CircleCI build openturns 16553

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)
@@ -361,25 +371,31 @@ 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
 X_train = myDistribution.getSample(sampleSize_train)
 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)

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"
       ]
     }
   ],