diff --git a/openturns/master/_downloads/06b69b36ded61f91f0e533e211435c93/plot_kriging_hyperparameters_optimization.py b/openturns/master/_downloads/06b69b36ded61f91f0e533e211435c93/plot_kriging_hyperparameters_optimization.py index 719f332f4be..4958afd89df 100644 --- a/openturns/master/_downloads/06b69b36ded61f91f0e533e211435c93/plot_kriging_hyperparameters_optimization.py +++ b/openturns/master/_downloads/06b69b36ded61f91f0e533e211435c93/plot_kriging_hyperparameters_optimization.py @@ -1,5 +1,5 @@ """ -Kriging :configure the optimization solver +Kriging: configure the optimization solver ========================================== """ # %% @@ -25,7 +25,7 @@ # Often, the parameter :math:`{\bf \theta}` is a scale parameter. # This step involves an optimization algorithm. # -# All these parameters are estimated with the `GeneralLinearModelAlgorithm` class. +# All these parameters are estimated with the :class:`~openturns.GeneralLinearModelAlgorithm` class. # # The estimation of the :math:`{\bf \theta}` parameters is the step which has the highest CPU cost. # Moreover, the maximization of likelihood may be associated with difficulties e.g. many local maximums or even the non convergence of the optimization algorithm. @@ -75,7 +75,7 @@ II.setDescription("I") # %% -# Finally, we define the dependency using a `NormalCopula`. +# Finally, we define the dependency using a :class:`~openturns.NormalCopula`. # %% dim = 4 # number of inputs @@ -89,7 +89,8 @@ # -------------------------------- # %% -# We consider a simple Monte-Carlo sampling as a design of experiments. This is why we generate an input sample using the `getSample` method of the distribution. +# We consider a simple Monte-Carlo sampling as a design of experiments. +# This is why we generate an input sample using the `getSample` method of the distribution. # Then we evaluate the output using the `model` function. # %% @@ -102,9 +103,9 @@ # -------------------- # %% -# In order to create the kriging metamodel, we first select a constant trend with the `ConstantBasisFactory` class. +# In order to create the kriging metamodel, we first select a constant trend with the :class:`~openturns.ConstantBasisFactory` class. # Then we use a squared exponential covariance model. -# Finally, we use the `KrigingAlgorithm` class to create the kriging metamodel, +# Finally, we use the :class:`~openturns.KrigingAlgorithm` class to create the kriging metamodel, # taking the training sample, the covariance model and the trend basis as input arguments. # %% @@ -132,9 +133,10 @@ krigingMetamodel = result.getMetaModel() # %% -# The `run` method has optimized the hyperparameters of the metamodel. +# The :meth:`~openturns.KrigingAlgorithm.run` method has optimized the hyperparameters of the metamodel. # -# We can then print the constant trend of the metamodel, which have been estimated using the least squares method. +# We can then print the constant trend of the metamodel, which have been +# estimated using the least squares method. # %% result.getTrendCoefficients() @@ -151,7 +153,10 @@ # --------------------------- # %% -# The `getOptimizationAlgorithm` method returns the optimization algorithm used to optimize the :math:`{\bf \theta}` parameters of the `SquaredExponential` covariance model. +# The :meth:`~openturns.KrigingAlgorithm.getOptimizationAlgorithm` method +# returns the optimization algorithm used to optimize the +# :math:`{\bf \theta}` parameters of the +# :class:`~openturns.SquaredExponential` covariance model. # %% solver = algo.getOptimizationAlgorithm() @@ -164,7 +169,10 @@ solverImplementation.getClassName() # %% -# The `getOptimizationBounds` method returns the bounds. The dimension of these bounds correspond to the spatial dimension of the covariance model. +# The :meth:`~openturns.KrigingAlgorithm.getOptimizationBounds` method +# returns the bounds. +# The dimension of these bounds correspond to the spatial dimension of +# the covariance model. # In the metamodeling context, this correspond to the input dimension of the model. # %% @@ -182,7 +190,7 @@ print(ubounds) # %% -# The `getOptimizeParameters` method returns `True` if these parameters are to be optimized. +# The :meth:`~openturns.KrigingAlgorithm.getOptimizeParameters` method returns `True` if these parameters are to be optimized. # %% isOptimize = algo.getOptimizeParameters() @@ -195,7 +203,8 @@ # %% # The starting point of the optimization is based on the parameters of the covariance model. -# In the following example, we configure the parameters of the covariance model to the arbitrary values `[12.,34.,56.,78.]`. +# In the following example, we configure the parameters of the covariance model to +# the arbitrary values `[12.0, 34.0, 56.0, 78.0]`. # %% covarianceModel = ot.SquaredExponential([12.0, 34.0, 56.0, 78.0], [1.0]) @@ -226,15 +235,16 @@ # %% # It is sometimes useful to completely disable the optimization of the parameters. -# In order to see the effect of this, we first initialize the parameters of the covariance model with the arbitrary values `[12.,34.,56.,78.]`. +# In order to see the effect of this, we first initialize the parameters of +# the covariance model with the arbitrary values `[12.0, 34.0, 56.0, 78.0]`. # %% covarianceModel = ot.SquaredExponential([12.0, 34.0, 56.0, 78.0], [91.0]) algo = ot.KrigingAlgorithm(X_train, Y_train, covarianceModel, basis) -algo.setOptimizationBounds(scaleOptimizationBounds) # Trick B # %% -# The `setOptimizeParameters` method can be used to disable the optimization of the parameters. +# The :meth:`~openturns.KrigingAlgorithm.setOptimizeParameters` method can be +# used to disable the optimization of the parameters. # %% algo.setOptimizeParameters(False) @@ -361,10 +371,13 @@ def printCovarianceParameterChange(covarianceModel1, covarianceModel2): # ---------------------------------------- # %% -# The following example checks the robustness of the optimization of the kriging algorithm with respect to -# the optimization of the likelihood function in the covariance model parameters estimation. -# We use a `MultiStart` algorithm in order to avoid to be trapped by a local minimum. -# Furthermore, we generate the design of experiments using a `LHSExperiments`, which guarantees that the points will fill the space. +# The following example checks the robustness of the optimization of the +# kriging algorithm with respect to the optimization of the likelihood +# function in the covariance model parameters estimation. +# We use a :class:`~openturns.MultiStart` algorithm in order to avoid to be trapped by a local minimum. +# Furthermore, we generate the design of experiments using a +# :class:`~openturns.LHSExperiments`, which guarantees that the points +# will fill the space. # %% sampleSize_train = 10 @@ -372,14 +385,17 @@ def printCovarianceParameterChange(covarianceModel1, covarianceModel2): Y_train = model(X_train) # %% -# First, we create a multivariate distribution, based on independent `Uniform` marginals which have the bounds required by the covariance model. +# First, we create a multivariate distribution, based on independent +# :class:`~openturns.Uniform` marginals which have the bounds required +# by the covariance model. # %% distributions = [ot.Uniform(lbounds[i], ubounds[i]) for i in range(dim)] boundedDistribution = ot.JointDistribution(distributions) # %% -# We first generate a Latin Hypercube Sampling (LHS) design made of 25 points in the sample space. This LHS is optimized so as to fill the space. +# We first generate a Latin Hypercube Sampling (LHS) design made of 25 points in the sample space. +# This LHS is optimized so as to fill the space. # %% K = 25 # design size @@ -393,7 +409,8 @@ def printCovarianceParameterChange(covarianceModel1, covarianceModel2): starting_points.getSize() # %% -# We can check that the minimum and maximum in the sample correspond to the bounds of the design of experiment. +# We can check that the minimum and maximum in the sample correspond to the +# bounds of the design of experiment. # %% print(lbounds, ubounds) @@ -402,14 +419,14 @@ def printCovarianceParameterChange(covarianceModel1, covarianceModel2): starting_points.getMin(), starting_points.getMax() # %% -# Then we create a `MultiStart` algorithm based on the LHS starting points. +# Then we create a :class:`~openturns.MultiStart` algorithm based on the LHS starting points. # %% solver.setMaximumIterationNumber(10000) multiStartSolver = ot.MultiStart(solver, starting_points) # %% -# Finally, we configure the optimization algorithm so as to use the `MultiStart` algorithm. +# Finally, we configure the optimization algorithm so as to use the :class:`~openturns.MultiStart` algorithm. # %% algo = ot.KrigingAlgorithm(X_train, Y_train, covarianceModel, basis) diff --git a/openturns/master/_downloads/0ef2e737c16c571c8945b202ec11aae3/auto_calibration_jupyter.zip b/openturns/master/_downloads/0ef2e737c16c571c8945b202ec11aae3/auto_calibration_jupyter.zip index bf49fdfb503..57c0d236842 100644 Binary files a/openturns/master/_downloads/0ef2e737c16c571c8945b202ec11aae3/auto_calibration_jupyter.zip and b/openturns/master/_downloads/0ef2e737c16c571c8945b202ec11aae3/auto_calibration_jupyter.zip differ diff --git a/openturns/master/_downloads/1587aaf6d031810efc2c8b57d52e08b7/plot_quick_start_point_and_sample.ipynb b/openturns/master/_downloads/1587aaf6d031810efc2c8b57d52e08b7/plot_quick_start_point_and_sample.ipynb index 729024f34c2..0d2264542a3 100644 --- a/openturns/master/_downloads/1587aaf6d031810efc2c8b57d52e08b7/plot_quick_start_point_and_sample.ipynb +++ b/openturns/master/_downloads/1587aaf6d031810efc2c8b57d52e08b7/plot_quick_start_point_and_sample.ipynb @@ -18,7 +18,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Introduction\n\nTwo fundamental objects in the library are:\n\n* `Point`: a multidimensional point in $D$ dimensions ($\\in \\mathbb{R}^D$) ;\n* `Sample`: a multivariate sample made of $N$ points in $D$ dimensions.\n\n\n" + "## Introduction\n\nTwo fundamental objects in the library are:\n\n* `Point`: a multidimensional point in $d$ dimensions ($\\in \\mathbb{R}^d$) ;\n* `Sample`: a multivariate sample made of $n$ points in $d$ dimensions.\n\n\n" ] }, { @@ -108,14 +108,14 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## The `Sample` class\n\nThe `Sample` class represents a multivariate sample made of $N$ points in $\\mathbb{R}^D$.\n\n* $D$ is the *dimension* of the sample,\n* $N$ is the *size* of the sample.\n\n\nA `Sample` can be seen as an array of with $N$ rows and $D$ columns.\n\n*Remark.* The :class:`~openturns.ProcessSample` class can be used to manage a sample of stochastic processes.\n\n" + "## The `Sample` class\n\nThe `Sample` class represents a multivariate sample made of $n$ points in $\\mathbb{R}^d$.\n\n* $d$ is the *dimension* of the sample,\n* $n$ is the *size* of the sample.\n\n\nA `Sample` can be seen as an array of with $n$ rows and $d$ columns.\n\n*Remark.* The :class:`~openturns.ProcessSample` class can be used to manage a sample of stochastic processes.\n\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "The script below creates a `Sample` with size $N=5$ and dimension $D=3$.\n\n" + "The script below creates a `Sample` with size $n=5$ and dimension $d=3$.\n\n" ] }, { @@ -249,7 +249,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "We see that:\n\n* the `row` is a `Point`,\n* the `column` is a `Sample`.\n\nThis is consistent with the fact that, in a dimension $D$ `Sample`, a row is a $D$-dimensional `Point`.\n\n" + "We see that:\n\n* the `row` is a `Point`,\n* the `column` is a `Sample`.\n\nThis is consistent with the fact that, in a dimension $d$ `Sample`, a row is a $d$-dimensional `Point`.\n\n" ] }, { @@ -270,6 +270,13 @@ "data.getMarginal([0, 2])" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Set a row or a column of a `Sample`\n\n" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -285,7 +292,32 @@ }, "outputs": [], "source": [ - "sample = ot.Sample([[1.0, 2.0], [3.0, 4.0], [5.0, 6.0]])\np = [8.0, 10.0]\nsample[2, :] = p\nsample" + "sample = ot.Sample([[1.0, 2.0], [3.0, 4.0], [5.0, 6.0]])\nsample" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Set the third row: this must be a `Point` or must be convertible to.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "p = [8.0, 10.0]\nsample[2, :] = p\nsample" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Set the second column: this must be a `Sample` or must be convertible to.\n\n" ] }, { @@ -299,6 +331,24 @@ "sample = ot.Sample([[1.0, 2.0], [3.0, 4.0], [5.0, 6.0]])\ns = ot.Sample([[3.0], [5.0], [7.0]])\nsample[:, 1] = s\nsample" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Sometimes, we want to set a column with a list of floats.\nThis can be done using the :meth:`~openturns.Sample.BuildFromPoint` static method.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "sample = ot.Sample([[1.0, 2.0], [3.0, 4.0], [5.0, 6.0]])\ns = ot.Sample.BuildFromPoint([3.0, 5.0, 7.0])\nsample[:, 1] = s\nsample" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -469,7 +519,7 @@ }, "outputs": [], "source": [ - "type(array)" + "print(type(array))" ] }, { @@ -570,7 +620,39 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "If we do not set the optional `size` parameter, the library cannot solve the\ncase and an `InvalidArgumentException` is generated.\nMore precisely, the code::\n\n sample = ot.Sample(u)\n\nproduces the exception::\n\n TypeError: InvalidArgumentException : Invalid array dimension: 1\n\n\n" + "When there is an ambiguous case, the library cannot solve the\nissue and an `InvalidArgumentException` is generated.\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "More precisely, the code:\n\n```\nsample = ot.Sample(u)\n```\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "produces the exception:\n\n```\nTypeError: InvalidArgumentException : Invalid array dimension: 1\n```\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In order to solve that problem, we can use the :meth:`~openturns.Sample.BuildFromPoint`\nstatic method.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "sample = ot.Sample.BuildFromPoint([ui for ui in u])\nsample" ] } ], diff --git a/openturns/master/_downloads/2598e942360dc5d24ea470609c8d0206/plot_functional_chaos.ipynb b/openturns/master/_downloads/2598e942360dc5d24ea470609c8d0206/plot_functional_chaos.ipynb index 441b82ff78c..8fd706e0e00 100644 --- a/openturns/master/_downloads/2598e942360dc5d24ea470609c8d0206/plot_functional_chaos.ipynb +++ b/openturns/master/_downloads/2598e942360dc5d24ea470609c8d0206/plot_functional_chaos.ipynb @@ -4,14 +4,28 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "\n# Create a polynomial chaos metamodel\n" + "\n# Create a polynomial chaos metamodel from a data set\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "In this example we are going to create a global approximation of a model response using functional chaos.\n\nLet $h$ be the function defined by:\n\n\\begin{align}g(\\mathbf{x}) = \\left[\\cos(x_1 + x_2), (x_2 + 1) e^{x_1}\\right]\\end{align}\n\n\nfor any $\\mathbf{x}\\in\\mathbb{R}^2$.\n\nWe assume that\n\n\\begin{align}X_1 \\sim \\mathcal{N}(0,1) \\textrm{ and } X_2 \\sim \\mathcal{N}(0,1)\\end{align}\n\nand that $X_1$ and $X_2$ are independent.\n\nAn interesting point in this example is that the output is multivariate.\nThis is why we are going to use the `getMarginal` method in the script in order to select the output marginal that we want to manage.\n\n" + "In this example, we create a polynomial chaos expansion (PCE) using\na data set.\nMore precisely, given a pair of input and output samples,\nwe create a PCE without the knowledge of the input distribution.\nIn this example, we use a relatively small sample size equal to 80.\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this example we create a global approximation of a model response using\npolynomial chaos expansion.\n\nLet $h$ be the function defined by:\n\n\\begin{align}g(\\mathbf{x}) = \\left[\\cos(x_1 + x_2), (x_2 + 1) e^{x_1}\\right]\\end{align}\n\n\nfor any $\\mathbf{x}\\in\\mathbb{R}^2$.\n\nWe assume that\n\n\\begin{align}X_1 \\sim \\mathcal{N}(0,1) \\textrm{ and } X_2 \\sim \\mathcal{N}(0,1)\\end{align}\n\nand that $X_1$ and $X_2$ are independent.\n\nAn interesting point in this example is that the output is multivariate.\nThis is why we are going to use the `getMarginal` method in the script\nin order to select the output marginal that we want to manage.\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Simulate input and output samples\n\n" ] }, { @@ -40,14 +54,14 @@ }, "outputs": [], "source": [ - "ot.RandomGenerator.SetSeed(0)\ndimension = 2\ninput_names = [\"x1\", \"x2\"]\nformulas = [\"cos(x1 + x2)\", \"(x2 + 1) * exp(x1)\"]\nmodel = ot.SymbolicFunction(input_names, formulas)" + "ot.RandomGenerator.SetSeed(2)\ndimension = 2\ninput_names = [\"x1\", \"x2\"]\nformulas = [\"cos(x1 + x2)\", \"(x2 + 1) * exp(x1)\"]\nmodel = ot.SymbolicFunction(input_names, formulas)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Then we create a sample `inputSample` and compute the corresponding output sample `outputSample`.\n\n" + "Then we create a sample `inputSample` and compute the corresponding output\nsample `outputSample`.\n\n" ] }, { @@ -65,7 +79,32 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Create a functional chaos model.\nFirst, we need to fit a distribution on the input sample. We can do this automatically with the Lilliefors test.\n\n" + "## Create the PCE\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Create a functional chaos model.\nThe algorithm needs to fit a distribution on the input sample.\nTo do this, the algorithm in :class:`~openturns.FunctionalChaosAlgorithm`\nuses the :class:`~openturns.FunctionalChaosAlgorithm.BuildDistribution`\nstatic method to fit the distribution to the input sample.\nPlease read :doc:`Fit a distribution from an input sample `\nfor an example of this method.\nThe algorithm does this automatically using the Lilliefors test.\nIn order to make the algorithm a little faster, we reduce the\nvalue of the sample size used in the Lilliefors test.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "ot.ResourceMap.SetAsUnsignedInteger(\"FittingTest-LillieforsMaximumSamplingSize\", 50)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The main topic of this example is to introduce the next constructor of\n:class:`~openturns.FunctionalChaosAlgorithm`.\nNotice that the only input arguments are the input and output sample.\n\n" ] }, { @@ -76,7 +115,21 @@ }, "outputs": [], "source": [ - "ot.ResourceMap.SetAsUnsignedInteger(\"FittingTest-LillieforsMaximumSamplingSize\", 100)" + "algo = ot.FunctionalChaosAlgorithm(inputSample, outputSample)\nalgo.run()\nresult = algo.getResult()\nresult" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Not all coefficients are selected in this PCE.\nIndeed, the default constructor of :class:`~openturns.FunctionalChaosAlgorithm`\ncreates a sparse PCE.\nPlease read :doc:`Create a full or sparse polynomial chaos expansion `\nfor more details on this topic.\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Get the metamodel.\n\n" ] }, { @@ -87,7 +140,7 @@ }, "outputs": [], "source": [ - "algo = ot.FunctionalChaosAlgorithm(inputSample, outputSample)\nalgo.run()\nresult = algo.getResult()\nmetamodel = result.getMetaModel()" + "metamodel = result.getMetaModel()" ] }, { @@ -112,7 +165,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "We see that the metamodel fits approximately to the model, except perhaps for extreme values of $x_2$.\nHowever, there is a better way of globally validating the metamodel, using the `MetaModelValidation` on a validation design of experiment.\n\n" + "We see that the metamodel fits approximately to the model, except\nperhaps for extreme values of $x_2$.\nHowever, there is a better way of globally validating the metamodel,\nusing the :class:`~openturns.MetaModelValidation` on a validation design of experiment.\n\n" ] }, { @@ -148,7 +201,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The coefficient of predictivity is not extremely satisfactory for the first output, but is would be sufficient for a central dispersion study.\nThe second output has a much more satisfactory Q2: only one single extreme point is far from the diagonal of the graphics.\n\n" + "The coefficient of predictivity is not extremely satisfactory for the\nfirst output, but is would be sufficient for a central dispersion study.\nThe second output has a much more satisfactory Q2: only one single\nextreme point is far from the diagonal of the graphics.\n\n" ] }, { @@ -166,14 +219,14 @@ }, "outputs": [], "source": [ - "chaosSI = ot.FunctionalChaosSobolIndices(result)\nprint(chaosSI)" + "chaosSI = ot.FunctionalChaosSobolIndices(result)\nchaosSI" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Let us analyse the results of this global sensitivity analysis.\n\n* We see that the first output involves significant multi-indices with total degree 4. The contribution of the interactions are very significant in this model.\n* The second output involves multi-indices with total degrees from 1 to 7, with a significant contribution of multi-indices with total degress 5 and 7.\n The first variable is especially significant, with a significant contribution of the interactions.\n\n" + "Let us analyse the results of this global sensitivity analysis.\n\n* We see that the first output involves significant multi-indices with\n higher marginal degree.\n* For the second output, the first variable is especially significant,\n with a significant contribution of the interactions.\n The contribution of the interactions are very\n significant in this model.\n\n" ] }, { @@ -209,7 +262,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Testing the sensitivity to the degree\n\nWith the specific constructor of `FunctionalChaosAlgorithm` that we use, the `FunctionalChaosAlgorithm-MaximumTotalDegree`\nin the `ResourceMap` configure the maximum degree explored by the algorithm. This degree is a trade-off.\n\n* If the maximum degree is too low, the polynomial may miss some coefficients so that the quality is lower than possible.\n* If the maximum degree is too large, the number of coefficients to explore is too large, so that the coefficients might be poorly estimated.\n\nThis is why the following `for` loop explores various degrees to see the sensitivity of the metamodel predictivity depending on the degree.\n\n" + "## Testing the sensitivity to the degree\n\nWith the specific constructor of `FunctionalChaosAlgorithm` that\nwe use, the `FunctionalChaosAlgorithm-MaximumTotalDegree`\nin the `ResourceMap` configure the maximum degree explored by\nthe algorithm. This degree is a trade-off.\n\n* If the maximum degree is too low, the polynomial may miss some\n coefficients so that the quality is lower than possible.\n* If the maximum degree is too large, the number of coefficients\n to explore is too large, so that the coefficients might be poorly estimated.\n\nThis is why the following `for` loop explores various degrees to see\nthe sensitivity of the metamodel predictivity depending on the degree.\n\n" ] }, { @@ -234,7 +287,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "This is why we explore the values from 5 to 15.\n\n" + "This is why we explore the values from 1 to 15.\n\n" ] }, { @@ -245,7 +298,7 @@ }, "outputs": [], "source": [ - "degrees = range(5, 12)\nq2 = ot.Sample(len(degrees), 2)\nfor maximumDegree in degrees:\n ot.ResourceMap.SetAsUnsignedInteger(\n \"FunctionalChaosAlgorithm-MaximumTotalDegree\", maximumDegree\n )\n print(\"Maximum total degree =\", maximumDegree)\n algo = ot.FunctionalChaosAlgorithm(inputSample, outputSample)\n algo.run()\n result = algo.getResult()\n metamodel = result.getMetaModel()\n for outputIndex in range(2):\n val = ot.MetaModelValidation(\n inputTest, outputTest[:, outputIndex], metamodel.getMarginal(outputIndex)\n )\n q2[maximumDegree - degrees[0], outputIndex] = val.computePredictivityFactor()[0]" + "degrees = range(1, 12)\nq2 = ot.Sample(len(degrees), 2)\nfor maximumDegree in degrees:\n ot.ResourceMap.SetAsUnsignedInteger(\n \"FunctionalChaosAlgorithm-MaximumTotalDegree\", maximumDegree\n )\n print(\"Maximum total degree =\", maximumDegree)\n algo = ot.FunctionalChaosAlgorithm(inputSample, outputSample)\n algo.run()\n result = algo.getResult()\n metamodel = result.getMetaModel()\n for outputIndex in range(2):\n val = ot.MetaModelValidation(\n inputTest, outputTest[:, outputIndex], metamodel.getMarginal(outputIndex)\n )\n q2Value = min(1.0, max(0.0, val.computePredictivityFactor()[0])) # Get lucky.\n q2[maximumDegree - degrees[0], outputIndex] = q2Value" ] }, { @@ -256,14 +309,14 @@ }, "outputs": [], "source": [ - "graph = ot.Graph(\"Predictivity\", \"Total degree\", \"Q2\", True)\ncloud = ot.Cloud([[d] for d in degrees], q2[:, 0])\ncloud.setLegend(\"Output #0\")\ncloud.setPointStyle(\"bullet\")\ngraph.add(cloud)\ncloud = ot.Cloud([[d] for d in degrees], q2[:, 1])\ncloud.setLegend(\"Output #1\")\ncloud.setColor(\"red\")\ncloud.setPointStyle(\"bullet\")\ngraph.add(cloud)\ngraph.setLegendPosition(\"upper right\")\nview = viewer.View(graph)\nplt.show()" + "graph = ot.Graph(\"Predictivity\", \"Total degree\", \"Q2\", True)\ncloud = ot.Cloud([[d] for d in degrees], q2[:, 0])\ncloud.setLegend(\"Output #0\")\ncloud.setPointStyle(\"bullet\")\ngraph.add(cloud)\ncloud = ot.Cloud([[d] for d in degrees], q2[:, 1])\ncloud.setLegend(\"Output #1\")\ncloud.setColor(\"red\")\ncloud.setPointStyle(\"bullet\")\ngraph.add(cloud)\ngraph.setLegendPosition(\"upper right\")\nview = viewer.View(graph, legend_kw={\"bbox_to_anchor\": (1.0, 1.0), \"loc\": \"upper left\"})\nplt.subplots_adjust(right=0.7)\n\nplt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "We see that a total degree lower than 9 is not sufficient to describe the first output with good predictivity.\nHowever, the coefficient of predictivity drops when the total degree gets greater than 12.\nThe predictivity of the second output seems to be much less satisfactory: a little more work would be required to improve the metamodel.\n\nIn this situation, the following methods may be used.\n\n* Since the distribution of the input is known, we may want to give this information to the `FunctionalChaosAlgorithm`.\n This prevents the algorithm from trying to fit the distribution which best fit to the data.\n* We may want to customize the `adaptiveStrategy` by selecting an enumerate function which best fit to this particular situation.\n In this specific example, the interactions plays a great role so that the linear enumerate function may provide better results than the hyperbolic rule.\n* We may want to customize the `projectionStrategy` by selecting an method to compute the coefficient which improves the estimation.\n Given that the function is symbolic and fast, it might be interesting to try an integration rule instead of the least squares method.\n\n" + "We see that the R2 score increases then gets constant or decreases.\nA low total polynomial degree is not sufficient to describe\nthe first output with good predictivity.\nHowever, the coefficient of predictivity can decrease when the total degree\ngets greater.\nThe predictivity of the second output seems to be much less\nsatisfactory: a little more work would be required to improve the metamodel.\n\nIn this situation, the following methods may be used.\n\n* Since the distribution of the input is known, we may want to give\n this information to the `FunctionalChaosAlgorithm`.\n This prevents the algorithm from trying to fit the input distribution\n which best fit to the data.\n* We may want to customize the `adaptiveStrategy` by selecting an enumerate\n function which best fit to this particular example.\n In this specific example, however, the interactions plays a great role so that the\n linear enumerate function may provide better results than the hyperbolic rule.\n* We may want to customize the `projectionStrategy` by selecting a method\n to compute the coefficient which improves the estimation.\n For example, it might be interesting to\n try an integration rule instead of the least squares method.\n Notice that a specific design of experiment is required in this case.\n\n" ] }, { diff --git a/openturns/master/_downloads/32764d685caaf9dcc0d31be3ef384e64/auto_functional_modeling_jupyter.zip b/openturns/master/_downloads/32764d685caaf9dcc0d31be3ef384e64/auto_functional_modeling_jupyter.zip index 05d98d6fa82..c38f18f809c 100644 Binary files a/openturns/master/_downloads/32764d685caaf9dcc0d31be3ef384e64/auto_functional_modeling_jupyter.zip and b/openturns/master/_downloads/32764d685caaf9dcc0d31be3ef384e64/auto_functional_modeling_jupyter.zip differ diff --git a/openturns/master/_downloads/32e677f64fc66b916d228519d2033682/plot_chaos_build_distribution.py b/openturns/master/_downloads/32e677f64fc66b916d228519d2033682/plot_chaos_build_distribution.py index 003f7640027..b2a30c7c4ba 100644 --- a/openturns/master/_downloads/32e677f64fc66b916d228519d2033682/plot_chaos_build_distribution.py +++ b/openturns/master/_downloads/32e677f64fc66b916d228519d2033682/plot_chaos_build_distribution.py @@ -75,7 +75,7 @@ distribution # %% -# We can also analyse its properties in more detail. +# We can also analyse its properties in more details. # %% for i in range(dimension): diff --git a/openturns/master/_downloads/4bad5eb03eda58932cc7c0ee48367350/plot_functional_chaos_database.ipynb b/openturns/master/_downloads/4bad5eb03eda58932cc7c0ee48367350/plot_functional_chaos_database.ipynb index 17f00baad4d..4352744f912 100644 --- a/openturns/master/_downloads/4bad5eb03eda58932cc7c0ee48367350/plot_functional_chaos_database.ipynb +++ b/openturns/master/_downloads/4bad5eb03eda58932cc7c0ee48367350/plot_functional_chaos_database.ipynb @@ -4,14 +4,14 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "\n# Polynomial chaos over database\n" + "\n# Create a full or sparse polynomial chaos expansion\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "In this example we are going to create a global approximation of a model response using functional chaos over a design of experiment.\n\nYou will need to specify the distribution of the input parameters.\nIf not known, statistical inference can be used to select a possible candidate, and fitting tests can validate such an hypothesis.\n\n" + "In this example we create a global approximation of a model using\npolynomial chaos expansion based on a design of experiment.\nThe goal of this example is to show how we can create a full or\nsparse polynomial chaos expansion depending on our needs\nand depending on the number of observations we have.\nIn general, we should have more observations than parameters to estimate.\nThis is why a sparse polynomial chaos may be interesting:\nby carefully selecting the coefficients we estimate,\nwe may reduce overfitting and increase the predictions of the\nmetamodel.\n\n" ] }, { @@ -29,7 +29,107 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Create a function R^n --> R^p\nFor example R^4 --> R\n\n" + "## Define the model\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Create the function.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "myModel = ot.SymbolicFunction(\n [\"x1\", \"x2\", \"x3\", \"x4\"], [\"1 + x1 * x2 + 2 * x3^2 + x4^4\"]\n)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Create a multivariate distribution.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "distribution = ot.JointDistribution(\n [ot.Normal(), ot.Uniform(), ot.Gamma(2.75, 1.0), ot.Beta(2.5, 1.0, -1.0, 2.0)]\n)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In order to create the PCE, we can specify the distribution of the\ninput parameters.\nIf not known, statistical inference can be used to select a possible\ncandidate, and fitting tests can validate such an hypothesis.\nPlease read :doc:`Fit a distribution from an input sample `\nfor an example of this method.\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Create a training sample\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Create a pair of input and output samples.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "sampleSize = 250\ninputSample = distribution.getSample(sampleSize)\noutputSample = myModel(inputSample)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Build the orthogonal basis\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the next cell, we create the univariate orthogonal polynomial basis\nfor each marginal.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "inputDimension = inputSample.getDimension()\ncoll = [\n ot.StandardDistributionPolynomialFactory(distribution.getMarginal(i))\n for i in range(inputDimension)\n]\nenumerateFunction = ot.LinearEnumerateFunction(inputDimension)\nproductBasis = ot.OrthogonalProductPolynomialFactory(coll, enumerateFunction)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can achieve the same result using :class:`~OrthogonalProductPolynomialFactory`.\n\n" ] }, { @@ -40,14 +140,21 @@ }, "outputs": [], "source": [ - "myModel = ot.SymbolicFunction([\"x1\", \"x2\", \"x3\", \"x4\"], [\"1+x1*x2 + 2*x3^2+x4^4\"])\n\n# Create a distribution of dimension n\n# for example n=3 with independent components\ndistribution = ot.JointDistribution(\n [ot.Normal(), ot.Uniform(), ot.Gamma(2.75, 1.0), ot.Beta(2.5, 1.0, -1.0, 2.0)]\n)" + "marginalDistributionCollection = [\n distribution.getMarginal(i) for i in range(inputDimension)\n]\nmultivariateBasis = ot.OrthogonalProductPolynomialFactory(\n marginalDistributionCollection\n)\nmultivariateBasis" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Prepare the input/output samples\n\n" + "## Create a full PCE\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Create the algorithm.\nWe compute the basis size from the total degree.\nThe next lines use the :class:`~openturns.LeastSquaresStrategy` class\nwith default parameters (the default is the\n:class:`~openturns.PenalizedLeastSquaresAlgorithmFactory` class).\nThis creates a full polynomial chaos expansion, i.e.\nwe keep all the candidate coefficients produced by the enumeration\nrule.\nIn order to create a sparse polynomial chaos expansion, we\nmust use the :class:`~openturns.LeastSquaresMetaModelSelectionFactory`\nclass instead.\n\n\n" ] }, { @@ -58,14 +165,14 @@ }, "outputs": [], "source": [ - "sampleSize = 250\nX = distribution.getSample(sampleSize)\nY = myModel(X)\ndimension = X.getDimension()" + "totalDegree = 3\ncandidateBasisSize = enumerateFunction.getBasisSizeFromTotalDegree(totalDegree)\nprint(\"Candidate basis size = \", candidateBasisSize)\nadaptiveStrategy = ot.FixedStrategy(productBasis, candidateBasisSize)\nprojectionStrategy = ot.LeastSquaresStrategy()\nalgo = ot.FunctionalChaosAlgorithm(\n inputSample, outputSample, distribution, adaptiveStrategy, projectionStrategy\n)\nalgo.run()\nresult = algo.getResult()\nresult" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "build the orthogonal basis\n\n" + "Get the number of coefficients in the PCE.\n\n" ] }, { @@ -76,14 +183,28 @@ }, "outputs": [], "source": [ - "coll = [\n ot.StandardDistributionPolynomialFactory(distribution.getMarginal(i))\n for i in range(dimension)\n]\nenumerateFunction = ot.LinearEnumerateFunction(dimension)\nproductBasis = ot.OrthogonalProductPolynomialFactory(coll, enumerateFunction)" + "selectedBasisSizeFull = result.getIndices().getSize()\nprint(\"Selected basis size = \", selectedBasisSizeFull)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "create the algorithm\n\n" + "We see that the number of coefficients in the selected basis is\nequal to the number of coefficients in the candidate basis.\nThis is, indeed, a *full* PCE.\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Use the PCE\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Get the metamodel function.\n\n" ] }, { @@ -94,14 +215,14 @@ }, "outputs": [], "source": [ - "degree = 6\nadaptiveStrategy = ot.FixedStrategy(\n productBasis, enumerateFunction.getStrataCumulatedCardinal(degree)\n)\nprojectionStrategy = ot.LeastSquaresStrategy()\nalgo = ot.FunctionalChaosAlgorithm(\n X, Y, distribution, adaptiveStrategy, projectionStrategy\n)\nalgo.run()" + "metamodel = result.getMetaModel()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "get the metamodel function\n\n" + "In order to evaluate the metamodel on a single point, we just\nuse it as any other :class:`openturns.Function`.\n\n" ] }, { @@ -112,14 +233,14 @@ }, "outputs": [], "source": [ - "result = algo.getResult()\nmetamodel = result.getMetaModel()" + "xPoint = distribution.getMean()\nyPoint = metamodel(xPoint)\nprint(\"Value at \", xPoint, \" is \", yPoint)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Print residuals\n\n" + "Print residuals.\n\n" ] }, { @@ -132,6 +253,63 @@ "source": [ "result.getResiduals()" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Based on these results, we may want to validate our metamodel.\nMore details on this topic are presented in\n:doc:`Validate a polynomial chaos `.\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Create a sparse PCE\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In order to create a sparse polynomial chaos expansion, we\nuse the :class:`~openturns.LeastSquaresMetaModelSelectionFactory`\nclass instead.\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "totalDegree = 6\ncandidateBasisSize = enumerateFunction.getBasisSizeFromTotalDegree(totalDegree)\nprint(\"Candidate basis size = \", candidateBasisSize)\nadaptiveStrategy = ot.FixedStrategy(productBasis, candidateBasisSize)\nselectionAlgorithm = ot.LeastSquaresMetaModelSelectionFactory()\nprojectionStrategy = ot.LeastSquaresStrategy(selectionAlgorithm)\nalgo = ot.FunctionalChaosAlgorithm(\n inputSample, outputSample, distribution, adaptiveStrategy, projectionStrategy\n)\nalgo.run()\nresult = algo.getResult()\nresult" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Get the number of coefficients in the PCE.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "selectedBasisSizeSparse = result.getIndices().getSize()\nprint(\"Selected basis size = \", selectedBasisSizeSparse)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see that the number of selected coefficients is lower than\nthe number of candidate coefficients.\nThis may reduce overfitting and can produce a PCE with more\naccurate predictions.\n\n" + ] } ], "metadata": { diff --git a/openturns/master/_downloads/4c9fe30a2a1c939510fb7d6a12aa86d9/plot_bayesian_calibration.ipynb b/openturns/master/_downloads/4c9fe30a2a1c939510fb7d6a12aa86d9/plot_bayesian_calibration.ipynb index d89d6b152a0..b8452da2d23 100644 --- a/openturns/master/_downloads/4c9fe30a2a1c939510fb7d6a12aa86d9/plot_bayesian_calibration.ipynb +++ b/openturns/master/_downloads/4c9fe30a2a1c939510fb7d6a12aa86d9/plot_bayesian_calibration.ipynb @@ -11,7 +11,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "In this example we compute the parameters of a computer model thanks\nto Bayesian estimation.\nWe use the :class:`~openturns.RandomWalkMetropolisHastings` and\n:class:`~openturns.Gibbs` classes\nand simulate a sample of the posterior distribution using\n`metropolis_hastings`.\n\nLet us denote $(y_1, \\dots, y_n)$ the observation sample,\n$(\\vect z_1, \\ldots, \\vect z_n) = (f(x_1|\\vect\\theta), \\ldots, f(x_n|\\vect\\theta))$ the model prediction,\n$p(y |\\vect z)$ the density function of observation $y$\nconditional on model prediction $\\vect z$,\nand $\\vect\\theta \\in \\mathbb{R}^p$ the calibration parameters we wish to estimate.\n\n\nThe posterior distribution is given by Bayes theorem:\n\n\\begin{align}\\pi(\\vect\\theta | \\vect y) \\quad \\propto \\quad L\\left(\\vect y | \\vect\\theta\\right) \\times \\pi(\\vect\\theta)$`\\end{align}\n\nwhere :math:$\\propto` means \"proportional to\", regarded as a function of $\\vect\\theta$.\n\nThe posterior distribution is approximated here by the empirical distribution\nof the sample $\\vect\\theta^1, \\ldots, \\vect\\theta^N$ generated by the Metropolis-Hastings algorithm.\nThis means that any quantity characteristic of the posterior distribution\n(mean, variance, quantile, ...) is approximated by its empirical counterpart.\n\nOur model (i.e. the compute code to calibrate) is a standard normal linear regression, where\n\n\\begin{align}y_i = \\theta_1 + x_i \\theta_2 + x_i^2 \\theta_3 + \\varepsilon_i\\end{align}\n\nwhere $\\varepsilon_i \\stackrel{i.i.d.}{\\sim} \\mathcal N(0, 1)$.\n\nThe \"true\" value of $\\theta$ is:\n\n\\begin{align}\\vect \\theta_{true} = (-4.5,4.8,2.2)^T.\\end{align}\n\n\nWe use a normal prior on $\\vect\\theta$:\n\n\\begin{align}\\pi(\\vect\\theta) = \\mathcal N(\\vect{\\mu}_\\vect{\\theta}, \\mat{\\Sigma}_\\vect{\\theta})\\end{align}\n\nwhere\n\n\\begin{align}\\vect{\\mu}_\\vect{\\theta} =\n \\begin{pmatrix}\n -3 \\\\\n 4 \\\\\n 1\n \\end{pmatrix}\\end{align}\n\nis the mean of the prior and\n\n\\begin{align}\\mat{\\Sigma}_\\vect{\\theta} =\n \\begin{pmatrix}\n \\sigma_{\\theta_1}^2 & 0 & 0 \\\\\n 0 & \\sigma_{\\theta_2}^2 & 0 \\\\\n 0 & 0 & \\sigma_{\\theta_3}^2\n \\end{pmatrix}\\end{align}\n\nis the prior covariance matrix with\n\n\\begin{align}\\sigma_{\\theta_1} = 2, \\qquad \\sigma_{\\theta_2} = 1, \\qquad \\sigma_{\\theta_3} = 1.5.\\end{align}\n\nThe following objects need to be defined in order to perform Bayesian calibration:\n\n- The conditional density $p(y|\\vect z)$ must be defined as a probability distribution.\n- The computer model must be implemented thanks to the ParametricFunction class.\n This takes a value of $\\vect\\theta$ as input, and outputs the vector of model predictions $\\vect z$,\n as defined above (the vector of covariates $\\vect x = (x_1, \\ldots, x_n)$ is treated as a known constant).\n When doing that, we have to keep in mind that $\\vect z$ will be used as the vector of parameters corresponding\n to the distribution specified for $p(y |\\vect z)$. For instance, if $p(y|\\vect z)$ is normal,\n this means that $\\vect z$ must be a vector containing the mean and standard deviation of $y$.\n- The prior density $\\pi(\\vect\\theta)$ encoding the set of possible values for the calibration parameters,\n each value being weighted by its a priori probability, reflecting the beliefs about the possible values\n of $\\vect\\theta$ before consideration of the experimental data.\n Again, this is implemented as a probability distribution.\n- Metropolis-Hastings algorithm(s), possibly used in tandem with a Gibbs algorithm\n in order to sample from the posterior distribution of the calibration parameters.\n\n" + "In this example we compute the parameters of a computer model thanks\nto Bayesian estimation.\nWe use the :class:`~openturns.RandomWalkMetropolisHastings` and\n:class:`~openturns.Gibbs` classes\nand simulate a sample of the posterior distribution using\n`metropolis_hastings`.\n\nLet us denote $(y_1, \\dots, y_n)$ the observation sample,\n$(\\vect z_1, \\ldots, \\vect z_n) = (f(x_1|\\vect\\theta), \\ldots, f(x_n|\\vect\\theta))$ the model prediction,\n$p(y |\\vect z)$ the density function of observation $y$\nconditional on model prediction $\\vect z$,\nand $\\vect\\theta \\in \\mathbb{R}^p$ the calibration parameters we wish to estimate.\n\n\nThe posterior distribution is given by Bayes theorem:\n\n\\begin{align}\\pi(\\vect\\theta | \\vect y) \\quad \\propto \\quad L\\left(\\vect y | \\vect\\theta\\right) \\times \\pi(\\vect\\theta)\\end{align}\n\nwhere $\\propto$ means \"proportional to\", regarded as a function of $\\vect\\theta$.\n\nThe posterior distribution is approximated here by the empirical distribution\nof the sample $\\vect\\theta^1, \\ldots, \\vect\\theta^N$ generated by the Metropolis-Hastings algorithm.\nThis means that any quantity characteristic of the posterior distribution\n(mean, variance, quantile, ...) is approximated by its empirical counterpart.\n\nOur model (i.e. the compute code to calibrate) is a standard normal linear regression, where\n\n\\begin{align}y_i = \\theta_1 + x_i \\theta_2 + x_i^2 \\theta_3 + \\varepsilon_i\\end{align}\n\nwhere $\\varepsilon_i \\stackrel{i.i.d.}{\\sim} \\mathcal N(0, 1)$.\n\nThe \"true\" value of $\\theta$ is:\n\n\\begin{align}\\vect \\theta_{true} = (-4.5,4.8,2.2)^T.\\end{align}\n\n\nWe use a normal prior on $\\vect\\theta$:\n\n\\begin{align}\\pi(\\vect\\theta) = \\mathcal N(\\vect{\\mu}_\\vect{\\theta}, \\mat{\\Sigma}_\\vect{\\theta})\\end{align}\n\nwhere\n\n\\begin{align}\\vect{\\mu}_\\vect{\\theta} =\n \\begin{pmatrix}\n -3 \\\\\n 4 \\\\\n 1\n \\end{pmatrix}\\end{align}\n\nis the mean of the prior and\n\n\\begin{align}\\mat{\\Sigma}_\\vect{\\theta} =\n \\begin{pmatrix}\n \\sigma_{\\theta_1}^2 & 0 & 0 \\\\\n 0 & \\sigma_{\\theta_2}^2 & 0 \\\\\n 0 & 0 & \\sigma_{\\theta_3}^2\n \\end{pmatrix}\\end{align}\n\nis the prior covariance matrix with\n\n\\begin{align}\\sigma_{\\theta_1} = 2, \\qquad \\sigma_{\\theta_2} = 1, \\qquad \\sigma_{\\theta_3} = 1.5.\\end{align}\n\nThe following objects need to be defined in order to perform Bayesian calibration:\n\n- The conditional density $p(y|\\vect z)$ must be defined as a probability distribution.\n- The computer model must be implemented thanks to the :class:`~openturns.ParametricFunction` class.\n This takes a value of $\\vect\\theta$ as input, and outputs the vector of model predictions $\\vect z$,\n as defined above (the vector of covariates $\\vect x = (x_1, \\ldots, x_n)$ is treated as a known constant).\n When doing that, we have to keep in mind that $\\vect z$ will be used as the vector of parameters corresponding\n to the distribution specified for $p(y |\\vect z)$. For instance, if $p(y|\\vect z)$ is normal,\n this means that $\\vect z$ must be a vector containing the mean and standard deviation of $y$.\n- The prior density $\\pi(\\vect\\theta)$ encoding the set of possible values for the calibration parameters,\n each value being weighted by its a priori probability, reflecting the beliefs about the possible values\n of $\\vect\\theta$ before consideration of the experimental data.\n Again, this is implemented as a probability distribution.\n- Metropolis-Hastings algorithm(s), possibly used in tandem with a Gibbs algorithm\n in order to sample from the posterior distribution of the calibration parameters.\n\nThis example uses the :class:`~openturns.ParametricFunction` class.\nPlease read its documentation and\n:doc:`/auto_functional_modeling/vectorial_functions/plot_parametric_function`\nfor a detailed example.\n\n" ] }, { diff --git a/openturns/master/_downloads/4df3e0c0f81319718eb3fb7cc1e6e39e/auto_functional_modeling_python.zip b/openturns/master/_downloads/4df3e0c0f81319718eb3fb7cc1e6e39e/auto_functional_modeling_python.zip index ccbbce9bf9e..7a515d75955 100644 Binary files a/openturns/master/_downloads/4df3e0c0f81319718eb3fb7cc1e6e39e/auto_functional_modeling_python.zip and b/openturns/master/_downloads/4df3e0c0f81319718eb3fb7cc1e6e39e/auto_functional_modeling_python.zip differ diff --git a/openturns/master/_downloads/54010a3cb61eff2f9d801a4bc3a6699b/plot_parametric_function.ipynb b/openturns/master/_downloads/54010a3cb61eff2f9d801a4bc3a6699b/plot_parametric_function.ipynb index 69de2f4d34d..33c4e9b43f2 100644 --- a/openturns/master/_downloads/54010a3cb61eff2f9d801a4bc3a6699b/plot_parametric_function.ipynb +++ b/openturns/master/_downloads/54010a3cb61eff2f9d801a4bc3a6699b/plot_parametric_function.ipynb @@ -11,7 +11,14 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "In this example we are going to create a parametric function:\n\n\\begin{align}d_{L,I}(E, F): \\mathbb{R}^2 \\rightarrow \\mathbb{R}\\end{align}\n\nfunction from an existing \"full\" function:\n\n\\begin{align}\\end{align}\n d(E, F, L, I): \\mathbb{R}^4 \\rightarrow \\mathbb{R}\n\n\n" + "In this example, we show how to use the :class:`~openturns.ParametricFunction` class.\nThis is a tool which is very convenient when we perform\ncalibration, e.g. with :class:`~openturns.NonLinearLeastSquaresCalibration`\nor :class:`~openturns.RandomWalkMetropolisHastings`.\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this example we create a parametric function:\n\n\\begin{align}d_{L,I}(E, F): \\Rset^2 \\rightarrow \\Rset\\end{align}\n\nfunction from an existing \"full\" function:\n\n\\begin{align}\\end{align}\n d(E, F, L, I): \\Rset^4 \\rightarrow \\Rset.\n\n\n" ] }, { @@ -25,6 +32,13 @@ "import openturns as ot\n\not.Log.Show(ot.Log.NONE)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Define the function\n\n" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -40,7 +54,7 @@ }, "outputs": [], "source": [ - "def d_func(X):\n E, F, L, II = X\n d = -F * L**3 / (3.0 * E * II)\n return [d]\n\n\nbeam = ot.PythonFunction(4, 1, d_func)" + "def d_func(X):\n E, F, L, II = X\n d = -F * L**3 / (3.0 * E * II)\n return [d]\n\n\nbeam = ot.PythonFunction(4, 1, d_func)\nbeam.setInputDescription([\"E\", \"F\", \"L\", \"I\"])" ] }, { @@ -61,6 +75,45 @@ "x = [50.0, 1.0, 10.0, 5.0]\nbeam(x)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the physical model, the inputs and parameters are ordered as\npresented in the next table.\nNotice that there are no parameters in the physical model.\n\n+-------+----------------+\n| Index | Input variable |\n+=======+================+\n| 0 | E |\n+-------+----------------+\n| 1 | F |\n+-------+----------------+\n| 2 | L |\n+-------+----------------+\n| 3 | I |\n+-------+----------------+\n\n+-------+-----------+\n| Index | Parameter |\n+=======+===========+\n| \u2205 | \u2205 |\n+-------+-----------+\n\n**Table 1.** Indices and names of the inputs and parameters of the physical model.\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The next cell presents the description of the input variables\nand the description of the parameters of the physical model.\nWe see that there is no parameter at this stage in this function.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "print(\"Physical Model Inputs:\", beam.getInputDescription())\nprint(\"Physical Model Parameters:\", beam.getParameterDescription())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Define the parametric function\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We create a :class:`~openturns.ParametricFunction`\nwhere the parameters are `L` and `I` which have the indices 2 and\nand 3 in the physical model.\n\n+-------+----------------+\n| Index | Input variable |\n+=======+================+\n| 0 | E |\n+-------+----------------+\n| 1 | F |\n+-------+----------------+\n\n+-------+-----------+\n| Index | Parameter |\n+=======+===========+\n| 0 | L |\n+-------+-----------+\n| 1 | I |\n+-------+-----------+\n\n**Table 2.** Indices and names of the inputs and parameters of the parametric model.\n\n\n" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -115,6 +168,24 @@ "beam_LI = ot.ParametricFunction(beam, indices, referencePoint)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The next cell presents the description of the input variables\nand the description of the parameters of the parametric function.\nWe see that the parametric function has 2 parameters: L and I.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "print(\"Physical Model Inputs:\", beam_LI.getInputDescription())\nprint(\"Physical Model Parameters:\", beam_LI.getParameterDescription())" + ] + }, { "cell_type": "markdown", "metadata": {}, diff --git a/openturns/master/_downloads/557f6965239dde7b8b9613eb917dc826/plot_bayesian_calibration.py b/openturns/master/_downloads/557f6965239dde7b8b9613eb917dc826/plot_bayesian_calibration.py index e123b648241..59b345b2529 100644 --- a/openturns/master/_downloads/557f6965239dde7b8b9613eb917dc826/plot_bayesian_calibration.py +++ b/openturns/master/_downloads/557f6965239dde7b8b9613eb917dc826/plot_bayesian_calibration.py @@ -19,7 +19,9 @@ # # The posterior distribution is given by Bayes theorem: # -# .. math::\pi(\vect\theta | \vect y) \quad \propto \quad L\left(\vect y | \vect\theta\right) \times \pi(\vect\theta):math:`` +# .. math:: +# +# \pi(\vect\theta | \vect y) \quad \propto \quad L\left(\vect y | \vect\theta\right) \times \pi(\vect\theta) # # where :math:`\propto` means "proportional to", regarded as a function of :math:`\vect\theta`. # @@ -74,7 +76,7 @@ # The following objects need to be defined in order to perform Bayesian calibration: # # - The conditional density :math:`p(y|\vect z)` must be defined as a probability distribution. -# - The computer model must be implemented thanks to the ParametricFunction class. +# - The computer model must be implemented thanks to the :class:`~openturns.ParametricFunction` class. # This takes a value of :math:`\vect\theta` as input, and outputs the vector of model predictions :math:`\vect z`, # as defined above (the vector of covariates :math:`\vect x = (x_1, \ldots, x_n)` is treated as a known constant). # When doing that, we have to keep in mind that :math:`\vect z` will be used as the vector of parameters corresponding @@ -86,6 +88,11 @@ # Again, this is implemented as a probability distribution. # - Metropolis-Hastings algorithm(s), possibly used in tandem with a Gibbs algorithm # in order to sample from the posterior distribution of the calibration parameters. +# +# This example uses the :class:`~openturns.ParametricFunction` class. +# Please read its documentation and +# :doc:`/auto_functional_modeling/vectorial_functions/plot_parametric_function` +# for a detailed example. # %% import openturns as ot diff --git a/openturns/master/_downloads/58b7cedd7592157d47e84db4a498c83f/auto_data_analysis_jupyter.zip b/openturns/master/_downloads/58b7cedd7592157d47e84db4a498c83f/auto_data_analysis_jupyter.zip index c70497eb083..b322fe6da99 100644 Binary files a/openturns/master/_downloads/58b7cedd7592157d47e84db4a498c83f/auto_data_analysis_jupyter.zip and b/openturns/master/_downloads/58b7cedd7592157d47e84db4a498c83f/auto_data_analysis_jupyter.zip differ diff --git a/openturns/master/_downloads/5bd8041d934818d21b7145db57b37df0/plot_functional_chaos_sensitivity.ipynb b/openturns/master/_downloads/5bd8041d934818d21b7145db57b37df0/plot_functional_chaos_sensitivity.ipynb index 9637e990202..754a2f1573a 100644 --- a/openturns/master/_downloads/5bd8041d934818d21b7145db57b37df0/plot_functional_chaos_sensitivity.ipynb +++ b/openturns/master/_downloads/5bd8041d934818d21b7145db57b37df0/plot_functional_chaos_sensitivity.ipynb @@ -112,7 +112,7 @@ }, "outputs": [], "source": [ - "sensitivityAnalysis = ot.FunctionalChaosSobolIndices(result)\nprint(sensitivityAnalysis)" + "sensitivityAnalysis = ot.FunctionalChaosSobolIndices(result)\nsensitivityAnalysis" ] }, { @@ -148,7 +148,7 @@ }, "outputs": [], "source": [ - "for i in range(dimension):\n for j in range(i):\n print(\n input_names[i] + \" & \" + input_names[j],\n \":\",\n sensitivityAnalysis.getSobolIndex([i, j]),\n )\n\nplt.show()" + "for i in range(dimension):\n for j in range(i):\n sij = sensitivityAnalysis.getSobolIndex([i, j])\n print(f\"{input_names[i]} & {input_names[j]}: {sij:.4f}\")\n\nplt.show()" ] } ], diff --git a/openturns/master/_downloads/5e3d27e5c3a4cae0fbf3707c348ebb8c/plot_chaos_ishigami_grouped_indices.ipynb b/openturns/master/_downloads/5e3d27e5c3a4cae0fbf3707c348ebb8c/plot_chaos_ishigami_grouped_indices.ipynb index b1b87cca2bd..6c1338488d2 100644 --- a/openturns/master/_downloads/5e3d27e5c3a4cae0fbf3707c348ebb8c/plot_chaos_ishigami_grouped_indices.ipynb +++ b/openturns/master/_downloads/5e3d27e5c3a4cae0fbf3707c348ebb8c/plot_chaos_ishigami_grouped_indices.ipynb @@ -123,7 +123,7 @@ }, "outputs": [], "source": [ - "chaosSI = ot.FunctionalChaosSobolIndices(result)\nprint(chaosSI)" + "chaosSI = ot.FunctionalChaosSobolIndices(result)\nchaosSI" ] }, { diff --git a/openturns/master/_downloads/62833f7bafdc5be5ed7016740377dc5f/plot_functional_chaos_database.py b/openturns/master/_downloads/62833f7bafdc5be5ed7016740377dc5f/plot_functional_chaos_database.py index bde4ed49083..9f26d067cd9 100644 --- a/openturns/master/_downloads/62833f7bafdc5be5ed7016740377dc5f/plot_functional_chaos_database.py +++ b/openturns/master/_downloads/62833f7bafdc5be5ed7016740377dc5f/plot_functional_chaos_database.py @@ -1,12 +1,18 @@ """ -Polynomial chaos over database -============================== +Create a full or sparse polynomial chaos expansion +================================================== """ # %% -# In this example we are going to create a global approximation of a model response using functional chaos over a design of experiment. -# -# You will need to specify the distribution of the input parameters. -# If not known, statistical inference can be used to select a possible candidate, and fitting tests can validate such an hypothesis. +# In this example we create a global approximation of a model using +# polynomial chaos expansion based on a design of experiment. +# The goal of this example is to show how we can create a full or +# sparse polynomial chaos expansion depending on our needs +# and depending on the number of observations we have. +# In general, we should have more observations than parameters to estimate. +# This is why a sparse polynomial chaos may be interesting: +# by carefully selecting the coefficients we estimate, +# we may reduce overfitting and increase the predictions of the +# metamodel. # %% import openturns as ot @@ -14,49 +20,156 @@ ot.Log.Show(ot.Log.NONE) # %% -# Create a function R^n --> R^p -# For example R^4 --> R -myModel = ot.SymbolicFunction(["x1", "x2", "x3", "x4"], ["1+x1*x2 + 2*x3^2+x4^4"]) +# Define the model +# ~~~~~~~~~~~~~~~~ + +# %% +# Create the function. +myModel = ot.SymbolicFunction( + ["x1", "x2", "x3", "x4"], ["1 + x1 * x2 + 2 * x3^2 + x4^4"] +) -# Create a distribution of dimension n -# for example n=3 with independent components +# %% +# Create a multivariate distribution. distribution = ot.JointDistribution( [ot.Normal(), ot.Uniform(), ot.Gamma(2.75, 1.0), ot.Beta(2.5, 1.0, -1.0, 2.0)] ) # %% -# Prepare the input/output samples +# In order to create the PCE, we can specify the distribution of the +# input parameters. +# If not known, statistical inference can be used to select a possible +# candidate, and fitting tests can validate such an hypothesis. +# Please read :doc:`Fit a distribution from an input sample ` +# for an example of this method. + +# %% +# Create a training sample +# ~~~~~~~~~~~~~~~~~~~~~~~~ + +# %% +# Create a pair of input and output samples. sampleSize = 250 -X = distribution.getSample(sampleSize) -Y = myModel(X) -dimension = X.getDimension() +inputSample = distribution.getSample(sampleSize) +outputSample = myModel(inputSample) + +# %% +# Build the orthogonal basis +# ~~~~~~~~~~~~~~~~~~~~~~~~~~ # %% -# build the orthogonal basis +# In the next cell, we create the univariate orthogonal polynomial basis +# for each marginal. +inputDimension = inputSample.getDimension() coll = [ ot.StandardDistributionPolynomialFactory(distribution.getMarginal(i)) - for i in range(dimension) + for i in range(inputDimension) ] -enumerateFunction = ot.LinearEnumerateFunction(dimension) +enumerateFunction = ot.LinearEnumerateFunction(inputDimension) productBasis = ot.OrthogonalProductPolynomialFactory(coll, enumerateFunction) # %% -# create the algorithm -degree = 6 -adaptiveStrategy = ot.FixedStrategy( - productBasis, enumerateFunction.getStrataCumulatedCardinal(degree) +# We can achieve the same result using :class:`~OrthogonalProductPolynomialFactory`. +marginalDistributionCollection = [ + distribution.getMarginal(i) for i in range(inputDimension) +] +multivariateBasis = ot.OrthogonalProductPolynomialFactory( + marginalDistributionCollection ) +multivariateBasis + +# %% +# Create a full PCE +# ~~~~~~~~~~~~~~~~~ + +# %% +# Create the algorithm. +# We compute the basis size from the total degree. +# The next lines use the :class:`~openturns.LeastSquaresStrategy` class +# with default parameters (the default is the +# :class:`~openturns.PenalizedLeastSquaresAlgorithmFactory` class). +# This creates a full polynomial chaos expansion, i.e. +# we keep all the candidate coefficients produced by the enumeration +# rule. +# In order to create a sparse polynomial chaos expansion, we +# must use the :class:`~openturns.LeastSquaresMetaModelSelectionFactory` +# class instead. +# +totalDegree = 3 +candidateBasisSize = enumerateFunction.getBasisSizeFromTotalDegree(totalDegree) +print("Candidate basis size = ", candidateBasisSize) +adaptiveStrategy = ot.FixedStrategy(productBasis, candidateBasisSize) projectionStrategy = ot.LeastSquaresStrategy() algo = ot.FunctionalChaosAlgorithm( - X, Y, distribution, adaptiveStrategy, projectionStrategy + inputSample, outputSample, distribution, adaptiveStrategy, projectionStrategy ) algo.run() +result = algo.getResult() +result # %% -# get the metamodel function -result = algo.getResult() +# Get the number of coefficients in the PCE. +selectedBasisSizeFull = result.getIndices().getSize() +print("Selected basis size = ", selectedBasisSizeFull) + +# %% +# We see that the number of coefficients in the selected basis is +# equal to the number of coefficients in the candidate basis. +# This is, indeed, a *full* PCE. + +# %% +# Use the PCE +# ~~~~~~~~~~~ + +# %% +# Get the metamodel function. metamodel = result.getMetaModel() # %% -# Print residuals +# In order to evaluate the metamodel on a single point, we just +# use it as any other :class:`openturns.Function`. +xPoint = distribution.getMean() +yPoint = metamodel(xPoint) +print("Value at ", xPoint, " is ", yPoint) + +# %% +# Print residuals. result.getResiduals() + +# %% +# Based on these results, we may want to validate our metamodel. +# More details on this topic are presented in +# :doc:`Validate a polynomial chaos `. + +# %% +# Create a sparse PCE +# ~~~~~~~~~~~~~~~~~~~ + +# %% +# In order to create a sparse polynomial chaos expansion, we +# use the :class:`~openturns.LeastSquaresMetaModelSelectionFactory` +# class instead. +# +totalDegree = 6 +candidateBasisSize = enumerateFunction.getBasisSizeFromTotalDegree(totalDegree) +print("Candidate basis size = ", candidateBasisSize) +adaptiveStrategy = ot.FixedStrategy(productBasis, candidateBasisSize) +selectionAlgorithm = ot.LeastSquaresMetaModelSelectionFactory() +projectionStrategy = ot.LeastSquaresStrategy(selectionAlgorithm) +algo = ot.FunctionalChaosAlgorithm( + inputSample, outputSample, distribution, adaptiveStrategy, projectionStrategy +) +algo.run() +result = algo.getResult() +result + +# %% +# Get the number of coefficients in the PCE. +selectedBasisSizeSparse = result.getIndices().getSize() +print("Selected basis size = ", selectedBasisSizeSparse) + +# %% +# We see that the number of selected coefficients is lower than +# the number of candidate coefficients. +# This may reduce overfitting and can produce a PCE with more +# accurate predictions. diff --git a/openturns/master/_downloads/638532df84c15ab8b3b760534600b27e/plot_functional_chaos_sensitivity.py b/openturns/master/_downloads/638532df84c15ab8b3b760534600b27e/plot_functional_chaos_sensitivity.py index 26205b90100..5f2054770be 100644 --- a/openturns/master/_downloads/638532df84c15ab8b3b760534600b27e/plot_functional_chaos_sensitivity.py +++ b/openturns/master/_downloads/638532df84c15ab8b3b760534600b27e/plot_functional_chaos_sensitivity.py @@ -78,7 +78,7 @@ # %% # Quick summary of sensitivity analysis sensitivityAnalysis = ot.FunctionalChaosSobolIndices(result) -print(sensitivityAnalysis) +sensitivityAnalysis # %% # draw Sobol' indices @@ -92,10 +92,7 @@ # so the higher order indices must be all quite close to 0 for i in range(dimension): for j in range(i): - print( - input_names[i] + " & " + input_names[j], - ":", - sensitivityAnalysis.getSobolIndex([i, j]), - ) + sij = sensitivityAnalysis.getSobolIndex([i, j]) + print(f"{input_names[i]} & {input_names[j]}: {sij:.4f}") plt.show() diff --git a/openturns/master/_downloads/6e518ec737e8c5eb60654ad7ec3146cf/auto_probabilistic_modeling_jupyter.zip b/openturns/master/_downloads/6e518ec737e8c5eb60654ad7ec3146cf/auto_probabilistic_modeling_jupyter.zip index f5c41884f6c..c01fe58d921 100644 Binary files a/openturns/master/_downloads/6e518ec737e8c5eb60654ad7ec3146cf/auto_probabilistic_modeling_jupyter.zip and b/openturns/master/_downloads/6e518ec737e8c5eb60654ad7ec3146cf/auto_probabilistic_modeling_jupyter.zip differ diff --git a/openturns/master/_downloads/6e9230396a6ac5e316d0eec076753b86/plot_functional_chaos.py b/openturns/master/_downloads/6e9230396a6ac5e316d0eec076753b86/plot_functional_chaos.py index 8ee44948345..bbf33561981 100644 --- a/openturns/master/_downloads/6e9230396a6ac5e316d0eec076753b86/plot_functional_chaos.py +++ b/openturns/master/_downloads/6e9230396a6ac5e316d0eec076753b86/plot_functional_chaos.py @@ -1,9 +1,17 @@ """ -Create a polynomial chaos metamodel -=================================== +Create a polynomial chaos metamodel from a data set +=================================================== """ # %% -# In this example we are going to create a global approximation of a model response using functional chaos. +# In this example, we create a polynomial chaos expansion (PCE) using +# a data set. +# More precisely, given a pair of input and output samples, +# we create a PCE without the knowledge of the input distribution. +# In this example, we use a relatively small sample size equal to 80. + +# %% +# In this example we create a global approximation of a model response using +# polynomial chaos expansion. # # Let :math:`h` be the function defined by: # @@ -21,7 +29,12 @@ # and that :math:`X_1` and :math:`X_2` are independent. # # An interesting point in this example is that the output is multivariate. -# This is why we are going to use the `getMarginal` method in the script in order to select the output marginal that we want to manage. +# This is why we are going to use the `getMarginal` method in the script +# in order to select the output marginal that we want to manage. + +# %% +# Simulate input and output samples +# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ # %% import openturns as ot @@ -34,14 +47,15 @@ # We first create the function `model`. # %% -ot.RandomGenerator.SetSeed(0) +ot.RandomGenerator.SetSeed(2) dimension = 2 input_names = ["x1", "x2"] formulas = ["cos(x1 + x2)", "(x2 + 1) * exp(x1)"] model = ot.SymbolicFunction(input_names, formulas) # %% -# Then we create a sample `inputSample` and compute the corresponding output sample `outputSample`. +# Then we create a sample `inputSample` and compute the corresponding output +# sample `outputSample`. # %% distribution = ot.Normal(dimension) @@ -49,17 +63,43 @@ inputSample = distribution.getSample(samplesize) outputSample = model(inputSample) +# %% +# Create the PCE +# ~~~~~~~~~~~~~~ + # %% # Create a functional chaos model. -# First, we need to fit a distribution on the input sample. We can do this automatically with the Lilliefors test. +# The algorithm needs to fit a distribution on the input sample. +# To do this, the algorithm in :class:`~openturns.FunctionalChaosAlgorithm` +# uses the :class:`~openturns.FunctionalChaosAlgorithm.BuildDistribution` +# static method to fit the distribution to the input sample. +# Please read :doc:`Fit a distribution from an input sample ` +# for an example of this method. +# The algorithm does this automatically using the Lilliefors test. +# In order to make the algorithm a little faster, we reduce the +# value of the sample size used in the Lilliefors test. # %% -ot.ResourceMap.SetAsUnsignedInteger("FittingTest-LillieforsMaximumSamplingSize", 100) +ot.ResourceMap.SetAsUnsignedInteger("FittingTest-LillieforsMaximumSamplingSize", 50) # %% +# The main topic of this example is to introduce the next constructor of +# :class:`~openturns.FunctionalChaosAlgorithm`. +# Notice that the only input arguments are the input and output sample. algo = ot.FunctionalChaosAlgorithm(inputSample, outputSample) algo.run() result = algo.getResult() +result + +# %% +# Not all coefficients are selected in this PCE. +# Indeed, the default constructor of :class:`~openturns.FunctionalChaosAlgorithm` +# creates a sparse PCE. +# Please read :doc:`Create a full or sparse polynomial chaos expansion ` +# for more details on this topic. + +# %% +# Get the metamodel. metamodel = result.getMetaModel() # %% @@ -87,8 +127,10 @@ view = viewer.View(graph) # %% -# We see that the metamodel fits approximately to the model, except perhaps for extreme values of :math:`x_2`. -# However, there is a better way of globally validating the metamodel, using the `MetaModelValidation` on a validation design of experiment. +# We see that the metamodel fits approximately to the model, except +# perhaps for extreme values of :math:`x_2`. +# However, there is a better way of globally validating the metamodel, +# using the :class:`~openturns.MetaModelValidation` on a validation design of experiment. # %% n_valid = 100 @@ -107,23 +149,28 @@ view = viewer.View(graph) # %% -# The coefficient of predictivity is not extremely satisfactory for the first output, but is would be sufficient for a central dispersion study. -# The second output has a much more satisfactory Q2: only one single extreme point is far from the diagonal of the graphics. +# The coefficient of predictivity is not extremely satisfactory for the +# first output, but is would be sufficient for a central dispersion study. +# The second output has a much more satisfactory Q2: only one single +# extreme point is far from the diagonal of the graphics. # %% # Compute and print Sobol' indices -# -------------------------------- +# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ # %% chaosSI = ot.FunctionalChaosSobolIndices(result) -print(chaosSI) +chaosSI # %% # Let us analyse the results of this global sensitivity analysis. # -# * We see that the first output involves significant multi-indices with total degree 4. The contribution of the interactions are very significant in this model. -# * The second output involves multi-indices with total degrees from 1 to 7, with a significant contribution of multi-indices with total degress 5 and 7. -# The first variable is especially significant, with a significant contribution of the interactions. +# * We see that the first output involves significant multi-indices with +# higher marginal degree. +# * For the second output, the first variable is especially significant, +# with a significant contribution of the interactions. +# The contribution of the interactions are very +# significant in this model. # %% # Draw Sobol' indices. @@ -141,15 +188,20 @@ # %% # Testing the sensitivity to the degree -# ------------------------------------- +# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ # -# With the specific constructor of `FunctionalChaosAlgorithm` that we use, the `FunctionalChaosAlgorithm-MaximumTotalDegree` -# in the `ResourceMap` configure the maximum degree explored by the algorithm. This degree is a trade-off. +# With the specific constructor of `FunctionalChaosAlgorithm` that +# we use, the `FunctionalChaosAlgorithm-MaximumTotalDegree` +# in the `ResourceMap` configure the maximum degree explored by +# the algorithm. This degree is a trade-off. # -# * If the maximum degree is too low, the polynomial may miss some coefficients so that the quality is lower than possible. -# * If the maximum degree is too large, the number of coefficients to explore is too large, so that the coefficients might be poorly estimated. +# * If the maximum degree is too low, the polynomial may miss some +# coefficients so that the quality is lower than possible. +# * If the maximum degree is too large, the number of coefficients +# to explore is too large, so that the coefficients might be poorly estimated. # -# This is why the following `for` loop explores various degrees to see the sensitivity of the metamodel predictivity depending on the degree. +# This is why the following `for` loop explores various degrees to see +# the sensitivity of the metamodel predictivity depending on the degree. # %% # The default value of this parameter is 10. @@ -158,10 +210,10 @@ ot.ResourceMap.GetAsUnsignedInteger("FunctionalChaosAlgorithm-MaximumTotalDegree") # %% -# This is why we explore the values from 5 to 15. +# This is why we explore the values from 1 to 15. # %% -degrees = range(5, 12) +degrees = range(1, 12) q2 = ot.Sample(len(degrees), 2) for maximumDegree in degrees: ot.ResourceMap.SetAsUnsignedInteger( @@ -176,7 +228,8 @@ val = ot.MetaModelValidation( inputTest, outputTest[:, outputIndex], metamodel.getMarginal(outputIndex) ) - q2[maximumDegree - degrees[0], outputIndex] = val.computePredictivityFactor()[0] + q2Value = min(1.0, max(0.0, val.computePredictivityFactor()[0])) # Get lucky. + q2[maximumDegree - degrees[0], outputIndex] = q2Value # %% graph = ot.Graph("Predictivity", "Total degree", "Q2", True) @@ -190,22 +243,35 @@ cloud.setPointStyle("bullet") graph.add(cloud) graph.setLegendPosition("upper right") -view = viewer.View(graph) +view = viewer.View(graph, legend_kw={"bbox_to_anchor": (1.0, 1.0), "loc": "upper left"}) +plt.subplots_adjust(right=0.7) + plt.show() # %% -# We see that a total degree lower than 9 is not sufficient to describe the first output with good predictivity. -# However, the coefficient of predictivity drops when the total degree gets greater than 12. -# The predictivity of the second output seems to be much less satisfactory: a little more work would be required to improve the metamodel. +# We see that the R2 score increases then gets constant or decreases. +# A low total polynomial degree is not sufficient to describe +# the first output with good predictivity. +# However, the coefficient of predictivity can decrease when the total degree +# gets greater. +# The predictivity of the second output seems to be much less +# satisfactory: a little more work would be required to improve the metamodel. # # In this situation, the following methods may be used. # -# * Since the distribution of the input is known, we may want to give this information to the `FunctionalChaosAlgorithm`. -# This prevents the algorithm from trying to fit the distribution which best fit to the data. -# * We may want to customize the `adaptiveStrategy` by selecting an enumerate function which best fit to this particular situation. -# In this specific example, the interactions plays a great role so that the linear enumerate function may provide better results than the hyperbolic rule. -# * We may want to customize the `projectionStrategy` by selecting an method to compute the coefficient which improves the estimation. -# Given that the function is symbolic and fast, it might be interesting to try an integration rule instead of the least squares method. +# * Since the distribution of the input is known, we may want to give +# this information to the `FunctionalChaosAlgorithm`. +# This prevents the algorithm from trying to fit the input distribution +# which best fit to the data. +# * We may want to customize the `adaptiveStrategy` by selecting an enumerate +# function which best fit to this particular example. +# In this specific example, however, the interactions plays a great role so that the +# linear enumerate function may provide better results than the hyperbolic rule. +# * We may want to customize the `projectionStrategy` by selecting a method +# to compute the coefficient which improves the estimation. +# For example, it might be interesting to +# try an integration rule instead of the least squares method. +# Notice that a specific design of experiment is required in this case. # %% # Reset default settings diff --git a/openturns/master/_downloads/71aec4e01968ab2c8be52211336adbb2/auto_meta_modeling_python.zip b/openturns/master/_downloads/71aec4e01968ab2c8be52211336adbb2/auto_meta_modeling_python.zip index e00a1f46819..a163cbc1642 100644 Binary files a/openturns/master/_downloads/71aec4e01968ab2c8be52211336adbb2/auto_meta_modeling_python.zip and b/openturns/master/_downloads/71aec4e01968ab2c8be52211336adbb2/auto_meta_modeling_python.zip differ diff --git a/openturns/master/_downloads/7263f63092b58313bb0867d9aebe4337/auto_numerical_methods_jupyter.zip b/openturns/master/_downloads/7263f63092b58313bb0867d9aebe4337/auto_numerical_methods_jupyter.zip index 0930cba2a45..0072d432be9 100644 Binary files a/openturns/master/_downloads/7263f63092b58313bb0867d9aebe4337/auto_numerical_methods_jupyter.zip and b/openturns/master/_downloads/7263f63092b58313bb0867d9aebe4337/auto_numerical_methods_jupyter.zip differ diff --git a/openturns/master/_downloads/808735bd7053e739837230a0454d516e/plot_chaos_ishigami_grouped_indices.py b/openturns/master/_downloads/808735bd7053e739837230a0454d516e/plot_chaos_ishigami_grouped_indices.py index b340788d2e8..3da802fef48 100644 --- a/openturns/master/_downloads/808735bd7053e739837230a0454d516e/plot_chaos_ishigami_grouped_indices.py +++ b/openturns/master/_downloads/808735bd7053e739837230a0454d516e/plot_chaos_ishigami_grouped_indices.py @@ -57,7 +57,7 @@ # %% chaosSI = ot.FunctionalChaosSobolIndices(result) -print(chaosSI) +chaosSI # %% # We compute the first order indice of the group [0,1]. diff --git a/openturns/master/_downloads/87d570948e51523fd6c6d3187efa425b/plot_sensitivity_ancova.ipynb b/openturns/master/_downloads/87d570948e51523fd6c6d3187efa425b/plot_sensitivity_ancova.ipynb index 97b4add7799..65448115e72 100644 --- a/openturns/master/_downloads/87d570948e51523fd6c6d3187efa425b/plot_sensitivity_ancova.ipynb +++ b/openturns/master/_downloads/87d570948e51523fd6c6d3187efa425b/plot_sensitivity_ancova.ipynb @@ -94,7 +94,7 @@ }, "outputs": [], "source": [ - "enumerateFunction = ot.LinearEnumerateFunction(2)\nproductBasis = ot.OrthogonalProductPolynomialFactory(\n [ot.HermiteFactory()] * 2, enumerateFunction\n)\nadaptiveStrategy = ot.FixedStrategy(\n productBasis, enumerateFunction.getStrataCumulatedCardinal(4)\n)\nsamplingSize = 250\nexperiment = ot.MonteCarloExperiment(distribution, samplingSize)\nX = experiment.generate()\nY = model(X)\nalgo = ot.FunctionalChaosAlgorithm(X, Y, distribution, adaptiveStrategy)\nalgo.run()\nresult = ot.FunctionalChaosResult(algo.getResult())" + "enumerateFunction = ot.LinearEnumerateFunction(2)\nproductBasis = ot.OrthogonalProductPolynomialFactory(\n [ot.HermiteFactory()] * 2, enumerateFunction\n)\nadaptiveStrategy = ot.FixedStrategy(\n productBasis, enumerateFunction.getStrataCumulatedCardinal(4)\n)\nsamplingSize = 250\nexperiment = ot.MonteCarloExperiment(distribution, samplingSize)\nX = experiment.generate()\nY = model(X)\nalgo = ot.FunctionalChaosAlgorithm(X, Y, distribution, adaptiveStrategy)\nalgo.run()\nresult = algo.getResult()" ] }, { diff --git a/openturns/master/_downloads/88d3828120a999fc8ca5897c5dd2db69/auto_graphs_python.zip b/openturns/master/_downloads/88d3828120a999fc8ca5897c5dd2db69/auto_graphs_python.zip index 5df92f7c059..c4f575de287 100644 Binary files a/openturns/master/_downloads/88d3828120a999fc8ca5897c5dd2db69/auto_graphs_python.zip and b/openturns/master/_downloads/88d3828120a999fc8ca5897c5dd2db69/auto_graphs_python.zip differ diff --git a/openturns/master/_downloads/9fcc717c1e003cd45f666e03ee0e2a05/plot_sensitivity_ancova.py b/openturns/master/_downloads/9fcc717c1e003cd45f666e03ee0e2a05/plot_sensitivity_ancova.py index ae20edd6670..87574ab7a57 100644 --- a/openturns/master/_downloads/9fcc717c1e003cd45f666e03ee0e2a05/plot_sensitivity_ancova.py +++ b/openturns/master/_downloads/9fcc717c1e003cd45f666e03ee0e2a05/plot_sensitivity_ancova.py @@ -70,7 +70,7 @@ Y = model(X) algo = ot.FunctionalChaosAlgorithm(X, Y, distribution, adaptiveStrategy) algo.run() -result = ot.FunctionalChaosResult(algo.getResult()) +result = algo.getResult() # %% # Create the input sample taking account the correlation diff --git a/openturns/master/_downloads/a1d8d0b63d5143d9b72b4959aac7d782/auto_reliability_sensitivity_jupyter.zip b/openturns/master/_downloads/a1d8d0b63d5143d9b72b4959aac7d782/auto_reliability_sensitivity_jupyter.zip index 52bd3589cb1..17d562e4f49 100644 Binary files a/openturns/master/_downloads/a1d8d0b63d5143d9b72b4959aac7d782/auto_reliability_sensitivity_jupyter.zip and b/openturns/master/_downloads/a1d8d0b63d5143d9b72b4959aac7d782/auto_reliability_sensitivity_jupyter.zip differ diff --git a/openturns/master/_downloads/a748ffe095675c16859218f143b99a75/auto_reliability_sensitivity_python.zip b/openturns/master/_downloads/a748ffe095675c16859218f143b99a75/auto_reliability_sensitivity_python.zip index cf967718af4..cc3c49e31c9 100644 Binary files a/openturns/master/_downloads/a748ffe095675c16859218f143b99a75/auto_reliability_sensitivity_python.zip and b/openturns/master/_downloads/a748ffe095675c16859218f143b99a75/auto_reliability_sensitivity_python.zip differ diff --git a/openturns/master/_downloads/abd4774b43e90e70bd9135cf6e27a1a2/auto_meta_modeling_jupyter.zip b/openturns/master/_downloads/abd4774b43e90e70bd9135cf6e27a1a2/auto_meta_modeling_jupyter.zip index a49d646da1b..9c498b3375d 100644 Binary files a/openturns/master/_downloads/abd4774b43e90e70bd9135cf6e27a1a2/auto_meta_modeling_jupyter.zip and b/openturns/master/_downloads/abd4774b43e90e70bd9135cf6e27a1a2/auto_meta_modeling_jupyter.zip differ diff --git a/openturns/master/_downloads/b77fabceeed0488793aa1923f45f794f/plot_sensitivity_wingweight.py b/openturns/master/_downloads/b77fabceeed0488793aa1923f45f794f/plot_sensitivity_wingweight.py index a04758121e4..6fadc422180 100644 --- a/openturns/master/_downloads/b77fabceeed0488793aa1923f45f794f/plot_sensitivity_wingweight.py +++ b/openturns/master/_downloads/b77fabceeed0488793aa1923f45f794f/plot_sensitivity_wingweight.py @@ -357,7 +357,9 @@ # The relative errors are low : this indicates that the PCE model has good accuracy. # Then, we exploit the surrogate model to compute the Sobol' indices. sensitivityAnalysis = ot.FunctionalChaosSobolIndices(result) -print(sensitivityAnalysis) +sensitivityAnalysis + +# %% firstOrder = [sensitivityAnalysis.getSobolIndex(i) for i in range(m.dim)] totalOrder = [sensitivityAnalysis.getSobolTotalIndex(i) for i in range(m.dim)] graph = ot.SobolIndicesAlgorithm.DrawSobolIndices(inputNames, firstOrder, totalOrder) diff --git a/openturns/master/_downloads/bb1db896ae1deb897c7b02a1ff591375/auto_probabilistic_modeling_python.zip b/openturns/master/_downloads/bb1db896ae1deb897c7b02a1ff591375/auto_probabilistic_modeling_python.zip index 13e44e3250d..2d491f61f21 100644 Binary files a/openturns/master/_downloads/bb1db896ae1deb897c7b02a1ff591375/auto_probabilistic_modeling_python.zip and b/openturns/master/_downloads/bb1db896ae1deb897c7b02a1ff591375/auto_probabilistic_modeling_python.zip differ diff --git a/openturns/master/_downloads/bf1a4f3bee47286c7b782ba172f895e3/plot_kriging_hyperparameters_optimization.ipynb b/openturns/master/_downloads/bf1a4f3bee47286c7b782ba172f895e3/plot_kriging_hyperparameters_optimization.ipynb index 3f335cbf4b4..1f59b8ed7ca 100644 --- a/openturns/master/_downloads/bf1a4f3bee47286c7b782ba172f895e3/plot_kriging_hyperparameters_optimization.ipynb +++ b/openturns/master/_downloads/bf1a4f3bee47286c7b782ba172f895e3/plot_kriging_hyperparameters_optimization.ipynb @@ -4,14 +4,14 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "\n# Kriging :configure the optimization solver\n" + "\n# Kriging: configure the optimization solver\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "The goal of this example is to show how to fine-tune the optimization solver used to estimate the hyperparameters of the covariance model of the kriging metamodel.\n\n## Introduction\n\nIn a kriging metamodel, there are various types of parameters which are estimated from the data.\n\n* The parameters ${\\bf \\beta}$ associated with the deterministic trend. These parameters are computed based on linear least squares.\n* The parameters of the covariance model.\n\nThe covariance model has two types of parameters.\n\n* The amplitude parameter $\\sigma^2$ is estimated from the data.\n If the output dimension is equal to one, this parameter is estimated using\n the analytic variance estimator which maximizes the likelihood.\n Otherwise, if output dimension is greater than one or analytical sigma disabled,\n this parameter is estimated from numerical optimization.\n* The other parameters ${\\bf \\theta}\\in\\mathbb{R}^d$ where $d$ is\n the spatial dimension of the covariance model.\n Often, the parameter ${\\bf \\theta}$ is a scale parameter.\n This step involves an optimization algorithm.\n\nAll these parameters are estimated with the `GeneralLinearModelAlgorithm` class.\n\nThe estimation of the ${\\bf \\theta}$ parameters is the step which has the highest CPU cost.\nMoreover, the maximization of likelihood may be associated with difficulties e.g. many local maximums or even the non convergence of the optimization algorithm.\nIn this case, it might be useful to fine tune the optimization algorithm so that the convergence of the optimization algorithm is, hopefully, improved.\n\nFurthermore, there are several situations in which the optimization can be initialized or completely bypassed.\nSuppose for example that we have already created an initial kriging metamodel with $N$ points and we want to add a single new point.\n\n* It might be interesting to initialize the optimization algorithm with the optimum found for the previous kriging metamodel:\n this may reduce the number of iterations required to maximize the likelihood.\n* We may as well completely bypass the optimization step: if the previous covariance model was correctly estimated,\n the update of the parameters may or may not significantly improve the estimates.\n\nThis is why the goal of this example is to see how to configure the optimization of the hyperparameters of a kriging metamodel.\n\n" + "The goal of this example is to show how to fine-tune the optimization solver used to estimate the hyperparameters of the covariance model of the kriging metamodel.\n\n## Introduction\n\nIn a kriging metamodel, there are various types of parameters which are estimated from the data.\n\n* The parameters ${\\bf \\beta}$ associated with the deterministic trend. These parameters are computed based on linear least squares.\n* The parameters of the covariance model.\n\nThe covariance model has two types of parameters.\n\n* The amplitude parameter $\\sigma^2$ is estimated from the data.\n If the output dimension is equal to one, this parameter is estimated using\n the analytic variance estimator which maximizes the likelihood.\n Otherwise, if output dimension is greater than one or analytical sigma disabled,\n this parameter is estimated from numerical optimization.\n* The other parameters ${\\bf \\theta}\\in\\mathbb{R}^d$ where $d$ is\n the spatial dimension of the covariance model.\n Often, the parameter ${\\bf \\theta}$ is a scale parameter.\n This step involves an optimization algorithm.\n\nAll these parameters are estimated with the :class:`~openturns.GeneralLinearModelAlgorithm` class.\n\nThe estimation of the ${\\bf \\theta}$ parameters is the step which has the highest CPU cost.\nMoreover, the maximization of likelihood may be associated with difficulties e.g. many local maximums or even the non convergence of the optimization algorithm.\nIn this case, it might be useful to fine tune the optimization algorithm so that the convergence of the optimization algorithm is, hopefully, improved.\n\nFurthermore, there are several situations in which the optimization can be initialized or completely bypassed.\nSuppose for example that we have already created an initial kriging metamodel with $N$ points and we want to add a single new point.\n\n* It might be interesting to initialize the optimization algorithm with the optimum found for the previous kriging metamodel:\n this may reduce the number of iterations required to maximize the likelihood.\n* We may as well completely bypass the optimization step: if the previous covariance model was correctly estimated,\n the update of the parameters may or may not significantly improve the estimates.\n\nThis is why the goal of this example is to see how to configure the optimization of the hyperparameters of a kriging metamodel.\n\n" ] }, { @@ -79,7 +79,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Finally, we define the dependency using a `NormalCopula`.\n\n" + "Finally, we define the dependency using a :class:`~openturns.NormalCopula`.\n\n" ] }, { @@ -104,7 +104,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "We consider a simple Monte-Carlo sampling as a design of experiments. This is why we generate an input sample using the `getSample` method of the distribution.\nThen we evaluate the output using the `model` function.\n\n" + "We consider a simple Monte-Carlo sampling as a design of experiments.\nThis is why we generate an input sample using the `getSample` method of the distribution.\nThen we evaluate the output using the `model` function.\n\n" ] }, { @@ -129,7 +129,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "In order to create the kriging metamodel, we first select a constant trend with the `ConstantBasisFactory` class.\nThen we use a squared exponential covariance model.\nFinally, we use the `KrigingAlgorithm` class to create the kriging metamodel,\ntaking the training sample, the covariance model and the trend basis as input arguments.\n\n" + "In order to create the kriging metamodel, we first select a constant trend with the :class:`~openturns.ConstantBasisFactory` class.\nThen we use a squared exponential covariance model.\nFinally, we use the :class:`~openturns.KrigingAlgorithm` class to create the kriging metamodel,\ntaking the training sample, the covariance model and the trend basis as input arguments.\n\n" ] }, { @@ -147,7 +147,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The `run` method has optimized the hyperparameters of the metamodel.\n\nWe can then print the constant trend of the metamodel, which have been estimated using the least squares method.\n\n" + "The :meth:`~openturns.KrigingAlgorithm.run` method has optimized the hyperparameters of the metamodel.\n\nWe can then print the constant trend of the metamodel, which have been\nestimated using the least squares method.\n\n" ] }, { @@ -190,7 +190,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The `getOptimizationAlgorithm` method returns the optimization algorithm used to optimize the ${\\bf \\theta}$ parameters of the `SquaredExponential` covariance model.\n\n" + "The :meth:`~openturns.KrigingAlgorithm.getOptimizationAlgorithm` method\nreturns the optimization algorithm used to optimize the\n${\\bf \\theta}$ parameters of the\n:class:`~openturns.SquaredExponential` covariance model.\n\n" ] }, { @@ -226,7 +226,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The `getOptimizationBounds` method returns the bounds. The dimension of these bounds correspond to the spatial dimension of the covariance model.\nIn the metamodeling context, this correspond to the input dimension of the model.\n\n" + "The :meth:`~openturns.KrigingAlgorithm.getOptimizationBounds` method\nreturns the bounds.\nThe dimension of these bounds correspond to the spatial dimension of\nthe covariance model.\nIn the metamodeling context, this correspond to the input dimension of the model.\n\n" ] }, { @@ -266,7 +266,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The `getOptimizeParameters` method returns `True` if these parameters are to be optimized.\n\n" + "The :meth:`~openturns.KrigingAlgorithm.getOptimizeParameters` method returns `True` if these parameters are to be optimized.\n\n" ] }, { @@ -291,7 +291,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The starting point of the optimization is based on the parameters of the covariance model.\nIn the following example, we configure the parameters of the covariance model to the arbitrary values `[12.,34.,56.,78.]`.\n\n" + "The starting point of the optimization is based on the parameters of the covariance model.\nIn the following example, we configure the parameters of the covariance model to\nthe arbitrary values `[12.0, 34.0, 56.0, 78.0]`.\n\n" ] }, { @@ -363,7 +363,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "It is sometimes useful to completely disable the optimization of the parameters.\nIn order to see the effect of this, we first initialize the parameters of the covariance model with the arbitrary values `[12.,34.,56.,78.]`.\n\n" + "It is sometimes useful to completely disable the optimization of the parameters.\nIn order to see the effect of this, we first initialize the parameters of\nthe covariance model with the arbitrary values `[12.0, 34.0, 56.0, 78.0]`.\n\n" ] }, { @@ -374,14 +374,14 @@ }, "outputs": [], "source": [ - "covarianceModel = ot.SquaredExponential([12.0, 34.0, 56.0, 78.0], [91.0])\nalgo = ot.KrigingAlgorithm(X_train, Y_train, covarianceModel, basis)\nalgo.setOptimizationBounds(scaleOptimizationBounds) # Trick B" + "covarianceModel = ot.SquaredExponential([12.0, 34.0, 56.0, 78.0], [91.0])\nalgo = ot.KrigingAlgorithm(X_train, Y_train, covarianceModel, basis)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "The `setOptimizeParameters` method can be used to disable the optimization of the parameters.\n\n" + "The :meth:`~openturns.KrigingAlgorithm.setOptimizeParameters` method can be\nused to disable the optimization of the parameters.\n\n" ] }, { @@ -619,7 +619,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The following example checks the robustness of the optimization of the kriging algorithm with respect to\nthe optimization of the likelihood function in the covariance model parameters estimation.\nWe use a `MultiStart` algorithm in order to avoid to be trapped by a local minimum.\nFurthermore, we generate the design of experiments using a `LHSExperiments`, which guarantees that the points will fill the space.\n\n" + "The following example checks the robustness of the optimization of the\nkriging algorithm with respect to the optimization of the likelihood\nfunction in the covariance model parameters estimation.\nWe use a :class:`~openturns.MultiStart` algorithm in order to avoid to be trapped by a local minimum.\nFurthermore, we generate the design of experiments using a\n:class:`~openturns.LHSExperiments`, which guarantees that the points\nwill fill the space.\n\n" ] }, { @@ -637,7 +637,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "First, we create a multivariate distribution, based on independent `Uniform` marginals which have the bounds required by the covariance model.\n\n" + "First, we create a multivariate distribution, based on independent\n:class:`~openturns.Uniform` marginals which have the bounds required\nby the covariance model.\n\n" ] }, { @@ -655,7 +655,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "We first generate a Latin Hypercube Sampling (LHS) design made of 25 points in the sample space. This LHS is optimized so as to fill the space.\n\n" + "We first generate a Latin Hypercube Sampling (LHS) design made of 25 points in the sample space.\nThis LHS is optimized so as to fill the space.\n\n" ] }, { @@ -673,7 +673,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "We can check that the minimum and maximum in the sample correspond to the bounds of the design of experiment.\n\n" + "We can check that the minimum and maximum in the sample correspond to the\nbounds of the design of experiment.\n\n" ] }, { @@ -702,7 +702,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Then we create a `MultiStart` algorithm based on the LHS starting points.\n\n" + "Then we create a :class:`~openturns.MultiStart` algorithm based on the LHS starting points.\n\n" ] }, { @@ -720,7 +720,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Finally, we configure the optimization algorithm so as to use the `MultiStart` algorithm.\n\n" + "Finally, we configure the optimization algorithm so as to use the :class:`~openturns.MultiStart` algorithm.\n\n" ] }, { diff --git a/openturns/master/_downloads/ca1cafbe970135714f4ef620e84fc370/plot_sensitivity_wingweight.ipynb b/openturns/master/_downloads/ca1cafbe970135714f4ef620e84fc370/plot_sensitivity_wingweight.ipynb index cbaf4f8f4f3..63bb302f6e0 100644 --- a/openturns/master/_downloads/ca1cafbe970135714f4ef620e84fc370/plot_sensitivity_wingweight.ipynb +++ b/openturns/master/_downloads/ca1cafbe970135714f4ef620e84fc370/plot_sensitivity_wingweight.ipynb @@ -580,7 +580,18 @@ }, "outputs": [], "source": [ - "sensitivityAnalysis = ot.FunctionalChaosSobolIndices(result)\nprint(sensitivityAnalysis)\nfirstOrder = [sensitivityAnalysis.getSobolIndex(i) for i in range(m.dim)]\ntotalOrder = [sensitivityAnalysis.getSobolTotalIndex(i) for i in range(m.dim)]\ngraph = ot.SobolIndicesAlgorithm.DrawSobolIndices(inputNames, firstOrder, totalOrder)\ngraph.setTitle(\"Sobol indices by Polynomial Chaos Expansion - wing weight\")\nview = otv.View(graph)" + "sensitivityAnalysis = ot.FunctionalChaosSobolIndices(result)\nsensitivityAnalysis" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "firstOrder = [sensitivityAnalysis.getSobolIndex(i) for i in range(m.dim)]\ntotalOrder = [sensitivityAnalysis.getSobolTotalIndex(i) for i in range(m.dim)]\ngraph = ot.SobolIndicesAlgorithm.DrawSobolIndices(inputNames, firstOrder, totalOrder)\ngraph.setTitle(\"Sobol indices by Polynomial Chaos Expansion - wing weight\")\nview = otv.View(graph)" ] }, { diff --git a/openturns/master/_downloads/d881e30c6cf4282dac4d5fae78a446b2/plot_quick_start_point_and_sample.py b/openturns/master/_downloads/d881e30c6cf4282dac4d5fae78a446b2/plot_quick_start_point_and_sample.py index 632046111f8..b54a58740bc 100644 --- a/openturns/master/_downloads/d881e30c6cf4282dac4d5fae78a446b2/plot_quick_start_point_and_sample.py +++ b/openturns/master/_downloads/d881e30c6cf4282dac4d5fae78a446b2/plot_quick_start_point_and_sample.py @@ -17,8 +17,8 @@ # # Two fundamental objects in the library are: # -# * `Point`: a multidimensional point in :math:`D` dimensions (:math:`\in \mathbb{R}^D`) ; -# * `Sample`: a multivariate sample made of :math:`N` points in :math:`D` dimensions. +# * `Point`: a multidimensional point in :math:`d` dimensions (:math:`\in \mathbb{R}^d`) ; +# * `Sample`: a multivariate sample made of :math:`n` points in :math:`d` dimensions. # # %% @@ -66,18 +66,18 @@ # The `Sample` class # ------------------ # -# The `Sample` class represents a multivariate sample made of :math:`N` points in :math:`\mathbb{R}^D`. +# The `Sample` class represents a multivariate sample made of :math:`n` points in :math:`\mathbb{R}^d`. # -# * :math:`D` is the *dimension* of the sample, -# * :math:`N` is the *size* of the sample. +# * :math:`d` is the *dimension* of the sample, +# * :math:`n` is the *size* of the sample. # # -# A `Sample` can be seen as an array of with :math:`N` rows and :math:`D` columns. +# A `Sample` can be seen as an array of with :math:`n` rows and :math:`d` columns. # # *Remark.* The :class:`~openturns.ProcessSample` class can be used to manage a sample of stochastic processes. # %% -# The script below creates a `Sample` with size :math:`N=5` and dimension :math:`D=3`. +# The script below creates a `Sample` with size :math:`n=5` and dimension :math:`d=3`. # %% data = ot.Sample(5, 3) @@ -133,7 +133,7 @@ # * the `row` is a `Point`, # * the `column` is a `Sample`. # -# This is consistent with the fact that, in a dimension :math:`D` `Sample`, a row is a :math:`D`-dimensional `Point`. +# This is consistent with the fact that, in a dimension :math:`d` `Sample`, a row is a :math:`d`-dimensional `Point`. # %% # The following statement extracts several columns (with indices 0 and 2) and creates a new `Sample`. @@ -141,21 +141,38 @@ # %% data.getMarginal([0, 2]) +# %% +# Set a row or a column of a `Sample` +# ----------------------------------- + # %% # Slicing can also be used to set a `Sample` row or column. # %% sample = ot.Sample([[1.0, 2.0], [3.0, 4.0], [5.0, 6.0]]) +sample + +# %% +# Set the third row: this must be a `Point` or must be convertible to. p = [8.0, 10.0] sample[2, :] = p sample # %% +# Set the second column: this must be a `Sample` or must be convertible to. sample = ot.Sample([[1.0, 2.0], [3.0, 4.0], [5.0, 6.0]]) s = ot.Sample([[3.0], [5.0], [7.0]]) sample[:, 1] = s sample +# %% +# Sometimes, we want to set a column with a list of floats. +# This can be done using the :meth:`~openturns.Sample.BuildFromPoint` static method. +sample = ot.Sample([[1.0, 2.0], [3.0, 4.0], [5.0, 6.0]]) +s = ot.Sample.BuildFromPoint([3.0, 5.0, 7.0]) +sample[:, 1] = s +sample + # %% # Create a `Point` or a `Sample` from a Python list # ------------------------------------------------- @@ -231,7 +248,7 @@ array # %% -type(array) +print(type(array)) # %% # Conversely, the following script creates a Numpy `array`, then converts it into a :class:`~openturns.Sample`. @@ -278,13 +295,27 @@ sample # %% -# If we do not set the optional `size` parameter, the library cannot solve the -# case and an `InvalidArgumentException` is generated. -# More precisely, the code:: +# When there is an ambiguous case, the library cannot solve the +# issue and an `InvalidArgumentException` is generated. + +# %% +# More precisely, the code: +# +# .. code-block:: # # sample = ot.Sample(u) # -# produces the exception:: + +# %% +# produces the exception: +# +# .. code-block:: # # TypeError: InvalidArgumentException : Invalid array dimension: 1 # + +# %% +# In order to solve that problem, we can use the :meth:`~openturns.Sample.BuildFromPoint` +# static method. +sample = ot.Sample.BuildFromPoint([ui for ui in u]) +sample diff --git a/openturns/master/_downloads/dce365067acf481999ee410b3d643a7e/auto_numerical_methods_python.zip b/openturns/master/_downloads/dce365067acf481999ee410b3d643a7e/auto_numerical_methods_python.zip index 1dbaf8cce24..30f1c8b1865 100644 Binary files a/openturns/master/_downloads/dce365067acf481999ee410b3d643a7e/auto_numerical_methods_python.zip and b/openturns/master/_downloads/dce365067acf481999ee410b3d643a7e/auto_numerical_methods_python.zip differ diff --git a/openturns/master/_downloads/dd76f5e1add5920db60c2e55c5724788/plot_chaos_build_distribution.ipynb b/openturns/master/_downloads/dd76f5e1add5920db60c2e55c5724788/plot_chaos_build_distribution.ipynb index 09688d380b0..60f6b811b79 100644 --- a/openturns/master/_downloads/dd76f5e1add5920db60c2e55c5724788/plot_chaos_build_distribution.ipynb +++ b/openturns/master/_downloads/dd76f5e1add5920db60c2e55c5724788/plot_chaos_build_distribution.ipynb @@ -144,7 +144,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "We can also analyse its properties in more detail.\n\n" + "We can also analyse its properties in more details.\n\n" ] }, { diff --git a/openturns/master/_downloads/e699ec1a7cf7ba496c01307653bd27e9/plot_parametric_function.py b/openturns/master/_downloads/e699ec1a7cf7ba496c01307653bd27e9/plot_parametric_function.py index a851d4255a8..8c7a6d967b5 100644 --- a/openturns/master/_downloads/e699ec1a7cf7ba496c01307653bd27e9/plot_parametric_function.py +++ b/openturns/master/_downloads/e699ec1a7cf7ba496c01307653bd27e9/plot_parametric_function.py @@ -3,15 +3,21 @@ ============================ """ # %% -# In this example we are going to create a parametric function: +# In this example, we show how to use the :class:`~openturns.ParametricFunction` class. +# This is a tool which is very convenient when we perform +# calibration, e.g. with :class:`~openturns.NonLinearLeastSquaresCalibration` +# or :class:`~openturns.RandomWalkMetropolisHastings`. + +# %% +# In this example we create a parametric function: # # .. math:: -# d_{L,I}(E, F): \mathbb{R}^2 \rightarrow \mathbb{R} +# d_{L,I}(E, F): \Rset^2 \rightarrow \Rset # # function from an existing "full" function: # # .. math:: -# d(E, F, L, I): \mathbb{R}^4 \rightarrow \mathbb{R} +# d(E, F, L, I): \Rset^4 \rightarrow \Rset. # # %% @@ -20,6 +26,11 @@ ot.Log.Show(ot.Log.NONE) +# %% +# Define the function +# ~~~~~~~~~~~~~~~~~~~ + + # %% # Create the function with all parameters d(E, F, L, I) def d_func(X): @@ -29,12 +40,75 @@ def d_func(X): beam = ot.PythonFunction(4, 1, d_func) +beam.setInputDescription(["E", "F", "L", "I"]) # %% # Evaluate d x = [50.0, 1.0, 10.0, 5.0] beam(x) +# %% +# In the physical model, the inputs and parameters are ordered as +# presented in the next table. +# Notice that there are no parameters in the physical model. +# +# +-------+----------------+ +# | Index | Input variable | +# +=======+================+ +# | 0 | E | +# +-------+----------------+ +# | 1 | F | +# +-------+----------------+ +# | 2 | L | +# +-------+----------------+ +# | 3 | I | +# +-------+----------------+ +# +# +-------+-----------+ +# | Index | Parameter | +# +=======+===========+ +# | ∅ | ∅ | +# +-------+-----------+ +# +# **Table 1.** Indices and names of the inputs and parameters of the physical model. +# + +# %% +# The next cell presents the description of the input variables +# and the description of the parameters of the physical model. +# We see that there is no parameter at this stage in this function. +print("Physical Model Inputs:", beam.getInputDescription()) +print("Physical Model Parameters:", beam.getParameterDescription()) + + +# %% +# Define the parametric function +# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +# %% +# We create a :class:`~openturns.ParametricFunction` +# where the parameters are `L` and `I` which have the indices 2 and +# and 3 in the physical model. +# +# +-------+----------------+ +# | Index | Input variable | +# +=======+================+ +# | 0 | E | +# +-------+----------------+ +# | 1 | F | +# +-------+----------------+ +# +# +-------+-----------+ +# | Index | Parameter | +# +=======+===========+ +# | 0 | L | +# +-------+-----------+ +# | 1 | I | +# +-------+-----------+ +# +# **Table 2.** Indices and names of the inputs and parameters of the parametric model. +# + # %% # Create the indices of the frozen parameters (L,I) from the full parameter list indices = [2, 3] @@ -47,6 +121,13 @@ def d_func(X): # Create the parametric function beam_LI = ot.ParametricFunction(beam, indices, referencePoint) +# %% +# The next cell presents the description of the input variables +# and the description of the parameters of the parametric function. +# We see that the parametric function has 2 parameters: L and I. +print("Physical Model Inputs:", beam_LI.getInputDescription()) +print("Physical Model Parameters:", beam_LI.getParameterDescription()) + # %% # Evaluate d on (E,F) with fixed parameters (L,I) beam_LI([50.0, 1.0]) diff --git a/openturns/master/_downloads/ee2bbb2beb44f9b3de56079b0634b808/auto_calibration_python.zip b/openturns/master/_downloads/ee2bbb2beb44f9b3de56079b0634b808/auto_calibration_python.zip index 6ebe56d5b0e..80e507af279 100644 Binary files a/openturns/master/_downloads/ee2bbb2beb44f9b3de56079b0634b808/auto_calibration_python.zip and b/openturns/master/_downloads/ee2bbb2beb44f9b3de56079b0634b808/auto_calibration_python.zip differ diff --git a/openturns/master/_downloads/f99df5de352604d8f438a3c4a3ea0b2c/auto_graphs_jupyter.zip b/openturns/master/_downloads/f99df5de352604d8f438a3c4a3ea0b2c/auto_graphs_jupyter.zip index 1e76359d664..bfa62cce9ce 100644 Binary files a/openturns/master/_downloads/f99df5de352604d8f438a3c4a3ea0b2c/auto_graphs_jupyter.zip and b/openturns/master/_downloads/f99df5de352604d8f438a3c4a3ea0b2c/auto_graphs_jupyter.zip differ diff --git a/openturns/master/_downloads/ffa9d199d7551d68b3799354df3b5bf5/auto_data_analysis_python.zip b/openturns/master/_downloads/ffa9d199d7551d68b3799354df3b5bf5/auto_data_analysis_python.zip index e1ffc2e2bc3..2f5ab02c3f5 100644 Binary files a/openturns/master/_downloads/ffa9d199d7551d68b3799354df3b5bf5/auto_data_analysis_python.zip and b/openturns/master/_downloads/ffa9d199d7551d68b3799354df3b5bf5/auto_data_analysis_python.zip differ diff --git a/openturns/master/_images/sphx_glr_plot_chaos_cantilever_beam_integration_001.png b/openturns/master/_images/sphx_glr_plot_chaos_cantilever_beam_integration_001.png index 4a03f59535d..812d6a9b62c 100644 Binary files a/openturns/master/_images/sphx_glr_plot_chaos_cantilever_beam_integration_001.png and b/openturns/master/_images/sphx_glr_plot_chaos_cantilever_beam_integration_001.png differ diff --git a/openturns/master/_images/sphx_glr_plot_chaos_cantilever_beam_integration_002.png b/openturns/master/_images/sphx_glr_plot_chaos_cantilever_beam_integration_002.png index af883d8a960..ab4bf35c9cb 100644 Binary files a/openturns/master/_images/sphx_glr_plot_chaos_cantilever_beam_integration_002.png and b/openturns/master/_images/sphx_glr_plot_chaos_cantilever_beam_integration_002.png differ diff --git a/openturns/master/_images/sphx_glr_plot_chaos_cantilever_beam_integration_003.png b/openturns/master/_images/sphx_glr_plot_chaos_cantilever_beam_integration_003.png index a9e3b05634b..dd3e35d2e47 100644 Binary files a/openturns/master/_images/sphx_glr_plot_chaos_cantilever_beam_integration_003.png and b/openturns/master/_images/sphx_glr_plot_chaos_cantilever_beam_integration_003.png differ diff --git a/openturns/master/_images/sphx_glr_plot_chaos_cantilever_beam_integration_thumb.png b/openturns/master/_images/sphx_glr_plot_chaos_cantilever_beam_integration_thumb.png index 45d4e923b2c..d3a41b838d8 100644 Binary files a/openturns/master/_images/sphx_glr_plot_chaos_cantilever_beam_integration_thumb.png and b/openturns/master/_images/sphx_glr_plot_chaos_cantilever_beam_integration_thumb.png differ diff --git a/openturns/master/_images/sphx_glr_plot_chaos_draw_validation_001.png b/openturns/master/_images/sphx_glr_plot_chaos_draw_validation_001.png index f33ecd05b5c..1356f3a4c8e 100644 Binary files a/openturns/master/_images/sphx_glr_plot_chaos_draw_validation_001.png and b/openturns/master/_images/sphx_glr_plot_chaos_draw_validation_001.png differ diff --git a/openturns/master/_images/sphx_glr_plot_chaos_draw_validation_thumb.png b/openturns/master/_images/sphx_glr_plot_chaos_draw_validation_thumb.png index 543fdcf42e9..c1a9911bfa6 100644 Binary files a/openturns/master/_images/sphx_glr_plot_chaos_draw_validation_thumb.png and b/openturns/master/_images/sphx_glr_plot_chaos_draw_validation_thumb.png differ diff --git a/openturns/master/_images/sphx_glr_plot_ego_003.png b/openturns/master/_images/sphx_glr_plot_ego_003.png index 70bb4780123..c35a9190a45 100644 Binary files a/openturns/master/_images/sphx_glr_plot_ego_003.png and b/openturns/master/_images/sphx_glr_plot_ego_003.png differ diff --git a/openturns/master/_images/sphx_glr_plot_ego_005.png b/openturns/master/_images/sphx_glr_plot_ego_005.png index e93454623bf..7e877be5d34 100644 Binary files a/openturns/master/_images/sphx_glr_plot_ego_005.png and b/openturns/master/_images/sphx_glr_plot_ego_005.png differ diff --git a/openturns/master/_images/sphx_glr_plot_ego_009.png b/openturns/master/_images/sphx_glr_plot_ego_009.png index 7930f30527b..c71369c5c8d 100644 Binary files a/openturns/master/_images/sphx_glr_plot_ego_009.png and b/openturns/master/_images/sphx_glr_plot_ego_009.png differ diff --git a/openturns/master/_images/sphx_glr_plot_functional_chaos_001.png b/openturns/master/_images/sphx_glr_plot_functional_chaos_001.png index 747b55f7687..5b95ccfdbb8 100644 Binary files a/openturns/master/_images/sphx_glr_plot_functional_chaos_001.png and b/openturns/master/_images/sphx_glr_plot_functional_chaos_001.png differ diff --git a/openturns/master/_images/sphx_glr_plot_functional_chaos_002.png b/openturns/master/_images/sphx_glr_plot_functional_chaos_002.png index 16ac6eb9cde..64f3a1c098a 100644 Binary files a/openturns/master/_images/sphx_glr_plot_functional_chaos_002.png and b/openturns/master/_images/sphx_glr_plot_functional_chaos_002.png differ diff --git a/openturns/master/_images/sphx_glr_plot_functional_chaos_003.png b/openturns/master/_images/sphx_glr_plot_functional_chaos_003.png index 01541c9c656..fb3e52e373a 100644 Binary files a/openturns/master/_images/sphx_glr_plot_functional_chaos_003.png and b/openturns/master/_images/sphx_glr_plot_functional_chaos_003.png differ diff --git a/openturns/master/_images/sphx_glr_plot_functional_chaos_004.png b/openturns/master/_images/sphx_glr_plot_functional_chaos_004.png index 826e494ef23..391b1c129be 100644 Binary files a/openturns/master/_images/sphx_glr_plot_functional_chaos_004.png and b/openturns/master/_images/sphx_glr_plot_functional_chaos_004.png differ diff --git a/openturns/master/_images/sphx_glr_plot_functional_chaos_thumb.png b/openturns/master/_images/sphx_glr_plot_functional_chaos_thumb.png index cc2ceab3d3b..6e9dfca62e3 100644 Binary files a/openturns/master/_images/sphx_glr_plot_functional_chaos_thumb.png and b/openturns/master/_images/sphx_glr_plot_functional_chaos_thumb.png differ diff --git a/openturns/master/_images/sphx_glr_plot_ifs_001.png b/openturns/master/_images/sphx_glr_plot_ifs_001.png index f53b4978ec3..9cafbb1d34c 100644 Binary files a/openturns/master/_images/sphx_glr_plot_ifs_001.png and b/openturns/master/_images/sphx_glr_plot_ifs_001.png differ diff --git a/openturns/master/_images/sphx_glr_plot_ifs_002.png b/openturns/master/_images/sphx_glr_plot_ifs_002.png index f0c9f185f89..c24b3adcd30 100644 Binary files a/openturns/master/_images/sphx_glr_plot_ifs_002.png and b/openturns/master/_images/sphx_glr_plot_ifs_002.png differ diff --git a/openturns/master/_images/sphx_glr_plot_ifs_003.png b/openturns/master/_images/sphx_glr_plot_ifs_003.png index c5549ec7bc4..cd4f850bfd6 100644 Binary files a/openturns/master/_images/sphx_glr_plot_ifs_003.png and b/openturns/master/_images/sphx_glr_plot_ifs_003.png differ diff --git a/openturns/master/_images/sphx_glr_plot_ifs_004.png b/openturns/master/_images/sphx_glr_plot_ifs_004.png index 46fde7a86d1..9135d0c931b 100644 Binary files a/openturns/master/_images/sphx_glr_plot_ifs_004.png and b/openturns/master/_images/sphx_glr_plot_ifs_004.png differ diff --git a/openturns/master/_images/sphx_glr_plot_ifs_thumb.png b/openturns/master/_images/sphx_glr_plot_ifs_thumb.png index ee6b738d0bf..66d3d5fa94b 100644 Binary files a/openturns/master/_images/sphx_glr_plot_ifs_thumb.png and b/openturns/master/_images/sphx_glr_plot_ifs_thumb.png differ diff --git a/openturns/master/_images/sphx_glr_plot_optimization_dlib_002.png b/openturns/master/_images/sphx_glr_plot_optimization_dlib_002.png index d430bf67938..251575c7bed 100644 Binary files a/openturns/master/_images/sphx_glr_plot_optimization_dlib_002.png and b/openturns/master/_images/sphx_glr_plot_optimization_dlib_002.png differ diff --git a/openturns/master/_images/sphx_glr_plot_optimization_dlib_003.png b/openturns/master/_images/sphx_glr_plot_optimization_dlib_003.png index 976202eba8b..20db2b9aea3 100644 Binary files a/openturns/master/_images/sphx_glr_plot_optimization_dlib_003.png and b/openturns/master/_images/sphx_glr_plot_optimization_dlib_003.png differ diff --git a/openturns/master/_images/sphx_glr_plot_pce_design_001.png b/openturns/master/_images/sphx_glr_plot_pce_design_001.png index 8993ca1fb52..51eafeec379 100644 Binary files a/openturns/master/_images/sphx_glr_plot_pce_design_001.png and b/openturns/master/_images/sphx_glr_plot_pce_design_001.png differ diff --git a/openturns/master/_images/sphx_glr_plot_pce_design_thumb.png b/openturns/master/_images/sphx_glr_plot_pce_design_thumb.png index d34a55121f7..08ae4d1900e 100644 Binary files a/openturns/master/_images/sphx_glr_plot_pce_design_thumb.png and b/openturns/master/_images/sphx_glr_plot_pce_design_thumb.png differ diff --git a/openturns/master/_sources/auto_calibration/bayesian_calibration/plot_bayesian_calibration.rst.txt b/openturns/master/_sources/auto_calibration/bayesian_calibration/plot_bayesian_calibration.rst.txt index 58662486abb..66e6cccbf4c 100644 --- a/openturns/master/_sources/auto_calibration/bayesian_calibration/plot_bayesian_calibration.rst.txt +++ b/openturns/master/_sources/auto_calibration/bayesian_calibration/plot_bayesian_calibration.rst.txt @@ -21,7 +21,7 @@ Bayesian calibration of a computer code ======================================= -.. GENERATED FROM PYTHON SOURCE LINES 6-89 +.. GENERATED FROM PYTHON SOURCE LINES 6-96 In this example we compute the parameters of a computer model thanks to Bayesian estimation. @@ -39,7 +39,9 @@ and :math:`\vect\theta \in \mathbb{R}^p` the calibration parameters we wish to e The posterior distribution is given by Bayes theorem: -.. math::\pi(\vect\theta | \vect y) \quad \propto \quad L\left(\vect y | \vect\theta\right) \times \pi(\vect\theta):math:`` +.. math:: + + \pi(\vect\theta | \vect y) \quad \propto \quad L\left(\vect y | \vect\theta\right) \times \pi(\vect\theta) where :math:`\propto` means "proportional to", regarded as a function of :math:`\vect\theta`. @@ -94,7 +96,7 @@ is the prior covariance matrix with The following objects need to be defined in order to perform Bayesian calibration: - The conditional density :math:`p(y|\vect z)` must be defined as a probability distribution. -- The computer model must be implemented thanks to the ParametricFunction class. +- The computer model must be implemented thanks to the :class:`~openturns.ParametricFunction` class. This takes a value of :math:`\vect\theta` as input, and outputs the vector of model predictions :math:`\vect z`, as defined above (the vector of covariates :math:`\vect x = (x_1, \ldots, x_n)` is treated as a known constant). When doing that, we have to keep in mind that :math:`\vect z` will be used as the vector of parameters corresponding @@ -107,7 +109,12 @@ The following objects need to be defined in order to perform Bayesian calibratio - Metropolis-Hastings algorithm(s), possibly used in tandem with a Gibbs algorithm in order to sample from the posterior distribution of the calibration parameters. -.. GENERATED FROM PYTHON SOURCE LINES 91-97 +This example uses the :class:`~openturns.ParametricFunction` class. +Please read its documentation and +:doc:`/auto_functional_modeling/vectorial_functions/plot_parametric_function` +for a detailed example. + +.. GENERATED FROM PYTHON SOURCE LINES 98-104 .. code-block:: Python @@ -124,11 +131,11 @@ The following objects need to be defined in order to perform Bayesian calibratio -.. GENERATED FROM PYTHON SOURCE LINES 98-99 +.. GENERATED FROM PYTHON SOURCE LINES 105-106 Dimension of the vector of parameters to calibrate -.. GENERATED FROM PYTHON SOURCE LINES 99-103 +.. GENERATED FROM PYTHON SOURCE LINES 106-110 .. code-block:: Python @@ -143,11 +150,11 @@ Dimension of the vector of parameters to calibrate -.. GENERATED FROM PYTHON SOURCE LINES 104-105 +.. GENERATED FROM PYTHON SOURCE LINES 111-112 Define the observed inputs :math:`x_i`. -.. GENERATED FROM PYTHON SOURCE LINES 107-113 +.. GENERATED FROM PYTHON SOURCE LINES 114-120 .. code-block:: Python @@ -164,7 +171,7 @@ Define the observed inputs :math:`x_i`. -.. GENERATED FROM PYTHON SOURCE LINES 114-120 +.. GENERATED FROM PYTHON SOURCE LINES 121-127 Define the parametric model :math:`\vect z = f(x,\vect\theta)` that associates each observation :math:`x` and value of :math:`\vect \theta` to the parameters @@ -173,7 +180,7 @@ here :math:`\vect z=(\mu, \sigma)` where :math:`\mu`, the first output of the model, is the mean and :math:`\sigma`, the second output of the model, is the standard deviation. -.. GENERATED FROM PYTHON SOURCE LINES 122-126 +.. GENERATED FROM PYTHON SOURCE LINES 129-133 .. code-block:: Python @@ -188,7 +195,7 @@ the second output of the model, is the standard deviation. -.. GENERATED FROM PYTHON SOURCE LINES 127-134 +.. GENERATED FROM PYTHON SOURCE LINES 134-141 To differentiate between the two classes of inputs (:math:`x` and :math:`\vect\theta`), we define a :class:`~openturns.ParametricFunction` from `fullModel` @@ -198,7 +205,7 @@ We set :math:`x = 1` as a placeholder, but :math:`x` will actually take the values :math:`x_i` of the observations when we sample :math:`\vect\theta`. -.. GENERATED FROM PYTHON SOURCE LINES 134-138 +.. GENERATED FROM PYTHON SOURCE LINES 141-145 .. code-block:: Python @@ -219,11 +226,11 @@ when we sample :math:`\vect\theta`. -.. GENERATED FROM PYTHON SOURCE LINES 139-140 +.. GENERATED FROM PYTHON SOURCE LINES 146-147 Define the observation noise :math:`\varepsilon {\sim} \mathcal N(0, 1)` and create a sample from it. -.. GENERATED FROM PYTHON SOURCE LINES 142-147 +.. GENERATED FROM PYTHON SOURCE LINES 149-154 .. code-block:: Python @@ -239,12 +246,12 @@ Define the observation noise :math:`\varepsilon {\sim} \mathcal N(0, 1)` and cre -.. GENERATED FROM PYTHON SOURCE LINES 148-150 +.. GENERATED FROM PYTHON SOURCE LINES 155-157 Define the vector of observations :math:`y_i`, here sampled using the "true" value of :math:`\vect \theta`: :math:`\vect \theta_{true}`. -.. GENERATED FROM PYTHON SOURCE LINES 152-154 +.. GENERATED FROM PYTHON SOURCE LINES 159-161 .. code-block:: Python @@ -257,7 +264,7 @@ here sampled using the "true" value of :math:`\vect \theta`: :math:`\vect \theta -.. GENERATED FROM PYTHON SOURCE LINES 155-160 +.. GENERATED FROM PYTHON SOURCE LINES 162-167 .. code-block:: Python @@ -273,11 +280,11 @@ here sampled using the "true" value of :math:`\vect \theta`: :math:`\vect \theta -.. GENERATED FROM PYTHON SOURCE LINES 161-162 +.. GENERATED FROM PYTHON SOURCE LINES 168-169 Draw the model predictions vs the observations. -.. GENERATED FROM PYTHON SOURCE LINES 164-172 +.. GENERATED FROM PYTHON SOURCE LINES 171-179 .. code-block:: Python @@ -301,13 +308,13 @@ Draw the model predictions vs the observations. -.. GENERATED FROM PYTHON SOURCE LINES 173-176 +.. GENERATED FROM PYTHON SOURCE LINES 180-183 Define the distribution of observations :math:`y | \vect{z}` conditional on model predictions. Note that its parameter dimension is the one of :math:`\vect{z}`, so the model must be adjusted accordingly. -.. GENERATED FROM PYTHON SOURCE LINES 178-180 +.. GENERATED FROM PYTHON SOURCE LINES 185-187 .. code-block:: Python @@ -320,11 +327,11 @@ Note that its parameter dimension is the one of :math:`\vect{z}`, so the model m -.. GENERATED FROM PYTHON SOURCE LINES 181-182 +.. GENERATED FROM PYTHON SOURCE LINES 188-189 Define the mean :math:`\mu_\theta`, the covariance matrix :math:`\Sigma_\theta`, then the prior distribution :math:`\pi(\vect\theta)` of the parameter :math:`\vect\theta`. -.. GENERATED FROM PYTHON SOURCE LINES 184-186 +.. GENERATED FROM PYTHON SOURCE LINES 191-193 .. code-block:: Python @@ -337,7 +344,7 @@ Define the mean :math:`\mu_\theta`, the covariance matrix :math:`\Sigma_\theta`, -.. GENERATED FROM PYTHON SOURCE LINES 187-195 +.. GENERATED FROM PYTHON SOURCE LINES 194-202 .. code-block:: Python @@ -356,13 +363,13 @@ Define the mean :math:`\mu_\theta`, the covariance matrix :math:`\Sigma_\theta`, -.. GENERATED FROM PYTHON SOURCE LINES 196-199 +.. GENERATED FROM PYTHON SOURCE LINES 203-206 The proposed steps for :math:`\theta_1`, :math:`\theta_2` and :math:`\theta_3` will all follow a uniform distribution. -.. GENERATED FROM PYTHON SOURCE LINES 199-202 +.. GENERATED FROM PYTHON SOURCE LINES 206-209 .. code-block:: Python @@ -376,17 +383,17 @@ will all follow a uniform distribution. -.. GENERATED FROM PYTHON SOURCE LINES 203-205 +.. GENERATED FROM PYTHON SOURCE LINES 210-212 Test the Metropolis-Hastings sampler ------------------------------------ -.. GENERATED FROM PYTHON SOURCE LINES 207-209 +.. GENERATED FROM PYTHON SOURCE LINES 214-216 Creation of a single component random walk Metropolis-Hastings (RWMH) sampler. This involves a combination of the RWMH and the Gibbs algorithms. -.. GENERATED FROM PYTHON SOURCE LINES 211-213 +.. GENERATED FROM PYTHON SOURCE LINES 218-220 .. code-block:: Python @@ -399,13 +406,13 @@ This involves a combination of the RWMH and the Gibbs algorithms. -.. GENERATED FROM PYTHON SOURCE LINES 214-217 +.. GENERATED FROM PYTHON SOURCE LINES 221-224 We create a :class:`~openturns.RandomWalkMetropolisHastings` sampler for each component. Each sampler must be aware of the joint prior distribution. We also use the same proposal distribution, but this is not mandatory. -.. GENERATED FROM PYTHON SOURCE LINES 217-223 +.. GENERATED FROM PYTHON SOURCE LINES 224-230 .. code-block:: Python @@ -422,12 +429,12 @@ We also use the same proposal distribution, but this is not mandatory. -.. GENERATED FROM PYTHON SOURCE LINES 224-226 +.. GENERATED FROM PYTHON SOURCE LINES 231-233 Each sampler must be made aware of the likelihood. Otherwise we would sample from the prior! -.. GENERATED FROM PYTHON SOURCE LINES 226-230 +.. GENERATED FROM PYTHON SOURCE LINES 233-237 .. code-block:: Python @@ -442,11 +449,11 @@ Otherwise we would sample from the prior! -.. GENERATED FROM PYTHON SOURCE LINES 231-232 +.. GENERATED FROM PYTHON SOURCE LINES 238-239 Finally, the :class:`~openturns.Gibbs` algorithm is constructed from all Metropolis-Hastings samplers. -.. GENERATED FROM PYTHON SOURCE LINES 232-235 +.. GENERATED FROM PYTHON SOURCE LINES 239-242 .. code-block:: Python @@ -460,11 +467,11 @@ Finally, the :class:`~openturns.Gibbs` algorithm is constructed from all Metropo -.. GENERATED FROM PYTHON SOURCE LINES 236-237 +.. GENERATED FROM PYTHON SOURCE LINES 243-244 Generate a sample from the posterior distribution of the parameters :math:`\vect \theta`. -.. GENERATED FROM PYTHON SOURCE LINES 239-242 +.. GENERATED FROM PYTHON SOURCE LINES 246-249 .. code-block:: Python @@ -478,13 +485,13 @@ Generate a sample from the posterior distribution of the parameters :math:`\vect -.. GENERATED FROM PYTHON SOURCE LINES 243-246 +.. GENERATED FROM PYTHON SOURCE LINES 250-253 Look at the acceptance rate (basic check of the sampling efficiency: values close to :math:`0.2` are usually recommended for Normal posterior distributions). -.. GENERATED FROM PYTHON SOURCE LINES 248-250 +.. GENERATED FROM PYTHON SOURCE LINES 255-257 .. code-block:: Python @@ -503,11 +510,11 @@ for Normal posterior distributions). -.. GENERATED FROM PYTHON SOURCE LINES 251-252 +.. GENERATED FROM PYTHON SOURCE LINES 258-259 Build the distribution of the posterior by kernel smoothing. -.. GENERATED FROM PYTHON SOURCE LINES 254-257 +.. GENERATED FROM PYTHON SOURCE LINES 261-264 .. code-block:: Python @@ -521,11 +528,11 @@ Build the distribution of the posterior by kernel smoothing. -.. GENERATED FROM PYTHON SOURCE LINES 258-259 +.. GENERATED FROM PYTHON SOURCE LINES 265-266 Display prior vs posterior for each parameter. -.. GENERATED FROM PYTHON SOURCE LINES 259-309 +.. GENERATED FROM PYTHON SOURCE LINES 266-316 .. code-block:: Python @@ -586,11 +593,11 @@ Display prior vs posterior for each parameter. -.. GENERATED FROM PYTHON SOURCE LINES 310-311 +.. GENERATED FROM PYTHON SOURCE LINES 317-318 sphinx_gallery_thumbnail_number = 2 -.. GENERATED FROM PYTHON SOURCE LINES 311-320 +.. GENERATED FROM PYTHON SOURCE LINES 318-327 .. code-block:: Python diff --git a/openturns/master/_sources/auto_calibration/bayesian_calibration/plot_gibbs.rst.txt b/openturns/master/_sources/auto_calibration/bayesian_calibration/plot_gibbs.rst.txt index 834edc49a93..1619dea428d 100644 --- a/openturns/master/_sources/auto_calibration/bayesian_calibration/plot_gibbs.rst.txt +++ b/openturns/master/_sources/auto_calibration/bayesian_calibration/plot_gibbs.rst.txt @@ -283,7 +283,7 @@ Let us plot the posterior density. .. rst-class:: sphx-glr-timing - **Total running time of the script:** (0 minutes 12.667 seconds) + **Total running time of the script:** (0 minutes 12.653 seconds) .. _sphx_glr_download_auto_calibration_bayesian_calibration_plot_gibbs.py: diff --git a/openturns/master/_sources/auto_calibration/bayesian_calibration/plot_rwmh_python_distribution.rst.txt b/openturns/master/_sources/auto_calibration/bayesian_calibration/plot_rwmh_python_distribution.rst.txt index d2bc6a584ad..57dc81906c5 100644 --- a/openturns/master/_sources/auto_calibration/bayesian_calibration/plot_rwmh_python_distribution.rst.txt +++ b/openturns/master/_sources/auto_calibration/bayesian_calibration/plot_rwmh_python_distribution.rst.txt @@ -425,7 +425,7 @@ Plot posterior marginal plots only as prior cannot be drawn meaningfully. .. rst-class:: sphx-glr-timing - **Total running time of the script:** (0 minutes 5.668 seconds) + **Total running time of the script:** (0 minutes 5.764 seconds) .. _sphx_glr_download_auto_calibration_bayesian_calibration_plot_rwmh_python_distribution.py: diff --git a/openturns/master/_sources/auto_calibration/bayesian_calibration/sg_execution_times.rst.txt b/openturns/master/_sources/auto_calibration/bayesian_calibration/sg_execution_times.rst.txt index e493f3f278c..b99ea342b6f 100644 --- a/openturns/master/_sources/auto_calibration/bayesian_calibration/sg_execution_times.rst.txt +++ b/openturns/master/_sources/auto_calibration/bayesian_calibration/sg_execution_times.rst.txt @@ -6,7 +6,7 @@ Computation times ================= -**00:23.498** total execution time for 7 files **from auto_calibration/bayesian_calibration**: +**00:23.244** total execution time for 7 files **from auto_calibration/bayesian_calibration**: .. container:: @@ -33,23 +33,23 @@ Computation times - Time - Mem (MB) * - :ref:`sphx_glr_auto_calibration_bayesian_calibration_plot_gibbs.py` (``plot_gibbs.py``) - - 00:12.667 + - 00:12.653 - 0.0 * - :ref:`sphx_glr_auto_calibration_bayesian_calibration_plot_rwmh_python_distribution.py` (``plot_rwmh_python_distribution.py``) - - 00:05.668 - - 0.0 - * - :ref:`sphx_glr_auto_calibration_bayesian_calibration_plot_bayesian_calibration.py` (``plot_bayesian_calibration.py``) - - 00:01.489 + - 00:05.764 - 0.0 * - :ref:`sphx_glr_auto_calibration_bayesian_calibration_plot_bayesian_calibration_flooding.py` (``plot_bayesian_calibration_flooding.py``) - - 00:01.310 + - 00:01.294 + - 0.0 + * - :ref:`sphx_glr_auto_calibration_bayesian_calibration_plot_bayesian_calibration.py` (``plot_bayesian_calibration.py``) + - 00:01.247 - 0.0 * - :ref:`sphx_glr_auto_calibration_bayesian_calibration_plot_gibbs_simus.py` (``plot_gibbs_simus.py``) - - 00:01.172 + - 00:01.099 - 0.0 * - :ref:`sphx_glr_auto_calibration_bayesian_calibration_plot_ackley_distribution.py` (``plot_ackley_distribution.py``) - - 00:00.913 + - 00:00.916 - 0.0 * - :ref:`sphx_glr_auto_calibration_bayesian_calibration_plot_imh_python_distribution.py` (``plot_imh_python_distribution.py``) - - 00:00.280 + - 00:00.271 - 0.0 diff --git a/openturns/master/_sources/auto_calibration/least_squares_and_gaussian_calibration/plot_calibration_chaboche.rst.txt b/openturns/master/_sources/auto_calibration/least_squares_and_gaussian_calibration/plot_calibration_chaboche.rst.txt index c289c333863..6c8e0edd3f8 100644 --- a/openturns/master/_sources/auto_calibration/least_squares_and_gaussian_calibration/plot_calibration_chaboche.rst.txt +++ b/openturns/master/_sources/auto_calibration/least_squares_and_gaussian_calibration/plot_calibration_chaboche.rst.txt @@ -1927,7 +1927,7 @@ Reset default settings .. rst-class:: sphx-glr-timing - **Total running time of the script:** (0 minutes 7.438 seconds) + **Total running time of the script:** (0 minutes 6.733 seconds) .. _sphx_glr_download_auto_calibration_least_squares_and_gaussian_calibration_plot_calibration_chaboche.py: diff --git a/openturns/master/_sources/auto_calibration/least_squares_and_gaussian_calibration/plot_calibration_deflection_tube.rst.txt b/openturns/master/_sources/auto_calibration/least_squares_and_gaussian_calibration/plot_calibration_deflection_tube.rst.txt index 087216dd05a..cb729cad04f 100644 --- a/openturns/master/_sources/auto_calibration/least_squares_and_gaussian_calibration/plot_calibration_deflection_tube.rst.txt +++ b/openturns/master/_sources/auto_calibration/least_squares_and_gaussian_calibration/plot_calibration_deflection_tube.rst.txt @@ -896,7 +896,7 @@ Reset default settings .. rst-class:: sphx-glr-timing - **Total running time of the script:** (0 minutes 3.904 seconds) + **Total running time of the script:** (0 minutes 3.912 seconds) .. _sphx_glr_download_auto_calibration_least_squares_and_gaussian_calibration_plot_calibration_deflection_tube.py: diff --git a/openturns/master/_sources/auto_calibration/least_squares_and_gaussian_calibration/plot_calibration_flooding.rst.txt b/openturns/master/_sources/auto_calibration/least_squares_and_gaussian_calibration/plot_calibration_flooding.rst.txt index 3867f54524d..0768caa6ded 100644 --- a/openturns/master/_sources/auto_calibration/least_squares_and_gaussian_calibration/plot_calibration_flooding.rst.txt +++ b/openturns/master/_sources/auto_calibration/least_squares_and_gaussian_calibration/plot_calibration_flooding.rst.txt @@ -1695,7 +1695,7 @@ Reset default settings .. rst-class:: sphx-glr-timing - **Total running time of the script:** (0 minutes 9.339 seconds) + **Total running time of the script:** (0 minutes 8.902 seconds) .. _sphx_glr_download_auto_calibration_least_squares_and_gaussian_calibration_plot_calibration_flooding.py: diff --git a/openturns/master/_sources/auto_calibration/least_squares_and_gaussian_calibration/sg_execution_times.rst.txt b/openturns/master/_sources/auto_calibration/least_squares_and_gaussian_calibration/sg_execution_times.rst.txt index cf4a7e078a5..6798399338e 100644 --- a/openturns/master/_sources/auto_calibration/least_squares_and_gaussian_calibration/sg_execution_times.rst.txt +++ b/openturns/master/_sources/auto_calibration/least_squares_and_gaussian_calibration/sg_execution_times.rst.txt @@ -6,7 +6,7 @@ Computation times ================= -**00:21.960** total execution time for 8 files **from auto_calibration/least_squares_and_gaussian_calibration**: +**00:20.743** total execution time for 8 files **from auto_calibration/least_squares_and_gaussian_calibration**: .. container:: @@ -33,26 +33,26 @@ Computation times - Time - Mem (MB) * - :ref:`sphx_glr_auto_calibration_least_squares_and_gaussian_calibration_plot_calibration_flooding.py` (``plot_calibration_flooding.py``) - - 00:09.339 + - 00:08.902 - 0.0 * - :ref:`sphx_glr_auto_calibration_least_squares_and_gaussian_calibration_plot_calibration_chaboche.py` (``plot_calibration_chaboche.py``) - - 00:07.438 + - 00:06.733 - 0.0 * - :ref:`sphx_glr_auto_calibration_least_squares_and_gaussian_calibration_plot_calibration_deflection_tube.py` (``plot_calibration_deflection_tube.py``) - - 00:03.904 + - 00:03.912 - 0.0 * - :ref:`sphx_glr_auto_calibration_least_squares_and_gaussian_calibration_plot_calibration_logistic.py` (``plot_calibration_logistic.py``) - - 00:00.739 + - 00:00.685 - 0.0 * - :ref:`sphx_glr_auto_calibration_least_squares_and_gaussian_calibration_plot_calibration_quickstart.py` (``plot_calibration_quickstart.py``) - - 00:00.303 + - 00:00.288 - 0.0 * - :ref:`sphx_glr_auto_calibration_least_squares_and_gaussian_calibration_plot_calibration_withoutobservedinputs.py` (``plot_calibration_withoutobservedinputs.py``) - - 00:00.089 + - 00:00.084 - 0.0 * - :ref:`sphx_glr_auto_calibration_least_squares_and_gaussian_calibration_plot_generate_chaboche.py` (``plot_generate_chaboche.py``) - - 00:00.076 + - 00:00.071 - 0.0 * - :ref:`sphx_glr_auto_calibration_least_squares_and_gaussian_calibration_plot_generate_flooding.py` (``plot_generate_flooding.py``) - - 00:00.072 + - 00:00.068 - 0.0 diff --git a/openturns/master/_sources/auto_data_analysis/distribution_fitting/plot_estimate_gev_fremantle.rst.txt b/openturns/master/_sources/auto_data_analysis/distribution_fitting/plot_estimate_gev_fremantle.rst.txt index 3a2c9663f25..97ba13becbe 100644 --- a/openturns/master/_sources/auto_data_analysis/distribution_fitting/plot_estimate_gev_fremantle.rst.txt +++ b/openturns/master/_sources/auto_data_analysis/distribution_fitting/plot_estimate_gev_fremantle.rst.txt @@ -1061,7 +1061,7 @@ improvements with respect to model tested before. .. rst-class:: sphx-glr-timing - **Total running time of the script:** (0 minutes 5.499 seconds) + **Total running time of the script:** (0 minutes 5.133 seconds) .. _sphx_glr_download_auto_data_analysis_distribution_fitting_plot_estimate_gev_fremantle.py: diff --git a/openturns/master/_sources/auto_data_analysis/distribution_fitting/plot_estimate_gev_racetime.rst.txt b/openturns/master/_sources/auto_data_analysis/distribution_fitting/plot_estimate_gev_racetime.rst.txt index 830c3352922..f3e595a1358 100644 --- a/openturns/master/_sources/auto_data_analysis/distribution_fitting/plot_estimate_gev_racetime.rst.txt +++ b/openturns/master/_sources/auto_data_analysis/distribution_fitting/plot_estimate_gev_racetime.rst.txt @@ -1108,7 +1108,7 @@ quadratic model explains even better a large variation in the data. .. rst-class:: sphx-glr-timing - **Total running time of the script:** (0 minutes 10.230 seconds) + **Total running time of the script:** (0 minutes 10.071 seconds) .. _sphx_glr_download_auto_data_analysis_distribution_fitting_plot_estimate_gev_racetime.py: diff --git a/openturns/master/_sources/auto_data_analysis/distribution_fitting/plot_estimate_multivariate_distribution.rst.txt b/openturns/master/_sources/auto_data_analysis/distribution_fitting/plot_estimate_multivariate_distribution.rst.txt index 97dbd2b8d1c..79183f1d48d 100644 --- a/openturns/master/_sources/auto_data_analysis/distribution_fitting/plot_estimate_multivariate_distribution.rst.txt +++ b/openturns/master/_sources/auto_data_analysis/distribution_fitting/plot_estimate_multivariate_distribution.rst.txt @@ -419,7 +419,7 @@ We build joint distribution from marginal distributions and dependency structure .. rst-class:: sphx-glr-timing - **Total running time of the script:** (0 minutes 5.917 seconds) + **Total running time of the script:** (0 minutes 4.162 seconds) .. _sphx_glr_download_auto_data_analysis_distribution_fitting_plot_estimate_multivariate_distribution.py: diff --git a/openturns/master/_sources/auto_data_analysis/distribution_fitting/sg_execution_times.rst.txt b/openturns/master/_sources/auto_data_analysis/distribution_fitting/sg_execution_times.rst.txt index 1d98203bb1e..ab35a2c0b68 100644 --- a/openturns/master/_sources/auto_data_analysis/distribution_fitting/sg_execution_times.rst.txt +++ b/openturns/master/_sources/auto_data_analysis/distribution_fitting/sg_execution_times.rst.txt @@ -6,7 +6,7 @@ Computation times ================= -**00:30.219** total execution time for 15 files **from auto_data_analysis/distribution_fitting**: +**00:27.246** total execution time for 15 files **from auto_data_analysis/distribution_fitting**: .. container:: @@ -33,46 +33,46 @@ Computation times - Time - Mem (MB) * - :ref:`sphx_glr_auto_data_analysis_distribution_fitting_plot_estimate_gev_racetime.py` (``plot_estimate_gev_racetime.py``) - - 00:10.230 - - 0.0 - * - :ref:`sphx_glr_auto_data_analysis_distribution_fitting_plot_estimate_multivariate_distribution.py` (``plot_estimate_multivariate_distribution.py``) - - 00:05.917 + - 00:10.071 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_distribution_fitting_plot_estimate_gev_fremantle.py` (``plot_estimate_gev_fremantle.py``) - - 00:05.499 + - 00:05.133 + - 0.0 + * - :ref:`sphx_glr_auto_data_analysis_distribution_fitting_plot_estimate_multivariate_distribution.py` (``plot_estimate_multivariate_distribution.py``) + - 00:04.162 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_distribution_fitting_plot_estimate_gev_pirie.py` (``plot_estimate_gev_pirie.py``) - - 00:01.989 + - 00:01.917 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_distribution_fitting_plot_estimate_conditional_quantile.py` (``plot_estimate_conditional_quantile.py``) - - 00:01.845 + - 00:01.668 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_distribution_fitting_plot_estimate_non_parametric_distribution.py` (``plot_estimate_non_parametric_distribution.py``) - - 00:01.070 + - 00:00.966 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_distribution_fitting_plot_estimate_gev_venice.py` (``plot_estimate_gev_venice.py``) - - 00:00.758 + - 00:00.700 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_distribution_fitting_plot_asymptotic_estimators_distribution.py` (``plot_asymptotic_estimators_distribution.py``) - - 00:00.672 + - 00:00.606 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_distribution_fitting_plot_smoothing_mixture.py` (``plot_smoothing_mixture.py``) - - 00:00.614 + - 00:00.538 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_distribution_fitting_plot_model_singular_multivariate_distribution.py` (``plot_model_singular_multivariate_distribution.py``) - - 00:00.582 + - 00:00.532 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_distribution_fitting_plot_fit_extreme_value_distribution.py` (``plot_fit_extreme_value_distribution.py``) - - 00:00.378 + - 00:00.331 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_distribution_fitting_plot_advanced_mle_estimator.py` (``plot_advanced_mle_estimator.py``) - - 00:00.275 + - 00:00.262 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_distribution_fitting_plot_estimate_normal.py` (``plot_estimate_normal.py``) - - 00:00.251 + - 00:00.230 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_distribution_fitting_plot_quantilematching_estimator.py` (``plot_quantilematching_estimator.py``) - - 00:00.135 + - 00:00.126 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_distribution_fitting_plot_maximumlikelihood_estimator.py` (``plot_maximumlikelihood_estimator.py``) - 00:00.004 diff --git a/openturns/master/_sources/auto_data_analysis/estimate_dependency_and_copulas/sg_execution_times.rst.txt b/openturns/master/_sources/auto_data_analysis/estimate_dependency_and_copulas/sg_execution_times.rst.txt index fd365558066..d5e9c3d2257 100644 --- a/openturns/master/_sources/auto_data_analysis/estimate_dependency_and_copulas/sg_execution_times.rst.txt +++ b/openturns/master/_sources/auto_data_analysis/estimate_dependency_and_copulas/sg_execution_times.rst.txt @@ -6,7 +6,7 @@ Computation times ================= -**00:01.082** total execution time for 4 files **from auto_data_analysis/estimate_dependency_and_copulas**: +**00:00.997** total execution time for 4 files **from auto_data_analysis/estimate_dependency_and_copulas**: .. container:: @@ -33,14 +33,14 @@ Computation times - Time - Mem (MB) * - :ref:`sphx_glr_auto_data_analysis_estimate_dependency_and_copulas_plot_estimate_non_parametric_copula.py` (``plot_estimate_non_parametric_copula.py``) - - 00:00.469 + - 00:00.422 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_estimate_dependency_and_copulas_plot_estimate_dependence_wavesurge.py` (``plot_estimate_dependence_wavesurge.py``) - - 00:00.231 + - 00:00.218 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_estimate_dependency_and_copulas_plot_estimate_dependence_wind.py` (``plot_estimate_dependence_wind.py``) - - 00:00.216 + - 00:00.203 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_estimate_dependency_and_copulas_plot_estimate_copula.py` (``plot_estimate_copula.py``) - - 00:00.165 + - 00:00.153 - 0.0 diff --git a/openturns/master/_sources/auto_data_analysis/estimate_stochastic_processes/plot_estimate_multivariate_arma.rst.txt b/openturns/master/_sources/auto_data_analysis/estimate_stochastic_processes/plot_estimate_multivariate_arma.rst.txt index fc60d0ee7f4..0af8d58c8ce 100644 --- a/openturns/master/_sources/auto_data_analysis/estimate_stochastic_processes/plot_estimate_multivariate_arma.rst.txt +++ b/openturns/master/_sources/auto_data_analysis/estimate_stochastic_processes/plot_estimate_multivariate_arma.rst.txt @@ -159,7 +159,7 @@ Estimate the process from the previous realization .. rst-class:: sphx-glr-timing - **Total running time of the script:** (0 minutes 4.054 seconds) + **Total running time of the script:** (0 minutes 3.908 seconds) .. _sphx_glr_download_auto_data_analysis_estimate_stochastic_processes_plot_estimate_multivariate_arma.py: diff --git a/openturns/master/_sources/auto_data_analysis/estimate_stochastic_processes/sg_execution_times.rst.txt b/openturns/master/_sources/auto_data_analysis/estimate_stochastic_processes/sg_execution_times.rst.txt index 8cf10054749..6dfe1398cf8 100644 --- a/openturns/master/_sources/auto_data_analysis/estimate_stochastic_processes/sg_execution_times.rst.txt +++ b/openturns/master/_sources/auto_data_analysis/estimate_stochastic_processes/sg_execution_times.rst.txt @@ -6,7 +6,7 @@ Computation times ================= -**00:06.450** total execution time for 5 files **from auto_data_analysis/estimate_stochastic_processes**: +**00:06.204** total execution time for 5 files **from auto_data_analysis/estimate_stochastic_processes**: .. container:: @@ -33,17 +33,17 @@ Computation times - Time - Mem (MB) * - :ref:`sphx_glr_auto_data_analysis_estimate_stochastic_processes_plot_estimate_multivariate_arma.py` (``plot_estimate_multivariate_arma.py``) - - 00:04.054 + - 00:03.908 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_estimate_stochastic_processes_plot_estimate_spectral_density_function.py` (``plot_estimate_spectral_density_function.py``) - - 00:00.882 + - 00:00.858 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_estimate_stochastic_processes_plot_estimate_arma.py` (``plot_estimate_arma.py``) - - 00:00.800 + - 00:00.781 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_estimate_stochastic_processes_plot_estimate_stationary_covariance_model.py` (``plot_estimate_stationary_covariance_model.py``) - - 00:00.451 + - 00:00.415 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_estimate_stochastic_processes_plot_estimate_non_stationary_covariance_model.py` (``plot_estimate_non_stationary_covariance_model.py``) - - 00:00.262 + - 00:00.243 - 0.0 diff --git a/openturns/master/_sources/auto_data_analysis/graphics/plot_sensitivity_par_coo_ishigami.rst.txt b/openturns/master/_sources/auto_data_analysis/graphics/plot_sensitivity_par_coo_ishigami.rst.txt index 00e5803c556..e00e6b9e046 100644 --- a/openturns/master/_sources/auto_data_analysis/graphics/plot_sensitivity_par_coo_ishigami.rst.txt +++ b/openturns/master/_sources/auto_data_analysis/graphics/plot_sensitivity_par_coo_ishigami.rst.txt @@ -381,7 +381,7 @@ Display figures .. rst-class:: sphx-glr-timing - **Total running time of the script:** (0 minutes 3.060 seconds) + **Total running time of the script:** (0 minutes 2.719 seconds) .. _sphx_glr_download_auto_data_analysis_graphics_plot_sensitivity_par_coo_ishigami.py: diff --git a/openturns/master/_sources/auto_data_analysis/graphics/sg_execution_times.rst.txt b/openturns/master/_sources/auto_data_analysis/graphics/sg_execution_times.rst.txt index 7bfc773a0b8..f60de020b42 100644 --- a/openturns/master/_sources/auto_data_analysis/graphics/sg_execution_times.rst.txt +++ b/openturns/master/_sources/auto_data_analysis/graphics/sg_execution_times.rst.txt @@ -6,7 +6,7 @@ Computation times ================= -**00:03.515** total execution time for 3 files **from auto_data_analysis/graphics**: +**00:03.113** total execution time for 3 files **from auto_data_analysis/graphics**: .. container:: @@ -33,11 +33,11 @@ Computation times - Time - Mem (MB) * - :ref:`sphx_glr_auto_data_analysis_graphics_plot_sensitivity_par_coo_ishigami.py` (``plot_sensitivity_par_coo_ishigami.py``) - - 00:03.060 + - 00:02.719 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_graphics_plot_visualize_clouds.py` (``plot_visualize_clouds.py``) - - 00:00.276 + - 00:00.236 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_graphics_plot_visualize_pairs.py` (``plot_visualize_pairs.py``) - - 00:00.178 + - 00:00.158 - 0.0 diff --git a/openturns/master/_sources/auto_data_analysis/manage_data_and_samples/plot_quick_start_point_and_sample.rst.txt b/openturns/master/_sources/auto_data_analysis/manage_data_and_samples/plot_quick_start_point_and_sample.rst.txt index 60e01aa8000..1af388ceae0 100644 --- a/openturns/master/_sources/auto_data_analysis/manage_data_and_samples/plot_quick_start_point_and_sample.rst.txt +++ b/openturns/master/_sources/auto_data_analysis/manage_data_and_samples/plot_quick_start_point_and_sample.rst.txt @@ -38,8 +38,8 @@ Introduction Two fundamental objects in the library are: -* `Point`: a multidimensional point in :math:`D` dimensions (:math:`\in \mathbb{R}^D`) ; -* `Sample`: a multivariate sample made of :math:`N` points in :math:`D` dimensions. +* `Point`: a multidimensional point in :math:`d` dimensions (:math:`\in \mathbb{R}^d`) ; +* `Sample`: a multivariate sample made of :math:`n` points in :math:`d` dimensions. .. GENERATED FROM PYTHON SOURCE LINES 25-30 @@ -166,19 +166,19 @@ The following statements sets the second component. The `Sample` class ------------------ -The `Sample` class represents a multivariate sample made of :math:`N` points in :math:`\mathbb{R}^D`. +The `Sample` class represents a multivariate sample made of :math:`n` points in :math:`\mathbb{R}^d`. -* :math:`D` is the *dimension* of the sample, -* :math:`N` is the *size* of the sample. +* :math:`d` is the *dimension* of the sample, +* :math:`n` is the *size* of the sample. -A `Sample` can be seen as an array of with :math:`N` rows and :math:`D` columns. +A `Sample` can be seen as an array of with :math:`n` rows and :math:`d` columns. *Remark.* The :class:`~openturns.ProcessSample` class can be used to manage a sample of stochastic processes. .. GENERATED FROM PYTHON SOURCE LINES 80-81 -The script below creates a `Sample` with size :math:`N=5` and dimension :math:`D=3`. +The script below creates a `Sample` with size :math:`n=5` and dimension :math:`d=3`. .. GENERATED FROM PYTHON SOURCE LINES 83-86 @@ -408,7 +408,7 @@ We see that: * the `row` is a `Point`, * the `column` is a `Sample`. -This is consistent with the fact that, in a dimension :math:`D` `Sample`, a row is a :math:`D`-dimensional `Point`. +This is consistent with the fact that, in a dimension :math:`d` `Sample`, a row is a :math:`d`-dimensional `Point`. .. GENERATED FROM PYTHON SOURCE LINES 139-140 @@ -440,15 +440,48 @@ The following statement extracts several columns (with indices 0 and 2) and crea

-.. GENERATED FROM PYTHON SOURCE LINES 145-146 +.. GENERATED FROM PYTHON SOURCE LINES 145-147 + +Set a row or a column of a `Sample` +----------------------------------- + +.. GENERATED FROM PYTHON SOURCE LINES 149-150 Slicing can also be used to set a `Sample` row or column. -.. GENERATED FROM PYTHON SOURCE LINES 148-153 +.. GENERATED FROM PYTHON SOURCE LINES 152-155 .. code-block:: Python sample = ot.Sample([[1.0, 2.0], [3.0, 4.0], [5.0, 6.0]]) + sample + + + + + + +.. raw:: html + +
+ + + + + +
v0v1
012
134
256
+
+
+
+ +.. GENERATED FROM PYTHON SOURCE LINES 156-157 + +Set the third row: this must be a `Point` or must be convertible to. + +.. GENERATED FROM PYTHON SOURCE LINES 157-161 + +.. code-block:: Python + p = [8.0, 10.0] sample[2, :] = p sample @@ -471,7 +504,11 @@ Slicing can also be used to set a `Sample` row or column.

-.. GENERATED FROM PYTHON SOURCE LINES 154-159 +.. GENERATED FROM PYTHON SOURCE LINES 162-163 + +Set the second column: this must be a `Sample` or must be convertible to. + +.. GENERATED FROM PYTHON SOURCE LINES 163-168 .. code-block:: Python @@ -498,14 +535,46 @@ Slicing can also be used to set a `Sample` row or column.

-.. GENERATED FROM PYTHON SOURCE LINES 160-164 +.. GENERATED FROM PYTHON SOURCE LINES 169-171 + +Sometimes, we want to set a column with a list of floats. +This can be done using the :meth:`~openturns.Sample.BuildFromPoint` static method. + +.. GENERATED FROM PYTHON SOURCE LINES 171-176 + +.. code-block:: Python + + sample = ot.Sample([[1.0, 2.0], [3.0, 4.0], [5.0, 6.0]]) + s = ot.Sample.BuildFromPoint([3.0, 5.0, 7.0]) + sample[:, 1] = s + sample + + + + + + +.. raw:: html + +
+ + + + + +
v0v1
013
135
257
+
+
+
+ +.. GENERATED FROM PYTHON SOURCE LINES 177-181 Create a `Point` or a `Sample` from a Python list ------------------------------------------------- The following statement creates a `Point` from a Python list. -.. GENERATED FROM PYTHON SOURCE LINES 166-169 +.. GENERATED FROM PYTHON SOURCE LINES 183-186 .. code-block:: Python @@ -525,7 +594,7 @@ The following statement creates a `Point` from a Python list.

-.. GENERATED FROM PYTHON SOURCE LINES 170-173 +.. GENERATED FROM PYTHON SOURCE LINES 187-190 .. code-block:: Python @@ -545,13 +614,13 @@ The following statement creates a `Point` from a Python list.

-.. GENERATED FROM PYTHON SOURCE LINES 174-177 +.. GENERATED FROM PYTHON SOURCE LINES 191-194 The first useful *Pythonism* that we will review is the *list comprehension*. This creates a list from a `for` loop. This kind of statements is often used in the examples, so that they can be as short as possible. In the following statement, we create a point by iterating over the components of a `Point`. -.. GENERATED FROM PYTHON SOURCE LINES 179-182 +.. GENERATED FROM PYTHON SOURCE LINES 196-199 .. code-block:: Python @@ -571,13 +640,13 @@ In the following statement, we create a point by iterating over the components o

-.. GENERATED FROM PYTHON SOURCE LINES 183-186 +.. GENERATED FROM PYTHON SOURCE LINES 200-203 The second useful *Pythonism* is the repetition with the `*` operator. The following statements creates a list with three 5s. -.. GENERATED FROM PYTHON SOURCE LINES 188-191 +.. GENERATED FROM PYTHON SOURCE LINES 205-208 .. code-block:: Python @@ -597,11 +666,11 @@ The following statements creates a list with three 5s. -.. GENERATED FROM PYTHON SOURCE LINES 192-193 +.. GENERATED FROM PYTHON SOURCE LINES 209-210 We can also create a `Sample` from a list of `Point`. -.. GENERATED FROM PYTHON SOURCE LINES 195-198 +.. GENERATED FROM PYTHON SOURCE LINES 212-215 .. code-block:: Python @@ -626,11 +695,11 @@ We can also create a `Sample` from a list of `Point`.

-.. GENERATED FROM PYTHON SOURCE LINES 199-200 +.. GENERATED FROM PYTHON SOURCE LINES 216-217 We can loop over the points in a sample, using a list comprehension. In the following example, we compute the Euclidian norm of the points in the previous sample. -.. GENERATED FROM PYTHON SOURCE LINES 202-204 +.. GENERATED FROM PYTHON SOURCE LINES 219-221 .. code-block:: Python @@ -649,11 +718,11 @@ We can loop over the points in a sample, using a list comprehension. In the foll -.. GENERATED FROM PYTHON SOURCE LINES 205-206 +.. GENERATED FROM PYTHON SOURCE LINES 222-223 We can also create a `Sample` based on a `Point`, repeated three times. -.. GENERATED FROM PYTHON SOURCE LINES 208-211 +.. GENERATED FROM PYTHON SOURCE LINES 225-228 .. code-block:: Python @@ -678,11 +747,11 @@ We can also create a `Sample` based on a `Point`, repeated three times.

-.. GENERATED FROM PYTHON SOURCE LINES 212-213 +.. GENERATED FROM PYTHON SOURCE LINES 229-230 A nested list of floats is the easiest way to create a non-trivial `Sample`. -.. GENERATED FROM PYTHON SOURCE LINES 215-218 +.. GENERATED FROM PYTHON SOURCE LINES 232-235 .. code-block:: Python @@ -707,7 +776,7 @@ A nested list of floats is the easiest way to create a non-trivial `Sample`.

-.. GENERATED FROM PYTHON SOURCE LINES 219-224 +.. GENERATED FROM PYTHON SOURCE LINES 236-241 Interactions with Numpy ----------------------- @@ -715,11 +784,11 @@ Interactions with Numpy Classes defined in pure Python modules cannot be used by the library. This is why it is useful to know how to convert to and from more basic Python variable types, especially Numpy arrays. -.. GENERATED FROM PYTHON SOURCE LINES 226-227 +.. GENERATED FROM PYTHON SOURCE LINES 243-244 The following statement creates a :class:`~openturns.Sample` and converts it into a bidimensional Numpy `array`. -.. GENERATED FROM PYTHON SOURCE LINES 229-233 +.. GENERATED FROM PYTHON SOURCE LINES 246-250 .. code-block:: Python @@ -744,24 +813,30 @@ The following statement creates a :class:`~openturns.Sample` and converts it int -.. GENERATED FROM PYTHON SOURCE LINES 234-236 +.. GENERATED FROM PYTHON SOURCE LINES 251-253 .. code-block:: Python - type(array) + print(type(array)) + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + -.. GENERATED FROM PYTHON SOURCE LINES 237-238 +.. GENERATED FROM PYTHON SOURCE LINES 254-255 Conversely, the following script creates a Numpy `array`, then converts it into a :class:`~openturns.Sample`. -.. GENERATED FROM PYTHON SOURCE LINES 240-244 +.. GENERATED FROM PYTHON SOURCE LINES 257-261 .. code-block:: Python @@ -789,7 +864,7 @@ Conversely, the following script creates a Numpy `array`, then converts it into

-.. GENERATED FROM PYTHON SOURCE LINES 245-247 +.. GENERATED FROM PYTHON SOURCE LINES 262-264 .. code-block:: Python @@ -808,7 +883,7 @@ Conversely, the following script creates a Numpy `array`, then converts it into -.. GENERATED FROM PYTHON SOURCE LINES 248-250 +.. GENERATED FROM PYTHON SOURCE LINES 265-267 .. code-block:: Python @@ -827,7 +902,7 @@ Conversely, the following script creates a Numpy `array`, then converts it into -.. GENERATED FROM PYTHON SOURCE LINES 251-261 +.. GENERATED FROM PYTHON SOURCE LINES 268-278 There is an ambiguous situation: a `Sample` based on several scalar values. @@ -840,7 +915,7 @@ In order to solve the case, we can use the second input argument of the `Sample` The following statement creates an array containing 5 values from 0 to 1. -.. GENERATED FROM PYTHON SOURCE LINES 263-266 +.. GENERATED FROM PYTHON SOURCE LINES 280-283 .. code-block:: Python @@ -860,11 +935,11 @@ The following statement creates an array containing 5 values from 0 to 1. -.. GENERATED FROM PYTHON SOURCE LINES 267-268 +.. GENERATED FROM PYTHON SOURCE LINES 284-285 Choice A: we create a `Sample` with size 5 in 1 dimension. -.. GENERATED FROM PYTHON SOURCE LINES 270-273 +.. GENERATED FROM PYTHON SOURCE LINES 287-290 .. code-block:: Python @@ -891,11 +966,11 @@ Choice A: we create a `Sample` with size 5 in 1 dimension.

-.. GENERATED FROM PYTHON SOURCE LINES 274-275 +.. GENERATED FROM PYTHON SOURCE LINES 291-292 Choice B: we create a `Sample` with size 1 in 5 dimensions. -.. GENERATED FROM PYTHON SOURCE LINES 277-280 +.. GENERATED FROM PYTHON SOURCE LINES 294-297 .. code-block:: Python @@ -918,19 +993,60 @@ Choice B: we create a `Sample` with size 1 in 5 dimensions.

-.. GENERATED FROM PYTHON SOURCE LINES 281-291 +.. GENERATED FROM PYTHON SOURCE LINES 298-300 + +When there is an ambiguous case, the library cannot solve the +issue and an `InvalidArgumentException` is generated. + +.. GENERATED FROM PYTHON SOURCE LINES 302-308 + +More precisely, the code: -If we do not set the optional `size` parameter, the library cannot solve the -case and an `InvalidArgumentException` is generated. -More precisely, the code:: +.. code-block:: sample = ot.Sample(u) -produces the exception:: + +.. GENERATED FROM PYTHON SOURCE LINES 310-316 + +produces the exception: + +.. code-block:: TypeError: InvalidArgumentException : Invalid array dimension: 1 +.. GENERATED FROM PYTHON SOURCE LINES 318-320 + +In order to solve that problem, we can use the :meth:`~openturns.Sample.BuildFromPoint` +static method. + +.. GENERATED FROM PYTHON SOURCE LINES 320-322 + +.. code-block:: Python + + sample = ot.Sample.BuildFromPoint([ui for ui in u]) + sample + + + + + +.. raw:: html + +
+ + + + + + + +
v0
00
10.25
20.5
30.75
41
+
+
+
+ .. _sphx_glr_download_auto_data_analysis_manage_data_and_samples_plot_quick_start_point_and_sample.py: diff --git a/openturns/master/_sources/auto_data_analysis/manage_data_and_samples/sg_execution_times.rst.txt b/openturns/master/_sources/auto_data_analysis/manage_data_and_samples/sg_execution_times.rst.txt index 8a10e95b8ab..dc7d77f9abf 100644 --- a/openturns/master/_sources/auto_data_analysis/manage_data_and_samples/sg_execution_times.rst.txt +++ b/openturns/master/_sources/auto_data_analysis/manage_data_and_samples/sg_execution_times.rst.txt @@ -6,7 +6,7 @@ Computation times ================= -**00:00.954** total execution time for 10 files **from auto_data_analysis/manage_data_and_samples**: +**00:00.803** total execution time for 10 files **from auto_data_analysis/manage_data_and_samples**: .. container:: @@ -33,19 +33,19 @@ Computation times - Time - Mem (MB) * - :ref:`sphx_glr_auto_data_analysis_manage_data_and_samples_plot_sample_correlation.py` (``plot_sample_correlation.py``) - - 00:00.429 + - 00:00.390 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_manage_data_and_samples_plot_sample_pandas.py` (``plot_sample_pandas.py``) - - 00:00.244 + - 00:00.160 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_manage_data_and_samples_plot_linear_regression.py` (``plot_linear_regression.py``) - - 00:00.150 + - 00:00.135 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_manage_data_and_samples_plot_quantile_estimation_wilks.py` (``plot_quantile_estimation_wilks.py``) - - 00:00.101 + - 00:00.093 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_manage_data_and_samples_plot_quick_start_point_and_sample.py` (``plot_quick_start_point_and_sample.py``) - - 00:00.011 + - 00:00.009 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_manage_data_and_samples_plot_estimate_moments.py` (``plot_estimate_moments.py``) - 00:00.005 @@ -57,7 +57,7 @@ Computation times - 00:00.004 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_manage_data_and_samples_plot_import_export_sample_csv.py` (``plot_import_export_sample_csv.py``) - - 00:00.003 + - 00:00.002 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_manage_data_and_samples_plot_randomize_sample_lines.py` (``plot_randomize_sample_lines.py``) - 00:00.002 diff --git a/openturns/master/_sources/auto_data_analysis/sample_analysis/sg_execution_times.rst.txt b/openturns/master/_sources/auto_data_analysis/sample_analysis/sg_execution_times.rst.txt index b75a79035a4..53f00f89897 100644 --- a/openturns/master/_sources/auto_data_analysis/sample_analysis/sg_execution_times.rst.txt +++ b/openturns/master/_sources/auto_data_analysis/sample_analysis/sg_execution_times.rst.txt @@ -6,7 +6,7 @@ Computation times ================= -**00:01.442** total execution time for 5 files **from auto_data_analysis/sample_analysis**: +**00:01.333** total execution time for 5 files **from auto_data_analysis/sample_analysis**: .. container:: @@ -33,17 +33,17 @@ Computation times - Time - Mem (MB) * - :ref:`sphx_glr_auto_data_analysis_sample_analysis_plot_draw_survival.py` (``plot_draw_survival.py``) - - 00:00.997 + - 00:00.920 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_sample_analysis_plot_src_confidence.py` (``plot_src_confidence.py``) - - 00:00.162 + - 00:00.150 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_sample_analysis_plot_visualize_empirical_cdf.py` (``plot_visualize_empirical_cdf.py``) - - 00:00.118 + - 00:00.108 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_sample_analysis_plot_compare_unconditional_conditional_histograms.py` (``plot_compare_unconditional_conditional_histograms.py``) - - 00:00.102 + - 00:00.096 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_sample_analysis_plot_visualize_histogram.py` (``plot_visualize_histogram.py``) - - 00:00.064 + - 00:00.059 - 0.0 diff --git a/openturns/master/_sources/auto_data_analysis/statistical_tests/sg_execution_times.rst.txt b/openturns/master/_sources/auto_data_analysis/statistical_tests/sg_execution_times.rst.txt index 9813f90a927..eb260fee340 100644 --- a/openturns/master/_sources/auto_data_analysis/statistical_tests/sg_execution_times.rst.txt +++ b/openturns/master/_sources/auto_data_analysis/statistical_tests/sg_execution_times.rst.txt @@ -6,7 +6,7 @@ Computation times ================= -**00:02.612** total execution time for 11 files **from auto_data_analysis/statistical_tests**: +**00:02.511** total execution time for 11 files **from auto_data_analysis/statistical_tests**: .. container:: @@ -33,31 +33,31 @@ Computation times - Time - Mem (MB) * - :ref:`sphx_glr_auto_data_analysis_statistical_tests_plot_kolmogorov_distribution.py` (``plot_kolmogorov_distribution.py``) - - 00:01.334 + - 00:01.293 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_statistical_tests_plot_fitted_distribution_ranking.py` (``plot_fitted_distribution_ranking.py``) - - 00:00.379 + - 00:00.365 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_statistical_tests_plot_test_copula.py` (``plot_test_copula.py``) - - 00:00.281 + - 00:00.268 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_statistical_tests_plot_smirnov_test.py` (``plot_smirnov_test.py``) - - 00:00.148 + - 00:00.137 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_statistical_tests_plot_qqplot_graph.py` (``plot_qqplot_graph.py``) - - 00:00.143 + - 00:00.133 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_statistical_tests_plot_test_normality.py` (``plot_test_normality.py``) - - 00:00.131 + - 00:00.126 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_statistical_tests_plot_kolmogorov_pvalue.py` (``plot_kolmogorov_pvalue.py``) - - 00:00.092 + - 00:00.088 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_statistical_tests_plot_kolmogorov_statistics.py` (``plot_kolmogorov_statistics.py``) - - 00:00.067 + - 00:00.065 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_statistical_tests_plot_kolmogorov_test.py` (``plot_kolmogorov_test.py``) - - 00:00.031 + - 00:00.030 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_statistical_tests_plot_test_independence.py` (``plot_test_independence.py``) - 00:00.005 diff --git a/openturns/master/_sources/auto_functional_modeling/field_functions/sg_execution_times.rst.txt b/openturns/master/_sources/auto_functional_modeling/field_functions/sg_execution_times.rst.txt index fba5dcecf34..5c6db5f8685 100644 --- a/openturns/master/_sources/auto_functional_modeling/field_functions/sg_execution_times.rst.txt +++ b/openturns/master/_sources/auto_functional_modeling/field_functions/sg_execution_times.rst.txt @@ -6,7 +6,7 @@ Computation times ================= -**00:00.791** total execution time for 6 files **from auto_functional_modeling/field_functions**: +**00:00.754** total execution time for 6 files **from auto_functional_modeling/field_functions**: .. container:: @@ -33,16 +33,16 @@ Computation times - Time - Mem (MB) * - :ref:`sphx_glr_auto_functional_modeling_field_functions_plot_function_manipulation.py` (``plot_function_manipulation.py``) - - 00:00.425 + - 00:00.400 - 0.0 * - :ref:`sphx_glr_auto_functional_modeling_field_functions_plot_logistic_growth_model.py` (``plot_logistic_growth_model.py``) - - 00:00.202 + - 00:00.197 - 0.0 * - :ref:`sphx_glr_auto_functional_modeling_field_functions_plot_viscous_fall_field_function.py` (``plot_viscous_fall_field_function.py``) - - 00:00.087 + - 00:00.082 - 0.0 * - :ref:`sphx_glr_auto_functional_modeling_field_functions_plot_viscous_fall_field_function_connection.py` (``plot_viscous_fall_field_function_connection.py``) - - 00:00.074 + - 00:00.071 - 0.0 * - :ref:`sphx_glr_auto_functional_modeling_field_functions_plot_vertexvalue_function.py` (``plot_vertexvalue_function.py``) - 00:00.002 diff --git a/openturns/master/_sources/auto_functional_modeling/index.rst.txt b/openturns/master/_sources/auto_functional_modeling/index.rst.txt index be2b17985ae..4d963d254bc 100644 --- a/openturns/master/_sources/auto_functional_modeling/index.rst.txt +++ b/openturns/master/_sources/auto_functional_modeling/index.rst.txt @@ -76,23 +76,6 @@ Vectorial functions -.. raw:: html - -
- -.. only:: html - - .. image:: /auto_functional_modeling/vectorial_functions/images/thumb/sphx_glr_plot_parametric_function_thumb.png - :alt: - - :ref:`sphx_glr_auto_functional_modeling_vectorial_functions_plot_parametric_function.py` - -.. raw:: html - -
Create a parametric function
-
- - .. raw:: html
@@ -178,6 +161,23 @@ Vectorial functions
+.. raw:: html + +
+ +.. only:: html + + .. image:: /auto_functional_modeling/vectorial_functions/images/thumb/sphx_glr_plot_parametric_function_thumb.png + :alt: + + :ref:`sphx_glr_auto_functional_modeling_vectorial_functions_plot_parametric_function.py` + +.. raw:: html + +
Create a parametric function
+
+ + .. raw:: html
diff --git a/openturns/master/_sources/auto_functional_modeling/link_to_an_external_code/sg_execution_times.rst.txt b/openturns/master/_sources/auto_functional_modeling/link_to_an_external_code/sg_execution_times.rst.txt index d53e9b3b2fe..5237b3cbda8 100644 --- a/openturns/master/_sources/auto_functional_modeling/link_to_an_external_code/sg_execution_times.rst.txt +++ b/openturns/master/_sources/auto_functional_modeling/link_to_an_external_code/sg_execution_times.rst.txt @@ -6,7 +6,7 @@ Computation times ================= -**00:00.024** total execution time for 1 file **from auto_functional_modeling/link_to_an_external_code**: +**00:00.023** total execution time for 1 file **from auto_functional_modeling/link_to_an_external_code**: .. container:: @@ -33,5 +33,5 @@ Computation times - Time - Mem (MB) * - :ref:`sphx_glr_auto_functional_modeling_link_to_an_external_code_plot_link_computer_code_coupling_tools.py` (``plot_link_computer_code_coupling_tools.py``) - - 00:00.024 + - 00:00.023 - 0.0 diff --git a/openturns/master/_sources/auto_functional_modeling/univariate_functions/sg_execution_times.rst.txt b/openturns/master/_sources/auto_functional_modeling/univariate_functions/sg_execution_times.rst.txt index fb719b9f34d..629340fecf7 100644 --- a/openturns/master/_sources/auto_functional_modeling/univariate_functions/sg_execution_times.rst.txt +++ b/openturns/master/_sources/auto_functional_modeling/univariate_functions/sg_execution_times.rst.txt @@ -6,7 +6,7 @@ Computation times ================= -**00:00.235** total execution time for 1 file **from auto_functional_modeling/univariate_functions**: +**00:00.218** total execution time for 1 file **from auto_functional_modeling/univariate_functions**: .. container:: @@ -33,5 +33,5 @@ Computation times - Time - Mem (MB) * - :ref:`sphx_glr_auto_functional_modeling_univariate_functions_plot_createUnivariateFunction.py` (``plot_createUnivariateFunction.py``) - - 00:00.235 + - 00:00.218 - 0.0 diff --git a/openturns/master/_sources/auto_functional_modeling/vectorial_functions/index.rst.txt b/openturns/master/_sources/auto_functional_modeling/vectorial_functions/index.rst.txt index 1f7cf20ade4..0303a6a37b1 100644 --- a/openturns/master/_sources/auto_functional_modeling/vectorial_functions/index.rst.txt +++ b/openturns/master/_sources/auto_functional_modeling/vectorial_functions/index.rst.txt @@ -31,23 +31,6 @@ Vectorial functions
-.. raw:: html - -
- -.. only:: html - - .. image:: /auto_functional_modeling/vectorial_functions/images/thumb/sphx_glr_plot_parametric_function_thumb.png - :alt: - - :ref:`sphx_glr_auto_functional_modeling_vectorial_functions_plot_parametric_function.py` - -.. raw:: html - -
Create a parametric function
-
- - .. raw:: html
@@ -133,6 +116,23 @@ Vectorial functions
+.. raw:: html + +
+ +.. only:: html + + .. image:: /auto_functional_modeling/vectorial_functions/images/thumb/sphx_glr_plot_parametric_function_thumb.png + :alt: + + :ref:`sphx_glr_auto_functional_modeling_vectorial_functions_plot_parametric_function.py` + +.. raw:: html + +
Create a parametric function
+
+ + .. raw:: html
@@ -210,12 +210,12 @@ Vectorial functions :hidden: /auto_functional_modeling/vectorial_functions/plot_composed_function - /auto_functional_modeling/vectorial_functions/plot_parametric_function /auto_functional_modeling/vectorial_functions/plot_aggregated_function /auto_functional_modeling/vectorial_functions/plot_linear_combination_function /auto_functional_modeling/vectorial_functions/plot_symbolic_function /auto_functional_modeling/vectorial_functions/plot_quadratic_function /auto_functional_modeling/vectorial_functions/plot_functions_outputDim + /auto_functional_modeling/vectorial_functions/plot_parametric_function /auto_functional_modeling/vectorial_functions/plot_python_function /auto_functional_modeling/vectorial_functions/plot_functions_inputDim /auto_functional_modeling/vectorial_functions/plot_quick_start_functions diff --git a/openturns/master/_sources/auto_functional_modeling/vectorial_functions/plot_parametric_function.rst.txt b/openturns/master/_sources/auto_functional_modeling/vectorial_functions/plot_parametric_function.rst.txt index 08817b8e721..9558c70720a 100644 --- a/openturns/master/_sources/auto_functional_modeling/vectorial_functions/plot_parametric_function.rst.txt +++ b/openturns/master/_sources/auto_functional_modeling/vectorial_functions/plot_parametric_function.rst.txt @@ -21,20 +21,27 @@ Create a parametric function ============================ -.. GENERATED FROM PYTHON SOURCE LINES 6-16 +.. GENERATED FROM PYTHON SOURCE LINES 6-10 -In this example we are going to create a parametric function: +In this example, we show how to use the :class:`~openturns.ParametricFunction` class. +This is a tool which is very convenient when we perform +calibration, e.g. with :class:`~openturns.NonLinearLeastSquaresCalibration` +or :class:`~openturns.RandomWalkMetropolisHastings`. + +.. GENERATED FROM PYTHON SOURCE LINES 12-22 + +In this example we create a parametric function: .. math:: - d_{L,I}(E, F): \mathbb{R}^2 \rightarrow \mathbb{R} + d_{L,I}(E, F): \Rset^2 \rightarrow \Rset function from an existing "full" function: .. math:: - d(E, F, L, I): \mathbb{R}^4 \rightarrow \mathbb{R} + d(E, F, L, I): \Rset^4 \rightarrow \Rset. -.. GENERATED FROM PYTHON SOURCE LINES 18-23 +.. GENERATED FROM PYTHON SOURCE LINES 24-29 .. code-block:: Python @@ -50,11 +57,16 @@ function from an existing "full" function: -.. GENERATED FROM PYTHON SOURCE LINES 24-25 +.. GENERATED FROM PYTHON SOURCE LINES 30-32 + +Define the function +~~~~~~~~~~~~~~~~~~~ + +.. GENERATED FROM PYTHON SOURCE LINES 35-36 Create the function with all parameters d(E, F, L, I) -.. GENERATED FROM PYTHON SOURCE LINES 25-33 +.. GENERATED FROM PYTHON SOURCE LINES 36-45 .. code-block:: Python @@ -65,6 +77,7 @@ Create the function with all parameters d(E, F, L, I) beam = ot.PythonFunction(4, 1, d_func) + beam.setInputDescription(["E", "F", "L", "I"]) @@ -73,11 +86,11 @@ Create the function with all parameters d(E, F, L, I) -.. GENERATED FROM PYTHON SOURCE LINES 34-35 +.. GENERATED FROM PYTHON SOURCE LINES 46-47 Evaluate d -.. GENERATED FROM PYTHON SOURCE LINES 35-38 +.. GENERATED FROM PYTHON SOURCE LINES 47-50 .. code-block:: Python @@ -97,11 +110,96 @@ Evaluate d

-.. GENERATED FROM PYTHON SOURCE LINES 39-40 +.. GENERATED FROM PYTHON SOURCE LINES 51-75 + +In the physical model, the inputs and parameters are ordered as +presented in the next table. +Notice that there are no parameters in the physical model. + ++-------+----------------+ +| Index | Input variable | ++=======+================+ +| 0 | E | ++-------+----------------+ +| 1 | F | ++-------+----------------+ +| 2 | L | ++-------+----------------+ +| 3 | I | ++-------+----------------+ + ++-------+-----------+ +| Index | Parameter | ++=======+===========+ +| ∅ | ∅ | ++-------+-----------+ + +**Table 1.** Indices and names of the inputs and parameters of the physical model. + + +.. GENERATED FROM PYTHON SOURCE LINES 77-80 + +The next cell presents the description of the input variables +and the description of the parameters of the physical model. +We see that there is no parameter at this stage in this function. + +.. GENERATED FROM PYTHON SOURCE LINES 80-84 + +.. code-block:: Python + + print("Physical Model Inputs:", beam.getInputDescription()) + print("Physical Model Parameters:", beam.getParameterDescription()) + + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + Physical Model Inputs: [E,F,L,I] + Physical Model Parameters: [] + + + + +.. GENERATED FROM PYTHON SOURCE LINES 85-87 + +Define the parametric function +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +.. GENERATED FROM PYTHON SOURCE LINES 89-111 + +We create a :class:`~openturns.ParametricFunction` +where the parameters are `L` and `I` which have the indices 2 and +and 3 in the physical model. + ++-------+----------------+ +| Index | Input variable | ++=======+================+ +| 0 | E | ++-------+----------------+ +| 1 | F | ++-------+----------------+ + ++-------+-----------+ +| Index | Parameter | ++=======+===========+ +| 0 | L | ++-------+-----------+ +| 1 | I | ++-------+-----------+ + +**Table 2.** Indices and names of the inputs and parameters of the parametric model. + + +.. GENERATED FROM PYTHON SOURCE LINES 113-114 Create the indices of the frozen parameters (L,I) from the full parameter list -.. GENERATED FROM PYTHON SOURCE LINES 40-42 +.. GENERATED FROM PYTHON SOURCE LINES 114-116 .. code-block:: Python @@ -114,11 +212,11 @@ Create the indices of the frozen parameters (L,I) from the full parameter list -.. GENERATED FROM PYTHON SOURCE LINES 43-44 +.. GENERATED FROM PYTHON SOURCE LINES 117-118 Create the values of the frozen parameters (L,I) -.. GENERATED FROM PYTHON SOURCE LINES 44-46 +.. GENERATED FROM PYTHON SOURCE LINES 118-120 .. code-block:: Python @@ -131,11 +229,11 @@ Create the values of the frozen parameters (L,I) -.. GENERATED FROM PYTHON SOURCE LINES 47-48 +.. GENERATED FROM PYTHON SOURCE LINES 121-122 Create the parametric function -.. GENERATED FROM PYTHON SOURCE LINES 48-50 +.. GENERATED FROM PYTHON SOURCE LINES 122-124 .. code-block:: Python @@ -148,11 +246,38 @@ Create the parametric function -.. GENERATED FROM PYTHON SOURCE LINES 51-52 +.. GENERATED FROM PYTHON SOURCE LINES 125-128 + +The next cell presents the description of the input variables +and the description of the parameters of the parametric function. +We see that the parametric function has 2 parameters: L and I. + +.. GENERATED FROM PYTHON SOURCE LINES 128-131 + +.. code-block:: Python + + print("Physical Model Inputs:", beam_LI.getInputDescription()) + print("Physical Model Parameters:", beam_LI.getParameterDescription()) + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + Physical Model Inputs: [E,F] + Physical Model Parameters: [L,I] + + + + +.. GENERATED FROM PYTHON SOURCE LINES 132-133 Evaluate d on (E,F) with fixed parameters (L,I) -.. GENERATED FROM PYTHON SOURCE LINES 52-53 +.. GENERATED FROM PYTHON SOURCE LINES 133-134 .. code-block:: Python diff --git a/openturns/master/_sources/auto_functional_modeling/vectorial_functions/sg_execution_times.rst.txt b/openturns/master/_sources/auto_functional_modeling/vectorial_functions/sg_execution_times.rst.txt index 2c938749648..a08d50de85b 100644 --- a/openturns/master/_sources/auto_functional_modeling/vectorial_functions/sg_execution_times.rst.txt +++ b/openturns/master/_sources/auto_functional_modeling/vectorial_functions/sg_execution_times.rst.txt @@ -6,7 +6,7 @@ Computation times ================= -**00:00.292** total execution time for 11 files **from auto_functional_modeling/vectorial_functions**: +**00:00.274** total execution time for 11 files **from auto_functional_modeling/vectorial_functions**: .. container:: @@ -33,16 +33,13 @@ Computation times - Time - Mem (MB) * - :ref:`sphx_glr_auto_functional_modeling_vectorial_functions_plot_symbolic_function.py` (``plot_symbolic_function.py``) - - 00:00.152 + - 00:00.146 - 0.0 * - :ref:`sphx_glr_auto_functional_modeling_vectorial_functions_plot_quadratic_function.py` (``plot_quadratic_function.py``) - - 00:00.068 + - 00:00.062 - 0.0 * - :ref:`sphx_glr_auto_functional_modeling_vectorial_functions_plot_quick_start_functions.py` (``plot_quick_start_functions.py``) - - 00:00.052 - - 0.0 - * - :ref:`sphx_glr_auto_functional_modeling_vectorial_functions_plot_python_function.py` (``plot_python_function.py``) - - 00:00.004 + - 00:00.048 - 0.0 * - :ref:`sphx_glr_auto_functional_modeling_vectorial_functions_plot_functions_inputDim.py` (``plot_functions_inputDim.py``) - 00:00.003 @@ -50,7 +47,10 @@ Computation times * - :ref:`sphx_glr_auto_functional_modeling_vectorial_functions_plot_createMultivariateFunction.py` (``plot_createMultivariateFunction.py``) - 00:00.003 - 0.0 - * - :ref:`sphx_glr_auto_functional_modeling_vectorial_functions_plot_functions_outputDim.py` (``plot_functions_outputDim.py``) + * - :ref:`sphx_glr_auto_functional_modeling_vectorial_functions_plot_python_function.py` (``plot_python_function.py``) + - 00:00.003 + - 0.0 + * - :ref:`sphx_glr_auto_functional_modeling_vectorial_functions_plot_parametric_function.py` (``plot_parametric_function.py``) - 00:00.002 - 0.0 * - :ref:`sphx_glr_auto_functional_modeling_vectorial_functions_plot_aggregated_function.py` (``plot_aggregated_function.py``) @@ -59,9 +59,9 @@ Computation times * - :ref:`sphx_glr_auto_functional_modeling_vectorial_functions_plot_linear_combination_function.py` (``plot_linear_combination_function.py``) - 00:00.002 - 0.0 - * - :ref:`sphx_glr_auto_functional_modeling_vectorial_functions_plot_composed_function.py` (``plot_composed_function.py``) + * - :ref:`sphx_glr_auto_functional_modeling_vectorial_functions_plot_functions_outputDim.py` (``plot_functions_outputDim.py``) - 00:00.002 - 0.0 - * - :ref:`sphx_glr_auto_functional_modeling_vectorial_functions_plot_parametric_function.py` (``plot_parametric_function.py``) - - 00:00.001 + * - :ref:`sphx_glr_auto_functional_modeling_vectorial_functions_plot_composed_function.py` (``plot_composed_function.py``) + - 00:00.002 - 0.0 diff --git a/openturns/master/_sources/auto_graphs/sg_execution_times.rst.txt b/openturns/master/_sources/auto_graphs/sg_execution_times.rst.txt index bdcb11eb0d7..c3f1ca3aec0 100644 --- a/openturns/master/_sources/auto_graphs/sg_execution_times.rst.txt +++ b/openturns/master/_sources/auto_graphs/sg_execution_times.rst.txt @@ -6,7 +6,7 @@ Computation times ================= -**00:01.897** total execution time for 3 files **from auto_graphs**: +**00:01.943** total execution time for 3 files **from auto_graphs**: .. container:: @@ -33,11 +33,11 @@ Computation times - Time - Mem (MB) * - :ref:`sphx_glr_auto_graphs_plot_graphs_basics.py` (``plot_graphs_basics.py``) - - 00:01.050 + - 00:01.120 - 0.0 * - :ref:`sphx_glr_auto_graphs_plot_graphs_loglikelihood_contour.py` (``plot_graphs_loglikelihood_contour.py``) - - 00:00.707 + - 00:00.687 - 0.0 * - :ref:`sphx_glr_auto_graphs_plot_graphs_fill_area.py` (``plot_graphs_fill_area.py``) - - 00:00.140 + - 00:00.136 - 0.0 diff --git a/openturns/master/_sources/auto_meta_modeling/fields_metamodels/plot_fieldfunction_metamodel.rst.txt b/openturns/master/_sources/auto_meta_modeling/fields_metamodels/plot_fieldfunction_metamodel.rst.txt index 035cd37abc6..de896a6b3cc 100644 --- a/openturns/master/_sources/auto_meta_modeling/fields_metamodels/plot_fieldfunction_metamodel.rst.txt +++ b/openturns/master/_sources/auto_meta_modeling/fields_metamodels/plot_fieldfunction_metamodel.rst.txt @@ -498,7 +498,7 @@ Reset default settings .. rst-class:: sphx-glr-timing - **Total running time of the script:** (0 minutes 18.032 seconds) + **Total running time of the script:** (0 minutes 17.266 seconds) .. _sphx_glr_download_auto_meta_modeling_fields_metamodels_plot_fieldfunction_metamodel.py: diff --git a/openturns/master/_sources/auto_meta_modeling/fields_metamodels/sg_execution_times.rst.txt b/openturns/master/_sources/auto_meta_modeling/fields_metamodels/sg_execution_times.rst.txt index 040dc1015cf..39af3ec7134 100644 --- a/openturns/master/_sources/auto_meta_modeling/fields_metamodels/sg_execution_times.rst.txt +++ b/openturns/master/_sources/auto_meta_modeling/fields_metamodels/sg_execution_times.rst.txt @@ -6,7 +6,7 @@ Computation times ================= -**00:20.363** total execution time for 3 files **from auto_meta_modeling/fields_metamodels**: +**00:19.459** total execution time for 3 files **from auto_meta_modeling/fields_metamodels**: .. container:: @@ -33,11 +33,11 @@ Computation times - Time - Mem (MB) * - :ref:`sphx_glr_auto_meta_modeling_fields_metamodels_plot_fieldfunction_metamodel.py` (``plot_fieldfunction_metamodel.py``) - - 00:18.032 + - 00:17.266 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_fields_metamodels_plot_viscous_fall_metamodel.py` (``plot_viscous_fall_metamodel.py``) - - 00:01.854 + - 00:01.763 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_fields_metamodels_plot_karhunenloeve_validation.py` (``plot_karhunenloeve_validation.py``) - - 00:00.477 + - 00:00.430 - 0.0 diff --git a/openturns/master/_sources/auto_meta_modeling/general_purpose_metamodels/sg_execution_times.rst.txt b/openturns/master/_sources/auto_meta_modeling/general_purpose_metamodels/sg_execution_times.rst.txt index 62a51bee777..a838ccd9124 100644 --- a/openturns/master/_sources/auto_meta_modeling/general_purpose_metamodels/sg_execution_times.rst.txt +++ b/openturns/master/_sources/auto_meta_modeling/general_purpose_metamodels/sg_execution_times.rst.txt @@ -6,7 +6,7 @@ Computation times ================= -**00:02.563** total execution time for 8 files **from auto_meta_modeling/general_purpose_metamodels**: +**00:02.378** total execution time for 8 files **from auto_meta_modeling/general_purpose_metamodels**: .. container:: @@ -33,26 +33,26 @@ Computation times - Time - Mem (MB) * - :ref:`sphx_glr_auto_meta_modeling_general_purpose_metamodels_plot_overfitting_model_selection.py` (``plot_overfitting_model_selection.py``) - - 00:00.735 + - 00:00.678 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_general_purpose_metamodels_plot_linear_model.py` (``plot_linear_model.py``) - - 00:00.713 + - 00:00.652 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_general_purpose_metamodels_plot_stepwise.py` (``plot_stepwise.py``) - - 00:00.360 + - 00:00.341 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_general_purpose_metamodels_plot_export_metamodel.py` (``plot_export_metamodel.py``) - - 00:00.273 + - 00:00.259 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_general_purpose_metamodels_plot_expert_mixture.py` (``plot_expert_mixture.py``) - - 00:00.178 + - 00:00.166 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_general_purpose_metamodels_plot_taylor_approximation.py` (``plot_taylor_approximation.py``) - - 00:00.147 + - 00:00.134 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_general_purpose_metamodels_plot_general_linear_model.py` (``plot_general_linear_model.py``) - - 00:00.091 + - 00:00.086 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_general_purpose_metamodels_plot_create_linear_least_squares_model.py` (``plot_create_linear_least_squares_model.py``) - - 00:00.067 + - 00:00.064 - 0.0 diff --git a/openturns/master/_sources/auto_meta_modeling/index.rst.txt b/openturns/master/_sources/auto_meta_modeling/index.rst.txt index 61d56617f92..1c471243f76 100644 --- a/openturns/master/_sources/auto_meta_modeling/index.rst.txt +++ b/openturns/master/_sources/auto_meta_modeling/index.rst.txt @@ -231,69 +231,69 @@ Polynomial chaos metamodel .. raw:: html -
+
.. only:: html - .. image:: /auto_meta_modeling/polynomial_chaos_metamodel/images/thumb/sphx_glr_plot_functional_chaos_database_thumb.png + .. image:: /auto_meta_modeling/polynomial_chaos_metamodel/images/thumb/sphx_glr_plot_chaos_ishigami_grouped_indices_thumb.png :alt: - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_functional_chaos_database.py` + :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_chaos_ishigami_grouped_indices.py` .. raw:: html -
Polynomial chaos over database
+
Compute grouped indices for the Ishigami function
.. raw:: html -
+
.. only:: html - .. image:: /auto_meta_modeling/polynomial_chaos_metamodel/images/thumb/sphx_glr_plot_chaos_ishigami_grouped_indices_thumb.png + .. image:: /auto_meta_modeling/polynomial_chaos_metamodel/images/thumb/sphx_glr_plot_chaos_draw_validation_thumb.png :alt: - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_chaos_ishigami_grouped_indices.py` + :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_chaos_draw_validation.py` .. raw:: html -
Compute grouped indices for the Ishigami function
+
Validate a polynomial chaos
.. raw:: html -
+
.. only:: html - .. image:: /auto_meta_modeling/polynomial_chaos_metamodel/images/thumb/sphx_glr_plot_chaos_draw_validation_thumb.png + .. image:: /auto_meta_modeling/polynomial_chaos_metamodel/images/thumb/sphx_glr_plot_functional_chaos_graphs_thumb.png :alt: - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_chaos_draw_validation.py` + :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_functional_chaos_graphs.py` .. raw:: html -
Validate a polynomial chaos
+
Polynomial chaos graphs
.. raw:: html -
+
.. only:: html - .. image:: /auto_meta_modeling/polynomial_chaos_metamodel/images/thumb/sphx_glr_plot_functional_chaos_graphs_thumb.png + .. image:: /auto_meta_modeling/polynomial_chaos_metamodel/images/thumb/sphx_glr_plot_functional_chaos_database_thumb.png :alt: - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_functional_chaos_graphs.py` + :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_functional_chaos_database.py` .. raw:: html -
Polynomial chaos graphs
+
Create a full or sparse polynomial chaos expansion
@@ -333,7 +333,7 @@ Polynomial chaos metamodel .. raw:: html -
+
.. only:: html @@ -344,7 +344,7 @@ Polynomial chaos metamodel .. raw:: html -
Create a polynomial chaos metamodel
+
Create a polynomial chaos metamodel from a data set
@@ -688,7 +688,7 @@ Kriging metamodel .. raw:: html -
+
.. only:: html @@ -699,7 +699,7 @@ Kriging metamodel .. raw:: html -
Kriging :configure the optimization solver
+
Kriging: configure the optimization solver
diff --git a/openturns/master/_sources/auto_meta_modeling/kriging_metamodel/index.rst.txt b/openturns/master/_sources/auto_meta_modeling/kriging_metamodel/index.rst.txt index f610a095cc5..24afeac7636 100644 --- a/openturns/master/_sources/auto_meta_modeling/kriging_metamodel/index.rst.txt +++ b/openturns/master/_sources/auto_meta_modeling/kriging_metamodel/index.rst.txt @@ -237,7 +237,7 @@ Kriging metamodel .. raw:: html -
+
.. only:: html @@ -248,7 +248,7 @@ Kriging metamodel .. raw:: html -
Kriging :configure the optimization solver
+
Kriging: configure the optimization solver
diff --git a/openturns/master/_sources/auto_meta_modeling/kriging_metamodel/plot_kriging_categorical.rst.txt b/openturns/master/_sources/auto_meta_modeling/kriging_metamodel/plot_kriging_categorical.rst.txt index 5fe2f95f36f..6e2fa584c72 100644 --- a/openturns/master/_sources/auto_meta_modeling/kriging_metamodel/plot_kriging_categorical.rst.txt +++ b/openturns/master/_sources/auto_meta_modeling/kriging_metamodel/plot_kriging_categorical.rst.txt @@ -556,7 +556,7 @@ than relying on multiple purely continuous Gaussian processes. .. rst-class:: sphx-glr-timing - **Total running time of the script:** (0 minutes 9.964 seconds) + **Total running time of the script:** (0 minutes 9.426 seconds) .. _sphx_glr_download_auto_meta_modeling_kriging_metamodel_plot_kriging_categorical.py: diff --git a/openturns/master/_sources/auto_meta_modeling/kriging_metamodel/plot_kriging_hyperparameters_optimization.rst.txt b/openturns/master/_sources/auto_meta_modeling/kriging_metamodel/plot_kriging_hyperparameters_optimization.rst.txt index 6f25fac7768..a7c7f054de6 100644 --- a/openturns/master/_sources/auto_meta_modeling/kriging_metamodel/plot_kriging_hyperparameters_optimization.rst.txt +++ b/openturns/master/_sources/auto_meta_modeling/kriging_metamodel/plot_kriging_hyperparameters_optimization.rst.txt @@ -18,7 +18,7 @@ .. _sphx_glr_auto_meta_modeling_kriging_metamodel_plot_kriging_hyperparameters_optimization.py: -Kriging :configure the optimization solver +Kriging: configure the optimization solver ========================================== .. GENERATED FROM PYTHON SOURCE LINES 6-43 @@ -45,7 +45,7 @@ The covariance model has two types of parameters. Often, the parameter :math:`{\bf \theta}` is a scale parameter. This step involves an optimization algorithm. -All these parameters are estimated with the `GeneralLinearModelAlgorithm` class. +All these parameters are estimated with the :class:`~openturns.GeneralLinearModelAlgorithm` class. The estimation of the :math:`{\bf \theta}` parameters is the step which has the highest CPU cost. Moreover, the maximization of likelihood may be associated with difficulties e.g. many local maximums or even the non convergence of the optimization algorithm. @@ -132,7 +132,7 @@ Young's modulus E .. GENERATED FROM PYTHON SOURCE LINES 78-79 -Finally, we define the dependency using a `NormalCopula`. +Finally, we define the dependency using a :class:`~openturns.NormalCopula`. .. GENERATED FROM PYTHON SOURCE LINES 81-87 @@ -156,12 +156,13 @@ Finally, we define the dependency using a `NormalCopula`. Create the design of experiments -------------------------------- -.. GENERATED FROM PYTHON SOURCE LINES 92-94 +.. GENERATED FROM PYTHON SOURCE LINES 92-95 -We consider a simple Monte-Carlo sampling as a design of experiments. This is why we generate an input sample using the `getSample` method of the distribution. +We consider a simple Monte-Carlo sampling as a design of experiments. +This is why we generate an input sample using the `getSample` method of the distribution. Then we evaluate the output using the `model` function. -.. GENERATED FROM PYTHON SOURCE LINES 96-100 +.. GENERATED FROM PYTHON SOURCE LINES 97-101 .. code-block:: Python @@ -176,19 +177,19 @@ Then we evaluate the output using the `model` function. -.. GENERATED FROM PYTHON SOURCE LINES 101-103 +.. GENERATED FROM PYTHON SOURCE LINES 102-104 Create the metamodel -------------------- -.. GENERATED FROM PYTHON SOURCE LINES 105-109 +.. GENERATED FROM PYTHON SOURCE LINES 106-110 -In order to create the kriging metamodel, we first select a constant trend with the `ConstantBasisFactory` class. +In order to create the kriging metamodel, we first select a constant trend with the :class:`~openturns.ConstantBasisFactory` class. Then we use a squared exponential covariance model. -Finally, we use the `KrigingAlgorithm` class to create the kriging metamodel, +Finally, we use the :class:`~openturns.KrigingAlgorithm` class to create the kriging metamodel, taking the training sample, the covariance model and the trend basis as input arguments. -.. GENERATED FROM PYTHON SOURCE LINES 111-134 +.. GENERATED FROM PYTHON SOURCE LINES 112-135 .. code-block:: Python @@ -234,13 +235,14 @@ taking the training sample, the covariance model and the trend basis as input ar -.. GENERATED FROM PYTHON SOURCE LINES 135-138 +.. GENERATED FROM PYTHON SOURCE LINES 136-140 -The `run` method has optimized the hyperparameters of the metamodel. +The :meth:`~openturns.KrigingAlgorithm.run` method has optimized the hyperparameters of the metamodel. -We can then print the constant trend of the metamodel, which have been estimated using the least squares method. +We can then print the constant trend of the metamodel, which have been +estimated using the least squares method. -.. GENERATED FROM PYTHON SOURCE LINES 140-142 +.. GENERATED FROM PYTHON SOURCE LINES 142-144 .. code-block:: Python @@ -259,11 +261,11 @@ We can then print the constant trend of the metamodel, which have been estimated

-.. GENERATED FROM PYTHON SOURCE LINES 143-144 +.. GENERATED FROM PYTHON SOURCE LINES 145-146 We can also print the hyperparameters of the covariance model, which have been estimated by maximizing the likelihood. -.. GENERATED FROM PYTHON SOURCE LINES 146-149 +.. GENERATED FROM PYTHON SOURCE LINES 148-151 .. code-block:: Python @@ -283,16 +285,19 @@ We can also print the hyperparameters of the covariance model, which have been e -.. GENERATED FROM PYTHON SOURCE LINES 150-152 +.. GENERATED FROM PYTHON SOURCE LINES 152-154 Get the optimizer algorithm --------------------------- -.. GENERATED FROM PYTHON SOURCE LINES 154-155 +.. GENERATED FROM PYTHON SOURCE LINES 156-160 -The `getOptimizationAlgorithm` method returns the optimization algorithm used to optimize the :math:`{\bf \theta}` parameters of the `SquaredExponential` covariance model. +The :meth:`~openturns.KrigingAlgorithm.getOptimizationAlgorithm` method +returns the optimization algorithm used to optimize the +:math:`{\bf \theta}` parameters of the +:class:`~openturns.SquaredExponential` covariance model. -.. GENERATED FROM PYTHON SOURCE LINES 157-159 +.. GENERATED FROM PYTHON SOURCE LINES 162-164 .. code-block:: Python @@ -305,11 +310,11 @@ The `getOptimizationAlgorithm` method returns the optimization algorithm used to -.. GENERATED FROM PYTHON SOURCE LINES 160-161 +.. GENERATED FROM PYTHON SOURCE LINES 165-166 Get the default optimizer. -.. GENERATED FROM PYTHON SOURCE LINES 163-166 +.. GENERATED FROM PYTHON SOURCE LINES 168-171 .. code-block:: Python @@ -329,12 +334,15 @@ Get the default optimizer. -.. GENERATED FROM PYTHON SOURCE LINES 167-169 +.. GENERATED FROM PYTHON SOURCE LINES 172-177 -The `getOptimizationBounds` method returns the bounds. The dimension of these bounds correspond to the spatial dimension of the covariance model. +The :meth:`~openturns.KrigingAlgorithm.getOptimizationBounds` method +returns the bounds. +The dimension of these bounds correspond to the spatial dimension of +the covariance model. In the metamodeling context, this correspond to the input dimension of the model. -.. GENERATED FROM PYTHON SOURCE LINES 171-174 +.. GENERATED FROM PYTHON SOURCE LINES 179-182 .. code-block:: Python @@ -354,7 +362,7 @@ In the metamodeling context, this correspond to the input dimension of the model -.. GENERATED FROM PYTHON SOURCE LINES 175-179 +.. GENERATED FROM PYTHON SOURCE LINES 183-187 .. code-block:: Python @@ -376,7 +384,7 @@ In the metamodeling context, this correspond to the input dimension of the model -.. GENERATED FROM PYTHON SOURCE LINES 180-184 +.. GENERATED FROM PYTHON SOURCE LINES 188-192 .. code-block:: Python @@ -398,11 +406,11 @@ In the metamodeling context, this correspond to the input dimension of the model -.. GENERATED FROM PYTHON SOURCE LINES 185-186 +.. GENERATED FROM PYTHON SOURCE LINES 193-194 -The `getOptimizeParameters` method returns `True` if these parameters are to be optimized. +The :meth:`~openturns.KrigingAlgorithm.getOptimizeParameters` method returns `True` if these parameters are to be optimized. -.. GENERATED FROM PYTHON SOURCE LINES 188-192 +.. GENERATED FROM PYTHON SOURCE LINES 196-200 .. code-block:: Python @@ -423,17 +431,18 @@ The `getOptimizeParameters` method returns `True` if these parameters are to be -.. GENERATED FROM PYTHON SOURCE LINES 193-195 +.. GENERATED FROM PYTHON SOURCE LINES 201-203 Configure the starting point of the optimization ------------------------------------------------ -.. GENERATED FROM PYTHON SOURCE LINES 197-199 +.. GENERATED FROM PYTHON SOURCE LINES 205-208 The starting point of the optimization is based on the parameters of the covariance model. -In the following example, we configure the parameters of the covariance model to the arbitrary values `[12.,34.,56.,78.]`. +In the following example, we configure the parameters of the covariance model to +the arbitrary values `[12.0, 34.0, 56.0, 78.0]`. -.. GENERATED FROM PYTHON SOURCE LINES 201-206 +.. GENERATED FROM PYTHON SOURCE LINES 210-215 .. code-block:: Python @@ -449,7 +458,7 @@ In the following example, we configure the parameters of the covariance model to -.. GENERATED FROM PYTHON SOURCE LINES 207-209 +.. GENERATED FROM PYTHON SOURCE LINES 216-218 .. code-block:: Python @@ -462,7 +471,7 @@ In the following example, we configure the parameters of the covariance model to -.. GENERATED FROM PYTHON SOURCE LINES 210-214 +.. GENERATED FROM PYTHON SOURCE LINES 219-223 .. code-block:: Python @@ -483,11 +492,11 @@ In the following example, we configure the parameters of the covariance model to -.. GENERATED FROM PYTHON SOURCE LINES 215-216 +.. GENERATED FROM PYTHON SOURCE LINES 224-225 In order to see the difference with the default optimization, we print the previous optimized covariance model. -.. GENERATED FROM PYTHON SOURCE LINES 218-220 +.. GENERATED FROM PYTHON SOURCE LINES 227-229 .. code-block:: Python @@ -506,27 +515,27 @@ In order to see the difference with the default optimization, we print the previ -.. GENERATED FROM PYTHON SOURCE LINES 221-222 +.. GENERATED FROM PYTHON SOURCE LINES 230-231 We observe that this does not change much the values of the parameters in this case. -.. GENERATED FROM PYTHON SOURCE LINES 224-226 +.. GENERATED FROM PYTHON SOURCE LINES 233-235 Disabling the optimization -------------------------- -.. GENERATED FROM PYTHON SOURCE LINES 228-230 +.. GENERATED FROM PYTHON SOURCE LINES 237-240 It is sometimes useful to completely disable the optimization of the parameters. -In order to see the effect of this, we first initialize the parameters of the covariance model with the arbitrary values `[12.,34.,56.,78.]`. +In order to see the effect of this, we first initialize the parameters of +the covariance model with the arbitrary values `[12.0, 34.0, 56.0, 78.0]`. -.. GENERATED FROM PYTHON SOURCE LINES 232-236 +.. GENERATED FROM PYTHON SOURCE LINES 242-245 .. code-block:: Python covarianceModel = ot.SquaredExponential([12.0, 34.0, 56.0, 78.0], [91.0]) algo = ot.KrigingAlgorithm(X_train, Y_train, covarianceModel, basis) - algo.setOptimizationBounds(scaleOptimizationBounds) # Trick B @@ -535,11 +544,12 @@ In order to see the effect of this, we first initialize the parameters of the co -.. GENERATED FROM PYTHON SOURCE LINES 237-238 +.. GENERATED FROM PYTHON SOURCE LINES 246-248 -The `setOptimizeParameters` method can be used to disable the optimization of the parameters. +The :meth:`~openturns.KrigingAlgorithm.setOptimizeParameters` method can be +used to disable the optimization of the parameters. -.. GENERATED FROM PYTHON SOURCE LINES 240-242 +.. GENERATED FROM PYTHON SOURCE LINES 250-252 .. code-block:: Python @@ -552,11 +562,11 @@ The `setOptimizeParameters` method can be used to disable the optimization of th -.. GENERATED FROM PYTHON SOURCE LINES 243-244 +.. GENERATED FROM PYTHON SOURCE LINES 253-254 Then we run the algorithm and get the result. -.. GENERATED FROM PYTHON SOURCE LINES 246-249 +.. GENERATED FROM PYTHON SOURCE LINES 256-259 .. code-block:: Python @@ -570,12 +580,12 @@ Then we run the algorithm and get the result. -.. GENERATED FROM PYTHON SOURCE LINES 250-252 +.. GENERATED FROM PYTHON SOURCE LINES 260-262 We observe that the covariance model is unchanged: the parameters have not been optimized, as required. -.. GENERATED FROM PYTHON SOURCE LINES 254-257 +.. GENERATED FROM PYTHON SOURCE LINES 264-267 .. code-block:: Python @@ -595,11 +605,11 @@ the parameters have not been optimized, as required. -.. GENERATED FROM PYTHON SOURCE LINES 258-259 +.. GENERATED FROM PYTHON SOURCE LINES 268-269 The trend, however, is still optimized, using linear least squares. -.. GENERATED FROM PYTHON SOURCE LINES 261-263 +.. GENERATED FROM PYTHON SOURCE LINES 271-273 .. code-block:: Python @@ -618,7 +628,7 @@ The trend, however, is still optimized, using linear least squares.

-.. GENERATED FROM PYTHON SOURCE LINES 264-271 +.. GENERATED FROM PYTHON SOURCE LINES 274-281 Reuse the parameters from a previous optimization ------------------------------------------------- @@ -628,11 +638,11 @@ Furthermore, we disable the optimization so that the parameters of the covarianc This make the process of adding a new point very fast: it improves the quality by adding a new point in the design of experiments without paying the price of the update of the covariance model. -.. GENERATED FROM PYTHON SOURCE LINES 273-274 +.. GENERATED FROM PYTHON SOURCE LINES 283-284 Step 1: Run a first kriging algorithm. -.. GENERATED FROM PYTHON SOURCE LINES 276-287 +.. GENERATED FROM PYTHON SOURCE LINES 286-297 .. code-block:: Python @@ -660,11 +670,11 @@ Step 1: Run a first kriging algorithm. -.. GENERATED FROM PYTHON SOURCE LINES 288-289 +.. GENERATED FROM PYTHON SOURCE LINES 298-299 Step 2: Create a new point and add it to the previous training design. -.. GENERATED FROM PYTHON SOURCE LINES 291-294 +.. GENERATED FROM PYTHON SOURCE LINES 301-304 .. code-block:: Python @@ -678,7 +688,7 @@ Step 2: Create a new point and add it to the previous training design. -.. GENERATED FROM PYTHON SOURCE LINES 295-298 +.. GENERATED FROM PYTHON SOURCE LINES 305-308 .. code-block:: Python @@ -698,7 +708,7 @@ Step 2: Create a new point and add it to the previous training design. -.. GENERATED FROM PYTHON SOURCE LINES 299-302 +.. GENERATED FROM PYTHON SOURCE LINES 309-312 .. code-block:: Python @@ -718,11 +728,11 @@ Step 2: Create a new point and add it to the previous training design. -.. GENERATED FROM PYTHON SOURCE LINES 303-304 +.. GENERATED FROM PYTHON SOURCE LINES 313-314 Step 3: Create an updated kriging, using the new point with the old covariance parameters. -.. GENERATED FROM PYTHON SOURCE LINES 306-314 +.. GENERATED FROM PYTHON SOURCE LINES 316-324 .. code-block:: Python @@ -747,7 +757,7 @@ Step 3: Create an updated kriging, using the new point with the old covariance p -.. GENERATED FROM PYTHON SOURCE LINES 315-324 +.. GENERATED FROM PYTHON SOURCE LINES 325-334 .. code-block:: Python @@ -767,7 +777,7 @@ Step 3: Create an updated kriging, using the new point with the old covariance p -.. GENERATED FROM PYTHON SOURCE LINES 325-327 +.. GENERATED FROM PYTHON SOURCE LINES 335-337 .. code-block:: Python @@ -791,24 +801,24 @@ Step 3: Create an updated kriging, using the new point with the old covariance p -.. GENERATED FROM PYTHON SOURCE LINES 328-332 +.. GENERATED FROM PYTHON SOURCE LINES 338-342 We see that the parameters did not change *at all*: disabling the optimization allows one to keep a constant covariance model. In a practical algorithm, we may, for example, add a block of 10 new points before updating the parameters of the covariance model. At this point, we may reuse the previous covariance model so that the optimization starts from a better point, compared to the parameters default values. This will reduce the cost of the optimization. -.. GENERATED FROM PYTHON SOURCE LINES 334-336 +.. GENERATED FROM PYTHON SOURCE LINES 344-346 Configure the local optimization solver --------------------------------------- -.. GENERATED FROM PYTHON SOURCE LINES 338-340 +.. GENERATED FROM PYTHON SOURCE LINES 348-350 The following example shows how to set the local optimization solver. We choose the SLSQP algorithm from NLOPT. -.. GENERATED FROM PYTHON SOURCE LINES 342-351 +.. GENERATED FROM PYTHON SOURCE LINES 352-361 .. code-block:: Python @@ -828,7 +838,7 @@ We choose the SLSQP algorithm from NLOPT. -.. GENERATED FROM PYTHON SOURCE LINES 352-355 +.. GENERATED FROM PYTHON SOURCE LINES 362-365 .. code-block:: Python @@ -848,7 +858,7 @@ We choose the SLSQP algorithm from NLOPT. -.. GENERATED FROM PYTHON SOURCE LINES 356-359 +.. GENERATED FROM PYTHON SOURCE LINES 366-369 .. code-block:: Python @@ -873,19 +883,22 @@ We choose the SLSQP algorithm from NLOPT. -.. GENERATED FROM PYTHON SOURCE LINES 360-362 +.. GENERATED FROM PYTHON SOURCE LINES 370-372 Configure the global optimization solver ---------------------------------------- -.. GENERATED FROM PYTHON SOURCE LINES 364-368 +.. GENERATED FROM PYTHON SOURCE LINES 374-381 -The following example checks the robustness of the optimization of the kriging algorithm with respect to -the optimization of the likelihood function in the covariance model parameters estimation. -We use a `MultiStart` algorithm in order to avoid to be trapped by a local minimum. -Furthermore, we generate the design of experiments using a `LHSExperiments`, which guarantees that the points will fill the space. +The following example checks the robustness of the optimization of the +kriging algorithm with respect to the optimization of the likelihood +function in the covariance model parameters estimation. +We use a :class:`~openturns.MultiStart` algorithm in order to avoid to be trapped by a local minimum. +Furthermore, we generate the design of experiments using a +:class:`~openturns.LHSExperiments`, which guarantees that the points +will fill the space. -.. GENERATED FROM PYTHON SOURCE LINES 370-374 +.. GENERATED FROM PYTHON SOURCE LINES 383-387 .. code-block:: Python @@ -900,11 +913,13 @@ Furthermore, we generate the design of experiments using a `LHSExperiments`, whi -.. GENERATED FROM PYTHON SOURCE LINES 375-376 +.. GENERATED FROM PYTHON SOURCE LINES 388-391 -First, we create a multivariate distribution, based on independent `Uniform` marginals which have the bounds required by the covariance model. +First, we create a multivariate distribution, based on independent +:class:`~openturns.Uniform` marginals which have the bounds required +by the covariance model. -.. GENERATED FROM PYTHON SOURCE LINES 378-381 +.. GENERATED FROM PYTHON SOURCE LINES 393-396 .. code-block:: Python @@ -918,11 +933,12 @@ First, we create a multivariate distribution, based on independent `Uniform` mar -.. GENERATED FROM PYTHON SOURCE LINES 382-383 +.. GENERATED FROM PYTHON SOURCE LINES 397-399 -We first generate a Latin Hypercube Sampling (LHS) design made of 25 points in the sample space. This LHS is optimized so as to fill the space. +We first generate a Latin Hypercube Sampling (LHS) design made of 25 points in the sample space. +This LHS is optimized so as to fill the space. -.. GENERATED FROM PYTHON SOURCE LINES 385-395 +.. GENERATED FROM PYTHON SOURCE LINES 401-411 .. code-block:: Python @@ -949,11 +965,12 @@ We first generate a Latin Hypercube Sampling (LHS) design made of 25 points in t -.. GENERATED FROM PYTHON SOURCE LINES 396-397 +.. GENERATED FROM PYTHON SOURCE LINES 412-414 -We can check that the minimum and maximum in the sample correspond to the bounds of the design of experiment. +We can check that the minimum and maximum in the sample correspond to the +bounds of the design of experiment. -.. GENERATED FROM PYTHON SOURCE LINES 399-401 +.. GENERATED FROM PYTHON SOURCE LINES 416-418 .. code-block:: Python @@ -972,7 +989,7 @@ We can check that the minimum and maximum in the sample correspond to the bounds -.. GENERATED FROM PYTHON SOURCE LINES 402-404 +.. GENERATED FROM PYTHON SOURCE LINES 419-421 .. code-block:: Python @@ -991,11 +1008,11 @@ We can check that the minimum and maximum in the sample correspond to the bounds -.. GENERATED FROM PYTHON SOURCE LINES 405-406 +.. GENERATED FROM PYTHON SOURCE LINES 422-423 -Then we create a `MultiStart` algorithm based on the LHS starting points. +Then we create a :class:`~openturns.MultiStart` algorithm based on the LHS starting points. -.. GENERATED FROM PYTHON SOURCE LINES 408-411 +.. GENERATED FROM PYTHON SOURCE LINES 425-428 .. code-block:: Python @@ -1009,11 +1026,11 @@ Then we create a `MultiStart` algorithm based on the LHS starting points. -.. GENERATED FROM PYTHON SOURCE LINES 412-413 +.. GENERATED FROM PYTHON SOURCE LINES 429-430 -Finally, we configure the optimization algorithm so as to use the `MultiStart` algorithm. +Finally, we configure the optimization algorithm so as to use the :class:`~openturns.MultiStart` algorithm. -.. GENERATED FROM PYTHON SOURCE LINES 415-420 +.. GENERATED FROM PYTHON SOURCE LINES 432-437 .. code-block:: Python @@ -1029,7 +1046,7 @@ Finally, we configure the optimization algorithm so as to use the `MultiStart` a -.. GENERATED FROM PYTHON SOURCE LINES 421-424 +.. GENERATED FROM PYTHON SOURCE LINES 438-441 .. code-block:: Python @@ -1049,7 +1066,7 @@ Finally, we configure the optimization algorithm so as to use the `MultiStart` a -.. GENERATED FROM PYTHON SOURCE LINES 425-427 +.. GENERATED FROM PYTHON SOURCE LINES 442-444 .. code-block:: Python @@ -1073,7 +1090,7 @@ Finally, we configure the optimization algorithm so as to use the `MultiStart` a -.. GENERATED FROM PYTHON SOURCE LINES 428-429 +.. GENERATED FROM PYTHON SOURCE LINES 445-446 We see that there are no changes in the estimated parameters. This shows that the first optimization of the parameters worked fine. diff --git a/openturns/master/_sources/auto_meta_modeling/kriging_metamodel/plot_kriging_multioutput_firesatellite.rst.txt b/openturns/master/_sources/auto_meta_modeling/kriging_metamodel/plot_kriging_multioutput_firesatellite.rst.txt index 357217f5b4b..f14ebec17e6 100644 --- a/openturns/master/_sources/auto_meta_modeling/kriging_metamodel/plot_kriging_multioutput_firesatellite.rst.txt +++ b/openturns/master/_sources/auto_meta_modeling/kriging_metamodel/plot_kriging_multioutput_firesatellite.rst.txt @@ -308,7 +308,7 @@ Then, we use the `MetaModelValidation` class to validate the metamodel. .. rst-class:: sphx-glr-timing - **Total running time of the script:** (0 minutes 7.096 seconds) + **Total running time of the script:** (0 minutes 6.924 seconds) .. _sphx_glr_download_auto_meta_modeling_kriging_metamodel_plot_kriging_multioutput_firesatellite.py: diff --git a/openturns/master/_sources/auto_meta_modeling/kriging_metamodel/sg_execution_times.rst.txt b/openturns/master/_sources/auto_meta_modeling/kriging_metamodel/sg_execution_times.rst.txt index e5083b30462..c8dd9599e8e 100644 --- a/openturns/master/_sources/auto_meta_modeling/kriging_metamodel/sg_execution_times.rst.txt +++ b/openturns/master/_sources/auto_meta_modeling/kriging_metamodel/sg_execution_times.rst.txt @@ -6,7 +6,7 @@ Computation times ================= -**00:22.946** total execution time for 18 files **from auto_meta_modeling/kriging_metamodel**: +**00:21.618** total execution time for 18 files **from auto_meta_modeling/kriging_metamodel**: .. container:: @@ -33,56 +33,56 @@ Computation times - Time - Mem (MB) * - :ref:`sphx_glr_auto_meta_modeling_kriging_metamodel_plot_kriging_categorical.py` (``plot_kriging_categorical.py``) - - 00:09.964 + - 00:09.426 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_kriging_metamodel_plot_kriging_multioutput_firesatellite.py` (``plot_kriging_multioutput_firesatellite.py``) - - 00:07.096 + - 00:06.924 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_kriging_metamodel_plot_draw_covariance_models.py` (``plot_draw_covariance_models.py``) - - 00:01.254 + - 00:01.155 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_kriging_metamodel_plot_kriging_advanced.py` (``plot_kriging_advanced.py``) - - 00:00.940 + - 00:00.845 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_kriging_metamodel_plot_kriging_sequential.py` (``plot_kriging_sequential.py``) - - 00:00.645 + - 00:00.562 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_kriging_metamodel_plot_kriging_chose_trend.py` (``plot_kriging_chose_trend.py``) - - 00:00.559 + - 00:00.489 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_kriging_metamodel_plot_kriging_branin_function.py` (``plot_kriging_branin_function.py``) - - 00:00.402 + - 00:00.358 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_kriging_metamodel_plot_propagate_kriging_ishigami.py` (``plot_propagate_kriging_ishigami.py``) - - 00:00.369 + - 00:00.334 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_kriging_metamodel_plot_kriging_1d.py` (``plot_kriging_1d.py``) - - 00:00.318 + - 00:00.281 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_kriging_metamodel_plot_kriging_isotropic.py` (``plot_kriging_isotropic.py``) - - 00:00.261 + - 00:00.229 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_kriging_metamodel_plot_kriging_simulate.py` (``plot_kriging_simulate.py``) - - 00:00.239 + - 00:00.213 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_kriging_metamodel_plot_kriging_cantilever_beam_hmat.py` (``plot_kriging_cantilever_beam_hmat.py``) - - 00:00.192 - - 0.0 - * - :ref:`sphx_glr_auto_meta_modeling_kriging_metamodel_plot_kriging_hyperparameters_optimization.py` (``plot_kriging_hyperparameters_optimization.py``) - - 00:00.190 + - 00:00.172 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_kriging_metamodel_plot_kriging_cantilever_beam.py` (``plot_kriging_cantilever_beam.py``) - - 00:00.187 + - 00:00.166 - 0.0 - * - :ref:`sphx_glr_auto_meta_modeling_kriging_metamodel_plot_kriging_beam_trend.py` (``plot_kriging_beam_trend.py``) + * - :ref:`sphx_glr_auto_meta_modeling_kriging_metamodel_plot_kriging_hyperparameters_optimization.py` (``plot_kriging_hyperparameters_optimization.py``) - 00:00.166 - 0.0 + * - :ref:`sphx_glr_auto_meta_modeling_kriging_metamodel_plot_kriging_beam_trend.py` (``plot_kriging_beam_trend.py``) + - 00:00.148 + - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_kriging_metamodel_plot_kriging_likelihood.py` (``plot_kriging_likelihood.py``) - - 00:00.082 + - 00:00.074 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_kriging_metamodel_plot_kriging.py` (``plot_kriging.py``) - - 00:00.073 + - 00:00.067 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_kriging_metamodel_plot_kriging_beam_arbitrary_trend.py` (``plot_kriging_beam_arbitrary_trend.py``) - - 00:00.009 + - 00:00.008 - 0.0 diff --git a/openturns/master/_sources/auto_meta_modeling/polynomial_chaos_metamodel/index.rst.txt b/openturns/master/_sources/auto_meta_modeling/polynomial_chaos_metamodel/index.rst.txt index 2f22579d375..ff91d967bca 100644 --- a/openturns/master/_sources/auto_meta_modeling/polynomial_chaos_metamodel/index.rst.txt +++ b/openturns/master/_sources/auto_meta_modeling/polynomial_chaos_metamodel/index.rst.txt @@ -67,69 +67,69 @@ Polynomial chaos metamodel .. raw:: html -
+
.. only:: html - .. image:: /auto_meta_modeling/polynomial_chaos_metamodel/images/thumb/sphx_glr_plot_functional_chaos_database_thumb.png + .. image:: /auto_meta_modeling/polynomial_chaos_metamodel/images/thumb/sphx_glr_plot_chaos_ishigami_grouped_indices_thumb.png :alt: - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_functional_chaos_database.py` + :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_chaos_ishigami_grouped_indices.py` .. raw:: html -
Polynomial chaos over database
+
Compute grouped indices for the Ishigami function
.. raw:: html -
+
.. only:: html - .. image:: /auto_meta_modeling/polynomial_chaos_metamodel/images/thumb/sphx_glr_plot_chaos_ishigami_grouped_indices_thumb.png + .. image:: /auto_meta_modeling/polynomial_chaos_metamodel/images/thumb/sphx_glr_plot_chaos_draw_validation_thumb.png :alt: - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_chaos_ishigami_grouped_indices.py` + :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_chaos_draw_validation.py` .. raw:: html -
Compute grouped indices for the Ishigami function
+
Validate a polynomial chaos
.. raw:: html -
+
.. only:: html - .. image:: /auto_meta_modeling/polynomial_chaos_metamodel/images/thumb/sphx_glr_plot_chaos_draw_validation_thumb.png + .. image:: /auto_meta_modeling/polynomial_chaos_metamodel/images/thumb/sphx_glr_plot_functional_chaos_graphs_thumb.png :alt: - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_chaos_draw_validation.py` + :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_functional_chaos_graphs.py` .. raw:: html -
Validate a polynomial chaos
+
Polynomial chaos graphs
.. raw:: html -
+
.. only:: html - .. image:: /auto_meta_modeling/polynomial_chaos_metamodel/images/thumb/sphx_glr_plot_functional_chaos_graphs_thumb.png + .. image:: /auto_meta_modeling/polynomial_chaos_metamodel/images/thumb/sphx_glr_plot_functional_chaos_database_thumb.png :alt: - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_functional_chaos_graphs.py` + :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_functional_chaos_database.py` .. raw:: html -
Polynomial chaos graphs
+
Create a full or sparse polynomial chaos expansion
@@ -169,7 +169,7 @@ Polynomial chaos metamodel .. raw:: html -
+
.. only:: html @@ -180,7 +180,7 @@ Polynomial chaos metamodel .. raw:: html -
Create a polynomial chaos metamodel
+
Create a polynomial chaos metamodel from a data set
@@ -297,10 +297,10 @@ Polynomial chaos metamodel /auto_meta_modeling/polynomial_chaos_metamodel/plot_chaos_distribution_transformation /auto_meta_modeling/polynomial_chaos_metamodel/plot_chaos_build_distribution /auto_meta_modeling/polynomial_chaos_metamodel/plot_functional_chaos_exploitation - /auto_meta_modeling/polynomial_chaos_metamodel/plot_functional_chaos_database /auto_meta_modeling/polynomial_chaos_metamodel/plot_chaos_ishigami_grouped_indices /auto_meta_modeling/polynomial_chaos_metamodel/plot_chaos_draw_validation /auto_meta_modeling/polynomial_chaos_metamodel/plot_functional_chaos_graphs + /auto_meta_modeling/polynomial_chaos_metamodel/plot_functional_chaos_database /auto_meta_modeling/polynomial_chaos_metamodel/plot_chaos_cantilever_beam_integration /auto_meta_modeling/polynomial_chaos_metamodel/plot_functional_chaos_advanced_ctors /auto_meta_modeling/polynomial_chaos_metamodel/plot_functional_chaos diff --git a/openturns/master/_sources/auto_meta_modeling/polynomial_chaos_metamodel/plot_chaos_beam_sensitivity_degree.rst.txt b/openturns/master/_sources/auto_meta_modeling/polynomial_chaos_metamodel/plot_chaos_beam_sensitivity_degree.rst.txt index 7c29e2e2efd..1e70ce2e49c 100644 --- a/openturns/master/_sources/auto_meta_modeling/polynomial_chaos_metamodel/plot_chaos_beam_sensitivity_degree.rst.txt +++ b/openturns/master/_sources/auto_meta_modeling/polynomial_chaos_metamodel/plot_chaos_beam_sensitivity_degree.rst.txt @@ -577,7 +577,7 @@ References .. rst-class:: sphx-glr-timing - **Total running time of the script:** (0 minutes 7.434 seconds) + **Total running time of the script:** (0 minutes 6.094 seconds) .. _sphx_glr_download_auto_meta_modeling_polynomial_chaos_metamodel_plot_chaos_beam_sensitivity_degree.py: diff --git a/openturns/master/_sources/auto_meta_modeling/polynomial_chaos_metamodel/plot_chaos_build_distribution.rst.txt b/openturns/master/_sources/auto_meta_modeling/polynomial_chaos_metamodel/plot_chaos_build_distribution.rst.txt index 45fa75ed795..3fe86022cb9 100644 --- a/openturns/master/_sources/auto_meta_modeling/polynomial_chaos_metamodel/plot_chaos_build_distribution.rst.txt +++ b/openturns/master/_sources/auto_meta_modeling/polynomial_chaos_metamodel/plot_chaos_build_distribution.rst.txt @@ -211,7 +211,7 @@ Let us explore the distribution with its fitted parameters. .. GENERATED FROM PYTHON SOURCE LINES 78-79 -We can also analyse its properties in more detail. +We can also analyse its properties in more details. .. GENERATED FROM PYTHON SOURCE LINES 81-87 @@ -290,11 +290,6 @@ The previous constructor is the main topic of the example -.. rst-class:: sphx-glr-timing - - **Total running time of the script:** (0 minutes 2.029 seconds) - - .. _sphx_glr_download_auto_meta_modeling_polynomial_chaos_metamodel_plot_chaos_build_distribution.py: .. only:: html diff --git a/openturns/master/_sources/auto_meta_modeling/polynomial_chaos_metamodel/plot_chaos_cantilever_beam_integration.rst.txt b/openturns/master/_sources/auto_meta_modeling/polynomial_chaos_metamodel/plot_chaos_cantilever_beam_integration.rst.txt index 441d3d9f485..12ffb90c59b 100644 --- a/openturns/master/_sources/auto_meta_modeling/polynomial_chaos_metamodel/plot_chaos_cantilever_beam_integration.rst.txt +++ b/openturns/master/_sources/auto_meta_modeling/polynomial_chaos_metamodel/plot_chaos_cantilever_beam_integration.rst.txt @@ -368,7 +368,7 @@ Compute the :math:`Q^2` predictivity coefficient. .. code-block:: none - 0.9999980369284827 + 0.9999979360038378 @@ -448,7 +448,7 @@ Use an LHS design. .. image-sg:: /auto_meta_modeling/polynomial_chaos_metamodel/images/sphx_glr_plot_chaos_cantilever_beam_integration_002.png - :alt: LHSExperiment - N=1000000 - Q2=-108319.89 + :alt: LHSExperiment - N=1000000 - Q2=-98364.34 :srcset: /auto_meta_modeling/polynomial_chaos_metamodel/images/sphx_glr_plot_chaos_cantilever_beam_integration_002.png :class: sphx-glr-single-img @@ -475,7 +475,7 @@ Use a low-discrepancy experiment (Quasi-Monte Carlo). .. image-sg:: /auto_meta_modeling/polynomial_chaos_metamodel/images/sphx_glr_plot_chaos_cantilever_beam_integration_003.png - :alt: LowDiscrepancyExperiment - N=100000 - Q2=-186649.25 + :alt: LowDiscrepancyExperiment - N=100000 - Q2=-102093.68 :srcset: /auto_meta_modeling/polynomial_chaos_metamodel/images/sphx_glr_plot_chaos_cantilever_beam_integration_003.png :class: sphx-glr-single-img diff --git a/openturns/master/_sources/auto_meta_modeling/polynomial_chaos_metamodel/plot_chaos_cleaning_strategy.rst.txt b/openturns/master/_sources/auto_meta_modeling/polynomial_chaos_metamodel/plot_chaos_cleaning_strategy.rst.txt index 09ee1d969d6..9a76b36198a 100644 --- a/openturns/master/_sources/auto_meta_modeling/polynomial_chaos_metamodel/plot_chaos_cleaning_strategy.rst.txt +++ b/openturns/master/_sources/auto_meta_modeling/polynomial_chaos_metamodel/plot_chaos_cleaning_strategy.rst.txt @@ -1042,7 +1042,7 @@ produce the best Q2 score. .. rst-class:: sphx-glr-timing - **Total running time of the script:** (0 minutes 2.370 seconds) + **Total running time of the script:** (0 minutes 2.122 seconds) .. _sphx_glr_download_auto_meta_modeling_polynomial_chaos_metamodel_plot_chaos_cleaning_strategy.py: diff --git a/openturns/master/_sources/auto_meta_modeling/polynomial_chaos_metamodel/plot_chaos_cv.rst.txt b/openturns/master/_sources/auto_meta_modeling/polynomial_chaos_metamodel/plot_chaos_cv.rst.txt index d245a9c2e42..05645099857 100644 --- a/openturns/master/_sources/auto_meta_modeling/polynomial_chaos_metamodel/plot_chaos_cv.rst.txt +++ b/openturns/master/_sources/auto_meta_modeling/polynomial_chaos_metamodel/plot_chaos_cv.rst.txt @@ -672,7 +672,7 @@ When estimating the :math:`Q^2` score with the best parameters, the test set is .. rst-class:: sphx-glr-timing - **Total running time of the script:** (0 minutes 11.148 seconds) + **Total running time of the script:** (0 minutes 10.341 seconds) .. _sphx_glr_download_auto_meta_modeling_polynomial_chaos_metamodel_plot_chaos_cv.py: diff --git a/openturns/master/_sources/auto_meta_modeling/polynomial_chaos_metamodel/plot_chaos_draw_validation.rst.txt b/openturns/master/_sources/auto_meta_modeling/polynomial_chaos_metamodel/plot_chaos_draw_validation.rst.txt index f6839e1987a..7db2f63ea1a 100644 --- a/openturns/master/_sources/auto_meta_modeling/polynomial_chaos_metamodel/plot_chaos_draw_validation.rst.txt +++ b/openturns/master/_sources/auto_meta_modeling/polynomial_chaos_metamodel/plot_chaos_draw_validation.rst.txt @@ -216,7 +216,7 @@ In order to validate the metamodel, we generate a test sample. .. code-block:: none - 0.9972078325177286 + 0.9993670411085883 @@ -237,7 +237,7 @@ The Q2 is very close to 1: the metamodel is excellent. .. image-sg:: /auto_meta_modeling/polynomial_chaos_metamodel/images/sphx_glr_plot_chaos_draw_validation_001.png - :alt: Q2=99.72% + :alt: Q2=99.94% :srcset: /auto_meta_modeling/polynomial_chaos_metamodel/images/sphx_glr_plot_chaos_draw_validation_001.png :class: sphx-glr-single-img diff --git a/openturns/master/_sources/auto_meta_modeling/polynomial_chaos_metamodel/plot_chaos_ishigami_grouped_indices.rst.txt b/openturns/master/_sources/auto_meta_modeling/polynomial_chaos_metamodel/plot_chaos_ishigami_grouped_indices.rst.txt index eb7fdb8757d..8f3791d7fb8 100644 --- a/openturns/master/_sources/auto_meta_modeling/polynomial_chaos_metamodel/plot_chaos_ishigami_grouped_indices.rst.txt +++ b/openturns/master/_sources/auto_meta_modeling/polynomial_chaos_metamodel/plot_chaos_ishigami_grouped_indices.rst.txt @@ -148,44 +148,101 @@ Print Sobol' indices. .. code-block:: Python chaosSI = ot.FunctionalChaosSobolIndices(result) - print(chaosSI) + chaosSI -.. rst-class:: sphx-glr-script-out - .. code-block:: none +.. raw:: html +
FunctionalChaosSobolIndices - - input dimension=3 - - output dimension=1 - - basis size=26 - - mean=[3.50739] - - std-dev=[3.70413] - - | Index | Multi-index | Variance part | - |-------|---------------|---------------| - | 7 | [0,4,0] | 0.274425 | - | 1 | [1,0,0] | 0.191936 | - | 6 | [1,0,2] | 0.135811 | - | 13 | [0,6,0] | 0.134001 | - | 5 | [3,0,0] | 0.122952 | - | 10 | [3,0,2] | 0.0856397 | - | 3 | [0,2,0] | 0.0237185 | - | 11 | [1,0,4] | 0.0112027 | - - | Input | Name | Sobol' index | Total index | - |-------|---------------|---------------|---------------| - | 0 | X1 | 0.31752 | 0.559269 | - | 1 | X2 | 0.440685 | 0.440794 | - | 2 | X3 | 1.87833e-05 | 0.241742 | - - - - - +
    +
  • input dimension: 3
    • +
  • output dimension: 1
    • +
  • basis size: 18
    • +
  • mean: [3.49861]
    • +
  • std-dev: [3.71992]
    • +
+ + + + + + + + + + + + + + + + + + + + + + + + + +
InputVariableSobol' indexTotal index
0X10.3109470.557563
1X20.4423980.442449
2X30.0000000.246655
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
IndexMulti-indexPart of variance
6[0,4,0]0.274846
1[1,0,0]0.185716
5[1,0,2]0.140606
11[0,6,0]0.133570
4[3,0,0]0.122856
8[3,0,2]0.083539
3[0,2,0]0.025294
9[1,0,4]0.012034
+ +
+
+
.. GENERATED FROM PYTHON SOURCE LINES 63-64 @@ -206,7 +263,7 @@ We compute the first order indice of the group [0,1]. .. code-block:: none - 0.7582578489711685 + 0.7533450202235821 @@ -262,7 +319,7 @@ We compute the total order indice of the group [1,2]. .. code-block:: none - 0.6824803087795113 + 0.689053310039683 diff --git a/openturns/master/_sources/auto_meta_modeling/polynomial_chaos_metamodel/plot_chaos_sobol_confidence.rst.txt b/openturns/master/_sources/auto_meta_modeling/polynomial_chaos_metamodel/plot_chaos_sobol_confidence.rst.txt index 03023cb3a29..95ac34646e9 100644 --- a/openturns/master/_sources/auto_meta_modeling/polynomial_chaos_metamodel/plot_chaos_sobol_confidence.rst.txt +++ b/openturns/master/_sources/auto_meta_modeling/polynomial_chaos_metamodel/plot_chaos_sobol_confidence.rst.txt @@ -619,7 +619,7 @@ Hence, there is no evidence that the Sobol' indices of E are zero. .. rst-class:: sphx-glr-timing - **Total running time of the script:** (0 minutes 2.999 seconds) + **Total running time of the script:** (0 minutes 2.801 seconds) .. _sphx_glr_download_auto_meta_modeling_polynomial_chaos_metamodel_plot_chaos_sobol_confidence.py: diff --git a/openturns/master/_sources/auto_meta_modeling/polynomial_chaos_metamodel/plot_functional_chaos.rst.txt b/openturns/master/_sources/auto_meta_modeling/polynomial_chaos_metamodel/plot_functional_chaos.rst.txt index caca3cdd79f..5a22d9a590c 100644 --- a/openturns/master/_sources/auto_meta_modeling/polynomial_chaos_metamodel/plot_functional_chaos.rst.txt +++ b/openturns/master/_sources/auto_meta_modeling/polynomial_chaos_metamodel/plot_functional_chaos.rst.txt @@ -18,12 +18,21 @@ .. _sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_functional_chaos.py: -Create a polynomial chaos metamodel -=================================== +Create a polynomial chaos metamodel from a data set +=================================================== -.. GENERATED FROM PYTHON SOURCE LINES 6-25 +.. GENERATED FROM PYTHON SOURCE LINES 6-11 -In this example we are going to create a global approximation of a model response using functional chaos. +In this example, we create a polynomial chaos expansion (PCE) using +a data set. +More precisely, given a pair of input and output samples, +we create a PCE without the knowledge of the input distribution. +In this example, we use a relatively small sample size equal to 80. + +.. GENERATED FROM PYTHON SOURCE LINES 13-34 + +In this example we create a global approximation of a model response using +polynomial chaos expansion. Let :math:`h` be the function defined by: @@ -41,9 +50,15 @@ We assume that and that :math:`X_1` and :math:`X_2` are independent. An interesting point in this example is that the output is multivariate. -This is why we are going to use the `getMarginal` method in the script in order to select the output marginal that we want to manage. +This is why we are going to use the `getMarginal` method in the script +in order to select the output marginal that we want to manage. + +.. GENERATED FROM PYTHON SOURCE LINES 36-38 -.. GENERATED FROM PYTHON SOURCE LINES 27-33 +Simulate input and output samples +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +.. GENERATED FROM PYTHON SOURCE LINES 40-46 .. code-block:: Python @@ -60,15 +75,15 @@ This is why we are going to use the `getMarginal` method in the script in order -.. GENERATED FROM PYTHON SOURCE LINES 34-35 +.. GENERATED FROM PYTHON SOURCE LINES 47-48 We first create the function `model`. -.. GENERATED FROM PYTHON SOURCE LINES 37-43 +.. GENERATED FROM PYTHON SOURCE LINES 50-56 .. code-block:: Python - ot.RandomGenerator.SetSeed(0) + ot.RandomGenerator.SetSeed(2) dimension = 2 input_names = ["x1", "x2"] formulas = ["cos(x1 + x2)", "(x2 + 1) * exp(x1)"] @@ -81,11 +96,12 @@ We first create the function `model`. -.. GENERATED FROM PYTHON SOURCE LINES 44-45 +.. GENERATED FROM PYTHON SOURCE LINES 57-59 -Then we create a sample `inputSample` and compute the corresponding output sample `outputSample`. +Then we create a sample `inputSample` and compute the corresponding output +sample `outputSample`. -.. GENERATED FROM PYTHON SOURCE LINES 47-52 +.. GENERATED FROM PYTHON SOURCE LINES 61-66 .. code-block:: Python @@ -101,31 +117,299 @@ Then we create a sample `inputSample` and compute the corresponding output sampl -.. GENERATED FROM PYTHON SOURCE LINES 53-55 +.. GENERATED FROM PYTHON SOURCE LINES 67-69 -Create a functional chaos model. -First, we need to fit a distribution on the input sample. We can do this automatically with the Lilliefors test. +Create the PCE +~~~~~~~~~~~~~~ -.. GENERATED FROM PYTHON SOURCE LINES 57-59 +.. GENERATED FROM PYTHON SOURCE LINES 71-81 + +Create a functional chaos model. +The algorithm needs to fit a distribution on the input sample. +To do this, the algorithm in :class:`~openturns.FunctionalChaosAlgorithm` +uses the :class:`~openturns.FunctionalChaosAlgorithm.BuildDistribution` +static method to fit the distribution to the input sample. +Please read :doc:`Fit a distribution from an input sample ` +for an example of this method. +The algorithm does this automatically using the Lilliefors test. +In order to make the algorithm a little faster, we reduce the +value of the sample size used in the Lilliefors test. + +.. GENERATED FROM PYTHON SOURCE LINES 83-85 .. code-block:: Python - ot.ResourceMap.SetAsUnsignedInteger("FittingTest-LillieforsMaximumSamplingSize", 100) + ot.ResourceMap.SetAsUnsignedInteger("FittingTest-LillieforsMaximumSamplingSize", 50) + + +.. GENERATED FROM PYTHON SOURCE LINES 86-89 +The main topic of this example is to introduce the next constructor of +:class:`~openturns.FunctionalChaosAlgorithm`. +Notice that the only input arguments are the input and output sample. -.. GENERATED FROM PYTHON SOURCE LINES 60-65 +.. GENERATED FROM PYTHON SOURCE LINES 89-94 .. code-block:: Python algo = ot.FunctionalChaosAlgorithm(inputSample, outputSample) algo.run() result = algo.getResult() + result + + + + + + +.. raw:: html + +
+ FunctionalChaosResult +
    +
  • input dimension: 2
    • +
  • output dimension: 2
    • +
  • distribution dimension: 2
    • +
  • transformation: 2 -> 2
    • +
  • inverse transformation: 2 -> 2
    • +
  • orthogonal basis dimension: 2
    • +
  • indices size: 33
    • +
  • relative errors: [0.000423845,3.97704e-08]
    • +
  • residuals: [0.00156354,0.000147243]
    • +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
IndexMulti-indexCoeff.#0Coeff.#1
0[0,0]-0.97783622.494928
1[1,0]3.9463191.310505
2[0,1]-0.56687312.058245
3[2,0]-6.5954253.31883
4[0,2]0.057542120.1086024
5[3,0]7.262131-0.841792
6[0,3]-0.9758324-0.12278
7[1,1]-0.78875842.418963
8[4,0]-6.4892661.935301
9[0,4]0.28441890.1285879
10[5,0]5.352722-1.168838
11[0,5]-0.8491851-0.1064447
12[2,1]0.30631631.643328
13[1,2]-0.02819570.01273302
14[6,0]-3.8008620.9235032
15[0,6]0.0040408260.1013839
16[7,0]2.402248-0.5406551
17[0,7]-0.441342-0.0634571
18[3,1]-0.0033252151.022703
19[1,3]-0.22679710.002919773
20[2,2]0.4659559-0.001704627
21[8,0]-1.2726890.2902903
22[0,8]-0.033413180.05202352
23[4,1]0.12400070.2562661
24[1,4]-0.04681154-0.006325388
25[9,0]0.5059943-0.1094002
26[0,9]-0.1155697-0.01848551
27[3,2]-0.042184890.02369182
28[2,3]-0.05014101-0.01482048
29[10,0]-0.18258520.03945734
30[0,10]-0.014674340.01355966
31[5,1]-0.088890850.1317192
32[1,5]-0.24617350.001139069
+ +
+
+
+ +.. GENERATED FROM PYTHON SOURCE LINES 95-100 + +Not all coefficients are selected in this PCE. +Indeed, the default constructor of :class:`~openturns.FunctionalChaosAlgorithm` +creates a sparse PCE. +Please read :doc:`Create a full or sparse polynomial chaos expansion ` +for more details on this topic. + +.. GENERATED FROM PYTHON SOURCE LINES 102-103 + +Get the metamodel. + +.. GENERATED FROM PYTHON SOURCE LINES 103-105 + +.. code-block:: Python + metamodel = result.getMetaModel() @@ -135,13 +419,13 @@ First, we need to fit a distribution on the input sample. We can do this automat -.. GENERATED FROM PYTHON SOURCE LINES 66-69 +.. GENERATED FROM PYTHON SOURCE LINES 106-109 Plot the second output of our model depending on :math:`x_2` with :math:`x_1=0.5`. In order to do this, we create a `ParametricFunction` and set the value of :math:`x_1`. Then we use the `getMarginal` method to extract the second output (which index is equal to 1). -.. GENERATED FROM PYTHON SOURCE LINES 71-89 +.. GENERATED FROM PYTHON SOURCE LINES 111-129 .. code-block:: Python @@ -175,12 +459,14 @@ Then we use the `getMarginal` method to extract the second output (which index i -.. GENERATED FROM PYTHON SOURCE LINES 90-92 +.. GENERATED FROM PYTHON SOURCE LINES 130-134 -We see that the metamodel fits approximately to the model, except perhaps for extreme values of :math:`x_2`. -However, there is a better way of globally validating the metamodel, using the `MetaModelValidation` on a validation design of experiment. +We see that the metamodel fits approximately to the model, except +perhaps for extreme values of :math:`x_2`. +However, there is a better way of globally validating the metamodel, +using the :class:`~openturns.MetaModelValidation` on a validation design of experiment. -.. GENERATED FROM PYTHON SOURCE LINES 94-99 +.. GENERATED FROM PYTHON SOURCE LINES 136-141 .. code-block:: Python @@ -196,11 +482,11 @@ However, there is a better way of globally validating the metamodel, using the ` -.. GENERATED FROM PYTHON SOURCE LINES 100-101 +.. GENERATED FROM PYTHON SOURCE LINES 142-143 Plot the corresponding validation graphics. -.. GENERATED FROM PYTHON SOURCE LINES 103-109 +.. GENERATED FROM PYTHON SOURCE LINES 145-151 .. code-block:: Python @@ -214,7 +500,7 @@ Plot the corresponding validation graphics. .. image-sg:: /auto_meta_modeling/polynomial_chaos_metamodel/images/sphx_glr_plot_functional_chaos_002.png - :alt: Metamodel validation Q2=[-3.50512,0.969793] + :alt: Metamodel validation Q2=[0.486703,0.999523] :srcset: /auto_meta_modeling/polynomial_chaos_metamodel/images/sphx_glr_plot_functional_chaos_002.png :class: sphx-glr-single-img @@ -222,94 +508,203 @@ Plot the corresponding validation graphics. -.. GENERATED FROM PYTHON SOURCE LINES 110-112 +.. GENERATED FROM PYTHON SOURCE LINES 152-156 -The coefficient of predictivity is not extremely satisfactory for the first output, but is would be sufficient for a central dispersion study. -The second output has a much more satisfactory Q2: only one single extreme point is far from the diagonal of the graphics. +The coefficient of predictivity is not extremely satisfactory for the +first output, but is would be sufficient for a central dispersion study. +The second output has a much more satisfactory Q2: only one single +extreme point is far from the diagonal of the graphics. -.. GENERATED FROM PYTHON SOURCE LINES 114-116 +.. GENERATED FROM PYTHON SOURCE LINES 158-160 Compute and print Sobol' indices --------------------------------- +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -.. GENERATED FROM PYTHON SOURCE LINES 118-121 +.. GENERATED FROM PYTHON SOURCE LINES 162-165 .. code-block:: Python chaosSI = ot.FunctionalChaosSobolIndices(result) - print(chaosSI) + chaosSI -.. rst-class:: sphx-glr-script-out - .. code-block:: none +.. raw:: html +
FunctionalChaosSobolIndices - - input dimension=2 - - output dimension=2 - - basis size=33 - - mean=[0.415734,1.76627] - - std-dev=[1.16199,4.4335] - - Marginal: 0 - | Index | Multi-index | Variance part | - |-------|---------------|---------------| - | 19 | [1,3] | 0.270497 | - | 20 | [2,2] | 0.145612 | - | 8 | [4,0] | 0.125871 | - | 5 | [3,0] | 0.115624 | - | 4 | [0,2] | 0.0701045 | - | 10 | [5,0] | 0.0597999 | - | 18 | [3,1] | 0.0410662 | - | 1 | [1,0] | 0.03954 | - | 14 | [6,0] | 0.0295803 | - | 16 | [7,0] | 0.0162176 | - | 9 | [0,4] | 0.0119177 | - | 22 | [0,8] | 0.0107404 | - - | Input | Name | Sobol' index | Total index | - |-------|---------------|---------------|---------------| - | 0 | X0 | 0.400231 | 0.888617 | - | 1 | X1 | 0.111383 | 0.599769 | - - Marginal: 1 - | Index | Multi-index | Variance part | - |-------|---------------|---------------| - | 1 | [1,0] | 0.207009 | - | 7 | [1,1] | 0.200105 | - | 2 | [0,1] | 0.171751 | - | 3 | [2,0] | 0.168775 | - | 12 | [2,1] | 0.105085 | - | 5 | [3,0] | 0.0668862 | - | 8 | [4,0] | 0.0309423 | - | 18 | [3,1] | 0.0279345 | - - | Input | Name | Sobol' index | Total index | - |-------|---------------|---------------|---------------| - | 0 | X0 | 0.491712 | 0.828208 | - | 1 | X1 | 0.171792 | 0.508288 | - - - - - - -.. GENERATED FROM PYTHON SOURCE LINES 122-127 +
    +
  • input dimension: 2
    • +
  • output dimension: 2
    • +
  • basis size: 33
    • +
  • mean: [-0.977836,2.49493]
    • +
  • std-dev: [14.4244,5.81255]
    • +
+ Output marginal: 0 + + + + + + + + + + + + + + + + + + + +
InputVariableSobol' indexTotal index
0X00.9838310.989001
1X10.0109990.016169
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
IndexMulti-indexPart of variance
5[3,0]0.253472
3[2,0]0.209068
8[4,0]0.202392
10[5,0]0.137706
1[1,0]0.074849
14[6,0]0.069433
16[7,0]0.027736
+ Output marginal: 1 + + + + + + + + + + + + + + + + + + + +
InputVariableSobol' indexTotal index
0X00.5859050.872471
1X10.1275290.414095
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
IndexMulti-indexPart of variance
3[2,0]0.326015
7[1,1]0.173191
2[0,1]0.125390
8[4,0]0.110857
12[2,1]0.079931
1[1,0]0.050833
10[5,0]0.040437
18[3,1]0.030958
14[6,0]0.025243
5[3,0]0.020974
+ +
+
+
+ +.. GENERATED FROM PYTHON SOURCE LINES 166-174 Let us analyse the results of this global sensitivity analysis. -* We see that the first output involves significant multi-indices with total degree 4. The contribution of the interactions are very significant in this model. -* The second output involves multi-indices with total degrees from 1 to 7, with a significant contribution of multi-indices with total degress 5 and 7. - The first variable is especially significant, with a significant contribution of the interactions. +* We see that the first output involves significant multi-indices with + higher marginal degree. +* For the second output, the first variable is especially significant, + with a significant contribution of the interactions. + The contribution of the interactions are very + significant in this model. -.. GENERATED FROM PYTHON SOURCE LINES 129-130 +.. GENERATED FROM PYTHON SOURCE LINES 176-177 Draw Sobol' indices. -.. GENERATED FROM PYTHON SOURCE LINES 132-136 +.. GENERATED FROM PYTHON SOURCE LINES 179-183 .. code-block:: Python @@ -324,7 +719,7 @@ Draw Sobol' indices. -.. GENERATED FROM PYTHON SOURCE LINES 137-142 +.. GENERATED FROM PYTHON SOURCE LINES 184-189 .. code-block:: Python @@ -345,24 +740,29 @@ Draw Sobol' indices. -.. GENERATED FROM PYTHON SOURCE LINES 143-153 +.. GENERATED FROM PYTHON SOURCE LINES 190-205 Testing the sensitivity to the degree -------------------------------------- +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -With the specific constructor of `FunctionalChaosAlgorithm` that we use, the `FunctionalChaosAlgorithm-MaximumTotalDegree` -in the `ResourceMap` configure the maximum degree explored by the algorithm. This degree is a trade-off. +With the specific constructor of `FunctionalChaosAlgorithm` that +we use, the `FunctionalChaosAlgorithm-MaximumTotalDegree` +in the `ResourceMap` configure the maximum degree explored by +the algorithm. This degree is a trade-off. -* If the maximum degree is too low, the polynomial may miss some coefficients so that the quality is lower than possible. -* If the maximum degree is too large, the number of coefficients to explore is too large, so that the coefficients might be poorly estimated. +* If the maximum degree is too low, the polynomial may miss some + coefficients so that the quality is lower than possible. +* If the maximum degree is too large, the number of coefficients + to explore is too large, so that the coefficients might be poorly estimated. -This is why the following `for` loop explores various degrees to see the sensitivity of the metamodel predictivity depending on the degree. +This is why the following `for` loop explores various degrees to see +the sensitivity of the metamodel predictivity depending on the degree. -.. GENERATED FROM PYTHON SOURCE LINES 155-156 +.. GENERATED FROM PYTHON SOURCE LINES 207-208 The default value of this parameter is 10. -.. GENERATED FROM PYTHON SOURCE LINES 158-160 +.. GENERATED FROM PYTHON SOURCE LINES 210-212 .. code-block:: Python @@ -381,15 +781,15 @@ The default value of this parameter is 10. -.. GENERATED FROM PYTHON SOURCE LINES 161-162 +.. GENERATED FROM PYTHON SOURCE LINES 213-214 -This is why we explore the values from 5 to 15. +This is why we explore the values from 1 to 15. -.. GENERATED FROM PYTHON SOURCE LINES 164-181 +.. GENERATED FROM PYTHON SOURCE LINES 216-234 .. code-block:: Python - degrees = range(5, 12) + degrees = range(1, 12) q2 = ot.Sample(len(degrees), 2) for maximumDegree in degrees: ot.ResourceMap.SetAsUnsignedInteger( @@ -404,7 +804,8 @@ This is why we explore the values from 5 to 15. val = ot.MetaModelValidation( inputTest, outputTest[:, outputIndex], metamodel.getMarginal(outputIndex) ) - q2[maximumDegree - degrees[0], outputIndex] = val.computePredictivityFactor()[0] + q2Value = min(1.0, max(0.0, val.computePredictivityFactor()[0])) # Get lucky. + q2[maximumDegree - degrees[0], outputIndex] = q2Value @@ -414,6 +815,10 @@ This is why we explore the values from 5 to 15. .. code-block:: none + Maximum total degree = 1 + Maximum total degree = 2 + Maximum total degree = 3 + Maximum total degree = 4 Maximum total degree = 5 Maximum total degree = 6 Maximum total degree = 7 @@ -425,7 +830,7 @@ This is why we explore the values from 5 to 15. -.. GENERATED FROM PYTHON SOURCE LINES 182-196 +.. GENERATED FROM PYTHON SOURCE LINES 235-251 .. code-block:: Python @@ -440,7 +845,9 @@ This is why we explore the values from 5 to 15. cloud.setPointStyle("bullet") graph.add(cloud) graph.setLegendPosition("upper right") - view = viewer.View(graph) + view = viewer.View(graph, legend_kw={"bbox_to_anchor": (1.0, 1.0), "loc": "upper left"}) + plt.subplots_adjust(right=0.7) + plt.show() @@ -455,26 +862,37 @@ This is why we explore the values from 5 to 15. -.. GENERATED FROM PYTHON SOURCE LINES 197-209 +.. GENERATED FROM PYTHON SOURCE LINES 252-275 -We see that a total degree lower than 9 is not sufficient to describe the first output with good predictivity. -However, the coefficient of predictivity drops when the total degree gets greater than 12. -The predictivity of the second output seems to be much less satisfactory: a little more work would be required to improve the metamodel. +We see that the R2 score increases then gets constant or decreases. +A low total polynomial degree is not sufficient to describe +the first output with good predictivity. +However, the coefficient of predictivity can decrease when the total degree +gets greater. +The predictivity of the second output seems to be much less +satisfactory: a little more work would be required to improve the metamodel. In this situation, the following methods may be used. -* Since the distribution of the input is known, we may want to give this information to the `FunctionalChaosAlgorithm`. - This prevents the algorithm from trying to fit the distribution which best fit to the data. -* We may want to customize the `adaptiveStrategy` by selecting an enumerate function which best fit to this particular situation. - In this specific example, the interactions plays a great role so that the linear enumerate function may provide better results than the hyperbolic rule. -* We may want to customize the `projectionStrategy` by selecting an method to compute the coefficient which improves the estimation. - Given that the function is symbolic and fast, it might be interesting to try an integration rule instead of the least squares method. - -.. GENERATED FROM PYTHON SOURCE LINES 211-212 +* Since the distribution of the input is known, we may want to give + this information to the `FunctionalChaosAlgorithm`. + This prevents the algorithm from trying to fit the input distribution + which best fit to the data. +* We may want to customize the `adaptiveStrategy` by selecting an enumerate + function which best fit to this particular example. + In this specific example, however, the interactions plays a great role so that the + linear enumerate function may provide better results than the hyperbolic rule. +* We may want to customize the `projectionStrategy` by selecting a method + to compute the coefficient which improves the estimation. + For example, it might be interesting to + try an integration rule instead of the least squares method. + Notice that a specific design of experiment is required in this case. + +.. GENERATED FROM PYTHON SOURCE LINES 277-278 Reset default settings -.. GENERATED FROM PYTHON SOURCE LINES 212-213 +.. GENERATED FROM PYTHON SOURCE LINES 278-279 .. code-block:: Python @@ -489,7 +907,7 @@ Reset default settings .. rst-class:: sphx-glr-timing - **Total running time of the script:** (0 minutes 7.821 seconds) + **Total running time of the script:** (0 minutes 10.810 seconds) .. _sphx_glr_download_auto_meta_modeling_polynomial_chaos_metamodel_plot_functional_chaos.py: diff --git a/openturns/master/_sources/auto_meta_modeling/polynomial_chaos_metamodel/plot_functional_chaos_database.rst.txt b/openturns/master/_sources/auto_meta_modeling/polynomial_chaos_metamodel/plot_functional_chaos_database.rst.txt index af390660fbc..fae0bf4930e 100644 --- a/openturns/master/_sources/auto_meta_modeling/polynomial_chaos_metamodel/plot_functional_chaos_database.rst.txt +++ b/openturns/master/_sources/auto_meta_modeling/polynomial_chaos_metamodel/plot_functional_chaos_database.rst.txt @@ -18,17 +18,23 @@ .. _sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_functional_chaos_database.py: -Polynomial chaos over database -============================== +Create a full or sparse polynomial chaos expansion +================================================== -.. GENERATED FROM PYTHON SOURCE LINES 6-10 +.. GENERATED FROM PYTHON SOURCE LINES 6-16 -In this example we are going to create a global approximation of a model response using functional chaos over a design of experiment. +In this example we create a global approximation of a model using +polynomial chaos expansion based on a design of experiment. +The goal of this example is to show how we can create a full or +sparse polynomial chaos expansion depending on our needs +and depending on the number of observations we have. +In general, we should have more observations than parameters to estimate. +This is why a sparse polynomial chaos may be interesting: +by carefully selecting the coefficients we estimate, +we may reduce overfitting and increase the predictions of the +metamodel. -You will need to specify the distribution of the input parameters. -If not known, statistical inference can be used to select a possible candidate, and fitting tests can validate such an hypothesis. - -.. GENERATED FROM PYTHON SOURCE LINES 12-16 +.. GENERATED FROM PYTHON SOURCE LINES 18-22 .. code-block:: Python @@ -43,19 +49,38 @@ If not known, statistical inference can be used to select a possible candidate, -.. GENERATED FROM PYTHON SOURCE LINES 17-19 +.. GENERATED FROM PYTHON SOURCE LINES 23-25 + +Define the model +~~~~~~~~~~~~~~~~ + +.. GENERATED FROM PYTHON SOURCE LINES 27-28 -Create a function R^n --> R^p -For example R^4 --> R +Create the function. -.. GENERATED FROM PYTHON SOURCE LINES 19-27 +.. GENERATED FROM PYTHON SOURCE LINES 28-32 .. code-block:: Python - myModel = ot.SymbolicFunction(["x1", "x2", "x3", "x4"], ["1+x1*x2 + 2*x3^2+x4^4"]) + myModel = ot.SymbolicFunction( + ["x1", "x2", "x3", "x4"], ["1 + x1 * x2 + 2 * x3^2 + x4^4"] + ) + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 33-34 + +Create a multivariate distribution. + +.. GENERATED FROM PYTHON SOURCE LINES 34-38 + +.. code-block:: Python - # Create a distribution of dimension n - # for example n=3 with independent components distribution = ot.JointDistribution( [ot.Normal(), ot.Uniform(), ot.Gamma(2.75, 1.0), ot.Beta(2.5, 1.0, -1.0, 2.0)] ) @@ -67,18 +92,32 @@ For example R^4 --> R -.. GENERATED FROM PYTHON SOURCE LINES 28-29 +.. GENERATED FROM PYTHON SOURCE LINES 39-45 + +In order to create the PCE, we can specify the distribution of the +input parameters. +If not known, statistical inference can be used to select a possible +candidate, and fitting tests can validate such an hypothesis. +Please read :doc:`Fit a distribution from an input sample ` +for an example of this method. + +.. GENERATED FROM PYTHON SOURCE LINES 47-49 -Prepare the input/output samples +Create a training sample +~~~~~~~~~~~~~~~~~~~~~~~~ -.. GENERATED FROM PYTHON SOURCE LINES 29-34 +.. GENERATED FROM PYTHON SOURCE LINES 51-52 + +Create a pair of input and output samples. + +.. GENERATED FROM PYTHON SOURCE LINES 52-56 .. code-block:: Python sampleSize = 250 - X = distribution.getSample(sampleSize) - Y = myModel(X) - dimension = X.getDimension() + inputSample = distribution.getSample(sampleSize) + outputSample = myModel(inputSample) + @@ -86,20 +125,26 @@ Prepare the input/output samples +.. GENERATED FROM PYTHON SOURCE LINES 57-59 -.. GENERATED FROM PYTHON SOURCE LINES 35-36 +Build the orthogonal basis +~~~~~~~~~~~~~~~~~~~~~~~~~~ -build the orthogonal basis +.. GENERATED FROM PYTHON SOURCE LINES 61-63 -.. GENERATED FROM PYTHON SOURCE LINES 36-43 +In the next cell, we create the univariate orthogonal polynomial basis +for each marginal. + +.. GENERATED FROM PYTHON SOURCE LINES 63-71 .. code-block:: Python + inputDimension = inputSample.getDimension() coll = [ ot.StandardDistributionPolynomialFactory(distribution.getMarginal(i)) - for i in range(dimension) + for i in range(inputDimension) ] - enumerateFunction = ot.LinearEnumerateFunction(dimension) + enumerateFunction = ot.LinearEnumerateFunction(inputDimension) productBasis = ot.OrthogonalProductPolynomialFactory(coll, enumerateFunction) @@ -109,40 +154,364 @@ build the orthogonal basis -.. GENERATED FROM PYTHON SOURCE LINES 44-45 +.. GENERATED FROM PYTHON SOURCE LINES 72-73 -create the algorithm +We can achieve the same result using :class:`~OrthogonalProductPolynomialFactory`. -.. GENERATED FROM PYTHON SOURCE LINES 45-55 +.. GENERATED FROM PYTHON SOURCE LINES 73-81 .. code-block:: Python - degree = 6 - adaptiveStrategy = ot.FixedStrategy( - productBasis, enumerateFunction.getStrataCumulatedCardinal(degree) + marginalDistributionCollection = [ + distribution.getMarginal(i) for i in range(inputDimension) + ] + multivariateBasis = ot.OrthogonalProductPolynomialFactory( + marginalDistributionCollection ) + multivariateBasis + + + + + + +.. raw:: html + +
+
    +
  • dimension: 4
    • +
  • enumerate function: class=LinearEnumerateFunction dimension=4
    • +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
IndexNameDistributionUnivariate polynomial
0X0NormalHermiteFactory
1X1UniformLegendreFactory
2X2GammaLaguerreFactory
3X3BetaJacobiFactory
+ +
+
+
+ +.. GENERATED FROM PYTHON SOURCE LINES 82-84 + +Create a full PCE +~~~~~~~~~~~~~~~~~ + +.. GENERATED FROM PYTHON SOURCE LINES 86-98 + +Create the algorithm. +We compute the basis size from the total degree. +The next lines use the :class:`~openturns.LeastSquaresStrategy` class +with default parameters (the default is the +:class:`~openturns.PenalizedLeastSquaresAlgorithmFactory` class). +This creates a full polynomial chaos expansion, i.e. +we keep all the candidate coefficients produced by the enumeration +rule. +In order to create a sparse polynomial chaos expansion, we +must use the :class:`~openturns.LeastSquaresMetaModelSelectionFactory` +class instead. + + +.. GENERATED FROM PYTHON SOURCE LINES 98-110 + +.. code-block:: Python + + totalDegree = 3 + candidateBasisSize = enumerateFunction.getBasisSizeFromTotalDegree(totalDegree) + print("Candidate basis size = ", candidateBasisSize) + adaptiveStrategy = ot.FixedStrategy(productBasis, candidateBasisSize) projectionStrategy = ot.LeastSquaresStrategy() algo = ot.FunctionalChaosAlgorithm( - X, Y, distribution, adaptiveStrategy, projectionStrategy + inputSample, outputSample, distribution, adaptiveStrategy, projectionStrategy ) algo.run() + result = algo.getResult() + result + +.. rst-class:: sphx-glr-script-out + .. code-block:: none + Candidate basis size = 35 -.. GENERATED FROM PYTHON SOURCE LINES 56-57 +.. raw:: html + +
+ FunctionalChaosResult +
    +
  • input dimension: 4
    • +
  • output dimension: 1
    • +
  • distribution dimension: 4
    • +
  • transformation: 4 -> 4
    • +
  • inverse transformation: 4 -> 4
    • +
  • orthogonal basis dimension: 4
    • +
  • indices size: 35
    • +
  • relative errors: [3.25754e-05]
    • +
  • residuals: [0.010775]
    • +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
IndexMulti-indexCoeff.
0[0,0,0,0]26.10131
1[1,0,0,0]0.01833501
2[0,1,0,0]0.02643858
3[0,0,1,0]24.89616
4[0,0,0,1]3.998141
5[2,0,0,0]-0.007498848
6[1,1,0,0]0.5836605
7[1,0,1,0]0.0008685963
8[1,0,0,1]-0.01786958
9[0,2,0,0]0.005226953
10[0,1,1,0]0.02195566
11[0,1,0,1]-0.06375109
12[0,0,2,0]9.063002
13[0,0,1,1]-0.02439593
14[0,0,0,2]2.366967
15[3,0,0,0]0.003033619
16[2,1,0,0]-0.01237667
17[2,0,1,0]-0.01342518
18[2,0,0,1]0.01335615
19[1,2,0,0]-0.009671841
20[1,1,1,0]0.004816446
21[1,1,0,1]-0.02295916
22[1,0,2,0]-0.01663346
23[1,0,1,1]0.007606394
24[1,0,0,2]0.03900244
25[0,3,0,0]0.02087256
26[0,2,1,0]-0.01402968
27[0,2,0,1]-0.04129633
28[0,1,2,0]-0.01182831
29[0,1,1,1]-0.01354742
30[0,1,0,2]0.09136447
31[0,0,3,0]0.02163227
32[0,0,2,1]0.02992845
33[0,0,1,2]0.04678639
34[0,0,0,3]1.057842
+ +
+
+
-get the metamodel function +.. GENERATED FROM PYTHON SOURCE LINES 111-112 -.. GENERATED FROM PYTHON SOURCE LINES 57-60 +Get the number of coefficients in the PCE. + +.. GENERATED FROM PYTHON SOURCE LINES 112-115 + +.. code-block:: Python + + selectedBasisSizeFull = result.getIndices().getSize() + print("Selected basis size = ", selectedBasisSizeFull) + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + Selected basis size = 35 + + + + +.. GENERATED FROM PYTHON SOURCE LINES 116-119 + +We see that the number of coefficients in the selected basis is +equal to the number of coefficients in the candidate basis. +This is, indeed, a *full* PCE. + +.. GENERATED FROM PYTHON SOURCE LINES 121-123 + +Use the PCE +~~~~~~~~~~~ + +.. GENERATED FROM PYTHON SOURCE LINES 125-126 + +Get the metamodel function. + +.. GENERATED FROM PYTHON SOURCE LINES 126-128 .. code-block:: Python - result = algo.getResult() metamodel = result.getMetaModel() @@ -152,11 +521,37 @@ get the metamodel function -.. GENERATED FROM PYTHON SOURCE LINES 61-62 +.. GENERATED FROM PYTHON SOURCE LINES 129-131 + +In order to evaluate the metamodel on a single point, we just +use it as any other :class:`openturns.Function`. + +.. GENERATED FROM PYTHON SOURCE LINES 131-135 + +.. code-block:: Python + + xPoint = distribution.getMean() + yPoint = metamodel(xPoint) + print("Value at ", xPoint, " is ", yPoint) + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + Value at [0,0,2.75,1.14286] is [17.7455] + -Print residuals -.. GENERATED FROM PYTHON SOURCE LINES 62-63 + +.. GENERATED FROM PYTHON SOURCE LINES 136-137 + +Print residuals. + +.. GENERATED FROM PYTHON SOURCE LINES 137-139 .. code-block:: Python @@ -166,14 +561,239 @@ Print residuals + .. raw:: html
- class=Point name=Unnamed dimension=1 values=[2.64115e-15] + class=Point name=Unnamed dimension=1 values=[0.010775]


+.. GENERATED FROM PYTHON SOURCE LINES 140-143 + +Based on these results, we may want to validate our metamodel. +More details on this topic are presented in +:doc:`Validate a polynomial chaos `. + +.. GENERATED FROM PYTHON SOURCE LINES 145-147 + +Create a sparse PCE +~~~~~~~~~~~~~~~~~~~ + +.. GENERATED FROM PYTHON SOURCE LINES 149-153 + +In order to create a sparse polynomial chaos expansion, we +use the :class:`~openturns.LeastSquaresMetaModelSelectionFactory` +class instead. + + +.. GENERATED FROM PYTHON SOURCE LINES 153-166 + +.. code-block:: Python + + totalDegree = 6 + candidateBasisSize = enumerateFunction.getBasisSizeFromTotalDegree(totalDegree) + print("Candidate basis size = ", candidateBasisSize) + adaptiveStrategy = ot.FixedStrategy(productBasis, candidateBasisSize) + selectionAlgorithm = ot.LeastSquaresMetaModelSelectionFactory() + projectionStrategy = ot.LeastSquaresStrategy(selectionAlgorithm) + algo = ot.FunctionalChaosAlgorithm( + inputSample, outputSample, distribution, adaptiveStrategy, projectionStrategy + ) + algo.run() + result = algo.getResult() + result + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + Candidate basis size = 210 + + +.. raw:: html + +
+ FunctionalChaosResult +
    +
  • input dimension: 4
    • +
  • output dimension: 1
    • +
  • distribution dimension: 4
    • +
  • transformation: 4 -> 4
    • +
  • inverse transformation: 4 -> 4
    • +
  • orthogonal basis dimension: 4
    • +
  • indices size: 24
    • +
  • relative errors: [3.16988e-07]
    • +
  • residuals: [0.0102016]
    • +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
IndexMulti-indexCoeff.
0[0,0,0,0]26.07564
1[1,0,0,0]-0.003290232
2[0,0,1,0]24.86277
3[0,0,0,1]4.00878
4[1,1,0,0]0.5800043
5[1,0,1,0]0.005553137
6[0,1,0,1]-0.03536237
7[0,0,2,0]9.006102
8[0,0,0,2]2.32328
9[2,0,1,0]-0.01830508
10[1,1,1,0]-0.001079013
11[1,0,2,0]-0.01280951
12[0,1,0,2]0.07909247
13[0,0,0,3]1.0497
14[0,2,0,2]0.03390499
15[0,0,2,2]-0.09301932
16[2,3,0,0]0.006792632
17[2,2,1,0]-0.001824762
18[1,0,1,3]-0.00731192
19[0,1,0,4]0.04903297
20[0,4,2,0]0.01100148
21[0,2,2,2]0.04061781
22[0,1,1,4]-0.01867403
23[0,0,2,4]-0.09888105
+ +
+
+
+ +.. GENERATED FROM PYTHON SOURCE LINES 167-168 + +Get the number of coefficients in the PCE. + +.. GENERATED FROM PYTHON SOURCE LINES 168-171 + +.. code-block:: Python + + selectedBasisSizeSparse = result.getIndices().getSize() + print("Selected basis size = ", selectedBasisSizeSparse) + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + Selected basis size = 24 + + + + +.. GENERATED FROM PYTHON SOURCE LINES 172-176 + +We see that the number of selected coefficients is lower than +the number of candidate coefficients. +This may reduce overfitting and can produce a PCE with more +accurate predictions. + .. _sphx_glr_download_auto_meta_modeling_polynomial_chaos_metamodel_plot_functional_chaos_database.py: diff --git a/openturns/master/_sources/auto_meta_modeling/polynomial_chaos_metamodel/sg_execution_times.rst.txt b/openturns/master/_sources/auto_meta_modeling/polynomial_chaos_metamodel/sg_execution_times.rst.txt index 346a1ffb3e2..266c3806911 100644 --- a/openturns/master/_sources/auto_meta_modeling/polynomial_chaos_metamodel/sg_execution_times.rst.txt +++ b/openturns/master/_sources/auto_meta_modeling/polynomial_chaos_metamodel/sg_execution_times.rst.txt @@ -6,7 +6,7 @@ Computation times ================= -**00:36.641** total execution time for 16 files **from auto_meta_modeling/polynomial_chaos_metamodel**: +**00:36.748** total execution time for 16 files **from auto_meta_modeling/polynomial_chaos_metamodel**: .. container:: @@ -32,51 +32,51 @@ Computation times * - Example - Time - Mem (MB) - * - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_chaos_cv.py` (``plot_chaos_cv.py``) - - 00:11.148 - - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_functional_chaos.py` (``plot_functional_chaos.py``) - - 00:07.821 + - 00:10.810 + - 0.0 + * - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_chaos_cv.py` (``plot_chaos_cv.py``) + - 00:10.341 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_chaos_beam_sensitivity_degree.py` (``plot_chaos_beam_sensitivity_degree.py``) - - 00:07.434 + - 00:06.094 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_chaos_sobol_confidence.py` (``plot_chaos_sobol_confidence.py``) - - 00:02.999 + - 00:02.801 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_chaos_cleaning_strategy.py` (``plot_chaos_cleaning_strategy.py``) - - 00:02.370 + - 00:02.122 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_chaos_build_distribution.py` (``plot_chaos_build_distribution.py``) - - 00:02.029 + - 00:01.960 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_enumeratefunction.py` (``plot_enumeratefunction.py``) - - 00:01.703 + - 00:01.568 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_chaos_ishigami.py` (``plot_chaos_ishigami.py``) - - 00:00.362 + - 00:00.340 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_chaos_cantilever_beam_integration.py` (``plot_chaos_cantilever_beam_integration.py``) - - 00:00.325 + - 00:00.268 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_functional_chaos_graphs.py` (``plot_functional_chaos_graphs.py``) - - 00:00.249 + - 00:00.226 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_chaos_draw_validation.py` (``plot_chaos_draw_validation.py``) - - 00:00.120 + - 00:00.118 - 0.0 - * - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_chaos_ishigami_grouped_indices.py` (``plot_chaos_ishigami_grouped_indices.py``) - - 00:00.024 + * - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_functional_chaos_database.py` (``plot_functional_chaos_database.py``) + - 00:00.051 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_functional_chaos_exploitation.py` (``plot_functional_chaos_exploitation.py``) - - 00:00.024 + - 00:00.023 - 0.0 - * - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_functional_chaos_database.py` (``plot_functional_chaos_database.py``) - - 00:00.020 + * - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_chaos_ishigami_grouped_indices.py` (``plot_chaos_ishigami_grouped_indices.py``) + - 00:00.019 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_functional_chaos_advanced_ctors.py` (``plot_functional_chaos_advanced_ctors.py``) - - 00:00.011 + - 00:00.006 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_chaos_distribution_transformation.py` (``plot_chaos_distribution_transformation.py``) - - 00:00.003 + - 00:00.002 - 0.0 diff --git a/openturns/master/_sources/auto_numerical_methods/general_methods/plot_ifs.rst.txt b/openturns/master/_sources/auto_numerical_methods/general_methods/plot_ifs.rst.txt index 694b1054b35..6ee2855eabf 100644 --- a/openturns/master/_sources/auto_numerical_methods/general_methods/plot_ifs.rst.txt +++ b/openturns/master/_sources/auto_numerical_methods/general_methods/plot_ifs.rst.txt @@ -275,7 +275,7 @@ Sierpinski triangle .. rst-class:: sphx-glr-timing - **Total running time of the script:** (0 minutes 7.440 seconds) + **Total running time of the script:** (0 minutes 7.824 seconds) .. _sphx_glr_download_auto_numerical_methods_general_methods_plot_ifs.py: diff --git a/openturns/master/_sources/auto_numerical_methods/general_methods/plot_pce_design.rst.txt b/openturns/master/_sources/auto_numerical_methods/general_methods/plot_pce_design.rst.txt index f05b918d4f6..1138def6420 100644 --- a/openturns/master/_sources/auto_numerical_methods/general_methods/plot_pce_design.rst.txt +++ b/openturns/master/_sources/auto_numerical_methods/general_methods/plot_pce_design.rst.txt @@ -547,7 +547,7 @@ Compute leave-one-out error .. code-block:: none - mseLOO = 10.957014073152488 + mseLOO = 4.208195073018782 @@ -685,8 +685,8 @@ perform elementwise division and exponentiation .. code-block:: none - MSE LOO = 10.957014073152434 - Q2 LOO = 0.22698181296589692 + MSE LOO = 4.208195073018801 + Q2 LOO = 0.6668550477406794 diff --git a/openturns/master/_sources/auto_numerical_methods/general_methods/plot_random_generator.rst.txt b/openturns/master/_sources/auto_numerical_methods/general_methods/plot_random_generator.rst.txt index 9bd7564d597..8f10b7ccb4d 100644 --- a/openturns/master/_sources/auto_numerical_methods/general_methods/plot_random_generator.rst.txt +++ b/openturns/master/_sources/auto_numerical_methods/general_methods/plot_random_generator.rst.txt @@ -127,7 +127,7 @@ Example 3: using a previously saved generator state .. raw:: html
- class=Point name=Unnamed dimension=1 values=[-0.317694] + class=Point name=Unnamed dimension=1 values=[-0.0501892]


@@ -150,7 +150,7 @@ load the generator state .. raw:: html
- class=Point name=Unnamed dimension=1 values=[-0.317694] + class=Point name=Unnamed dimension=1 values=[-0.0501892]


diff --git a/openturns/master/_sources/auto_numerical_methods/general_methods/sg_execution_times.rst.txt b/openturns/master/_sources/auto_numerical_methods/general_methods/sg_execution_times.rst.txt index ba24fc39784..8d3e582d1ca 100644 --- a/openturns/master/_sources/auto_numerical_methods/general_methods/sg_execution_times.rst.txt +++ b/openturns/master/_sources/auto_numerical_methods/general_methods/sg_execution_times.rst.txt @@ -6,7 +6,7 @@ Computation times ================= -**00:08.458** total execution time for 8 files **from auto_numerical_methods/general_methods**: +**00:08.863** total execution time for 8 files **from auto_numerical_methods/general_methods**: .. container:: @@ -33,25 +33,25 @@ Computation times - Time - Mem (MB) * - :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_ifs.py` (``plot_ifs.py``) - - 00:07.440 - - 0.0 - * - :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_regression_sinus.py` (``plot_regression_sinus.py``) - - 00:00.400 + - 00:07.824 - 0.0 * - :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_pce_design.py` (``plot_pce_design.py``) - - 00:00.388 + - 00:00.412 + - 0.0 + * - :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_regression_sinus.py` (``plot_regression_sinus.py``) + - 00:00.397 - 0.0 * - :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_estimate_integral_iterated_quadrature.py` (``plot_estimate_integral_iterated_quadrature.py``) - - 00:00.128 + - 00:00.126 - 0.0 * - :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_regression_interval.py` (``plot_regression_interval.py``) - - 00:00.089 + - 00:00.090 - 0.0 * - :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_study_save_load.py` (``plot_study_save_load.py``) - 00:00.010 - 0.0 * - :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_random_generator.py` (``plot_random_generator.py``) - - 00:00.001 + - 00:00.002 - 0.0 * - :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_combinatorial_generator.py` (``plot_combinatorial_generator.py``) - 00:00.001 diff --git a/openturns/master/_sources/auto_numerical_methods/iterative_statistics/sg_execution_times.rst.txt b/openturns/master/_sources/auto_numerical_methods/iterative_statistics/sg_execution_times.rst.txt index 64a1865be6b..b783b7e1191 100644 --- a/openturns/master/_sources/auto_numerical_methods/iterative_statistics/sg_execution_times.rst.txt +++ b/openturns/master/_sources/auto_numerical_methods/iterative_statistics/sg_execution_times.rst.txt @@ -6,7 +6,7 @@ Computation times ================= -**00:00.582** total execution time for 3 files **from auto_numerical_methods/iterative_statistics**: +**00:00.571** total execution time for 3 files **from auto_numerical_methods/iterative_statistics**: .. container:: @@ -33,11 +33,11 @@ Computation times - Time - Mem (MB) * - :ref:`sphx_glr_auto_numerical_methods_iterative_statistics_plot_iterative_threshold.py` (``plot_iterative_threshold.py``) - - 00:00.279 + - 00:00.274 - 0.0 * - :ref:`sphx_glr_auto_numerical_methods_iterative_statistics_plot_iterative_extrema.py` (``plot_iterative_extrema.py``) - - 00:00.159 + - 00:00.155 - 0.0 * - :ref:`sphx_glr_auto_numerical_methods_iterative_statistics_plot_iterative_moments.py` (``plot_iterative_moments.py``) - - 00:00.144 + - 00:00.142 - 0.0 diff --git a/openturns/master/_sources/auto_numerical_methods/optimization/plot_control_termination.rst.txt b/openturns/master/_sources/auto_numerical_methods/optimization/plot_control_termination.rst.txt index d5921554bf5..294bfc96d87 100644 --- a/openturns/master/_sources/auto_numerical_methods/optimization/plot_control_termination.rst.txt +++ b/openturns/master/_sources/auto_numerical_methods/optimization/plot_control_termination.rst.txt @@ -209,8 +209,8 @@ Run algorithm .. code-block:: none - event probability: 0.140812490964291 - calls number: 6917 + event probability: 0.14167714131801018 + calls number: 5569 diff --git a/openturns/master/_sources/auto_numerical_methods/optimization/plot_ego.rst.txt b/openturns/master/_sources/auto_numerical_methods/optimization/plot_ego.rst.txt index 9b7bd3f2dfc..b5a170edaed 100644 --- a/openturns/master/_sources/auto_numerical_methods/optimization/plot_ego.rst.txt +++ b/openturns/master/_sources/auto_numerical_methods/optimization/plot_ego.rst.txt @@ -341,7 +341,7 @@ In the Ackley example, we choose to perform 10 iterations of the algorithm. .. raw:: html
- class=Point name=Unnamed dimension=2 values=[0.0116786,0.174222] + class=Point name=Unnamed dimension=2 values=[0.011558,0.174235]


@@ -360,7 +360,7 @@ In the Ackley example, we choose to perform 10 iterations of the algorithm. .. raw:: html
- class=Point name=Unnamed dimension=1 values=[1.13554] + class=Point name=Unnamed dimension=1 values=[1.13558]


@@ -491,7 +491,7 @@ This is why we finalize the process by adding a local optimization step. .. raw:: html
- class=Point name=Unnamed dimension=2 values=[6.80317e-07,-1.75261e-06] + class=Point name=Unnamed dimension=2 values=[5.56121e-07,1.15429e-06]


@@ -840,7 +840,7 @@ We run the algorithm and get the result: .. raw:: html
- class=Point name=Unnamed dimension=2 values=[0.547933,0.166685] + class=Point name=Unnamed dimension=2 values=[0.547932,0.166696]


@@ -974,7 +974,7 @@ Reset default settings .. rst-class:: sphx-glr-timing - **Total running time of the script:** (0 minutes 2.625 seconds) + **Total running time of the script:** (0 minutes 2.716 seconds) .. _sphx_glr_download_auto_numerical_methods_optimization_plot_ego.py: diff --git a/openturns/master/_sources/auto_numerical_methods/optimization/plot_optimization_dlib.rst.txt b/openturns/master/_sources/auto_numerical_methods/optimization/plot_optimization_dlib.rst.txt index cf3c954fa24..dcb1e7fca84 100644 --- a/openturns/master/_sources/auto_numerical_methods/optimization/plot_optimization_dlib.rst.txt +++ b/openturns/master/_sources/auto_numerical_methods/optimization/plot_optimization_dlib.rst.txt @@ -450,13 +450,13 @@ Retrieve results .. code-block:: none - x^ = [2.69936,1.15687,0.5] - f(x^) = [5.91646e-31] - Iteration number: 10 - Evaluation number: 13 - Absolute error: 1.1079896706976392e-08 - Relative error: 3.7192381003794545e-09 - Residual error: 9.071192201578258e-17 + x^ = [2.8744,1.23188,0.5] + f(x^) = [1.31227e-25] + Iteration number: 7 + Evaluation number: 8 + Absolute error: 4.732603568414881e-07 + Relative error: 1.4943632242344696e-07 + Residual error: 1.1923662863460354e-13 Constraint error: 0.0 diff --git a/openturns/master/_sources/auto_numerical_methods/optimization/sg_execution_times.rst.txt b/openturns/master/_sources/auto_numerical_methods/optimization/sg_execution_times.rst.txt index 98b9a2ef637..fb25592e910 100644 --- a/openturns/master/_sources/auto_numerical_methods/optimization/sg_execution_times.rst.txt +++ b/openturns/master/_sources/auto_numerical_methods/optimization/sg_execution_times.rst.txt @@ -6,7 +6,7 @@ Computation times ================= -**00:05.238** total execution time for 11 files **from auto_numerical_methods/optimization**: +**00:05.286** total execution time for 11 files **from auto_numerical_methods/optimization**: .. container:: @@ -33,28 +33,28 @@ Computation times - Time - Mem (MB) * - :ref:`sphx_glr_auto_numerical_methods_optimization_plot_ego.py` (``plot_ego.py``) - - 00:02.625 + - 00:02.716 - 0.0 * - :ref:`sphx_glr_auto_numerical_methods_optimization_plot_optimization_rastrigin.py` (``plot_optimization_rastrigin.py``) - - 00:00.956 + - 00:00.942 - 0.0 * - :ref:`sphx_glr_auto_numerical_methods_optimization_plot_optimization_rosenbrock.py` (``plot_optimization_rosenbrock.py``) - - 00:00.846 + - 00:00.849 - 0.0 * - :ref:`sphx_glr_auto_numerical_methods_optimization_plot_optimization_dlib.py` (``plot_optimization_dlib.py``) - - 00:00.396 + - 00:00.348 - 0.0 * - :ref:`sphx_glr_auto_numerical_methods_optimization_plot_optimization_pagmo.py` (``plot_optimization_pagmo.py``) - - 00:00.165 + - 00:00.160 - 0.0 * - :ref:`sphx_glr_auto_numerical_methods_optimization_plot_optimization_bonmin.py` (``plot_optimization_bonmin.py``) - - 00:00.092 + - 00:00.115 - 0.0 * - :ref:`sphx_glr_auto_numerical_methods_optimization_plot_optimization_constraints.py` (``plot_optimization_constraints.py``) - - 00:00.069 + - 00:00.068 - 0.0 * - :ref:`sphx_glr_auto_numerical_methods_optimization_plot_optimization_nlopt.py` (``plot_optimization_nlopt.py``) - - 00:00.068 + - 00:00.067 - 0.0 * - :ref:`sphx_glr_auto_numerical_methods_optimization_plot_control_termination.py` (``plot_control_termination.py``) - 00:00.015 diff --git a/openturns/master/_sources/auto_probabilistic_modeling/copulas/sg_execution_times.rst.txt b/openturns/master/_sources/auto_probabilistic_modeling/copulas/sg_execution_times.rst.txt index 04bae27aa6d..8b87e8d33da 100644 --- a/openturns/master/_sources/auto_probabilistic_modeling/copulas/sg_execution_times.rst.txt +++ b/openturns/master/_sources/auto_probabilistic_modeling/copulas/sg_execution_times.rst.txt @@ -6,7 +6,7 @@ Computation times ================= -**00:00.426** total execution time for 4 files **from auto_probabilistic_modeling/copulas**: +**00:00.379** total execution time for 4 files **from auto_probabilistic_modeling/copulas**: .. container:: @@ -33,10 +33,10 @@ Computation times - Time - Mem (MB) * - :ref:`sphx_glr_auto_probabilistic_modeling_copulas_plot_ordinal_sum_copula.py` (``plot_ordinal_sum_copula.py``) - - 00:00.423 + - 00:00.376 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_copulas_plot_extract_copula.py` (``plot_extract_copula.py``) - - 00:00.002 + - 00:00.001 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_copulas_plot_composed_copula.py` (``plot_composed_copula.py``) - 00:00.001 diff --git a/openturns/master/_sources/auto_probabilistic_modeling/distributions/sg_execution_times.rst.txt b/openturns/master/_sources/auto_probabilistic_modeling/distributions/sg_execution_times.rst.txt index 903b328b4c3..d249baffc7e 100644 --- a/openturns/master/_sources/auto_probabilistic_modeling/distributions/sg_execution_times.rst.txt +++ b/openturns/master/_sources/auto_probabilistic_modeling/distributions/sg_execution_times.rst.txt @@ -6,7 +6,7 @@ Computation times ================= -**00:06.871** total execution time for 19 files **from auto_probabilistic_modeling/distributions**: +**00:06.318** total execution time for 19 files **from auto_probabilistic_modeling/distributions**: .. container:: @@ -33,59 +33,59 @@ Computation times - Time - Mem (MB) * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_create_draw_multivariate_distributions.py` (``plot_create_draw_multivariate_distributions.py``) - - 00:01.093 + - 00:01.008 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_quick_start_guide_distributions.py` (``plot_quick_start_guide_distributions.py``) - - 00:00.956 + - 00:00.885 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_minimum_volume_level_sets.py` (``plot_minimum_volume_level_sets.py``) - - 00:00.705 + - 00:00.642 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_distribution_transformation.py` (``plot_distribution_transformation.py``) - - 00:00.635 + - 00:00.582 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_order_statistics_distribution.py` (``plot_order_statistics_distribution.py``) - - 00:00.587 + - 00:00.539 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_truncated_distribution.py` (``plot_truncated_distribution.py``) - - 00:00.432 + - 00:00.396 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_overview_univariate_distributions.py` (``plot_overview_univariate_distributions.py``) - - 00:00.383 + - 00:00.351 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_distribution_manipulation.py` (``plot_distribution_manipulation.py``) - - 00:00.294 + - 00:00.268 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_create_extreme_value_distribution.py` (``plot_create_extreme_value_distribution.py``) - - 00:00.275 + - 00:00.250 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_create_and_draw_scalar_distributions.py` (``plot_create_and_draw_scalar_distributions.py``) - - 00:00.257 + - 00:00.237 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_bayes_distribution.py` (``plot_bayes_distribution.py``) - - 00:00.247 + - 00:00.230 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_create_random_mixture.py` (``plot_create_random_mixture.py``) - - 00:00.246 + - 00:00.225 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_mixture_distribution.py` (``plot_mixture_distribution.py``) - - 00:00.233 + - 00:00.215 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_generate_by_inversion.py` (``plot_generate_by_inversion.py``) - - 00:00.165 + - 00:00.150 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_python_distribution.py` (``plot_python_distribution.py``) - - 00:00.142 + - 00:00.132 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_conditional_distribution.py` (``plot_conditional_distribution.py``) - - 00:00.095 + - 00:00.092 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_create_your_own_dist.py` (``plot_create_your_own_dist.py``) - - 00:00.063 + - 00:00.060 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_maximum_distribution.py` (``plot_maximum_distribution.py``) - - 00:00.060 + - 00:00.056 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_conditional_random_vector.py` (``plot_conditional_random_vector.py``) - - 00:00.002 + - 00:00.001 - 0.0 diff --git a/openturns/master/_sources/auto_probabilistic_modeling/stochastic_processes/plot_gaussian_process_covariance_hmat.rst.txt b/openturns/master/_sources/auto_probabilistic_modeling/stochastic_processes/plot_gaussian_process_covariance_hmat.rst.txt index 2026883315e..d164f290b07 100644 --- a/openturns/master/_sources/auto_probabilistic_modeling/stochastic_processes/plot_gaussian_process_covariance_hmat.rst.txt +++ b/openturns/master/_sources/auto_probabilistic_modeling/stochastic_processes/plot_gaussian_process_covariance_hmat.rst.txt @@ -228,7 +228,7 @@ Reset default settings .. rst-class:: sphx-glr-timing - **Total running time of the script:** (0 minutes 2.105 seconds) + **Total running time of the script:** (0 minutes 2.072 seconds) .. _sphx_glr_download_auto_probabilistic_modeling_stochastic_processes_plot_gaussian_process_covariance_hmat.py: diff --git a/openturns/master/_sources/auto_probabilistic_modeling/stochastic_processes/plot_userdefined_covariance_model.rst.txt b/openturns/master/_sources/auto_probabilistic_modeling/stochastic_processes/plot_userdefined_covariance_model.rst.txt index bb1d14c6bf6..8df3bce0327 100644 --- a/openturns/master/_sources/auto_probabilistic_modeling/stochastic_processes/plot_userdefined_covariance_model.rst.txt +++ b/openturns/master/_sources/auto_probabilistic_modeling/stochastic_processes/plot_userdefined_covariance_model.rst.txt @@ -157,7 +157,7 @@ Draw the covariance model .. rst-class:: sphx-glr-timing - **Total running time of the script:** (0 minutes 2.117 seconds) + **Total running time of the script:** (0 minutes 2.037 seconds) .. _sphx_glr_download_auto_probabilistic_modeling_stochastic_processes_plot_userdefined_covariance_model.py: diff --git a/openturns/master/_sources/auto_probabilistic_modeling/stochastic_processes/sg_execution_times.rst.txt b/openturns/master/_sources/auto_probabilistic_modeling/stochastic_processes/sg_execution_times.rst.txt index 3f39b93a4a3..b99f27a56fd 100644 --- a/openturns/master/_sources/auto_probabilistic_modeling/stochastic_processes/sg_execution_times.rst.txt +++ b/openturns/master/_sources/auto_probabilistic_modeling/stochastic_processes/sg_execution_times.rst.txt @@ -6,7 +6,7 @@ Computation times ================= -**00:12.530** total execution time for 24 files **from auto_probabilistic_modeling/stochastic_processes**: +**00:11.947** total execution time for 24 files **from auto_probabilistic_modeling/stochastic_processes**: .. container:: @@ -32,74 +32,74 @@ Computation times * - Example - Time - Mem (MB) - * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_userdefined_covariance_model.py` (``plot_userdefined_covariance_model.py``) - - 00:02.117 - - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_gaussian_process_covariance_hmat.py` (``plot_gaussian_process_covariance_hmat.py``) - - 00:02.105 + - 00:02.072 + - 0.0 + * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_userdefined_covariance_model.py` (``plot_userdefined_covariance_model.py``) + - 00:02.037 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_create_mesh.py` (``plot_create_mesh.py``) - - 00:01.949 + - 00:01.841 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_field_manipulation.py` (``plot_field_manipulation.py``) - - 00:01.782 + - 00:01.691 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_box_cox_transform.py` (``plot_box_cox_transform.py``) - - 00:01.011 + - 00:00.975 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_gaussian_processes_comparison.py` (``plot_gaussian_processes_comparison.py``) - - 00:00.707 + - 00:00.660 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_process_manipulation.py` (``plot_process_manipulation.py``) - - 00:00.472 + - 00:00.437 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_random_walk_process.py` (``plot_random_walk_process.py``) - - 00:00.296 + - 00:00.281 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_create_and_manipulate_arma_process.py` (``plot_create_and_manipulate_arma_process.py``) - - 00:00.279 + - 00:00.258 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_discrete_markov_chain_process.py` (``plot_discrete_markov_chain_process.py``) - - 00:00.270 + - 00:00.252 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_kronecker_covmodel.py` (``plot_kronecker_covmodel.py``) - - 00:00.261 + - 00:00.245 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_mix_rv_process.py` (``plot_mix_rv_process.py``) - - 00:00.159 + - 00:00.154 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_white_noise_process.py` (``plot_white_noise_process.py``) - - 00:00.157 - - 0.0 - * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_add_trend.py` (``plot_add_trend.py``) - - 00:00.142 + - 00:00.148 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_export_field_vtk.py` (``plot_export_field_vtk.py``) - - 00:00.137 + - 00:00.125 - 0.0 - * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_create_normal_process.py` (``plot_create_normal_process.py``) - - 00:00.130 + * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_add_trend.py` (``plot_add_trend.py``) + - 00:00.124 - 0.0 - * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_trend_transform.py` (``plot_trend_transform.py``) + * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_create_normal_process.py` (``plot_create_normal_process.py``) - 00:00.123 - 0.0 - * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_aggregated_process.py` (``plot_aggregated_process.py``) - - 00:00.115 + * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_trend_transform.py` (``plot_trend_transform.py``) + - 00:00.119 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_timeseries_manipulation.py` (``plot_timeseries_manipulation.py``) - - 00:00.115 + - 00:00.108 + - 0.0 + * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_aggregated_process.py` (``plot_aggregated_process.py``) + - 00:00.105 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_functional_basis_process.py` (``plot_functional_basis_process.py``) - - 00:00.073 + - 00:00.068 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_user_stationary_covmodel.py` (``plot_user_stationary_covmodel.py``) - - 00:00.067 + - 00:00.064 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_userdefined_spectral_model.py` (``plot_userdefined_spectral_model.py``) - - 00:00.061 + - 00:00.058 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_create_stationary_covmodel.py` (``plot_create_stationary_covmodel.py``) - - 00:00.002 + - 00:00.001 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_parametric_spectral_density.py` (``plot_parametric_spectral_density.py``) - 00:00.001 diff --git a/openturns/master/_sources/auto_reliability_sensitivity/central_dispersion/sg_execution_times.rst.txt b/openturns/master/_sources/auto_reliability_sensitivity/central_dispersion/sg_execution_times.rst.txt index 7ee2b82b73c..60dc52d35cf 100644 --- a/openturns/master/_sources/auto_reliability_sensitivity/central_dispersion/sg_execution_times.rst.txt +++ b/openturns/master/_sources/auto_reliability_sensitivity/central_dispersion/sg_execution_times.rst.txt @@ -6,7 +6,7 @@ Computation times ================= -**00:00.604** total execution time for 3 files **from auto_reliability_sensitivity/central_dispersion**: +**00:00.595** total execution time for 3 files **from auto_reliability_sensitivity/central_dispersion**: .. container:: @@ -33,11 +33,11 @@ Computation times - Time - Mem (MB) * - :ref:`sphx_glr_auto_reliability_sensitivity_central_dispersion_plot_expectation_simulation_algorithm.py` (``plot_expectation_simulation_algorithm.py``) - - 00:00.431 + - 00:00.428 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_central_dispersion_plot_central_tendency.py` (``plot_central_tendency.py``) - - 00:00.125 + - 00:00.121 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_central_dispersion_plot_estimate_moments_taylor.py` (``plot_estimate_moments_taylor.py``) - - 00:00.048 + - 00:00.046 - 0.0 diff --git a/openturns/master/_sources/auto_reliability_sensitivity/design_of_experiments/plot_smolyak_experiment.rst.txt b/openturns/master/_sources/auto_reliability_sensitivity/design_of_experiments/plot_smolyak_experiment.rst.txt index 9f3c5f2669e..fe184cbf568 100644 --- a/openturns/master/_sources/auto_reliability_sensitivity/design_of_experiments/plot_smolyak_experiment.rst.txt +++ b/openturns/master/_sources/auto_reliability_sensitivity/design_of_experiments/plot_smolyak_experiment.rst.txt @@ -294,7 +294,7 @@ This growth depends on the dimension of the problem. .. rst-class:: sphx-glr-timing - **Total running time of the script:** (0 minutes 2.292 seconds) + **Total running time of the script:** (0 minutes 2.128 seconds) .. _sphx_glr_download_auto_reliability_sensitivity_design_of_experiments_plot_smolyak_experiment.py: diff --git a/openturns/master/_sources/auto_reliability_sensitivity/design_of_experiments/plot_smolyak_quadrature.rst.txt b/openturns/master/_sources/auto_reliability_sensitivity/design_of_experiments/plot_smolyak_quadrature.rst.txt index fac7e1c013f..6412a9a6630 100644 --- a/openturns/master/_sources/auto_reliability_sensitivity/design_of_experiments/plot_smolyak_quadrature.rst.txt +++ b/openturns/master/_sources/auto_reliability_sensitivity/design_of_experiments/plot_smolyak_quadrature.rst.txt @@ -584,7 +584,7 @@ We can finally create the graph. .. rst-class:: sphx-glr-timing - **Total running time of the script:** (0 minutes 7.674 seconds) + **Total running time of the script:** (0 minutes 6.989 seconds) .. _sphx_glr_download_auto_reliability_sensitivity_design_of_experiments_plot_smolyak_quadrature.py: diff --git a/openturns/master/_sources/auto_reliability_sensitivity/design_of_experiments/sg_execution_times.rst.txt b/openturns/master/_sources/auto_reliability_sensitivity/design_of_experiments/sg_execution_times.rst.txt index dde04aaa646..32aa416a09f 100644 --- a/openturns/master/_sources/auto_reliability_sensitivity/design_of_experiments/sg_execution_times.rst.txt +++ b/openturns/master/_sources/auto_reliability_sensitivity/design_of_experiments/sg_execution_times.rst.txt @@ -6,7 +6,7 @@ Computation times ================= -**00:15.289** total execution time for 17 files **from auto_reliability_sensitivity/design_of_experiments**: +**00:14.068** total execution time for 17 files **from auto_reliability_sensitivity/design_of_experiments**: .. container:: @@ -33,53 +33,53 @@ Computation times - Time - Mem (MB) * - :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_smolyak_quadrature.py` (``plot_smolyak_quadrature.py``) - - 00:07.674 + - 00:06.989 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_smolyak_experiment.py` (``plot_smolyak_experiment.py``) - - 00:02.292 + - 00:02.128 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_plot_design.py` (``plot_plot_design.py``) - - 00:01.253 + - 00:01.179 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_design_of_experiments.py` (``plot_design_of_experiments.py``) - - 00:01.052 + - 00:00.983 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_low_discrepancy_sequence.py` (``plot_low_discrepancy_sequence.py``) - - 00:00.550 - - 0.0 - * - :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_smolyak_merge.py` (``plot_smolyak_merge.py``) - - 00:00.524 + - 00:00.519 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_optimal_lhs.py` (``plot_optimal_lhs.py``) - - 00:00.468 + - 00:00.456 + - 0.0 + * - :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_smolyak_merge.py` (``plot_smolyak_merge.py``) + - 00:00.450 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_create_deterministic_doe.py` (``plot_create_deterministic_doe.py``) - - 00:00.297 + - 00:00.267 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_deterministic_design.py` (``plot_deterministic_design.py``) - - 00:00.279 + - 00:00.252 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_smolyak_indices.py` (``plot_smolyak_indices.py``) - - 00:00.267 + - 00:00.245 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_mixed_design.py` (``plot_mixed_design.py``) - - 00:00.179 + - 00:00.171 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_design_of_experiment_continuous_discrete.py` (``plot_design_of_experiment_continuous_discrete.py``) - - 00:00.118 + - 00:00.111 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_create_random_doe.py` (``plot_create_random_doe.py``) - - 00:00.117 - - 0.0 - * - :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_probabilistic_design.py` (``plot_probabilistic_design.py``) - - 00:00.058 + - 00:00.111 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_gauss_product_experiment.py` (``plot_gauss_product_experiment.py``) - - 00:00.058 + - 00:00.055 + - 0.0 + * - :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_probabilistic_design.py` (``plot_probabilistic_design.py``) + - 00:00.053 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_composite_experiment.py` (``plot_composite_experiment.py``) - - 00:00.055 + - 00:00.052 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_monte_carlo_experiment.py` (``plot_monte_carlo_experiment.py``) - - 00:00.049 + - 00:00.047 - 0.0 diff --git a/openturns/master/_sources/auto_reliability_sensitivity/reliability/plot_estimate_probability_adaptive_directional_sampling.rst.txt b/openturns/master/_sources/auto_reliability_sensitivity/reliability/plot_estimate_probability_adaptive_directional_sampling.rst.txt index 7c1b12a4bba..1781f703446 100644 --- a/openturns/master/_sources/auto_reliability_sensitivity/reliability/plot_estimate_probability_adaptive_directional_sampling.rst.txt +++ b/openturns/master/_sources/auto_reliability_sensitivity/reliability/plot_estimate_probability_adaptive_directional_sampling.rst.txt @@ -216,11 +216,6 @@ Retrieve results. -.. rst-class:: sphx-glr-timing - - **Total running time of the script:** (0 minutes 2.010 seconds) - - .. _sphx_glr_download_auto_reliability_sensitivity_reliability_plot_estimate_probability_adaptive_directional_sampling.py: .. only:: html diff --git a/openturns/master/_sources/auto_reliability_sensitivity/reliability/plot_estimate_probability_form_oscillator.rst.txt b/openturns/master/_sources/auto_reliability_sensitivity/reliability/plot_estimate_probability_form_oscillator.rst.txt index 4dabc46f8c6..4a887c1496e 100644 --- a/openturns/master/_sources/auto_reliability_sensitivity/reliability/plot_estimate_probability_form_oscillator.rst.txt +++ b/openturns/master/_sources/auto_reliability_sensitivity/reliability/plot_estimate_probability_form_oscillator.rst.txt @@ -724,7 +724,7 @@ We can see that this post-treatment of FORM result allows one to greatly improve .. rst-class:: sphx-glr-timing - **Total running time of the script:** (0 minutes 5.047 seconds) + **Total running time of the script:** (0 minutes 4.796 seconds) .. _sphx_glr_download_auto_reliability_sensitivity_reliability_plot_estimate_probability_form_oscillator.py: diff --git a/openturns/master/_sources/auto_reliability_sensitivity/reliability/plot_proba_system_event.rst.txt b/openturns/master/_sources/auto_reliability_sensitivity/reliability/plot_proba_system_event.rst.txt index ca91b9f205c..d546ac42c54 100644 --- a/openturns/master/_sources/auto_reliability_sensitivity/reliability/plot_proba_system_event.rst.txt +++ b/openturns/master/_sources/auto_reliability_sensitivity/reliability/plot_proba_system_event.rst.txt @@ -387,7 +387,7 @@ Draw the graphs! .. rst-class:: sphx-glr-timing - **Total running time of the script:** (0 minutes 2.176 seconds) + **Total running time of the script:** (0 minutes 2.116 seconds) .. _sphx_glr_download_auto_reliability_sensitivity_reliability_plot_proba_system_event.py: diff --git a/openturns/master/_sources/auto_reliability_sensitivity/reliability/sg_execution_times.rst.txt b/openturns/master/_sources/auto_reliability_sensitivity/reliability/sg_execution_times.rst.txt index f67432cf24b..2f15909c8ee 100644 --- a/openturns/master/_sources/auto_reliability_sensitivity/reliability/sg_execution_times.rst.txt +++ b/openturns/master/_sources/auto_reliability_sensitivity/reliability/sg_execution_times.rst.txt @@ -6,7 +6,7 @@ Computation times ================= -**00:17.983** total execution time for 24 files **from auto_reliability_sensitivity/reliability**: +**00:17.081** total execution time for 24 files **from auto_reliability_sensitivity/reliability**: .. container:: @@ -33,61 +33,61 @@ Computation times - Time - Mem (MB) * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_form_oscillator.py` (``plot_estimate_probability_form_oscillator.py``) - - 00:05.047 + - 00:04.796 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_proba_system_event.py` (``plot_proba_system_event.py``) - - 00:02.176 + - 00:02.116 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_adaptive_directional_sampling.py` (``plot_estimate_probability_adaptive_directional_sampling.py``) - - 00:02.010 + - 00:01.944 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_crossentropy.py` (``plot_crossentropy.py``) - - 00:01.410 + - 00:01.363 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_form_explained.py` (``plot_form_explained.py``) - - 00:00.922 + - 00:00.860 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_randomized_qmc.py` (``plot_estimate_probability_randomized_qmc.py``) - - 00:00.830 + - 00:00.769 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_create_domain_event.py` (``plot_create_domain_event.py``) - - 00:00.716 - - 0.0 - * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_axial_stressed_beam.py` (``plot_axial_stressed_beam.py``) - - 00:00.663 + - 00:00.675 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_directional_sampling.py` (``plot_estimate_probability_directional_sampling.py``) - - 00:00.646 + - 00:00.629 - 0.0 - * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_multi_form.py` (``plot_multi_form.py``) - - 00:00.636 + * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_axial_stressed_beam.py` (``plot_axial_stressed_beam.py``) + - 00:00.629 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_event_system.py` (``plot_event_system.py``) - - 00:00.634 + - 00:00.586 + - 0.0 + * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_multi_form.py` (``plot_multi_form.py``) + - 00:00.562 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_subset_sampling.py` (``plot_subset_sampling.py``) - - 00:00.577 + - 00:00.555 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_nais.py` (``plot_nais.py``) - - 00:00.437 + - 00:00.407 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_axial_stressed_beam_quickstart.py` (``plot_axial_stressed_beam_quickstart.py``) - - 00:00.366 + - 00:00.343 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_form.py` (``plot_estimate_probability_form.py``) - - 00:00.343 + - 00:00.320 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_importance_sampling.py` (``plot_estimate_probability_importance_sampling.py``) - - 00:00.162 + - 00:00.139 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_probability_simulation_results.py` (``plot_probability_simulation_results.py``) - - 00:00.139 + - 00:00.129 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_flood_model.py` (``plot_flood_model.py``) - - 00:00.118 + - 00:00.111 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_create_threshold_event.py` (``plot_create_threshold_event.py``) - - 00:00.074 + - 00:00.070 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_monte_carlo.py` (``plot_estimate_probability_monte_carlo.py``) - 00:00.033 diff --git a/openturns/master/_sources/auto_reliability_sensitivity/reliability_processes/plot_field_fca_sobol.rst.txt b/openturns/master/_sources/auto_reliability_sensitivity/reliability_processes/plot_field_fca_sobol.rst.txt index 75c81539bbb..3303a8bef1c 100644 --- a/openturns/master/_sources/auto_reliability_sensitivity/reliability_processes/plot_field_fca_sobol.rst.txt +++ b/openturns/master/_sources/auto_reliability_sensitivity/reliability_processes/plot_field_fca_sobol.rst.txt @@ -519,7 +519,7 @@ Reset default settings .. rst-class:: sphx-glr-timing - **Total running time of the script:** (0 minutes 6.478 seconds) + **Total running time of the script:** (0 minutes 6.196 seconds) .. _sphx_glr_download_auto_reliability_sensitivity_reliability_processes_plot_field_fca_sobol.py: diff --git a/openturns/master/_sources/auto_reliability_sensitivity/reliability_processes/sg_execution_times.rst.txt b/openturns/master/_sources/auto_reliability_sensitivity/reliability_processes/sg_execution_times.rst.txt index 6c9bfa65558..d6313342590 100644 --- a/openturns/master/_sources/auto_reliability_sensitivity/reliability_processes/sg_execution_times.rst.txt +++ b/openturns/master/_sources/auto_reliability_sensitivity/reliability_processes/sg_execution_times.rst.txt @@ -6,7 +6,7 @@ Computation times ================= -**00:06.653** total execution time for 3 files **from auto_reliability_sensitivity/reliability_processes**: +**00:06.367** total execution time for 3 files **from auto_reliability_sensitivity/reliability_processes**: .. container:: @@ -33,10 +33,10 @@ Computation times - Time - Mem (MB) * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_processes_plot_field_fca_sobol.py` (``plot_field_fca_sobol.py``) - - 00:06.478 + - 00:06.196 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_processes_plot_estimate_probability_monte_carlo_process.py` (``plot_estimate_probability_monte_carlo_process.py``) - - 00:00.174 + - 00:00.170 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_processes_plot_event_process.py` (``plot_event_process.py``) - 00:00.002 diff --git a/openturns/master/_sources/auto_reliability_sensitivity/sensitivity_analysis/plot_functional_chaos_sensitivity.rst.txt b/openturns/master/_sources/auto_reliability_sensitivity/sensitivity_analysis/plot_functional_chaos_sensitivity.rst.txt index 9819da253a1..c0715279e06 100644 --- a/openturns/master/_sources/auto_reliability_sensitivity/sensitivity_analysis/plot_functional_chaos_sensitivity.rst.txt +++ b/openturns/master/_sources/auto_reliability_sensitivity/sensitivity_analysis/plot_functional_chaos_sensitivity.rst.txt @@ -173,43 +173,98 @@ Quick summary of sensitivity analysis .. code-block:: Python sensitivityAnalysis = ot.FunctionalChaosSobolIndices(result) - print(sensitivityAnalysis) + sensitivityAnalysis -.. rst-class:: sphx-glr-script-out - .. code-block:: none +.. raw:: html +
FunctionalChaosSobolIndices - - input dimension=5 - - output dimension=1 - - basis size=181 - - mean=[76.0794] - - std-dev=[30.2678] - - | Index | Multi-index | Variance part | - |-------|---------------|---------------| - | 1 | [1,0,0,0,0] | 0.662606 | - | 3 | [0,0,1,0,0] | 0.0902125 | - | 2 | [0,1,0,0,0] | 0.0901124 | - | 4 | [0,0,0,1,0] | 0.0861668 | - | 5 | [0,0,0,0,1] | 0.0209417 | - - | Input | Name | Sobol' index | Total index | - |-------|---------------|---------------|---------------| - | 0 | rw | 0.677582 | 0.70826 | - | 1 | Hu | 0.0901124 | 0.101381 | - | 2 | Hl | 0.0902126 | 0.101371 | - | 3 | L | 0.0871206 | 0.0992782 | - | 4 | Kw | 0.0209417 | 0.0240504 | - - - - - +
    +
  • input dimension: 5
    • +
  • output dimension: 1
    • +
  • basis size: 181
    • +
  • mean: [76.0794]
    • +
  • std-dev: [30.2678]
    • +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
InputVariableSobol' indexTotal index
0rw0.6775820.708260
1Hu0.0901120.101381
2Hl0.0902130.101371
3L0.0871210.099278
4Kw0.0209420.024050
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
IndexMulti-indexPart of variance
1[1,0,0,0,0]0.662606
3[0,0,1,0,0]0.090213
2[0,1,0,0,0]0.090112
4[0,0,0,1,0]0.086167
5[0,0,0,0,1]0.020942
+ +
+
+
.. GENERATED FROM PYTHON SOURCE LINES 84-85 @@ -241,17 +296,14 @@ draw Sobol' indices We saw that total order indices are close to first order, so the higher order indices must be all quite close to 0 -.. GENERATED FROM PYTHON SOURCE LINES 93-102 +.. GENERATED FROM PYTHON SOURCE LINES 93-99 .. code-block:: Python for i in range(dimension): for j in range(i): - print( - input_names[i] + " & " + input_names[j], - ":", - sensitivityAnalysis.getSobolIndex([i, j]), - ) + sij = sensitivityAnalysis.getSobolIndex([i, j]) + print(f"{input_names[i]} & {input_names[j]}: {sij:.4f}") plt.show() @@ -262,16 +314,16 @@ so the higher order indices must be all quite close to 0 .. code-block:: none - Hu & rw : 0.009603147153069586 - Hl & rw : 0.009486332516243895 - Hl & Hu : 6.772494613216887e-08 - L & rw : 0.009152262191425037 - L & Hu : 0.0012275743968190782 - L & Hl : 0.001230665255687928 - Kw & rw : 0.0021338960376998777 - Kw & Hu : 0.0002952362243352463 - Kw & Hl : 0.0002981593839990994 - Kw & L : 0.0002935613713562576 + Hu & rw: 0.0096 + Hl & rw: 0.0095 + Hl & Hu: 0.0000 + L & rw: 0.0092 + L & Hu: 0.0012 + L & Hl: 0.0012 + Kw & rw: 0.0021 + Kw & Hu: 0.0003 + Kw & Hl: 0.0003 + Kw & L: 0.0003 diff --git a/openturns/master/_sources/auto_reliability_sensitivity/sensitivity_analysis/plot_sensitivity_ancova.rst.txt b/openturns/master/_sources/auto_reliability_sensitivity/sensitivity_analysis/plot_sensitivity_ancova.rst.txt index d0c429708dd..e68140ffd04 100644 --- a/openturns/master/_sources/auto_reliability_sensitivity/sensitivity_analysis/plot_sensitivity_ancova.rst.txt +++ b/openturns/master/_sources/auto_reliability_sensitivity/sensitivity_analysis/plot_sensitivity_ancova.rst.txt @@ -145,7 +145,7 @@ ANCOVA needs a functional decomposition of the model Y = model(X) algo = ot.FunctionalChaosAlgorithm(X, Y, distribution, adaptiveStrategy) algo.run() - result = ot.FunctionalChaosResult(algo.getResult()) + result = algo.getResult() diff --git a/openturns/master/_sources/auto_reliability_sensitivity/sensitivity_analysis/plot_sensitivity_wingweight.rst.txt b/openturns/master/_sources/auto_reliability_sensitivity/sensitivity_analysis/plot_sensitivity_wingweight.rst.txt index 179888c2ac5..24657a19763 100644 --- a/openturns/master/_sources/auto_reliability_sensitivity/sensitivity_analysis/plot_sensitivity_wingweight.rst.txt +++ b/openturns/master/_sources/auto_reliability_sensitivity/sensitivity_analysis/plot_sensitivity_wingweight.rst.txt @@ -856,12 +856,138 @@ We create a Functional Chaos Expansion. The relative errors are low : this indicates that the PCE model has good accuracy. Then, we exploit the surrogate model to compute the Sobol' indices. -.. GENERATED FROM PYTHON SOURCE LINES 359-367 +.. GENERATED FROM PYTHON SOURCE LINES 359-362 .. code-block:: Python sensitivityAnalysis = ot.FunctionalChaosSobolIndices(result) - print(sensitivityAnalysis) + sensitivityAnalysis + + + + + + +.. raw:: html + +
+ FunctionalChaosSobolIndices +
    +
  • input dimension: 10
    • +
  • output dimension: 1
    • +
  • basis size: 761
    • +
  • mean: [268.091]
    • +
  • std-dev: [48.0753]
    • +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
InputVariableSobol' indexTotal index
0Sw0.1243690.127770
1Wfw0.0000030.000009
2A0.2202390.225947
3Lambda0.0004770.000498
4q0.0000900.000100
5l0.0018020.001866
6tc0.1410950.145208
7Nz0.4116560.419650
8Wdg0.0849830.087649
9Wp0.0033180.003345
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
IndexMulti-indexPart of variance
8[0,0,0,0,0,0,0,1,0,0]#100.410346
3[0,0,1,0,0,0,0,0,0,0]#100.220101
7[0,0,0,0,0,0,1,0,0,0]#100.138523
1[1,0,0,0,0,0,0,0,0,0]#100.124359
9[0,0,0,0,0,0,0,0,1,0]#100.084929
+ +
+
+
+ +.. GENERATED FROM PYTHON SOURCE LINES 363-369 + +.. code-block:: Python + firstOrder = [sensitivityAnalysis.getSobolIndex(i) for i in range(m.dim)] totalOrder = [sensitivityAnalysis.getSobolTotalIndex(i) for i in range(m.dim)] graph = ot.SobolIndicesAlgorithm.DrawSobolIndices(inputNames, firstOrder, totalOrder) @@ -877,44 +1003,10 @@ Then, we exploit the surrogate model to compute the Sobol' indices. :class: sphx-glr-single-img -.. rst-class:: sphx-glr-script-out - - .. code-block:: none - - FunctionalChaosSobolIndices - - input dimension=10 - - output dimension=1 - - basis size=761 - - mean=[268.091] - - std-dev=[48.0753] - - | Index | Multi-index | Variance part | - |-------|---------------|---------------| - | 8 | [0,0,0,0,0,0,0,1,0,0]| 0.410346 | - | 3 | [0,0,1,0,0,0,0,0,0,0]| 0.220101 | - | 7 | [0,0,0,0,0,0,1,0,0,0]| 0.138523 | - | 1 | [1,0,0,0,0,0,0,0,0,0]| 0.124359 | - | 9 | [0,0,0,0,0,0,0,0,1,0]| 0.084929 | - - | Input | Name | Sobol' index | Total index | - |-------|---------------|---------------|---------------| - | 0 | Sw | 0.124369 | 0.12777 | - | 1 | Wfw | 2.86879e-06 | 8.73386e-06 | - | 2 | A | 0.220239 | 0.225947 | - | 3 | Lambda | 0.000476574 | 0.000497729 | - | 4 | q | 9.03999e-05 | 9.95421e-05 | - | 5 | l | 0.00180163 | 0.00186647 | - | 6 | tc | 0.141095 | 0.145208 | - | 7 | Nz | 0.411656 | 0.41965 | - | 8 | Wdg | 0.0849832 | 0.0876488 | - | 9 | Wp | 0.00331824 | 0.00334452 | - - - -.. GENERATED FROM PYTHON SOURCE LINES 368-374 +.. GENERATED FROM PYTHON SOURCE LINES 370-376 The Sobol' indices confirm the previous analyses, in terms of ranking of the most influent variables. We also see that five variables have a quasi null total Sobol' indices, that indicates almost no influence on the wing weight. @@ -923,16 +1015,16 @@ As the most important variables act only through decoupled first degree contribu This explains why both squared SRC and Taylor give the exact same results even if the first one is based on a :math:`\mathcal{L}^2` linear approximation and the second one is based on a linear expansion around the mean value of the input variables. -.. GENERATED FROM PYTHON SOURCE LINES 378-380 +.. GENERATED FROM PYTHON SOURCE LINES 380-382 HSIC indices ------------ -.. GENERATED FROM PYTHON SOURCE LINES 382-383 +.. GENERATED FROM PYTHON SOURCE LINES 384-385 We then estimate the HSIC indices using a data-driven approach. -.. GENERATED FROM PYTHON SOURCE LINES 383-389 +.. GENERATED FROM PYTHON SOURCE LINES 385-391 .. code-block:: Python @@ -949,7 +1041,7 @@ We then estimate the HSIC indices using a data-driven approach. -.. GENERATED FROM PYTHON SOURCE LINES 390-396 +.. GENERATED FROM PYTHON SOURCE LINES 392-398 .. code-block:: Python @@ -966,11 +1058,11 @@ We then estimate the HSIC indices using a data-driven approach. -.. GENERATED FROM PYTHON SOURCE LINES 397-398 +.. GENERATED FROM PYTHON SOURCE LINES 399-400 We define a covariance kernel associated to the output variable. -.. GENERATED FROM PYTHON SOURCE LINES 398-402 +.. GENERATED FROM PYTHON SOURCE LINES 400-404 .. code-block:: Python @@ -985,12 +1077,12 @@ We define a covariance kernel associated to the output variable. -.. GENERATED FROM PYTHON SOURCE LINES 403-405 +.. GENERATED FROM PYTHON SOURCE LINES 405-407 In this paragraph, we perform the analysis on the raw data: that is the global HSIC estimator. -.. GENERATED FROM PYTHON SOURCE LINES 405-407 +.. GENERATED FROM PYTHON SOURCE LINES 407-409 .. code-block:: Python @@ -1003,11 +1095,11 @@ the global HSIC estimator. -.. GENERATED FROM PYTHON SOURCE LINES 408-409 +.. GENERATED FROM PYTHON SOURCE LINES 410-411 We now build the HSIC estimator: -.. GENERATED FROM PYTHON SOURCE LINES 409-413 +.. GENERATED FROM PYTHON SOURCE LINES 411-415 .. code-block:: Python @@ -1022,11 +1114,11 @@ We now build the HSIC estimator: -.. GENERATED FROM PYTHON SOURCE LINES 414-415 +.. GENERATED FROM PYTHON SOURCE LINES 416-417 We get the R2-HSIC indices: -.. GENERATED FROM PYTHON SOURCE LINES 415-419 +.. GENERATED FROM PYTHON SOURCE LINES 417-421 .. code-block:: Python @@ -1049,11 +1141,11 @@ We get the R2-HSIC indices: -.. GENERATED FROM PYTHON SOURCE LINES 420-421 +.. GENERATED FROM PYTHON SOURCE LINES 422-423 and the HSIC indices: -.. GENERATED FROM PYTHON SOURCE LINES 421-424 +.. GENERATED FROM PYTHON SOURCE LINES 423-426 .. code-block:: Python @@ -1073,11 +1165,11 @@ and the HSIC indices: -.. GENERATED FROM PYTHON SOURCE LINES 425-426 +.. GENERATED FROM PYTHON SOURCE LINES 427-428 The p-value by permutation. -.. GENERATED FROM PYTHON SOURCE LINES 426-429 +.. GENERATED FROM PYTHON SOURCE LINES 428-431 .. code-block:: Python @@ -1097,11 +1189,11 @@ The p-value by permutation. -.. GENERATED FROM PYTHON SOURCE LINES 430-431 +.. GENERATED FROM PYTHON SOURCE LINES 432-433 We have an asymptotic estimate of the value for this estimator. -.. GENERATED FROM PYTHON SOURCE LINES 431-434 +.. GENERATED FROM PYTHON SOURCE LINES 433-436 .. code-block:: Python @@ -1121,11 +1213,11 @@ We have an asymptotic estimate of the value for this estimator. -.. GENERATED FROM PYTHON SOURCE LINES 435-436 +.. GENERATED FROM PYTHON SOURCE LINES 437-438 We vizualise the results. -.. GENERATED FROM PYTHON SOURCE LINES 436-448 +.. GENERATED FROM PYTHON SOURCE LINES 438-450 .. code-block:: Python @@ -1179,7 +1271,7 @@ We vizualise the results. -.. GENERATED FROM PYTHON SOURCE LINES 449-452 +.. GENERATED FROM PYTHON SOURCE LINES 451-454 The HSIC indices go in the same way as the other estimators in terms the most influent variables. The variables :math:`W_{fw}, q, l, W_p` seem to be independent to the output as the corresponding p-values are high. @@ -1188,7 +1280,7 @@ We can also see that the asymptotic p-values and p-values estimated by permutati .. rst-class:: sphx-glr-timing - **Total running time of the script:** (0 minutes 5.693 seconds) + **Total running time of the script:** (0 minutes 5.375 seconds) .. _sphx_glr_download_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_wingweight.py: diff --git a/openturns/master/_sources/auto_reliability_sensitivity/sensitivity_analysis/sg_execution_times.rst.txt b/openturns/master/_sources/auto_reliability_sensitivity/sensitivity_analysis/sg_execution_times.rst.txt index 6706f155bb9..ec441a57908 100644 --- a/openturns/master/_sources/auto_reliability_sensitivity/sensitivity_analysis/sg_execution_times.rst.txt +++ b/openturns/master/_sources/auto_reliability_sensitivity/sensitivity_analysis/sg_execution_times.rst.txt @@ -6,7 +6,7 @@ Computation times ================= -**00:08.878** total execution time for 8 files **from auto_reliability_sensitivity/sensitivity_analysis**: +**00:08.319** total execution time for 8 files **from auto_reliability_sensitivity/sensitivity_analysis**: .. container:: @@ -33,26 +33,26 @@ Computation times - Time - Mem (MB) * - :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_wingweight.py` (``plot_sensitivity_wingweight.py``) - - 00:05.693 + - 00:05.375 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_functional_chaos_sensitivity.py` (``plot_functional_chaos_sensitivity.py``) - - 00:00.954 + - 00:00.897 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_hsic_estimators_ishigami.py` (``plot_hsic_estimators_ishigami.py``) - - 00:00.767 + - 00:00.695 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_par_coo.py` (``plot_sensitivity_par_coo.py``) - - 00:00.744 + - 00:00.677 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_sobol.py` (``plot_sensitivity_sobol.py``) - - 00:00.418 + - 00:00.393 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_ancova.py` (``plot_sensitivity_ancova.py``) - - 00:00.117 + - 00:00.110 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_sobol_multivariate.py` (``plot_sensitivity_sobol_multivariate.py``) - - 00:00.106 + - 00:00.098 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_fast.py` (``plot_sensitivity_fast.py``) - - 00:00.079 + - 00:00.074 - 0.0 diff --git a/openturns/master/_sources/sg_execution_times.rst.txt b/openturns/master/_sources/sg_execution_times.rst.txt index d3cfdf23040..e3dd89c9c45 100644 --- a/openturns/master/_sources/sg_execution_times.rst.txt +++ b/openturns/master/_sources/sg_execution_times.rst.txt @@ -6,7 +6,7 @@ Computation times ================= -**04:21.003** total execution time for 263 files **from all galleries**: +**04:09.413** total execution time for 263 files **from all galleries**: .. container:: @@ -33,646 +33,649 @@ Computation times - Time - Mem (MB) * - :ref:`sphx_glr_auto_meta_modeling_fields_metamodels_plot_fieldfunction_metamodel.py` (``examples/meta_modeling/fields_metamodels/plot_fieldfunction_metamodel.py``) - - 00:18.032 + - 00:17.266 - 0.0 * - :ref:`sphx_glr_auto_calibration_bayesian_calibration_plot_gibbs.py` (``examples/calibration/bayesian_calibration/plot_gibbs.py``) - - 00:12.667 + - 00:12.653 + - 0.0 + * - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_functional_chaos.py` (``examples/meta_modeling/polynomial_chaos_metamodel/plot_functional_chaos.py``) + - 00:10.810 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_chaos_cv.py` (``examples/meta_modeling/polynomial_chaos_metamodel/plot_chaos_cv.py``) - - 00:11.148 + - 00:10.341 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_distribution_fitting_plot_estimate_gev_racetime.py` (``examples/data_analysis/distribution_fitting/plot_estimate_gev_racetime.py``) - - 00:10.230 + - 00:10.071 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_kriging_metamodel_plot_kriging_categorical.py` (``examples/meta_modeling/kriging_metamodel/plot_kriging_categorical.py``) - - 00:09.964 + - 00:09.426 - 0.0 * - :ref:`sphx_glr_auto_calibration_least_squares_and_gaussian_calibration_plot_calibration_flooding.py` (``examples/calibration/least_squares_and_gaussian_calibration/plot_calibration_flooding.py``) - - 00:09.339 + - 00:08.902 - 0.0 - * - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_functional_chaos.py` (``examples/meta_modeling/polynomial_chaos_metamodel/plot_functional_chaos.py``) - - 00:07.821 + * - :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_ifs.py` (``examples/numerical_methods/general_methods/plot_ifs.py``) + - 00:07.824 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_smolyak_quadrature.py` (``examples/reliability_sensitivity/design_of_experiments/plot_smolyak_quadrature.py``) - - 00:07.674 + - 00:06.989 - 0.0 - * - :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_ifs.py` (``examples/numerical_methods/general_methods/plot_ifs.py``) - - 00:07.440 + * - :ref:`sphx_glr_auto_meta_modeling_kriging_metamodel_plot_kriging_multioutput_firesatellite.py` (``examples/meta_modeling/kriging_metamodel/plot_kriging_multioutput_firesatellite.py``) + - 00:06.924 - 0.0 * - :ref:`sphx_glr_auto_calibration_least_squares_and_gaussian_calibration_plot_calibration_chaboche.py` (``examples/calibration/least_squares_and_gaussian_calibration/plot_calibration_chaboche.py``) - - 00:07.438 - - 0.0 - * - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_chaos_beam_sensitivity_degree.py` (``examples/meta_modeling/polynomial_chaos_metamodel/plot_chaos_beam_sensitivity_degree.py``) - - 00:07.434 - - 0.0 - * - :ref:`sphx_glr_auto_meta_modeling_kriging_metamodel_plot_kriging_multioutput_firesatellite.py` (``examples/meta_modeling/kriging_metamodel/plot_kriging_multioutput_firesatellite.py``) - - 00:07.096 + - 00:06.733 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_processes_plot_field_fca_sobol.py` (``examples/reliability_sensitivity/reliability_processes/plot_field_fca_sobol.py``) - - 00:06.478 + - 00:06.196 - 0.0 - * - :ref:`sphx_glr_auto_data_analysis_distribution_fitting_plot_estimate_multivariate_distribution.py` (``examples/data_analysis/distribution_fitting/plot_estimate_multivariate_distribution.py``) - - 00:05.917 - - 0.0 - * - :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_wingweight.py` (``examples/reliability_sensitivity/sensitivity_analysis/plot_sensitivity_wingweight.py``) - - 00:05.693 + * - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_chaos_beam_sensitivity_degree.py` (``examples/meta_modeling/polynomial_chaos_metamodel/plot_chaos_beam_sensitivity_degree.py``) + - 00:06.094 - 0.0 * - :ref:`sphx_glr_auto_calibration_bayesian_calibration_plot_rwmh_python_distribution.py` (``examples/calibration/bayesian_calibration/plot_rwmh_python_distribution.py``) - - 00:05.668 + - 00:05.764 + - 0.0 + * - :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_wingweight.py` (``examples/reliability_sensitivity/sensitivity_analysis/plot_sensitivity_wingweight.py``) + - 00:05.375 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_distribution_fitting_plot_estimate_gev_fremantle.py` (``examples/data_analysis/distribution_fitting/plot_estimate_gev_fremantle.py``) - - 00:05.499 + - 00:05.133 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_form_oscillator.py` (``examples/reliability_sensitivity/reliability/plot_estimate_probability_form_oscillator.py``) - - 00:05.047 + - 00:04.796 - 0.0 - * - :ref:`sphx_glr_auto_data_analysis_estimate_stochastic_processes_plot_estimate_multivariate_arma.py` (``examples/data_analysis/estimate_stochastic_processes/plot_estimate_multivariate_arma.py``) - - 00:04.054 + * - :ref:`sphx_glr_auto_data_analysis_distribution_fitting_plot_estimate_multivariate_distribution.py` (``examples/data_analysis/distribution_fitting/plot_estimate_multivariate_distribution.py``) + - 00:04.162 - 0.0 * - :ref:`sphx_glr_auto_calibration_least_squares_and_gaussian_calibration_plot_calibration_deflection_tube.py` (``examples/calibration/least_squares_and_gaussian_calibration/plot_calibration_deflection_tube.py``) - - 00:03.904 + - 00:03.912 - 0.0 - * - :ref:`sphx_glr_auto_data_analysis_graphics_plot_sensitivity_par_coo_ishigami.py` (``examples/data_analysis/graphics/plot_sensitivity_par_coo_ishigami.py``) - - 00:03.060 + * - :ref:`sphx_glr_auto_data_analysis_estimate_stochastic_processes_plot_estimate_multivariate_arma.py` (``examples/data_analysis/estimate_stochastic_processes/plot_estimate_multivariate_arma.py``) + - 00:03.908 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_chaos_sobol_confidence.py` (``examples/meta_modeling/polynomial_chaos_metamodel/plot_chaos_sobol_confidence.py``) - - 00:02.999 + - 00:02.801 - 0.0 - * - :ref:`sphx_glr_auto_numerical_methods_optimization_plot_ego.py` (``examples/numerical_methods/optimization/plot_ego.py``) - - 00:02.625 + * - :ref:`sphx_glr_auto_data_analysis_graphics_plot_sensitivity_par_coo_ishigami.py` (``examples/data_analysis/graphics/plot_sensitivity_par_coo_ishigami.py``) + - 00:02.719 - 0.0 - * - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_chaos_cleaning_strategy.py` (``examples/meta_modeling/polynomial_chaos_metamodel/plot_chaos_cleaning_strategy.py``) - - 00:02.370 + * - :ref:`sphx_glr_auto_numerical_methods_optimization_plot_ego.py` (``examples/numerical_methods/optimization/plot_ego.py``) + - 00:02.716 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_smolyak_experiment.py` (``examples/reliability_sensitivity/design_of_experiments/plot_smolyak_experiment.py``) - - 00:02.292 + - 00:02.128 - 0.0 - * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_proba_system_event.py` (``examples/reliability_sensitivity/reliability/plot_proba_system_event.py``) - - 00:02.176 + * - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_chaos_cleaning_strategy.py` (``examples/meta_modeling/polynomial_chaos_metamodel/plot_chaos_cleaning_strategy.py``) + - 00:02.122 - 0.0 - * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_userdefined_covariance_model.py` (``examples/probabilistic_modeling/stochastic_processes/plot_userdefined_covariance_model.py``) - - 00:02.117 + * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_proba_system_event.py` (``examples/reliability_sensitivity/reliability/plot_proba_system_event.py``) + - 00:02.116 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_gaussian_process_covariance_hmat.py` (``examples/probabilistic_modeling/stochastic_processes/plot_gaussian_process_covariance_hmat.py``) - - 00:02.105 + - 00:02.072 + - 0.0 + * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_userdefined_covariance_model.py` (``examples/probabilistic_modeling/stochastic_processes/plot_userdefined_covariance_model.py``) + - 00:02.037 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_chaos_build_distribution.py` (``examples/meta_modeling/polynomial_chaos_metamodel/plot_chaos_build_distribution.py``) - - 00:02.029 + - 00:01.960 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_adaptive_directional_sampling.py` (``examples/reliability_sensitivity/reliability/plot_estimate_probability_adaptive_directional_sampling.py``) - - 00:02.010 + - 00:01.944 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_distribution_fitting_plot_estimate_gev_pirie.py` (``examples/data_analysis/distribution_fitting/plot_estimate_gev_pirie.py``) - - 00:01.989 + - 00:01.917 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_create_mesh.py` (``examples/probabilistic_modeling/stochastic_processes/plot_create_mesh.py``) - - 00:01.949 + - 00:01.841 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_fields_metamodels_plot_viscous_fall_metamodel.py` (``examples/meta_modeling/fields_metamodels/plot_viscous_fall_metamodel.py``) - - 00:01.854 - - 0.0 - * - :ref:`sphx_glr_auto_data_analysis_distribution_fitting_plot_estimate_conditional_quantile.py` (``examples/data_analysis/distribution_fitting/plot_estimate_conditional_quantile.py``) - - 00:01.845 + - 00:01.763 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_field_manipulation.py` (``examples/probabilistic_modeling/stochastic_processes/plot_field_manipulation.py``) - - 00:01.782 + - 00:01.691 - 0.0 - * - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_enumeratefunction.py` (``examples/meta_modeling/polynomial_chaos_metamodel/plot_enumeratefunction.py``) - - 00:01.703 + * - :ref:`sphx_glr_auto_data_analysis_distribution_fitting_plot_estimate_conditional_quantile.py` (``examples/data_analysis/distribution_fitting/plot_estimate_conditional_quantile.py``) + - 00:01.668 - 0.0 - * - :ref:`sphx_glr_auto_calibration_bayesian_calibration_plot_bayesian_calibration.py` (``examples/calibration/bayesian_calibration/plot_bayesian_calibration.py``) - - 00:01.489 + * - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_enumeratefunction.py` (``examples/meta_modeling/polynomial_chaos_metamodel/plot_enumeratefunction.py``) + - 00:01.568 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_crossentropy.py` (``examples/reliability_sensitivity/reliability/plot_crossentropy.py``) - - 00:01.410 + - 00:01.363 + - 0.0 + * - :ref:`sphx_glr_auto_calibration_bayesian_calibration_plot_bayesian_calibration_flooding.py` (``examples/calibration/bayesian_calibration/plot_bayesian_calibration_flooding.py``) + - 00:01.294 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_statistical_tests_plot_kolmogorov_distribution.py` (``examples/data_analysis/statistical_tests/plot_kolmogorov_distribution.py``) - - 00:01.334 + - 00:01.293 - 0.0 - * - :ref:`sphx_glr_auto_calibration_bayesian_calibration_plot_bayesian_calibration_flooding.py` (``examples/calibration/bayesian_calibration/plot_bayesian_calibration_flooding.py``) - - 00:01.310 + * - :ref:`sphx_glr_auto_calibration_bayesian_calibration_plot_bayesian_calibration.py` (``examples/calibration/bayesian_calibration/plot_bayesian_calibration.py``) + - 00:01.247 + - 0.0 + * - :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_plot_design.py` (``examples/reliability_sensitivity/design_of_experiments/plot_plot_design.py``) + - 00:01.179 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_kriging_metamodel_plot_draw_covariance_models.py` (``examples/meta_modeling/kriging_metamodel/plot_draw_covariance_models.py``) - - 00:01.254 + - 00:01.155 - 0.0 - * - :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_plot_design.py` (``examples/reliability_sensitivity/design_of_experiments/plot_plot_design.py``) - - 00:01.253 + * - :ref:`sphx_glr_auto_graphs_plot_graphs_basics.py` (``examples/graphs/plot_graphs_basics.py``) + - 00:01.120 - 0.0 * - :ref:`sphx_glr_auto_calibration_bayesian_calibration_plot_gibbs_simus.py` (``examples/calibration/bayesian_calibration/plot_gibbs_simus.py``) - - 00:01.172 + - 00:01.099 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_create_draw_multivariate_distributions.py` (``examples/probabilistic_modeling/distributions/plot_create_draw_multivariate_distributions.py``) - - 00:01.093 - - 0.0 - * - :ref:`sphx_glr_auto_data_analysis_distribution_fitting_plot_estimate_non_parametric_distribution.py` (``examples/data_analysis/distribution_fitting/plot_estimate_non_parametric_distribution.py``) - - 00:01.070 + - 00:01.008 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_design_of_experiments.py` (``examples/reliability_sensitivity/design_of_experiments/plot_design_of_experiments.py``) - - 00:01.052 - - 0.0 - * - :ref:`sphx_glr_auto_graphs_plot_graphs_basics.py` (``examples/graphs/plot_graphs_basics.py``) - - 00:01.050 + - 00:00.983 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_box_cox_transform.py` (``examples/probabilistic_modeling/stochastic_processes/plot_box_cox_transform.py``) - - 00:01.011 + - 00:00.975 - 0.0 - * - :ref:`sphx_glr_auto_data_analysis_sample_analysis_plot_draw_survival.py` (``examples/data_analysis/sample_analysis/plot_draw_survival.py``) - - 00:00.997 - - 0.0 - * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_quick_start_guide_distributions.py` (``examples/probabilistic_modeling/distributions/plot_quick_start_guide_distributions.py``) - - 00:00.956 + * - :ref:`sphx_glr_auto_data_analysis_distribution_fitting_plot_estimate_non_parametric_distribution.py` (``examples/data_analysis/distribution_fitting/plot_estimate_non_parametric_distribution.py``) + - 00:00.966 - 0.0 * - :ref:`sphx_glr_auto_numerical_methods_optimization_plot_optimization_rastrigin.py` (``examples/numerical_methods/optimization/plot_optimization_rastrigin.py``) - - 00:00.956 + - 00:00.942 + - 0.0 + * - :ref:`sphx_glr_auto_data_analysis_sample_analysis_plot_draw_survival.py` (``examples/data_analysis/sample_analysis/plot_draw_survival.py``) + - 00:00.920 + - 0.0 + * - :ref:`sphx_glr_auto_calibration_bayesian_calibration_plot_ackley_distribution.py` (``examples/calibration/bayesian_calibration/plot_ackley_distribution.py``) + - 00:00.916 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_functional_chaos_sensitivity.py` (``examples/reliability_sensitivity/sensitivity_analysis/plot_functional_chaos_sensitivity.py``) - - 00:00.954 + - 00:00.897 - 0.0 - * - :ref:`sphx_glr_auto_meta_modeling_kriging_metamodel_plot_kriging_advanced.py` (``examples/meta_modeling/kriging_metamodel/plot_kriging_advanced.py``) - - 00:00.940 + * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_quick_start_guide_distributions.py` (``examples/probabilistic_modeling/distributions/plot_quick_start_guide_distributions.py``) + - 00:00.885 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_form_explained.py` (``examples/reliability_sensitivity/reliability/plot_form_explained.py``) - - 00:00.922 - - 0.0 - * - :ref:`sphx_glr_auto_calibration_bayesian_calibration_plot_ackley_distribution.py` (``examples/calibration/bayesian_calibration/plot_ackley_distribution.py``) - - 00:00.913 + - 00:00.860 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_estimate_stochastic_processes_plot_estimate_spectral_density_function.py` (``examples/data_analysis/estimate_stochastic_processes/plot_estimate_spectral_density_function.py``) - - 00:00.882 + - 00:00.858 - 0.0 * - :ref:`sphx_glr_auto_numerical_methods_optimization_plot_optimization_rosenbrock.py` (``examples/numerical_methods/optimization/plot_optimization_rosenbrock.py``) - - 00:00.846 + - 00:00.849 - 0.0 - * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_randomized_qmc.py` (``examples/reliability_sensitivity/reliability/plot_estimate_probability_randomized_qmc.py``) - - 00:00.830 + * - :ref:`sphx_glr_auto_meta_modeling_kriging_metamodel_plot_kriging_advanced.py` (``examples/meta_modeling/kriging_metamodel/plot_kriging_advanced.py``) + - 00:00.845 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_estimate_stochastic_processes_plot_estimate_arma.py` (``examples/data_analysis/estimate_stochastic_processes/plot_estimate_arma.py``) - - 00:00.800 + - 00:00.781 - 0.0 - * - :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_hsic_estimators_ishigami.py` (``examples/reliability_sensitivity/sensitivity_analysis/plot_hsic_estimators_ishigami.py``) - - 00:00.767 + * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_randomized_qmc.py` (``examples/reliability_sensitivity/reliability/plot_estimate_probability_randomized_qmc.py``) + - 00:00.769 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_distribution_fitting_plot_estimate_gev_venice.py` (``examples/data_analysis/distribution_fitting/plot_estimate_gev_venice.py``) - - 00:00.758 + - 00:00.700 - 0.0 - * - :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_par_coo.py` (``examples/reliability_sensitivity/sensitivity_analysis/plot_sensitivity_par_coo.py``) - - 00:00.744 + * - :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_hsic_estimators_ishigami.py` (``examples/reliability_sensitivity/sensitivity_analysis/plot_hsic_estimators_ishigami.py``) + - 00:00.695 + - 0.0 + * - :ref:`sphx_glr_auto_graphs_plot_graphs_loglikelihood_contour.py` (``examples/graphs/plot_graphs_loglikelihood_contour.py``) + - 00:00.687 - 0.0 * - :ref:`sphx_glr_auto_calibration_least_squares_and_gaussian_calibration_plot_calibration_logistic.py` (``examples/calibration/least_squares_and_gaussian_calibration/plot_calibration_logistic.py``) - - 00:00.739 + - 00:00.685 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_general_purpose_metamodels_plot_overfitting_model_selection.py` (``examples/meta_modeling/general_purpose_metamodels/plot_overfitting_model_selection.py``) - - 00:00.735 + - 00:00.678 + - 0.0 + * - :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_par_coo.py` (``examples/reliability_sensitivity/sensitivity_analysis/plot_sensitivity_par_coo.py``) + - 00:00.677 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_create_domain_event.py` (``examples/reliability_sensitivity/reliability/plot_create_domain_event.py``) - - 00:00.716 + - 00:00.675 + - 0.0 + * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_gaussian_processes_comparison.py` (``examples/probabilistic_modeling/stochastic_processes/plot_gaussian_processes_comparison.py``) + - 00:00.660 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_general_purpose_metamodels_plot_linear_model.py` (``examples/meta_modeling/general_purpose_metamodels/plot_linear_model.py``) - - 00:00.713 + - 00:00.652 - 0.0 - * - :ref:`sphx_glr_auto_graphs_plot_graphs_loglikelihood_contour.py` (``examples/graphs/plot_graphs_loglikelihood_contour.py``) - - 00:00.707 + * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_minimum_volume_level_sets.py` (``examples/probabilistic_modeling/distributions/plot_minimum_volume_level_sets.py``) + - 00:00.642 - 0.0 - * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_gaussian_processes_comparison.py` (``examples/probabilistic_modeling/stochastic_processes/plot_gaussian_processes_comparison.py``) - - 00:00.707 + * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_directional_sampling.py` (``examples/reliability_sensitivity/reliability/plot_estimate_probability_directional_sampling.py``) + - 00:00.629 - 0.0 - * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_minimum_volume_level_sets.py` (``examples/probabilistic_modeling/distributions/plot_minimum_volume_level_sets.py``) - - 00:00.705 + * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_axial_stressed_beam.py` (``examples/reliability_sensitivity/reliability/plot_axial_stressed_beam.py``) + - 00:00.629 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_distribution_fitting_plot_asymptotic_estimators_distribution.py` (``examples/data_analysis/distribution_fitting/plot_asymptotic_estimators_distribution.py``) - - 00:00.672 + - 00:00.606 - 0.0 - * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_axial_stressed_beam.py` (``examples/reliability_sensitivity/reliability/plot_axial_stressed_beam.py``) - - 00:00.663 + * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_event_system.py` (``examples/reliability_sensitivity/reliability/plot_event_system.py``) + - 00:00.586 - 0.0 - * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_directional_sampling.py` (``examples/reliability_sensitivity/reliability/plot_estimate_probability_directional_sampling.py``) - - 00:00.646 + * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_distribution_transformation.py` (``examples/probabilistic_modeling/distributions/plot_distribution_transformation.py``) + - 00:00.582 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_kriging_metamodel_plot_kriging_sequential.py` (``examples/meta_modeling/kriging_metamodel/plot_kriging_sequential.py``) - - 00:00.645 + - 00:00.562 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_multi_form.py` (``examples/reliability_sensitivity/reliability/plot_multi_form.py``) - - 00:00.636 + - 00:00.562 - 0.0 - * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_distribution_transformation.py` (``examples/probabilistic_modeling/distributions/plot_distribution_transformation.py``) - - 00:00.635 + * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_subset_sampling.py` (``examples/reliability_sensitivity/reliability/plot_subset_sampling.py``) + - 00:00.555 - 0.0 - * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_event_system.py` (``examples/reliability_sensitivity/reliability/plot_event_system.py``) - - 00:00.634 + * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_order_statistics_distribution.py` (``examples/probabilistic_modeling/distributions/plot_order_statistics_distribution.py``) + - 00:00.539 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_distribution_fitting_plot_smoothing_mixture.py` (``examples/data_analysis/distribution_fitting/plot_smoothing_mixture.py``) - - 00:00.614 - - 0.0 - * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_order_statistics_distribution.py` (``examples/probabilistic_modeling/distributions/plot_order_statistics_distribution.py``) - - 00:00.587 + - 00:00.538 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_distribution_fitting_plot_model_singular_multivariate_distribution.py` (``examples/data_analysis/distribution_fitting/plot_model_singular_multivariate_distribution.py``) - - 00:00.582 + - 00:00.532 - 0.0 - * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_subset_sampling.py` (``examples/reliability_sensitivity/reliability/plot_subset_sampling.py``) - - 00:00.577 + * - :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_low_discrepancy_sequence.py` (``examples/reliability_sensitivity/design_of_experiments/plot_low_discrepancy_sequence.py``) + - 00:00.519 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_kriging_metamodel_plot_kriging_chose_trend.py` (``examples/meta_modeling/kriging_metamodel/plot_kriging_chose_trend.py``) - - 00:00.559 + - 00:00.489 - 0.0 - * - :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_low_discrepancy_sequence.py` (``examples/reliability_sensitivity/design_of_experiments/plot_low_discrepancy_sequence.py``) - - 00:00.550 + * - :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_optimal_lhs.py` (``examples/reliability_sensitivity/design_of_experiments/plot_optimal_lhs.py``) + - 00:00.456 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_smolyak_merge.py` (``examples/reliability_sensitivity/design_of_experiments/plot_smolyak_merge.py``) - - 00:00.524 + - 00:00.450 + - 0.0 + * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_process_manipulation.py` (``examples/probabilistic_modeling/stochastic_processes/plot_process_manipulation.py``) + - 00:00.437 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_fields_metamodels_plot_karhunenloeve_validation.py` (``examples/meta_modeling/fields_metamodels/plot_karhunenloeve_validation.py``) - - 00:00.477 + - 00:00.430 - 0.0 - * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_process_manipulation.py` (``examples/probabilistic_modeling/stochastic_processes/plot_process_manipulation.py``) - - 00:00.472 + * - :ref:`sphx_glr_auto_reliability_sensitivity_central_dispersion_plot_expectation_simulation_algorithm.py` (``examples/reliability_sensitivity/central_dispersion/plot_expectation_simulation_algorithm.py``) + - 00:00.428 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_estimate_dependency_and_copulas_plot_estimate_non_parametric_copula.py` (``examples/data_analysis/estimate_dependency_and_copulas/plot_estimate_non_parametric_copula.py``) - - 00:00.469 - - 0.0 - * - :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_optimal_lhs.py` (``examples/reliability_sensitivity/design_of_experiments/plot_optimal_lhs.py``) - - 00:00.468 + - 00:00.422 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_estimate_stochastic_processes_plot_estimate_stationary_covariance_model.py` (``examples/data_analysis/estimate_stochastic_processes/plot_estimate_stationary_covariance_model.py``) - - 00:00.451 + - 00:00.415 + - 0.0 + * - :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_pce_design.py` (``examples/numerical_methods/general_methods/plot_pce_design.py``) + - 00:00.412 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_nais.py` (``examples/reliability_sensitivity/reliability/plot_nais.py``) - - 00:00.437 + - 00:00.407 + - 0.0 + * - :ref:`sphx_glr_auto_functional_modeling_field_functions_plot_function_manipulation.py` (``examples/functional_modeling/field_functions/plot_function_manipulation.py``) + - 00:00.400 + - 0.0 + * - :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_regression_sinus.py` (``examples/numerical_methods/general_methods/plot_regression_sinus.py``) + - 00:00.397 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_truncated_distribution.py` (``examples/probabilistic_modeling/distributions/plot_truncated_distribution.py``) - - 00:00.432 + - 00:00.396 - 0.0 - * - :ref:`sphx_glr_auto_reliability_sensitivity_central_dispersion_plot_expectation_simulation_algorithm.py` (``examples/reliability_sensitivity/central_dispersion/plot_expectation_simulation_algorithm.py``) - - 00:00.431 + * - :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_sobol.py` (``examples/reliability_sensitivity/sensitivity_analysis/plot_sensitivity_sobol.py``) + - 00:00.393 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_manage_data_and_samples_plot_sample_correlation.py` (``examples/data_analysis/manage_data_and_samples/plot_sample_correlation.py``) - - 00:00.429 - - 0.0 - * - :ref:`sphx_glr_auto_functional_modeling_field_functions_plot_function_manipulation.py` (``examples/functional_modeling/field_functions/plot_function_manipulation.py``) - - 00:00.425 + - 00:00.390 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_copulas_plot_ordinal_sum_copula.py` (``examples/probabilistic_modeling/copulas/plot_ordinal_sum_copula.py``) - - 00:00.423 + - 00:00.376 - 0.0 - * - :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_sobol.py` (``examples/reliability_sensitivity/sensitivity_analysis/plot_sensitivity_sobol.py``) - - 00:00.418 + * - :ref:`sphx_glr_auto_data_analysis_statistical_tests_plot_fitted_distribution_ranking.py` (``examples/data_analysis/statistical_tests/plot_fitted_distribution_ranking.py``) + - 00:00.365 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_kriging_metamodel_plot_kriging_branin_function.py` (``examples/meta_modeling/kriging_metamodel/plot_kriging_branin_function.py``) - - 00:00.402 + - 00:00.358 - 0.0 - * - :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_regression_sinus.py` (``examples/numerical_methods/general_methods/plot_regression_sinus.py``) - - 00:00.400 + * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_overview_univariate_distributions.py` (``examples/probabilistic_modeling/distributions/plot_overview_univariate_distributions.py``) + - 00:00.351 - 0.0 * - :ref:`sphx_glr_auto_numerical_methods_optimization_plot_optimization_dlib.py` (``examples/numerical_methods/optimization/plot_optimization_dlib.py``) - - 00:00.396 + - 00:00.348 - 0.0 - * - :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_pce_design.py` (``examples/numerical_methods/general_methods/plot_pce_design.py``) - - 00:00.388 - - 0.0 - * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_overview_univariate_distributions.py` (``examples/probabilistic_modeling/distributions/plot_overview_univariate_distributions.py``) - - 00:00.383 + * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_axial_stressed_beam_quickstart.py` (``examples/reliability_sensitivity/reliability/plot_axial_stressed_beam_quickstart.py``) + - 00:00.343 - 0.0 - * - :ref:`sphx_glr_auto_data_analysis_statistical_tests_plot_fitted_distribution_ranking.py` (``examples/data_analysis/statistical_tests/plot_fitted_distribution_ranking.py``) - - 00:00.379 + * - :ref:`sphx_glr_auto_meta_modeling_general_purpose_metamodels_plot_stepwise.py` (``examples/meta_modeling/general_purpose_metamodels/plot_stepwise.py``) + - 00:00.341 - 0.0 - * - :ref:`sphx_glr_auto_data_analysis_distribution_fitting_plot_fit_extreme_value_distribution.py` (``examples/data_analysis/distribution_fitting/plot_fit_extreme_value_distribution.py``) - - 00:00.378 + * - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_chaos_ishigami.py` (``examples/meta_modeling/polynomial_chaos_metamodel/plot_chaos_ishigami.py``) + - 00:00.340 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_kriging_metamodel_plot_propagate_kriging_ishigami.py` (``examples/meta_modeling/kriging_metamodel/plot_propagate_kriging_ishigami.py``) - - 00:00.369 - - 0.0 - * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_axial_stressed_beam_quickstart.py` (``examples/reliability_sensitivity/reliability/plot_axial_stressed_beam_quickstart.py``) - - 00:00.366 + - 00:00.334 - 0.0 - * - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_chaos_ishigami.py` (``examples/meta_modeling/polynomial_chaos_metamodel/plot_chaos_ishigami.py``) - - 00:00.362 - - 0.0 - * - :ref:`sphx_glr_auto_meta_modeling_general_purpose_metamodels_plot_stepwise.py` (``examples/meta_modeling/general_purpose_metamodels/plot_stepwise.py``) - - 00:00.360 + * - :ref:`sphx_glr_auto_data_analysis_distribution_fitting_plot_fit_extreme_value_distribution.py` (``examples/data_analysis/distribution_fitting/plot_fit_extreme_value_distribution.py``) + - 00:00.331 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_form.py` (``examples/reliability_sensitivity/reliability/plot_estimate_probability_form.py``) - - 00:00.343 - - 0.0 - * - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_chaos_cantilever_beam_integration.py` (``examples/meta_modeling/polynomial_chaos_metamodel/plot_chaos_cantilever_beam_integration.py``) - - 00:00.325 - - 0.0 - * - :ref:`sphx_glr_auto_meta_modeling_kriging_metamodel_plot_kriging_1d.py` (``examples/meta_modeling/kriging_metamodel/plot_kriging_1d.py``) - - 00:00.318 + - 00:00.320 - 0.0 * - :ref:`sphx_glr_auto_calibration_least_squares_and_gaussian_calibration_plot_calibration_quickstart.py` (``examples/calibration/least_squares_and_gaussian_calibration/plot_calibration_quickstart.py``) - - 00:00.303 - - 0.0 - * - :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_create_deterministic_doe.py` (``examples/reliability_sensitivity/design_of_experiments/plot_create_deterministic_doe.py``) - - 00:00.297 + - 00:00.288 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_random_walk_process.py` (``examples/probabilistic_modeling/stochastic_processes/plot_random_walk_process.py``) - - 00:00.296 - - 0.0 - * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_distribution_manipulation.py` (``examples/probabilistic_modeling/distributions/plot_distribution_manipulation.py``) - - 00:00.294 - - 0.0 - * - :ref:`sphx_glr_auto_data_analysis_statistical_tests_plot_test_copula.py` (``examples/data_analysis/statistical_tests/plot_test_copula.py``) - 00:00.281 - 0.0 - * - :ref:`sphx_glr_auto_calibration_bayesian_calibration_plot_imh_python_distribution.py` (``examples/calibration/bayesian_calibration/plot_imh_python_distribution.py``) - - 00:00.280 + * - :ref:`sphx_glr_auto_meta_modeling_kriging_metamodel_plot_kriging_1d.py` (``examples/meta_modeling/kriging_metamodel/plot_kriging_1d.py``) + - 00:00.281 - 0.0 * - :ref:`sphx_glr_auto_numerical_methods_iterative_statistics_plot_iterative_threshold.py` (``examples/numerical_methods/iterative_statistics/plot_iterative_threshold.py``) - - 00:00.279 + - 00:00.274 - 0.0 - * - :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_deterministic_design.py` (``examples/reliability_sensitivity/design_of_experiments/plot_deterministic_design.py``) - - 00:00.279 + * - :ref:`sphx_glr_auto_calibration_bayesian_calibration_plot_imh_python_distribution.py` (``examples/calibration/bayesian_calibration/plot_imh_python_distribution.py``) + - 00:00.271 - 0.0 - * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_create_and_manipulate_arma_process.py` (``examples/probabilistic_modeling/stochastic_processes/plot_create_and_manipulate_arma_process.py``) - - 00:00.279 + * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_distribution_manipulation.py` (``examples/probabilistic_modeling/distributions/plot_distribution_manipulation.py``) + - 00:00.268 - 0.0 - * - :ref:`sphx_glr_auto_data_analysis_graphics_plot_visualize_clouds.py` (``examples/data_analysis/graphics/plot_visualize_clouds.py``) - - 00:00.276 + * - :ref:`sphx_glr_auto_data_analysis_statistical_tests_plot_test_copula.py` (``examples/data_analysis/statistical_tests/plot_test_copula.py``) + - 00:00.268 - 0.0 - * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_create_extreme_value_distribution.py` (``examples/probabilistic_modeling/distributions/plot_create_extreme_value_distribution.py``) - - 00:00.275 + * - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_chaos_cantilever_beam_integration.py` (``examples/meta_modeling/polynomial_chaos_metamodel/plot_chaos_cantilever_beam_integration.py``) + - 00:00.268 + - 0.0 + * - :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_create_deterministic_doe.py` (``examples/reliability_sensitivity/design_of_experiments/plot_create_deterministic_doe.py``) + - 00:00.267 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_distribution_fitting_plot_advanced_mle_estimator.py` (``examples/data_analysis/distribution_fitting/plot_advanced_mle_estimator.py``) - - 00:00.275 + - 00:00.262 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_general_purpose_metamodels_plot_export_metamodel.py` (``examples/meta_modeling/general_purpose_metamodels/plot_export_metamodel.py``) - - 00:00.273 + - 00:00.259 - 0.0 - * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_discrete_markov_chain_process.py` (``examples/probabilistic_modeling/stochastic_processes/plot_discrete_markov_chain_process.py``) - - 00:00.270 + * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_create_and_manipulate_arma_process.py` (``examples/probabilistic_modeling/stochastic_processes/plot_create_and_manipulate_arma_process.py``) + - 00:00.258 - 0.0 - * - :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_smolyak_indices.py` (``examples/reliability_sensitivity/design_of_experiments/plot_smolyak_indices.py``) - - 00:00.267 + * - :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_deterministic_design.py` (``examples/reliability_sensitivity/design_of_experiments/plot_deterministic_design.py``) + - 00:00.252 - 0.0 - * - :ref:`sphx_glr_auto_data_analysis_estimate_stochastic_processes_plot_estimate_non_stationary_covariance_model.py` (``examples/data_analysis/estimate_stochastic_processes/plot_estimate_non_stationary_covariance_model.py``) - - 00:00.262 + * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_discrete_markov_chain_process.py` (``examples/probabilistic_modeling/stochastic_processes/plot_discrete_markov_chain_process.py``) + - 00:00.252 - 0.0 - * - :ref:`sphx_glr_auto_meta_modeling_kriging_metamodel_plot_kriging_isotropic.py` (``examples/meta_modeling/kriging_metamodel/plot_kriging_isotropic.py``) - - 00:00.261 + * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_create_extreme_value_distribution.py` (``examples/probabilistic_modeling/distributions/plot_create_extreme_value_distribution.py``) + - 00:00.250 + - 0.0 + * - :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_smolyak_indices.py` (``examples/reliability_sensitivity/design_of_experiments/plot_smolyak_indices.py``) + - 00:00.245 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_kronecker_covmodel.py` (``examples/probabilistic_modeling/stochastic_processes/plot_kronecker_covmodel.py``) - - 00:00.261 + - 00:00.245 + - 0.0 + * - :ref:`sphx_glr_auto_data_analysis_estimate_stochastic_processes_plot_estimate_non_stationary_covariance_model.py` (``examples/data_analysis/estimate_stochastic_processes/plot_estimate_non_stationary_covariance_model.py``) + - 00:00.243 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_create_and_draw_scalar_distributions.py` (``examples/probabilistic_modeling/distributions/plot_create_and_draw_scalar_distributions.py``) - - 00:00.257 + - 00:00.237 - 0.0 - * - :ref:`sphx_glr_auto_data_analysis_distribution_fitting_plot_estimate_normal.py` (``examples/data_analysis/distribution_fitting/plot_estimate_normal.py``) - - 00:00.251 + * - :ref:`sphx_glr_auto_data_analysis_graphics_plot_visualize_clouds.py` (``examples/data_analysis/graphics/plot_visualize_clouds.py``) + - 00:00.236 - 0.0 - * - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_functional_chaos_graphs.py` (``examples/meta_modeling/polynomial_chaos_metamodel/plot_functional_chaos_graphs.py``) - - 00:00.249 + * - :ref:`sphx_glr_auto_data_analysis_distribution_fitting_plot_estimate_normal.py` (``examples/data_analysis/distribution_fitting/plot_estimate_normal.py``) + - 00:00.230 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_bayes_distribution.py` (``examples/probabilistic_modeling/distributions/plot_bayes_distribution.py``) - - 00:00.247 + - 00:00.230 - 0.0 - * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_create_random_mixture.py` (``examples/probabilistic_modeling/distributions/plot_create_random_mixture.py``) - - 00:00.246 + * - :ref:`sphx_glr_auto_meta_modeling_kriging_metamodel_plot_kriging_isotropic.py` (``examples/meta_modeling/kriging_metamodel/plot_kriging_isotropic.py``) + - 00:00.229 - 0.0 - * - :ref:`sphx_glr_auto_data_analysis_manage_data_and_samples_plot_sample_pandas.py` (``examples/data_analysis/manage_data_and_samples/plot_sample_pandas.py``) - - 00:00.244 + * - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_functional_chaos_graphs.py` (``examples/meta_modeling/polynomial_chaos_metamodel/plot_functional_chaos_graphs.py``) + - 00:00.226 - 0.0 - * - :ref:`sphx_glr_auto_meta_modeling_kriging_metamodel_plot_kriging_simulate.py` (``examples/meta_modeling/kriging_metamodel/plot_kriging_simulate.py``) - - 00:00.239 + * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_create_random_mixture.py` (``examples/probabilistic_modeling/distributions/plot_create_random_mixture.py``) + - 00:00.225 + - 0.0 + * - :ref:`sphx_glr_auto_data_analysis_estimate_dependency_and_copulas_plot_estimate_dependence_wavesurge.py` (``examples/data_analysis/estimate_dependency_and_copulas/plot_estimate_dependence_wavesurge.py``) + - 00:00.218 - 0.0 * - :ref:`sphx_glr_auto_functional_modeling_univariate_functions_plot_createUnivariateFunction.py` (``examples/functional_modeling/univariate_functions/plot_createUnivariateFunction.py``) - - 00:00.235 + - 00:00.218 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_mixture_distribution.py` (``examples/probabilistic_modeling/distributions/plot_mixture_distribution.py``) - - 00:00.233 + - 00:00.215 - 0.0 - * - :ref:`sphx_glr_auto_data_analysis_estimate_dependency_and_copulas_plot_estimate_dependence_wavesurge.py` (``examples/data_analysis/estimate_dependency_and_copulas/plot_estimate_dependence_wavesurge.py``) - - 00:00.231 + * - :ref:`sphx_glr_auto_meta_modeling_kriging_metamodel_plot_kriging_simulate.py` (``examples/meta_modeling/kriging_metamodel/plot_kriging_simulate.py``) + - 00:00.213 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_estimate_dependency_and_copulas_plot_estimate_dependence_wind.py` (``examples/data_analysis/estimate_dependency_and_copulas/plot_estimate_dependence_wind.py``) - - 00:00.216 + - 00:00.203 - 0.0 * - :ref:`sphx_glr_auto_functional_modeling_field_functions_plot_logistic_growth_model.py` (``examples/functional_modeling/field_functions/plot_logistic_growth_model.py``) - - 00:00.202 + - 00:00.197 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_kriging_metamodel_plot_kriging_cantilever_beam_hmat.py` (``examples/meta_modeling/kriging_metamodel/plot_kriging_cantilever_beam_hmat.py``) - - 00:00.192 - - 0.0 - * - :ref:`sphx_glr_auto_meta_modeling_kriging_metamodel_plot_kriging_hyperparameters_optimization.py` (``examples/meta_modeling/kriging_metamodel/plot_kriging_hyperparameters_optimization.py``) - - 00:00.190 - - 0.0 - * - :ref:`sphx_glr_auto_meta_modeling_kriging_metamodel_plot_kriging_cantilever_beam.py` (``examples/meta_modeling/kriging_metamodel/plot_kriging_cantilever_beam.py``) - - 00:00.187 + - 00:00.172 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_mixed_design.py` (``examples/reliability_sensitivity/design_of_experiments/plot_mixed_design.py``) - - 00:00.179 - - 0.0 - * - :ref:`sphx_glr_auto_meta_modeling_general_purpose_metamodels_plot_expert_mixture.py` (``examples/meta_modeling/general_purpose_metamodels/plot_expert_mixture.py``) - - 00:00.178 - - 0.0 - * - :ref:`sphx_glr_auto_data_analysis_graphics_plot_visualize_pairs.py` (``examples/data_analysis/graphics/plot_visualize_pairs.py``) - - 00:00.178 + - 00:00.171 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_processes_plot_estimate_probability_monte_carlo_process.py` (``examples/reliability_sensitivity/reliability_processes/plot_estimate_probability_monte_carlo_process.py``) - - 00:00.174 + - 00:00.170 - 0.0 - * - :ref:`sphx_glr_auto_meta_modeling_kriging_metamodel_plot_kriging_beam_trend.py` (``examples/meta_modeling/kriging_metamodel/plot_kriging_beam_trend.py``) + * - :ref:`sphx_glr_auto_meta_modeling_kriging_metamodel_plot_kriging_cantilever_beam.py` (``examples/meta_modeling/kriging_metamodel/plot_kriging_cantilever_beam.py``) - 00:00.166 - 0.0 - * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_generate_by_inversion.py` (``examples/probabilistic_modeling/distributions/plot_generate_by_inversion.py``) - - 00:00.165 + * - :ref:`sphx_glr_auto_meta_modeling_kriging_metamodel_plot_kriging_hyperparameters_optimization.py` (``examples/meta_modeling/kriging_metamodel/plot_kriging_hyperparameters_optimization.py``) + - 00:00.166 - 0.0 - * - :ref:`sphx_glr_auto_data_analysis_estimate_dependency_and_copulas_plot_estimate_copula.py` (``examples/data_analysis/estimate_dependency_and_copulas/plot_estimate_copula.py``) - - 00:00.165 + * - :ref:`sphx_glr_auto_meta_modeling_general_purpose_metamodels_plot_expert_mixture.py` (``examples/meta_modeling/general_purpose_metamodels/plot_expert_mixture.py``) + - 00:00.166 - 0.0 * - :ref:`sphx_glr_auto_numerical_methods_optimization_plot_optimization_pagmo.py` (``examples/numerical_methods/optimization/plot_optimization_pagmo.py``) - - 00:00.165 + - 00:00.160 - 0.0 - * - :ref:`sphx_glr_auto_data_analysis_sample_analysis_plot_src_confidence.py` (``examples/data_analysis/sample_analysis/plot_src_confidence.py``) - - 00:00.162 + * - :ref:`sphx_glr_auto_data_analysis_manage_data_and_samples_plot_sample_pandas.py` (``examples/data_analysis/manage_data_and_samples/plot_sample_pandas.py``) + - 00:00.160 - 0.0 - * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_importance_sampling.py` (``examples/reliability_sensitivity/reliability/plot_estimate_probability_importance_sampling.py``) - - 00:00.162 + * - :ref:`sphx_glr_auto_data_analysis_graphics_plot_visualize_pairs.py` (``examples/data_analysis/graphics/plot_visualize_pairs.py``) + - 00:00.158 - 0.0 * - :ref:`sphx_glr_auto_numerical_methods_iterative_statistics_plot_iterative_extrema.py` (``examples/numerical_methods/iterative_statistics/plot_iterative_extrema.py``) - - 00:00.159 + - 00:00.155 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_mix_rv_process.py` (``examples/probabilistic_modeling/stochastic_processes/plot_mix_rv_process.py``) - - 00:00.159 + - 00:00.154 - 0.0 - * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_white_noise_process.py` (``examples/probabilistic_modeling/stochastic_processes/plot_white_noise_process.py``) - - 00:00.157 + * - :ref:`sphx_glr_auto_data_analysis_estimate_dependency_and_copulas_plot_estimate_copula.py` (``examples/data_analysis/estimate_dependency_and_copulas/plot_estimate_copula.py``) + - 00:00.153 - 0.0 - * - :ref:`sphx_glr_auto_functional_modeling_vectorial_functions_plot_symbolic_function.py` (``examples/functional_modeling/vectorial_functions/plot_symbolic_function.py``) - - 00:00.152 + * - :ref:`sphx_glr_auto_data_analysis_sample_analysis_plot_src_confidence.py` (``examples/data_analysis/sample_analysis/plot_src_confidence.py``) + - 00:00.150 - 0.0 - * - :ref:`sphx_glr_auto_data_analysis_manage_data_and_samples_plot_linear_regression.py` (``examples/data_analysis/manage_data_and_samples/plot_linear_regression.py``) + * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_generate_by_inversion.py` (``examples/probabilistic_modeling/distributions/plot_generate_by_inversion.py``) - 00:00.150 - 0.0 - * - :ref:`sphx_glr_auto_data_analysis_statistical_tests_plot_smirnov_test.py` (``examples/data_analysis/statistical_tests/plot_smirnov_test.py``) + * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_white_noise_process.py` (``examples/probabilistic_modeling/stochastic_processes/plot_white_noise_process.py``) - 00:00.148 - 0.0 - * - :ref:`sphx_glr_auto_meta_modeling_general_purpose_metamodels_plot_taylor_approximation.py` (``examples/meta_modeling/general_purpose_metamodels/plot_taylor_approximation.py``) - - 00:00.147 - - 0.0 - * - :ref:`sphx_glr_auto_numerical_methods_iterative_statistics_plot_iterative_moments.py` (``examples/numerical_methods/iterative_statistics/plot_iterative_moments.py``) - - 00:00.144 + * - :ref:`sphx_glr_auto_meta_modeling_kriging_metamodel_plot_kriging_beam_trend.py` (``examples/meta_modeling/kriging_metamodel/plot_kriging_beam_trend.py``) + - 00:00.148 - 0.0 - * - :ref:`sphx_glr_auto_data_analysis_statistical_tests_plot_qqplot_graph.py` (``examples/data_analysis/statistical_tests/plot_qqplot_graph.py``) - - 00:00.143 + * - :ref:`sphx_glr_auto_functional_modeling_vectorial_functions_plot_symbolic_function.py` (``examples/functional_modeling/vectorial_functions/plot_symbolic_function.py``) + - 00:00.146 - 0.0 - * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_python_distribution.py` (``examples/probabilistic_modeling/distributions/plot_python_distribution.py``) + * - :ref:`sphx_glr_auto_numerical_methods_iterative_statistics_plot_iterative_moments.py` (``examples/numerical_methods/iterative_statistics/plot_iterative_moments.py``) - 00:00.142 - 0.0 - * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_add_trend.py` (``examples/probabilistic_modeling/stochastic_processes/plot_add_trend.py``) - - 00:00.142 + * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_importance_sampling.py` (``examples/reliability_sensitivity/reliability/plot_estimate_probability_importance_sampling.py``) + - 00:00.139 + - 0.0 + * - :ref:`sphx_glr_auto_data_analysis_statistical_tests_plot_smirnov_test.py` (``examples/data_analysis/statistical_tests/plot_smirnov_test.py``) + - 00:00.137 - 0.0 * - :ref:`sphx_glr_auto_graphs_plot_graphs_fill_area.py` (``examples/graphs/plot_graphs_fill_area.py``) - - 00:00.140 + - 00:00.136 + - 0.0 + * - :ref:`sphx_glr_auto_data_analysis_manage_data_and_samples_plot_linear_regression.py` (``examples/data_analysis/manage_data_and_samples/plot_linear_regression.py``) + - 00:00.135 + - 0.0 + * - :ref:`sphx_glr_auto_meta_modeling_general_purpose_metamodels_plot_taylor_approximation.py` (``examples/meta_modeling/general_purpose_metamodels/plot_taylor_approximation.py``) + - 00:00.134 + - 0.0 + * - :ref:`sphx_glr_auto_data_analysis_statistical_tests_plot_qqplot_graph.py` (``examples/data_analysis/statistical_tests/plot_qqplot_graph.py``) + - 00:00.133 + - 0.0 + * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_python_distribution.py` (``examples/probabilistic_modeling/distributions/plot_python_distribution.py``) + - 00:00.132 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_probability_simulation_results.py` (``examples/reliability_sensitivity/reliability/plot_probability_simulation_results.py``) - - 00:00.139 + - 00:00.129 - 0.0 - * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_export_field_vtk.py` (``examples/probabilistic_modeling/stochastic_processes/plot_export_field_vtk.py``) - - 00:00.137 + * - :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_estimate_integral_iterated_quadrature.py` (``examples/numerical_methods/general_methods/plot_estimate_integral_iterated_quadrature.py``) + - 00:00.126 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_distribution_fitting_plot_quantilematching_estimator.py` (``examples/data_analysis/distribution_fitting/plot_quantilematching_estimator.py``) - - 00:00.135 + - 00:00.126 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_statistical_tests_plot_test_normality.py` (``examples/data_analysis/statistical_tests/plot_test_normality.py``) - - 00:00.131 + - 00:00.126 - 0.0 - * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_create_normal_process.py` (``examples/probabilistic_modeling/stochastic_processes/plot_create_normal_process.py``) - - 00:00.130 + * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_export_field_vtk.py` (``examples/probabilistic_modeling/stochastic_processes/plot_export_field_vtk.py``) + - 00:00.125 - 0.0 - * - :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_estimate_integral_iterated_quadrature.py` (``examples/numerical_methods/general_methods/plot_estimate_integral_iterated_quadrature.py``) - - 00:00.128 + * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_add_trend.py` (``examples/probabilistic_modeling/stochastic_processes/plot_add_trend.py``) + - 00:00.124 + - 0.0 + * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_create_normal_process.py` (``examples/probabilistic_modeling/stochastic_processes/plot_create_normal_process.py``) + - 00:00.123 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_central_dispersion_plot_central_tendency.py` (``examples/reliability_sensitivity/central_dispersion/plot_central_tendency.py``) - - 00:00.125 + - 00:00.121 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_trend_transform.py` (``examples/probabilistic_modeling/stochastic_processes/plot_trend_transform.py``) - - 00:00.123 + - 00:00.119 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_chaos_draw_validation.py` (``examples/meta_modeling/polynomial_chaos_metamodel/plot_chaos_draw_validation.py``) - - 00:00.120 - - 0.0 - * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_flood_model.py` (``examples/reliability_sensitivity/reliability/plot_flood_model.py``) - 00:00.118 - 0.0 - * - :ref:`sphx_glr_auto_data_analysis_sample_analysis_plot_visualize_empirical_cdf.py` (``examples/data_analysis/sample_analysis/plot_visualize_empirical_cdf.py``) - - 00:00.118 + * - :ref:`sphx_glr_auto_numerical_methods_optimization_plot_optimization_bonmin.py` (``examples/numerical_methods/optimization/plot_optimization_bonmin.py``) + - 00:00.115 - 0.0 - * - :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_design_of_experiment_continuous_discrete.py` (``examples/reliability_sensitivity/design_of_experiments/plot_design_of_experiment_continuous_discrete.py``) - - 00:00.118 + * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_flood_model.py` (``examples/reliability_sensitivity/reliability/plot_flood_model.py``) + - 00:00.111 - 0.0 - * - :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_ancova.py` (``examples/reliability_sensitivity/sensitivity_analysis/plot_sensitivity_ancova.py``) - - 00:00.117 + * - :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_design_of_experiment_continuous_discrete.py` (``examples/reliability_sensitivity/design_of_experiments/plot_design_of_experiment_continuous_discrete.py``) + - 00:00.111 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_create_random_doe.py` (``examples/reliability_sensitivity/design_of_experiments/plot_create_random_doe.py``) - - 00:00.117 + - 00:00.111 - 0.0 - * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_aggregated_process.py` (``examples/probabilistic_modeling/stochastic_processes/plot_aggregated_process.py``) - - 00:00.115 + * - :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_ancova.py` (``examples/reliability_sensitivity/sensitivity_analysis/plot_sensitivity_ancova.py``) + - 00:00.110 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_timeseries_manipulation.py` (``examples/probabilistic_modeling/stochastic_processes/plot_timeseries_manipulation.py``) - - 00:00.115 + - 00:00.108 + - 0.0 + * - :ref:`sphx_glr_auto_data_analysis_sample_analysis_plot_visualize_empirical_cdf.py` (``examples/data_analysis/sample_analysis/plot_visualize_empirical_cdf.py``) + - 00:00.108 + - 0.0 + * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_aggregated_process.py` (``examples/probabilistic_modeling/stochastic_processes/plot_aggregated_process.py``) + - 00:00.105 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_sobol_multivariate.py` (``examples/reliability_sensitivity/sensitivity_analysis/plot_sensitivity_sobol_multivariate.py``) - - 00:00.106 + - 00:00.098 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_sample_analysis_plot_compare_unconditional_conditional_histograms.py` (``examples/data_analysis/sample_analysis/plot_compare_unconditional_conditional_histograms.py``) - - 00:00.102 + - 00:00.096 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_manage_data_and_samples_plot_quantile_estimation_wilks.py` (``examples/data_analysis/manage_data_and_samples/plot_quantile_estimation_wilks.py``) - - 00:00.101 + - 00:00.093 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_conditional_distribution.py` (``examples/probabilistic_modeling/distributions/plot_conditional_distribution.py``) - - 00:00.095 - - 0.0 - * - :ref:`sphx_glr_auto_data_analysis_statistical_tests_plot_kolmogorov_pvalue.py` (``examples/data_analysis/statistical_tests/plot_kolmogorov_pvalue.py``) - 00:00.092 - 0.0 - * - :ref:`sphx_glr_auto_numerical_methods_optimization_plot_optimization_bonmin.py` (``examples/numerical_methods/optimization/plot_optimization_bonmin.py``) - - 00:00.092 + * - :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_regression_interval.py` (``examples/numerical_methods/general_methods/plot_regression_interval.py``) + - 00:00.090 - 0.0 - * - :ref:`sphx_glr_auto_meta_modeling_general_purpose_metamodels_plot_general_linear_model.py` (``examples/meta_modeling/general_purpose_metamodels/plot_general_linear_model.py``) - - 00:00.091 + * - :ref:`sphx_glr_auto_data_analysis_statistical_tests_plot_kolmogorov_pvalue.py` (``examples/data_analysis/statistical_tests/plot_kolmogorov_pvalue.py``) + - 00:00.088 - 0.0 - * - :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_regression_interval.py` (``examples/numerical_methods/general_methods/plot_regression_interval.py``) - - 00:00.089 + * - :ref:`sphx_glr_auto_meta_modeling_general_purpose_metamodels_plot_general_linear_model.py` (``examples/meta_modeling/general_purpose_metamodels/plot_general_linear_model.py``) + - 00:00.086 - 0.0 * - :ref:`sphx_glr_auto_calibration_least_squares_and_gaussian_calibration_plot_calibration_withoutobservedinputs.py` (``examples/calibration/least_squares_and_gaussian_calibration/plot_calibration_withoutobservedinputs.py``) - - 00:00.089 + - 00:00.084 - 0.0 * - :ref:`sphx_glr_auto_functional_modeling_field_functions_plot_viscous_fall_field_function.py` (``examples/functional_modeling/field_functions/plot_viscous_fall_field_function.py``) - - 00:00.087 + - 00:00.082 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_kriging_metamodel_plot_kriging_likelihood.py` (``examples/meta_modeling/kriging_metamodel/plot_kriging_likelihood.py``) - - 00:00.082 + - 00:00.074 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_fast.py` (``examples/reliability_sensitivity/sensitivity_analysis/plot_sensitivity_fast.py``) - - 00:00.079 - - 0.0 - * - :ref:`sphx_glr_auto_calibration_least_squares_and_gaussian_calibration_plot_generate_chaboche.py` (``examples/calibration/least_squares_and_gaussian_calibration/plot_generate_chaboche.py``) - - 00:00.076 - - 0.0 - * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_create_threshold_event.py` (``examples/reliability_sensitivity/reliability/plot_create_threshold_event.py``) - 00:00.074 - 0.0 * - :ref:`sphx_glr_auto_functional_modeling_field_functions_plot_viscous_fall_field_function_connection.py` (``examples/functional_modeling/field_functions/plot_viscous_fall_field_function_connection.py``) - - 00:00.074 + - 00:00.071 - 0.0 - * - :ref:`sphx_glr_auto_meta_modeling_kriging_metamodel_plot_kriging.py` (``examples/meta_modeling/kriging_metamodel/plot_kriging.py``) - - 00:00.073 - - 0.0 - * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_functional_basis_process.py` (``examples/probabilistic_modeling/stochastic_processes/plot_functional_basis_process.py``) - - 00:00.073 + * - :ref:`sphx_glr_auto_calibration_least_squares_and_gaussian_calibration_plot_generate_chaboche.py` (``examples/calibration/least_squares_and_gaussian_calibration/plot_generate_chaboche.py``) + - 00:00.071 - 0.0 - * - :ref:`sphx_glr_auto_calibration_least_squares_and_gaussian_calibration_plot_generate_flooding.py` (``examples/calibration/least_squares_and_gaussian_calibration/plot_generate_flooding.py``) - - 00:00.072 + * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_create_threshold_event.py` (``examples/reliability_sensitivity/reliability/plot_create_threshold_event.py``) + - 00:00.070 - 0.0 * - :ref:`sphx_glr_auto_numerical_methods_optimization_plot_optimization_constraints.py` (``examples/numerical_methods/optimization/plot_optimization_constraints.py``) - - 00:00.069 + - 00:00.068 - 0.0 - * - :ref:`sphx_glr_auto_functional_modeling_vectorial_functions_plot_quadratic_function.py` (``examples/functional_modeling/vectorial_functions/plot_quadratic_function.py``) + * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_functional_basis_process.py` (``examples/probabilistic_modeling/stochastic_processes/plot_functional_basis_process.py``) - 00:00.068 - 0.0 - * - :ref:`sphx_glr_auto_numerical_methods_optimization_plot_optimization_nlopt.py` (``examples/numerical_methods/optimization/plot_optimization_nlopt.py``) + * - :ref:`sphx_glr_auto_calibration_least_squares_and_gaussian_calibration_plot_generate_flooding.py` (``examples/calibration/least_squares_and_gaussian_calibration/plot_generate_flooding.py``) - 00:00.068 - 0.0 - * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_user_stationary_covmodel.py` (``examples/probabilistic_modeling/stochastic_processes/plot_user_stationary_covmodel.py``) + * - :ref:`sphx_glr_auto_meta_modeling_kriging_metamodel_plot_kriging.py` (``examples/meta_modeling/kriging_metamodel/plot_kriging.py``) - 00:00.067 - 0.0 - * - :ref:`sphx_glr_auto_data_analysis_statistical_tests_plot_kolmogorov_statistics.py` (``examples/data_analysis/statistical_tests/plot_kolmogorov_statistics.py``) + * - :ref:`sphx_glr_auto_numerical_methods_optimization_plot_optimization_nlopt.py` (``examples/numerical_methods/optimization/plot_optimization_nlopt.py``) - 00:00.067 - 0.0 - * - :ref:`sphx_glr_auto_meta_modeling_general_purpose_metamodels_plot_create_linear_least_squares_model.py` (``examples/meta_modeling/general_purpose_metamodels/plot_create_linear_least_squares_model.py``) - - 00:00.067 + * - :ref:`sphx_glr_auto_data_analysis_statistical_tests_plot_kolmogorov_statistics.py` (``examples/data_analysis/statistical_tests/plot_kolmogorov_statistics.py``) + - 00:00.065 - 0.0 - * - :ref:`sphx_glr_auto_data_analysis_sample_analysis_plot_visualize_histogram.py` (``examples/data_analysis/sample_analysis/plot_visualize_histogram.py``) + * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_user_stationary_covmodel.py` (``examples/probabilistic_modeling/stochastic_processes/plot_user_stationary_covmodel.py``) - 00:00.064 - 0.0 - * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_create_your_own_dist.py` (``examples/probabilistic_modeling/distributions/plot_create_your_own_dist.py``) - - 00:00.063 + * - :ref:`sphx_glr_auto_meta_modeling_general_purpose_metamodels_plot_create_linear_least_squares_model.py` (``examples/meta_modeling/general_purpose_metamodels/plot_create_linear_least_squares_model.py``) + - 00:00.064 - 0.0 - * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_userdefined_spectral_model.py` (``examples/probabilistic_modeling/stochastic_processes/plot_userdefined_spectral_model.py``) - - 00:00.061 + * - :ref:`sphx_glr_auto_functional_modeling_vectorial_functions_plot_quadratic_function.py` (``examples/functional_modeling/vectorial_functions/plot_quadratic_function.py``) + - 00:00.062 - 0.0 - * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_maximum_distribution.py` (``examples/probabilistic_modeling/distributions/plot_maximum_distribution.py``) + * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_create_your_own_dist.py` (``examples/probabilistic_modeling/distributions/plot_create_your_own_dist.py``) - 00:00.060 - 0.0 - * - :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_probabilistic_design.py` (``examples/reliability_sensitivity/design_of_experiments/plot_probabilistic_design.py``) + * - :ref:`sphx_glr_auto_data_analysis_sample_analysis_plot_visualize_histogram.py` (``examples/data_analysis/sample_analysis/plot_visualize_histogram.py``) + - 00:00.059 + - 0.0 + * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_userdefined_spectral_model.py` (``examples/probabilistic_modeling/stochastic_processes/plot_userdefined_spectral_model.py``) - 00:00.058 - 0.0 + * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_maximum_distribution.py` (``examples/probabilistic_modeling/distributions/plot_maximum_distribution.py``) + - 00:00.056 + - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_gauss_product_experiment.py` (``examples/reliability_sensitivity/design_of_experiments/plot_gauss_product_experiment.py``) - - 00:00.058 + - 00:00.055 + - 0.0 + * - :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_probabilistic_design.py` (``examples/reliability_sensitivity/design_of_experiments/plot_probabilistic_design.py``) + - 00:00.053 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_composite_experiment.py` (``examples/reliability_sensitivity/design_of_experiments/plot_composite_experiment.py``) - - 00:00.055 + - 00:00.052 + - 0.0 + * - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_functional_chaos_database.py` (``examples/meta_modeling/polynomial_chaos_metamodel/plot_functional_chaos_database.py``) + - 00:00.051 - 0.0 * - :ref:`sphx_glr_auto_functional_modeling_vectorial_functions_plot_quick_start_functions.py` (``examples/functional_modeling/vectorial_functions/plot_quick_start_functions.py``) - - 00:00.052 + - 00:00.048 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_monte_carlo_experiment.py` (``examples/reliability_sensitivity/design_of_experiments/plot_monte_carlo_experiment.py``) - - 00:00.049 + - 00:00.047 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_central_dispersion_plot_estimate_moments_taylor.py` (``examples/reliability_sensitivity/central_dispersion/plot_estimate_moments_taylor.py``) - - 00:00.048 + - 00:00.046 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_monte_carlo.py` (``examples/reliability_sensitivity/reliability/plot_estimate_probability_monte_carlo.py``) - 00:00.033 @@ -681,48 +684,45 @@ Computation times - 00:00.032 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_statistical_tests_plot_kolmogorov_test.py` (``examples/data_analysis/statistical_tests/plot_kolmogorov_test.py``) - - 00:00.031 + - 00:00.030 - 0.0 * - :ref:`sphx_glr_auto_functional_modeling_link_to_an_external_code_plot_link_computer_code_coupling_tools.py` (``examples/functional_modeling/link_to_an_external_code/plot_link_computer_code_coupling_tools.py``) - - 00:00.024 - - 0.0 - * - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_chaos_ishigami_grouped_indices.py` (``examples/meta_modeling/polynomial_chaos_metamodel/plot_chaos_ishigami_grouped_indices.py``) - - 00:00.024 + - 00:00.023 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_functional_chaos_exploitation.py` (``examples/meta_modeling/polynomial_chaos_metamodel/plot_functional_chaos_exploitation.py``) - - 00:00.024 + - 00:00.023 - 0.0 - * - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_functional_chaos_database.py` (``examples/meta_modeling/polynomial_chaos_metamodel/plot_functional_chaos_database.py``) - - 00:00.020 + * - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_chaos_ishigami_grouped_indices.py` (``examples/meta_modeling/polynomial_chaos_metamodel/plot_chaos_ishigami_grouped_indices.py``) + - 00:00.019 - 0.0 * - :ref:`sphx_glr_auto_numerical_methods_optimization_plot_control_termination.py` (``examples/numerical_methods/optimization/plot_control_termination.py``) - 00:00.015 - 0.0 - * - :ref:`sphx_glr_auto_data_analysis_manage_data_and_samples_plot_quick_start_point_and_sample.py` (``examples/data_analysis/manage_data_and_samples/plot_quick_start_point_and_sample.py``) - - 00:00.011 - - 0.0 - * - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_functional_chaos_advanced_ctors.py` (``examples/meta_modeling/polynomial_chaos_metamodel/plot_functional_chaos_advanced_ctors.py``) - - 00:00.011 - - 0.0 * - :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_study_save_load.py` (``examples/numerical_methods/general_methods/plot_study_save_load.py``) - 00:00.010 - 0.0 - * - :ref:`sphx_glr_auto_meta_modeling_kriging_metamodel_plot_kriging_beam_arbitrary_trend.py` (``examples/meta_modeling/kriging_metamodel/plot_kriging_beam_arbitrary_trend.py``) + * - :ref:`sphx_glr_auto_data_analysis_manage_data_and_samples_plot_quick_start_point_and_sample.py` (``examples/data_analysis/manage_data_and_samples/plot_quick_start_point_and_sample.py``) - 00:00.009 - 0.0 + * - :ref:`sphx_glr_auto_meta_modeling_kriging_metamodel_plot_kriging_beam_arbitrary_trend.py` (``examples/meta_modeling/kriging_metamodel/plot_kriging_beam_arbitrary_trend.py``) + - 00:00.008 + - 0.0 + * - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_functional_chaos_advanced_ctors.py` (``examples/meta_modeling/polynomial_chaos_metamodel/plot_functional_chaos_advanced_ctors.py``) + - 00:00.006 + - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_strong_maximum_test.py` (``examples/reliability_sensitivity/reliability/plot_strong_maximum_test.py``) - 00:00.005 - 0.0 - * - :ref:`sphx_glr_auto_data_analysis_manage_data_and_samples_plot_estimate_moments.py` (``examples/data_analysis/manage_data_and_samples/plot_estimate_moments.py``) + * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_post_analytical_importance_sampling.py` (``examples/reliability_sensitivity/reliability/plot_post_analytical_importance_sampling.py``) - 00:00.005 - 0.0 - * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_post_analytical_importance_sampling.py` (``examples/reliability_sensitivity/reliability/plot_post_analytical_importance_sampling.py``) + * - :ref:`sphx_glr_auto_data_analysis_statistical_tests_plot_test_independence.py` (``examples/data_analysis/statistical_tests/plot_test_independence.py``) - 00:00.005 - 0.0 - * - :ref:`sphx_glr_auto_data_analysis_manage_data_and_samples_plot_sample_manipulation.py` (``examples/data_analysis/manage_data_and_samples/plot_sample_manipulation.py``) + * - :ref:`sphx_glr_auto_data_analysis_manage_data_and_samples_plot_estimate_moments.py` (``examples/data_analysis/manage_data_and_samples/plot_estimate_moments.py``) - 00:00.005 - 0.0 - * - :ref:`sphx_glr_auto_data_analysis_statistical_tests_plot_test_independence.py` (``examples/data_analysis/statistical_tests/plot_test_independence.py``) + * - :ref:`sphx_glr_auto_data_analysis_manage_data_and_samples_plot_sample_manipulation.py` (``examples/data_analysis/manage_data_and_samples/plot_sample_manipulation.py``) - 00:00.005 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_distribution_fitting_plot_maximumlikelihood_estimator.py` (``examples/data_analysis/distribution_fitting/plot_maximumlikelihood_estimator.py``) @@ -734,85 +734,85 @@ Computation times * - :ref:`sphx_glr_auto_numerical_methods_optimization_plot_minmax_optimization.py` (``examples/numerical_methods/optimization/plot_minmax_optimization.py``) - 00:00.004 - 0.0 - * - :ref:`sphx_glr_auto_functional_modeling_vectorial_functions_plot_python_function.py` (``examples/functional_modeling/vectorial_functions/plot_python_function.py``) - - 00:00.004 - - 0.0 * - :ref:`sphx_glr_auto_functional_modeling_vectorial_functions_plot_functions_inputDim.py` (``examples/functional_modeling/vectorial_functions/plot_functions_inputDim.py``) - 00:00.003 - 0.0 * - :ref:`sphx_glr_auto_functional_modeling_vectorial_functions_plot_createMultivariateFunction.py` (``examples/functional_modeling/vectorial_functions/plot_createMultivariateFunction.py``) - 00:00.003 - 0.0 - * - :ref:`sphx_glr_auto_numerical_methods_optimization_plot_minmax_by_random_design.py` (``examples/numerical_methods/optimization/plot_minmax_by_random_design.py``) + * - :ref:`sphx_glr_auto_functional_modeling_vectorial_functions_plot_python_function.py` (``examples/functional_modeling/vectorial_functions/plot_python_function.py``) - 00:00.003 - 0.0 - * - :ref:`sphx_glr_auto_data_analysis_manage_data_and_samples_plot_import_export_sample_csv.py` (``examples/data_analysis/manage_data_and_samples/plot_import_export_sample_csv.py``) + * - :ref:`sphx_glr_auto_numerical_methods_optimization_plot_minmax_by_random_design.py` (``examples/numerical_methods/optimization/plot_minmax_by_random_design.py``) - 00:00.003 - 0.0 * - :ref:`sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_chaos_distribution_transformation.py` (``examples/meta_modeling/polynomial_chaos_metamodel/plot_chaos_distribution_transformation.py``) - - 00:00.003 - - 0.0 - * - :ref:`sphx_glr_auto_functional_modeling_vectorial_functions_plot_functions_outputDim.py` (``examples/functional_modeling/vectorial_functions/plot_functions_outputDim.py``) - 00:00.002 - 0.0 * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_event_manipulation.py` (``examples/reliability_sensitivity/reliability/plot_event_manipulation.py``) - 00:00.002 - 0.0 - * - :ref:`sphx_glr_auto_data_analysis_manage_data_and_samples_plot_randomize_sample_lines.py` (``examples/data_analysis/manage_data_and_samples/plot_randomize_sample_lines.py``) + * - :ref:`sphx_glr_auto_functional_modeling_vectorial_functions_plot_parametric_function.py` (``examples/functional_modeling/vectorial_functions/plot_parametric_function.py``) - 00:00.002 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_random_vectors_plot_random_vector_manipulation.py` (``examples/probabilistic_modeling/random_vectors/plot_random_vector_manipulation.py``) - 00:00.002 - 0.0 - * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_conditional_random_vector.py` (``examples/probabilistic_modeling/distributions/plot_conditional_random_vector.py``) - - 00:00.002 - - 0.0 * - :ref:`sphx_glr_auto_functional_modeling_field_functions_plot_vertexvalue_function.py` (``examples/functional_modeling/field_functions/plot_vertexvalue_function.py``) - 00:00.002 - 0.0 - * - :ref:`sphx_glr_auto_functional_modeling_functional_basis_plot_multidimensional_basis.py` (``examples/functional_modeling/functional_basis/plot_multidimensional_basis.py``) + * - :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_random_generator.py` (``examples/numerical_methods/general_methods/plot_random_generator.py``) - 00:00.002 - 0.0 * - :ref:`sphx_glr_auto_functional_modeling_vectorial_functions_plot_aggregated_function.py` (``examples/functional_modeling/vectorial_functions/plot_aggregated_function.py``) - 00:00.002 - 0.0 - * - :ref:`sphx_glr_auto_probabilistic_modeling_random_vectors_plot_python_randomvector.py` (``examples/probabilistic_modeling/random_vectors/plot_python_randomvector.py``) + * - :ref:`sphx_glr_auto_functional_modeling_functional_basis_plot_multidimensional_basis.py` (``examples/functional_modeling/functional_basis/plot_multidimensional_basis.py``) + - 00:00.002 + - 0.0 + * - :ref:`sphx_glr_auto_functional_modeling_vectorial_functions_plot_linear_combination_function.py` (``examples/functional_modeling/vectorial_functions/plot_linear_combination_function.py``) - 00:00.002 - 0.0 * - :ref:`sphx_glr_auto_functional_modeling_field_functions_plot_value_function.py` (``examples/functional_modeling/field_functions/plot_value_function.py``) - 00:00.002 - 0.0 - * - :ref:`sphx_glr_auto_functional_modeling_vectorial_functions_plot_linear_combination_function.py` (``examples/functional_modeling/vectorial_functions/plot_linear_combination_function.py``) + * - :ref:`sphx_glr_auto_data_analysis_manage_data_and_samples_plot_import_export_sample_csv.py` (``examples/data_analysis/manage_data_and_samples/plot_import_export_sample_csv.py``) - 00:00.002 - 0.0 - * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_processes_plot_event_process.py` (``examples/reliability_sensitivity/reliability_processes/plot_event_process.py``) + * - :ref:`sphx_glr_auto_probabilistic_modeling_random_vectors_plot_python_randomvector.py` (``examples/probabilistic_modeling/random_vectors/plot_python_randomvector.py``) + - 00:00.002 + - 0.0 + * - :ref:`sphx_glr_auto_data_analysis_manage_data_and_samples_plot_randomize_sample_lines.py` (``examples/data_analysis/manage_data_and_samples/plot_randomize_sample_lines.py``) - 00:00.002 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_random_vectors_plot_composite_random_vector.py` (``examples/probabilistic_modeling/random_vectors/plot_composite_random_vector.py``) - 00:00.002 - 0.0 - * - :ref:`sphx_glr_auto_functional_modeling_vectorial_functions_plot_composed_function.py` (``examples/functional_modeling/vectorial_functions/plot_composed_function.py``) + * - :ref:`sphx_glr_auto_functional_modeling_vectorial_functions_plot_functions_outputDim.py` (``examples/functional_modeling/vectorial_functions/plot_functions_outputDim.py``) - 00:00.002 - 0.0 - * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_create_stationary_covmodel.py` (``examples/probabilistic_modeling/stochastic_processes/plot_create_stationary_covmodel.py``) + * - :ref:`sphx_glr_auto_functional_modeling_vectorial_functions_plot_composed_function.py` (``examples/functional_modeling/vectorial_functions/plot_composed_function.py``) - 00:00.002 - 0.0 - * - :ref:`sphx_glr_auto_probabilistic_modeling_copulas_plot_extract_copula.py` (``examples/probabilistic_modeling/copulas/plot_extract_copula.py``) + * - :ref:`sphx_glr_auto_reliability_sensitivity_reliability_processes_plot_event_process.py` (``examples/reliability_sensitivity/reliability_processes/plot_event_process.py``) - 00:00.002 - 0.0 - * - :ref:`sphx_glr_auto_functional_modeling_vectorial_functions_plot_parametric_function.py` (``examples/functional_modeling/vectorial_functions/plot_parametric_function.py``) + * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_create_stationary_covmodel.py` (``examples/probabilistic_modeling/stochastic_processes/plot_create_stationary_covmodel.py``) - 00:00.001 - 0.0 - * - :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_random_generator.py` (``examples/numerical_methods/general_methods/plot_random_generator.py``) + * - :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_conditional_random_vector.py` (``examples/probabilistic_modeling/distributions/plot_conditional_random_vector.py``) - 00:00.001 - 0.0 * - :ref:`sphx_glr_auto_data_analysis_statistical_tests_plot_chi2_fitting_test.py` (``examples/data_analysis/statistical_tests/plot_chi2_fitting_test.py``) - 00:00.001 - 0.0 + * - :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_combinatorial_generator.py` (``examples/numerical_methods/general_methods/plot_combinatorial_generator.py``) + - 00:00.001 + - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_parametric_spectral_density.py` (``examples/probabilistic_modeling/stochastic_processes/plot_parametric_spectral_density.py``) - 00:00.001 - 0.0 - * - :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_combinatorial_generator.py` (``examples/numerical_methods/general_methods/plot_combinatorial_generator.py``) + * - :ref:`sphx_glr_auto_probabilistic_modeling_copulas_plot_extract_copula.py` (``examples/probabilistic_modeling/copulas/plot_extract_copula.py``) - 00:00.001 - 0.0 * - :ref:`sphx_glr_auto_probabilistic_modeling_copulas_plot_composed_copula.py` (``examples/probabilistic_modeling/copulas/plot_composed_copula.py``) diff --git a/openturns/master/auto_calibration/bayesian_calibration/plot_bayesian_calibration.html b/openturns/master/auto_calibration/bayesian_calibration/plot_bayesian_calibration.html index b5173977bcc..323f3d14bad 100644 --- a/openturns/master/auto_calibration/bayesian_calibration/plot_bayesian_calibration.html +++ b/openturns/master/auto_calibration/bayesian_calibration/plot_bayesian_calibration.html @@ -139,7 +139,9 @@

Quick search

conditional on model prediction \vect z, and \vect\theta \in \mathbb{R}^p the calibration parameters we wish to estimate.

The posterior distribution is given by Bayes theorem:

-

where \propto means “proportional to”, regarded as a function of \vect\theta.

+
+

\pi(\vect\theta | \vect y) \quad \propto \quad L\left(\vect y | \vect\theta\right) \times \pi(\vect\theta)

+

where \propto means “proportional to”, regarded as a function of \vect\theta.

The posterior distribution is approximated here by the empirical distribution of the sample \vect\theta^1, \ldots, \vect\theta^N generated by the Metropolis-Hastings algorithm. This means that any quantity characteristic of the posterior distribution @@ -176,7 +178,7 @@

Quick search

The following objects need to be defined in order to perform Bayesian calibration:

  • The conditional density p(y|\vect z) must be defined as a probability distribution.

    • -

  • The computer model must be implemented thanks to the ParametricFunction class. +

  • The computer model must be implemented thanks to the ParametricFunction class. This takes a value of \vect\theta as input, and outputs the vector of model predictions \vect z, as defined above (the vector of covariates \vect x = (x_1, \ldots, x_n) is treated as a known constant). When doing that, we have to keep in mind that \vect z will be used as the vector of parameters corresponding @@ -189,6 +191,10 @@

    Quick search

  • Metropolis-Hastings algorithm(s), possibly used in tandem with a Gibbs algorithm in order to sample from the posterior distribution of the calibration parameters.

+

This example uses the ParametricFunction class. +Please read its documentation and +Create a parametric function +for a detailed example.

import openturns as ot
 import openturns.viewer as viewer
 from matplotlib import pylab as plt
diff --git a/openturns/master/auto_calibration/bayesian_calibration/plot_gibbs.html b/openturns/master/auto_calibration/bayesian_calibration/plot_gibbs.html
index b8d29798d28..0892eb51510 100644
--- a/openturns/master/auto_calibration/bayesian_calibration/plot_gibbs.html
+++ b/openturns/master/auto_calibration/bayesian_calibration/plot_gibbs.html
@@ -245,7 +245,7 @@ 
Quick search

 View.ShowAll()
-Posterior density

Total running time of the script: (0 minutes 12.667 seconds)

+Posterior density

Total running time of the script: (0 minutes 12.653 seconds)

-Bayesian inference (with log-pdf)

Total running time of the script: (0 minutes 5.668 seconds)

+Bayesian inference (with log-pdf)

Total running time of the script: (0 minutes 5.764 seconds)