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FTmTM(wtN5p delta 650 zcmZqkI_%Bbz&dq@>PFULCJsX@BLh7XBZJ8eOyL?Zj+WMx4EES583sL^1~9QHty3DO z)K1aJP{?qeJb_+ir#KhI2q+(}!@$bGSkKVVeDiO1 zWlqM($?}3ymiVl~>z2tuf*OowATuOznK5~;pcbS4?z?+;Zd`}7%XfWlV7=r}k=2($bMn-dxheSXgLJ!Qz&qZY!RYB6sKIcxK`Oa{N#S!{PvDAvf54lV^!P69vWuOqA0A9ye1ZyqWlnVG=Ax21dr4 J-$_Yu0RWd@-dX?v diff --git a/_downloads/349e24ddf4c2a9f9f1903b6c1d4ed115/plot_post_stack_inversion.py b/_downloads/1001629eacd23bb9b9df42b1d6da8075/poststack.py similarity index 86% rename from _downloads/349e24ddf4c2a9f9f1903b6c1d4ed115/plot_post_stack_inversion.py rename to _downloads/1001629eacd23bb9b9df42b1d6da8075/poststack.py index b350147e..7ba87b74 100644 --- a/_downloads/349e24ddf4c2a9f9f1903b6c1d4ed115/plot_post_stack_inversion.py +++ b/_downloads/1001629eacd23bb9b9df42b1d6da8075/poststack.py @@ -187,7 +187,19 @@ sampling=(1, 1, 1), dtype=BDiag.dtype) NormEqOp = BDiag.H @ BDiag + epsR * LapOp.H @ LapOp dnorm_dist = BDiag.H @ d_dist -minv3d_reg_dist = pylops_mpi.optimization.basic.cg(NormEqOp, dnorm_dist, x0=mback3d_dist, niter=100, show=True)[0] +minv3d_ne_dist = pylops_mpi.optimization.basic.cg(NormEqOp, dnorm_dist, x0=mback3d_dist, niter=100, show=True)[0] +minv3d_ne = minv3d_ne_dist.asarray().reshape((ny, nx, nz)) + +############################################################################### + +# Regularized inversion with regularized equations +StackOp = pylops_mpi.MPIStackedVStack([BDiag, np.sqrt(epsR) * LapOp]) +d0_dist = pylops_mpi.DistributedArray(global_shape=ny * nx * nz) +d0_dist[:] = 0. +dstack_dist = pylops_mpi.StackedDistributedArray([d_dist, d0_dist]) + +dnorm_dist = BDiag.H @ d_dist +minv3d_reg_dist = pylops_mpi.optimization.basic.cgls(StackOp, dstack_dist, x0=mback3d_dist, niter=100, show=False)[0] minv3d_reg = minv3d_reg_dist.asarray().reshape((ny, nx, nz)) ############################################################################### @@ -205,7 +217,7 @@ print('Smooth Distr == Local', np.allclose(d_0, d0_0)) # Visualize - fig, axs = plt.subplots(nrows=5, ncols=3, figsize=(9, 14), constrained_layout=True) + fig, axs = plt.subplots(nrows=6, ncols=3, figsize=(9, 14), constrained_layout=True) axs[0][0].imshow(m3d[5, :, :].T, cmap="gist_rainbow", vmin=m.min(), vmax=m.max()) axs[0][0].set_title("Model x-z") axs[0][0].axis("tight") @@ -246,12 +258,22 @@ axs[3][2].set_title('Inverted Model iter x-y') axs[3][2].axis('tight') - axs[4][0].imshow(minv3d_reg[5, :, :].T, cmap="gist_rainbow", vmin=m.min(), vmax=m.max()) - axs[4][0].set_title("Regularized Inverted Model iter x-z") + axs[4][0].imshow(minv3d_ne[5, :, :].T, cmap="gist_rainbow", vmin=m.min(), vmax=m.max()) + axs[4][0].set_title("Normal Equations Inverted Model iter x-z") axs[4][0].axis("tight") - axs[4][1].imshow(minv3d_reg[:, 200, :].T, cmap='gist_rainbow', vmin=m.min(), vmax=m.max()) - axs[4][1].set_title('Regularized Inverted Model iter y-z') + axs[4][1].imshow(minv3d_ne[:, 200, :].T, cmap='gist_rainbow', vmin=m.min(), vmax=m.max()) + axs[4][1].set_title('Normal Equations Inverted Model iter y-z') axs[4][1].axis('tight') - axs[4][2].imshow(minv3d_reg[:, :, 220].T, cmap='gist_rainbow', vmin=m.min(), vmax=m.max()) - axs[4][2].set_title('Regularized Inverted Model iter x-y') + axs[4][2].imshow(minv3d_ne[:, :, 220].T, cmap='gist_rainbow', vmin=m.min(), vmax=m.max()) + axs[4][2].set_title('Normal Equations Inverted Model iter x-y') axs[4][2].axis('tight') + + axs[5][0].imshow(minv3d_reg[5, :, :].T, cmap="gist_rainbow", vmin=m.min(), vmax=m.max()) + axs[5][0].set_title("Regularized Inverted Model iter x-z") + axs[5][0].axis("tight") + axs[5][1].imshow(minv3d_reg[:, 200, :].T, cmap='gist_rainbow', vmin=m.min(), vmax=m.max()) + axs[5][1].set_title('Regularized Inverted Model iter y-z') + axs[5][1].axis('tight') + axs[5][2].imshow(minv3d_reg[:, :, 220].T, cmap='gist_rainbow', vmin=m.min(), vmax=m.max()) + axs[5][2].set_title('Regularized Inverted Model iter x-y') + axs[5][2].axis('tight') diff --git a/_downloads/b1d8138fba244a3a8c36115409e884d3/plot_post_stack_inversion.ipynb b/_downloads/25d0d43c288bbcf46dfd5c529fe808c5/poststack.ipynb similarity index 84% rename from _downloads/b1d8138fba244a3a8c36115409e884d3/plot_post_stack_inversion.ipynb rename to _downloads/25d0d43c288bbcf46dfd5c529fe808c5/poststack.ipynb index cfb31501..3ad893a2 100644 --- a/_downloads/b1d8138fba244a3a8c36115409e884d3/plot_post_stack_inversion.ipynb +++ b/_downloads/25d0d43c288bbcf46dfd5c529fe808c5/poststack.ipynb @@ -80,7 +80,18 @@ }, "outputs": [], "source": [ - "# Regularized inversion with normal equations\nepsR = 1e2\nLapOp = pylops_mpi.MPILaplacian(dims=(ny, nx, nz), axes=(0, 1, 2), weights=(1, 1, 1),\n sampling=(1, 1, 1), dtype=BDiag.dtype)\nNormEqOp = BDiag.H @ BDiag + epsR * LapOp.H @ LapOp\ndnorm_dist = BDiag.H @ d_dist\nminv3d_reg_dist = pylops_mpi.optimization.basic.cg(NormEqOp, dnorm_dist, x0=mback3d_dist, niter=100, show=True)[0]\nminv3d_reg = minv3d_reg_dist.asarray().reshape((ny, nx, nz))" + "# Regularized inversion with normal equations\nepsR = 1e2\nLapOp = pylops_mpi.MPILaplacian(dims=(ny, nx, nz), axes=(0, 1, 2), weights=(1, 1, 1),\n sampling=(1, 1, 1), dtype=BDiag.dtype)\nNormEqOp = BDiag.H @ BDiag + epsR * LapOp.H @ LapOp\ndnorm_dist = BDiag.H @ d_dist\nminv3d_ne_dist = pylops_mpi.optimization.basic.cg(NormEqOp, dnorm_dist, x0=mback3d_dist, niter=100, show=True)[0]\nminv3d_ne = minv3d_ne_dist.asarray().reshape((ny, nx, nz))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Regularized inversion with regularized equations\nStackOp = pylops_mpi.MPIStackedVStack([BDiag, np.sqrt(epsR) * LapOp])\nd0_dist = pylops_mpi.DistributedArray(global_shape=ny * nx * nz)\nd0_dist[:] = 0.\ndstack_dist = pylops_mpi.StackedDistributedArray([d_dist, d0_dist])\n\ndnorm_dist = BDiag.H @ d_dist\nminv3d_reg_dist = pylops_mpi.optimization.basic.cgls(StackOp, dstack_dist, x0=mback3d_dist, niter=100, show=False)[0]\nminv3d_reg = minv3d_reg_dist.asarray().reshape((ny, nx, nz))" ] }, { @@ -98,7 +109,7 @@ }, "outputs": [], "source": [ - "if rank == 0:\n # Check the distributed implementation gives the same result\n # as the one running only on rank0\n PPop0 = PoststackLinearModelling(wav, nt0=nz, spatdims=(ny, nx))\n d0 = (PPop0 @ m3d.transpose(2, 0, 1)).transpose(1, 2, 0)\n d0_0 = (PPop0 @ m3d.transpose(2, 0, 1)).transpose(1, 2, 0)\n\n # Check the two distributed implementations give the same modelling results\n print('Distr == Local', np.allclose(d, d0))\n print('Smooth Distr == Local', np.allclose(d_0, d0_0))\n\n # Visualize\n fig, axs = plt.subplots(nrows=5, ncols=3, figsize=(9, 14), constrained_layout=True)\n axs[0][0].imshow(m3d[5, :, :].T, cmap=\"gist_rainbow\", vmin=m.min(), vmax=m.max())\n axs[0][0].set_title(\"Model x-z\")\n axs[0][0].axis(\"tight\")\n axs[0][1].imshow(m3d[:, 200, :].T, cmap=\"gist_rainbow\", vmin=m.min(), vmax=m.max())\n axs[0][1].set_title(\"Model y-z\")\n axs[0][1].axis(\"tight\")\n axs[0][2].imshow(m3d[:, :, 220].T, cmap=\"gist_rainbow\", vmin=m.min(), vmax=m.max())\n axs[0][2].set_title(\"Model y-z\")\n axs[0][2].axis(\"tight\")\n\n axs[1][0].imshow(mback3d[5, :, :].T, cmap=\"gist_rainbow\", vmin=m.min(), vmax=m.max())\n axs[1][0].set_title(\"Smooth Model x-z\")\n axs[1][0].axis(\"tight\")\n axs[1][1].imshow(mback3d[:, 200, :].T, cmap=\"gist_rainbow\", vmin=m.min(), vmax=m.max())\n axs[1][1].set_title(\"Smooth Model y-z\")\n axs[1][1].axis(\"tight\")\n axs[1][2].imshow(mback3d[:, :, 220].T, cmap=\"gist_rainbow\", vmin=m.min(), vmax=m.max())\n axs[1][2].set_title(\"Smooth Model y-z\")\n axs[1][2].axis(\"tight\")\n\n axs[2][0].imshow(d[5, :, :].T, cmap=\"gray\", vmin=-1, vmax=1)\n axs[2][0].set_title(\"Data x-z\")\n axs[2][0].axis(\"tight\")\n axs[2][1].imshow(d[:, 200, :].T, cmap='gray', vmin=-1, vmax=1)\n axs[2][1].set_title('Data y-z')\n axs[2][1].axis('tight')\n axs[2][2].imshow(d[:, :, 220].T, cmap='gray', vmin=-1, vmax=1)\n axs[2][2].set_title('Data x-y')\n axs[2][2].axis('tight')\n\n axs[3][0].imshow(minv3d_iter[5, :, :].T, cmap=\"gist_rainbow\", vmin=m.min(), vmax=m.max())\n axs[3][0].set_title(\"Inverted Model iter x-z\")\n axs[3][0].axis(\"tight\")\n axs[3][1].imshow(minv3d_iter[:, 200, :].T, cmap='gist_rainbow', vmin=m.min(), vmax=m.max())\n axs[3][1].set_title('Inverted Model iter y-z')\n axs[3][1].axis('tight')\n axs[3][2].imshow(minv3d_iter[:, :, 220].T, cmap='gist_rainbow', vmin=m.min(), vmax=m.max())\n axs[3][2].set_title('Inverted Model iter x-y')\n axs[3][2].axis('tight')\n\n axs[4][0].imshow(minv3d_reg[5, :, :].T, cmap=\"gist_rainbow\", vmin=m.min(), vmax=m.max())\n axs[4][0].set_title(\"Regularized Inverted Model iter x-z\")\n axs[4][0].axis(\"tight\")\n axs[4][1].imshow(minv3d_reg[:, 200, :].T, cmap='gist_rainbow', vmin=m.min(), vmax=m.max())\n axs[4][1].set_title('Regularized Inverted Model iter y-z')\n axs[4][1].axis('tight')\n axs[4][2].imshow(minv3d_reg[:, :, 220].T, cmap='gist_rainbow', vmin=m.min(), vmax=m.max())\n axs[4][2].set_title('Regularized Inverted Model iter x-y')\n axs[4][2].axis('tight')" + "if rank == 0:\n # Check the distributed implementation gives the same result\n # as the one running only on rank0\n PPop0 = PoststackLinearModelling(wav, nt0=nz, spatdims=(ny, nx))\n d0 = (PPop0 @ m3d.transpose(2, 0, 1)).transpose(1, 2, 0)\n d0_0 = (PPop0 @ m3d.transpose(2, 0, 1)).transpose(1, 2, 0)\n\n # Check the two distributed implementations give the same modelling results\n print('Distr == Local', np.allclose(d, d0))\n print('Smooth Distr == Local', np.allclose(d_0, d0_0))\n\n # Visualize\n fig, axs = plt.subplots(nrows=6, ncols=3, figsize=(9, 14), constrained_layout=True)\n axs[0][0].imshow(m3d[5, :, :].T, cmap=\"gist_rainbow\", vmin=m.min(), vmax=m.max())\n axs[0][0].set_title(\"Model x-z\")\n axs[0][0].axis(\"tight\")\n axs[0][1].imshow(m3d[:, 200, :].T, cmap=\"gist_rainbow\", vmin=m.min(), vmax=m.max())\n axs[0][1].set_title(\"Model y-z\")\n axs[0][1].axis(\"tight\")\n axs[0][2].imshow(m3d[:, :, 220].T, cmap=\"gist_rainbow\", vmin=m.min(), vmax=m.max())\n axs[0][2].set_title(\"Model y-z\")\n axs[0][2].axis(\"tight\")\n\n axs[1][0].imshow(mback3d[5, :, :].T, cmap=\"gist_rainbow\", vmin=m.min(), vmax=m.max())\n axs[1][0].set_title(\"Smooth Model x-z\")\n axs[1][0].axis(\"tight\")\n axs[1][1].imshow(mback3d[:, 200, :].T, cmap=\"gist_rainbow\", vmin=m.min(), vmax=m.max())\n axs[1][1].set_title(\"Smooth Model y-z\")\n axs[1][1].axis(\"tight\")\n axs[1][2].imshow(mback3d[:, :, 220].T, cmap=\"gist_rainbow\", vmin=m.min(), vmax=m.max())\n axs[1][2].set_title(\"Smooth Model y-z\")\n axs[1][2].axis(\"tight\")\n\n axs[2][0].imshow(d[5, :, :].T, cmap=\"gray\", vmin=-1, vmax=1)\n axs[2][0].set_title(\"Data x-z\")\n axs[2][0].axis(\"tight\")\n axs[2][1].imshow(d[:, 200, :].T, cmap='gray', vmin=-1, vmax=1)\n axs[2][1].set_title('Data y-z')\n axs[2][1].axis('tight')\n axs[2][2].imshow(d[:, :, 220].T, cmap='gray', vmin=-1, vmax=1)\n axs[2][2].set_title('Data x-y')\n axs[2][2].axis('tight')\n\n axs[3][0].imshow(minv3d_iter[5, :, :].T, cmap=\"gist_rainbow\", vmin=m.min(), vmax=m.max())\n axs[3][0].set_title(\"Inverted Model iter x-z\")\n axs[3][0].axis(\"tight\")\n axs[3][1].imshow(minv3d_iter[:, 200, :].T, cmap='gist_rainbow', vmin=m.min(), vmax=m.max())\n axs[3][1].set_title('Inverted Model iter y-z')\n axs[3][1].axis('tight')\n axs[3][2].imshow(minv3d_iter[:, :, 220].T, cmap='gist_rainbow', vmin=m.min(), vmax=m.max())\n axs[3][2].set_title('Inverted Model iter x-y')\n axs[3][2].axis('tight')\n\n axs[4][0].imshow(minv3d_ne[5, :, :].T, cmap=\"gist_rainbow\", vmin=m.min(), vmax=m.max())\n axs[4][0].set_title(\"Normal Equations Inverted Model iter x-z\")\n axs[4][0].axis(\"tight\")\n axs[4][1].imshow(minv3d_ne[:, 200, :].T, cmap='gist_rainbow', vmin=m.min(), vmax=m.max())\n axs[4][1].set_title('Normal Equations Inverted Model iter y-z')\n axs[4][1].axis('tight')\n axs[4][2].imshow(minv3d_ne[:, :, 220].T, cmap='gist_rainbow', vmin=m.min(), vmax=m.max())\n axs[4][2].set_title('Normal Equations Inverted Model iter x-y')\n axs[4][2].axis('tight')\n\n axs[5][0].imshow(minv3d_reg[5, :, :].T, cmap=\"gist_rainbow\", vmin=m.min(), vmax=m.max())\n axs[5][0].set_title(\"Regularized Inverted Model iter x-z\")\n axs[5][0].axis(\"tight\")\n axs[5][1].imshow(minv3d_reg[:, 200, :].T, cmap='gist_rainbow', vmin=m.min(), vmax=m.max())\n axs[5][1].set_title('Regularized Inverted Model iter y-z')\n axs[5][1].axis('tight')\n axs[5][2].imshow(minv3d_reg[:, :, 220].T, cmap='gist_rainbow', vmin=m.min(), vmax=m.max())\n axs[5][2].set_title('Regularized Inverted Model iter x-y')\n axs[5][2].axis('tight')" ] } ], diff --git a/_downloads/475cd62e887dac3f4cecf3ef64657324/plot_distributed_array.py b/_downloads/475cd62e887dac3f4cecf3ef64657324/plot_distributed_array.py index 6d428406..6e1168a3 100644 --- a/_downloads/475cd62e887dac3f4cecf3ef64657324/plot_distributed_array.py +++ b/_downloads/475cd62e887dac3f4cecf3ef64657324/plot_distributed_array.py @@ -71,12 +71,25 @@ pylops_mpi.plot_local_arrays(arr1, "Distributed Array - 1", vmin=0, vmax=1) pylops_mpi.plot_local_arrays(arr2, "Distributed Array - 2", vmin=0, vmax=1) +############################################################################### +# **Scaling** - Each process operates on its local portion of +# the array and scales the corresponding elements by a given scalar. +scale_arr = .5 * arr1 +pylops_mpi.plot_local_arrays(scale_arr, "Scaling", vmin=0, vmax=1) + ############################################################################### # **Element-wise Addition** - Each process operates on its local portion of # the array and adds the corresponding elements together. sum_arr = arr1 + arr2 pylops_mpi.plot_local_arrays(sum_arr, "Addition", vmin=0, vmax=1) +############################################################################### +# **Element-wise In-place Addition** - Similar to the previous one but the +# addition is performed directly on one of the addends without creating a new +# distributed array. +sum_arr += arr2 +pylops_mpi.plot_local_arrays(sum_arr, "Addition", vmin=0, vmax=1) + ############################################################################### # **Element-wise Subtraction** - Each process operates on its local portion # of the array and subtracts the corresponding elements together. diff --git a/_downloads/6b4bdf99ba907d36440c6747c4b6c693/plot_stacked_array.py b/_downloads/6b4bdf99ba907d36440c6747c4b6c693/plot_stacked_array.py new file mode 100644 index 00000000..a92a98f5 --- /dev/null +++ b/_downloads/6b4bdf99ba907d36440c6747c4b6c693/plot_stacked_array.py @@ -0,0 +1,155 @@ +""" +Stacked Array +========================= +This example shows how to use the :py:class:`pylops_mpi.StackedDistributedArray`. +This class provides a way to combine and act on multiple :py:class:`pylops_mpi.DistributedArray` +within the same program. This is very useful in scenarios where an array can be logically +divided in subarrays and each of them lends naturally to distribution across multiple processes in +a parallel computing environment. +""" + +from matplotlib import pyplot as plt +import numpy as np +from mpi4py import MPI + +import pylops +import pylops_mpi + +plt.close("all") +np.random.seed(42) +rank = MPI.COMM_WORLD.Get_rank() +size = MPI.COMM_WORLD.Get_size() + +############################################################################### +# Let's start by defining two distributed array +subarr1 = pylops_mpi.DistributedArray(global_shape=size * 10, + partition=pylops_mpi.Partition.SCATTER, + axis=0) +subarr2 = pylops_mpi.DistributedArray(global_shape=size * 4, + partition=pylops_mpi.Partition.SCATTER, + axis=0) +# Filling the local arrays +subarr1[:], subarr2[:] = 1, 2 + +############################################################################### +# We combine them into a single +# :py:class:`pylops_mpi.StackedDistributedArray` object. +arr1 = pylops_mpi.StackedDistributedArray([subarr1, subarr2]) +if rank == 0: + print('Stacked array:', arr1) + +# Extract and print full array +full_arr1 = arr1.asarray() +if rank == 0: + print('Full array:', full_arr1) + +# Modify the part of the first array in rank0 +if rank == 0: + arr1[0][:] = 10 +full_arr1 = arr1.asarray() +if rank == 0: + print('Modified full array:', full_arr1) + +############################################################################### +# Let's now create a second :py:class:`pylops_mpi.StackedDistributedArray` object +# and perform different mathematical operations on those two objects. +subarr1_ = pylops_mpi.DistributedArray(global_shape=size * 10, + partition=pylops_mpi.Partition.SCATTER, + axis=0) +subarr2_ = pylops_mpi.DistributedArray(global_shape=size * 4, + partition=pylops_mpi.Partition.SCATTER, + axis=0) +# Filling the local arrays +subarr1_[:], subarr2_[:] = 5, 6 +arr2 = pylops_mpi.StackedDistributedArray([subarr1_, subarr2_]) +if rank == 0: + print('Stacked array 2:', arr2) + +full_arr2 = arr2.asarray() +if rank == 0: + print('Full array2:', full_arr2) + +############################################################################### +# **Negation** +neg_arr = -arr1 +full_neg_arr = neg_arr.asarray() +if rank == 0: + print('Negated full array:', full_neg_arr) + +############################################################################### +# **Element-wise Addition** +sum_arr = arr1 + arr2 +full_sum_arr = sum_arr.asarray() +if rank == 0: + print('Summed full array:', full_sum_arr) + +############################################################################### +# **Element-wise Subtraction** +sub_arr = arr1 - arr2 +full_sub_arr = sub_arr.asarray() +if rank == 0: + print('Subtracted full array:', full_sub_arr) + +############################################################################### +# **Multiplication** +mult_arr = arr1 * arr2 +full_mult_arr = mult_arr.asarray() +if rank == 0: + print('Multipled full array:', full_mult_arr) + +############################################################################### +# **Dot-product** +dot_arr = arr1.dot(arr2) +if rank == 0: + print('Dot-product:', dot_arr) + print('Dot-product (np):', np.dot(full_arr1, full_arr2)) + +############################################################################### +# **Norms** +l0norm = arr1.norm(0) +l1norm = arr1.norm(1) +l2norm = arr1.norm(2) +linfnorm = arr1.norm(np.inf) + +if rank == 0: + print('L0 norm', l0norm, np.linalg.norm(full_arr1, 0)) + print('L1 norm', l1norm, np.linalg.norm(full_arr1, 1)) + print('L2 norm', l2norm, np.linalg.norm(full_arr1, 2)) + print('Linf norm', linfnorm, np.linalg.norm(full_arr1, np.inf)) + +############################################################################### +# Now that we have a way to stack multiple :py:class:`pylops_mpi.StackedDistributedArray` objects, +# let's see how we can apply operators to them. More specifically this can be +# done using the :py:class:`pylops_mpi.MPIStackedVStack` operator that takes multiple +# :py:class:`pylops_mpi.MPILinearOperator` objects, each acting on one specific +# distributed array +x = pylops_mpi.DistributedArray(global_shape=size * 10, + partition=pylops_mpi.Partition.SCATTER, + axis=0) +# Filling the local arrays +x[:] = 1. + +# Make stacked operator +mop1 = pylops_mpi.MPIBlockDiag([pylops.MatrixMult(np.ones((5, 10))), ]) +mop2 = pylops_mpi.MPIBlockDiag([pylops.MatrixMult(2 * np.ones((8, 10))), ]) +mop = pylops_mpi.MPIStackedVStack([mop1, mop2]) + +y = mop.matvec(x) +y_arr = y.asarray() +xadj = mop.rmatvec(y) +xadj_arr = xadj.asarray() + +if rank == 0: + print('StackedVStack y', y, y_arr, y_arr.shape) + print('StackedVStack xadj', xadj, xadj_arr, xadj_arr.shape) + +############################################################################### +# Finally, let's solve now an inverse problem using stacked arrays instead +# of distributed arrays +x0 = x.copy() +x0[:] = 0. +xinv = pylops_mpi.cgls(mop, y, x0=x0, niter=15, tol=1e-10, show=False)[0] +xinv_array = xinv.asarray() + +if rank == 0: + print('xinv_array', xinv_array) diff --git a/_downloads/82a21537237fa28c9fd15bc39c8c4644/plot_distributed_array.ipynb b/_downloads/82a21537237fa28c9fd15bc39c8c4644/plot_distributed_array.ipynb index bd4b0a8b..69944386 100644 --- a/_downloads/82a21537237fa28c9fd15bc39c8c4644/plot_distributed_array.ipynb +++ b/_downloads/82a21537237fa28c9fd15bc39c8c4644/plot_distributed_array.ipynb @@ -90,6 +90,24 @@ "n = global_shape[0] * global_shape[1]\n# Array to be distributed\narray = np.arange(n) / float(n)\narr1 = pylops_mpi.DistributedArray.to_dist(x=array.reshape(global_shape), axis=1)\narray = array / 2.0\narr2 = pylops_mpi.DistributedArray.to_dist(x=array.reshape(global_shape), axis=1)\n# plot local arrays\npylops_mpi.plot_local_arrays(arr1, \"Distributed Array - 1\", vmin=0, vmax=1)\npylops_mpi.plot_local_arrays(arr2, \"Distributed Array - 2\", vmin=0, vmax=1)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Scaling** - Each process operates on its local portion of\nthe array and scales the corresponding elements by a given scalar.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "scale_arr = .5 * arr1\npylops_mpi.plot_local_arrays(scale_arr, \"Scaling\", vmin=0, vmax=1)" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -108,6 +126,24 @@ "sum_arr = arr1 + arr2\npylops_mpi.plot_local_arrays(sum_arr, \"Addition\", vmin=0, vmax=1)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Element-wise In-place Addition** - Similar to the previous one but the\naddition is performed directly on one of the addends without creating a new\ndistributed array.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "sum_arr += arr2\npylops_mpi.plot_local_arrays(sum_arr, \"Addition\", vmin=0, vmax=1)" + ] + }, { "cell_type": "markdown", "metadata": {}, diff --git a/_downloads/301c43d9a19e3d4d0f37142b751e1aa2/plot_lsm.py b/_downloads/afacec718d3958430d53150fa3b27203/lsm.py similarity index 100% rename from _downloads/301c43d9a19e3d4d0f37142b751e1aa2/plot_lsm.py rename to _downloads/afacec718d3958430d53150fa3b27203/lsm.py diff --git a/_downloads/8b92f8d1ffe6a0e19e55cdb3a43cad08/plot_lsm.ipynb b/_downloads/d5dae76a02f3b395d667034f44fd5555/lsm.ipynb similarity index 100% rename from _downloads/8b92f8d1ffe6a0e19e55cdb3a43cad08/plot_lsm.ipynb rename to _downloads/d5dae76a02f3b395d667034f44fd5555/lsm.ipynb diff --git a/_downloads/ebaf2650b017800d8a38733a44fc1d32/plot_stacked_array.ipynb b/_downloads/ebaf2650b017800d8a38733a44fc1d32/plot_stacked_array.ipynb new file mode 100644 index 00000000..05b3d5f6 --- /dev/null +++ b/_downloads/ebaf2650b017800d8a38733a44fc1d32/plot_stacked_array.ipynb @@ -0,0 +1,241 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n# Stacked Array\nThis example shows how to use the :py:class:`pylops_mpi.StackedDistributedArray`.\nThis class provides a way to combine and act on multiple :py:class:`pylops_mpi.DistributedArray`\nwithin the same program. This is very useful in scenarios where an array can be logically\ndivided in subarrays and each of them lends naturally to distribution across multiple processes in\na parallel computing environment.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "from matplotlib import pyplot as plt\nimport numpy as np\nfrom mpi4py import MPI\n\nimport pylops\nimport pylops_mpi\n\nplt.close(\"all\")\nnp.random.seed(42)\nrank = MPI.COMM_WORLD.Get_rank()\nsize = MPI.COMM_WORLD.Get_size()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's start by defining two distributed array\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "subarr1 = pylops_mpi.DistributedArray(global_shape=size * 10,\n partition=pylops_mpi.Partition.SCATTER,\n axis=0)\nsubarr2 = pylops_mpi.DistributedArray(global_shape=size * 4,\n partition=pylops_mpi.Partition.SCATTER,\n axis=0)\n# Filling the local arrays\nsubarr1[:], subarr2[:] = 1, 2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We combine them into a single\n:py:class:`pylops_mpi.StackedDistributedArray` object.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "arr1 = pylops_mpi.StackedDistributedArray([subarr1, subarr2])\nif rank == 0:\n print('Stacked array:', arr1)\n\n# Extract and print full array\nfull_arr1 = arr1.asarray()\nif rank == 0:\n print('Full array:', full_arr1)\n\n# Modify the part of the first array in rank0\nif rank == 0:\n arr1[0][:] = 10\nfull_arr1 = arr1.asarray()\nif rank == 0:\n print('Modified full array:', full_arr1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's now create a second :py:class:`pylops_mpi.StackedDistributedArray` object\nand perform different mathematical operations on those two objects.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "subarr1_ = pylops_mpi.DistributedArray(global_shape=size * 10,\n partition=pylops_mpi.Partition.SCATTER,\n axis=0)\nsubarr2_ = pylops_mpi.DistributedArray(global_shape=size * 4,\n partition=pylops_mpi.Partition.SCATTER,\n axis=0)\n# Filling the local arrays\nsubarr1_[:], subarr2_[:] = 5, 6\narr2 = pylops_mpi.StackedDistributedArray([subarr1_, subarr2_])\nif rank == 0:\n print('Stacked array 2:', arr2)\n\nfull_arr2 = arr2.asarray()\nif rank == 0:\n print('Full array2:', full_arr2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Negation**\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "neg_arr = -arr1\nfull_neg_arr = neg_arr.asarray()\nif rank == 0:\n print('Negated full array:', full_neg_arr)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Element-wise Addition**\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "sum_arr = arr1 + arr2\nfull_sum_arr = sum_arr.asarray()\nif rank == 0:\n print('Summed full array:', full_sum_arr)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Element-wise Subtraction**\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "sub_arr = arr1 - arr2\nfull_sub_arr = sub_arr.asarray()\nif rank == 0:\n print('Subtracted full array:', full_sub_arr)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Multiplication**\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "mult_arr = arr1 * arr2\nfull_mult_arr = mult_arr.asarray()\nif rank == 0:\n print('Multipled full array:', full_mult_arr)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Dot-product**\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "dot_arr = arr1.dot(arr2)\nif rank == 0:\n print('Dot-product:', dot_arr)\n print('Dot-product (np):', np.dot(full_arr1, full_arr2))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Norms**\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "l0norm = arr1.norm(0)\nl1norm = arr1.norm(1)\nl2norm = arr1.norm(2)\nlinfnorm = arr1.norm(np.inf)\n\nif rank == 0:\n print('L0 norm', l0norm, np.linalg.norm(full_arr1, 0))\n print('L1 norm', l1norm, np.linalg.norm(full_arr1, 1))\n print('L2 norm', l2norm, np.linalg.norm(full_arr1, 2))\n print('Linf norm', linfnorm, np.linalg.norm(full_arr1, np.inf))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now that we have a way to stack multiple :py:class:`pylops_mpi.StackedDistributedArray` objects,\nlet's see how we can apply operators to them. More specifically this can be\ndone using the :py:class:`pylops_mpi.MPIStackedVStack` operator that takes multiple\n:py:class:`pylops_mpi.MPILinearOperator` objects, each acting on one specific\ndistributed array\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "x = pylops_mpi.DistributedArray(global_shape=size * 10,\n partition=pylops_mpi.Partition.SCATTER,\n axis=0)\n# Filling the local arrays\nx[:] = 1.\n\n# Make stacked operator\nmop1 = pylops_mpi.MPIBlockDiag([pylops.MatrixMult(np.ones((5, 10))), ])\nmop2 = pylops_mpi.MPIBlockDiag([pylops.MatrixMult(2 * np.ones((8, 10))), ])\nmop = pylops_mpi.MPIStackedVStack([mop1, mop2])\n\ny = mop.matvec(x)\ny_arr = y.asarray()\nxadj = mop.rmatvec(y)\nxadj_arr = xadj.asarray()\n\nif rank == 0:\n print('StackedVStack y', y, y_arr, y_arr.shape)\n print('StackedVStack xadj', xadj, xadj_arr, xadj_arr.shape)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, let's solve now an inverse problem using stacked arrays instead\nof distributed arrays\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "x0 = x.copy()\nx0[:] = 0.\nxinv = pylops_mpi.cgls(mop, y, x0=x0, niter=15, tol=1e-10, show=False)[0]\nxinv_array = xinv.asarray()\n\nif rank == 0:\n print('xinv_array', xinv_array)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.18" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} \ No newline at end of file diff --git a/_images/sphx_glr_plot_lsm_001.png b/_images/sphx_glr_lsm_001.png similarity 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      Source code for pylops_mpi.StackedLinearOperator

      +from typing import Optional, Union, Callable
      +from abc import abstractmethod, ABC
      +import numpy as np
      +from mpi4py import MPI
      +from pylops.utils import ShapeLike, DTypeLike
      +
      +from scipy.sparse._sputils import isintlike
      +from scipy.sparse.linalg._interface import _get_dtype
      +
      +from pylops_mpi.DistributedArray import DistributedArray, StackedDistributedArray
      +
      +
      +
      +[docs] +class MPIStackedLinearOperator(ABC): + """Common interface for performing matrix-vector products in distributed fashion + for StackedLinearOperators. + + This class provides methods to perform matrix-vector product and adjoint matrix-vector + products on a stack of MPILinearOperator objects. + + .. note:: End users of pylops-mpi should not use this class directly but simply + use operators that are already implemented. This class is meant for + developers only, it has to be used as the parent class of any new operator + developed within pylops-mpi. + + Parameters + ---------- + shape : :obj:`tuple(int, int)`, optional + Shape of the MPIStackedLinearOperator. Defaults to ``None``. + dtype : :obj:`str`, optional + Type of elements in input array. Defaults to ``None``. + base_comm : :obj:`mpi4py.MPI.Comm`, optional + MPI Base Communicator. Defaults to ``mpi4py.MPI.COMM_WORLD``. + """ + + def __init__(self, shape: Optional[ShapeLike] = None, + dtype: Optional[DTypeLike] = None, + base_comm: MPI.Comm = MPI.COMM_WORLD): + if shape: + self.shape = shape + if dtype: + self.dtype = dtype + # For MPI + self.base_comm = base_comm + self.size = self.base_comm.Get_size() + self.rank = self.base_comm.Get_rank() + + def matvec(self, x: Union[DistributedArray, StackedDistributedArray]) -> Union[DistributedArray, StackedDistributedArray]: + M, N = self.shape + if isinstance(x, StackedDistributedArray): + stacked_shape = (np.sum([a.global_shape for a in x.distarrays]), ) + if stacked_shape != (N, ): + raise ValueError("dimension mismatch") + if isinstance(x, DistributedArray) and x.global_shape != (N,): + raise ValueError("dimension mismatch") + return self._matvec(x) + + @abstractmethod + def _matvec(self, x: Union[DistributedArray, StackedDistributedArray]) -> Union[DistributedArray, StackedDistributedArray]: + pass + + def rmatvec(self, x: Union[DistributedArray, StackedDistributedArray]) -> Union[DistributedArray, StackedDistributedArray]: + M, N = self.shape + if isinstance(x, StackedDistributedArray): + stacked_shape = (np.sum([a.global_shape for a in x.distarrays]), ) + if stacked_shape != (M, ): + raise ValueError("dimension mismatch") + if isinstance(x, DistributedArray) and x.global_shape != (M,): + raise ValueError("dimension mismatch") + return self._rmatvec(x) + + @abstractmethod + def _rmatvec(self, x: Union[DistributedArray, StackedDistributedArray]) -> Union[DistributedArray, StackedDistributedArray]: + pass + + def dot(self, x): + """Matrix Vector Multiplication + + Parameters + ---------- + x : :obj:`pylops_mpi.DistributedArray` or :obj:`pylops_mpi.StackedDistributedArray` or + :obj:`pylops_mpi.StackedMPILinearOperator + StackedDistributedArray, DistributedArray or StackedMPILinearOperator. + + Returns + ------- + y : :obj:`pylops_mpi.DistributedArray` or :obj:`pylops_mpi.StackedDistributedArray` or + :obj:`pylops_mpi.StackedMPILinearOperator + StackedDistributedArray, DistributedArray or a StackedMPILinearOperator. + + """ + if isinstance(x, MPIStackedLinearOperator): + return _ProductStackedLinearOperator(self, x) + elif np.isscalar(x): + return _ScaledStackedLinearOperator(self, x) + else: + if x is None or (isinstance(x, DistributedArray) and x.ndim == 1): + return self.matvec(x) + elif isinstance(x, StackedDistributedArray): + ndims = np.unique([dis.ndim for dis in x.distarrays]) + if len(ndims) == 1 and ndims[0] == 1: + return self.matvec(x) + else: + raise ValueError('expected 1-d DistributedArray or StackedDistributedArray') + + def adjoint(self): + """Adjoint MPIStackedLinearOperator + + Returns + ------- + op : :obj:`pylops_mpi.MPIStackedLinearOperator` + Adjoint of Operator + + """ + return self._adjoint() + + H = property(adjoint) + + def transpose(self): + """Transposition of MPIStackedLinearOperator + + Returns + ------- + op : :obj:`pylops_mpi.MPIStackedLinearOperator` + Transpose MPIStackedLinearOperator + + """ + return self._transpose() + + T = property(transpose) + + def __mul__(self, x): + return self.dot(x) + + def __rmul__(self, x): + if np.isscalar(x): + return _ScaledStackedLinearOperator(self, x) + else: + return NotImplemented + + def __matmul__(self, x): + if np.isscalar(x): + raise ValueError("Scalar not allowed, use * instead") + return self.__mul__(x) + + def __rmatmul__(self, x): + if np.isscalar(x): + raise ValueError("Scalar not allowed, use * instead") + return self.__rmul__(x) + + def __pow__(self, p): + return _PowerLinearOperator(self, p) + + def __add__(self, x): + return _SumStackedLinearOperator(self, x) + + def __neg__(self): + return _ScaledStackedLinearOperator(self, -1) + + def __sub__(self, x): + return self.__add__(-x) + + def _adjoint(self): + return _AdjointStackedLinearOperator(self) + + def _transpose(self): + return _TransposedStackedLinearOperator(self) + + def conj(self): + """Complex conjugate operator + + Returns + ------- + conjop : :obj:`pylops_mpi.MPIStackedLinearOperator` + Complex conjugate operator + + """ + return _ConjLinearOperator(self) + + def __repr__(self): + M, N = self.shape + if self.dtype is None: + dt = "unspecified dtype" + else: + dt = f"dtype={self.dtype}" + return f"<{M}x{N} {self.__class__.__name__} with {dt}>"
      + + + +class _AdjointStackedLinearOperator(MPIStackedLinearOperator): + """Adjoint of MPIStackedLinearOperator""" + + def __init__(self, A: MPIStackedLinearOperator): + self.A = A + self.args = (A,) + super().__init__(shape=(A.shape[1], A.shape[0]), dtype=A.dtype, + base_comm=MPI.COMM_WORLD) + + def _matvec(self, x: Union[DistributedArray, StackedDistributedArray]) -> Union[DistributedArray, StackedDistributedArray]: + return self.A.rmatvec(x) + + def _rmatvec(self, x: Union[DistributedArray, StackedDistributedArray]) -> Union[DistributedArray, StackedDistributedArray]: + return self.A.matvec(x) + + +class _TransposedStackedLinearOperator(MPIStackedLinearOperator): + """Transpose of MPIStackedLinearOperator""" + + def __init__(self, A: MPIStackedLinearOperator): + self.A = A + self.args = (A,) + super().__init__(shape=(A.shape[1], A.shape[0]), dtype=A.dtype, + base_comm=MPI.COMM_WORLD) + + def _matvec(self, x: Union[DistributedArray, StackedDistributedArray]) -> Union[DistributedArray, StackedDistributedArray]: + x = x.conj() + y = self.A.rmatvec(x) + y = y.conj() + return y + + def _rmatvec(self, x: Union[DistributedArray, StackedDistributedArray]) -> Union[DistributedArray, StackedDistributedArray]: + x = x.conj() + y = self.A.matvec(x) + y = y.conj() + return y + + +class _ProductStackedLinearOperator(MPIStackedLinearOperator): + """Product of MPI Stacked Linear Operators""" + def __init__(self, A: MPIStackedLinearOperator, B: MPIStackedLinearOperator): + from pylops_mpi.basicoperators.VStack import MPIStackedVStack + from pylops_mpi.basicoperators.BlockDiag import MPIStackedBlockDiag + if not isinstance(A, MPIStackedLinearOperator) or not isinstance(B, MPIStackedLinearOperator): + raise ValueError('both operands have to be a MPIStackedLinearOperator') + if isinstance(A, MPIStackedVStack) and isinstance(B, MPIStackedVStack): + raise ValueError('both operands cannot be MPIStackedVStack') + if isinstance(A, MPIStackedBlockDiag) and isinstance(B, MPIStackedBlockDiag) and len(A.ops) != len(B.ops): + raise ValueError(f'both MPIStackedBlockDiag cannot have different number of ops, {A.ops} != {B.ops}') + if A.shape[1] != B.shape[0]: + raise ValueError('cannot multiply %r and %r: shape mismatch' % (A, B)) + self.args = (A, B) + super().__init__(shape=(A.shape[0], B.shape[1]), dtype=_get_dtype([A, B]), + base_comm=MPI.COMM_WORLD) + + def _matvec(self, x: Union[StackedDistributedArray, DistributedArray]) -> Union[StackedDistributedArray, DistributedArray]: + return self.args[0].matvec(self.args[1].matvec(x)) + + def _rmatvec(self, x: Union[StackedDistributedArray, DistributedArray]) -> Union[StackedDistributedArray, DistributedArray]: + return self.args[1].rmatvec(self.args[0].rmatvec(x)) + + def _adjoint(self) -> MPIStackedLinearOperator: + A, B = self.args + return B.H * A.H + + +class _ScaledStackedLinearOperator(MPIStackedLinearOperator): + """Scaled MPI StackedLinearOperator + """ + + def __init__(self, A: MPIStackedLinearOperator, alpha): + if not isinstance(A, MPIStackedLinearOperator): + raise ValueError('MPILinearOperator expected as A') + if not np.isscalar(alpha): + raise ValueError('scalar expected as alpha') + self.args = (A, alpha) + super().__init__(shape=A.shape, dtype=_get_dtype([A], [type(alpha)]), + base_comm=MPI.COMM_WORLD) + + def _matvec(self, x: Union[DistributedArray, StackedDistributedArray]) -> Union[DistributedArray, StackedDistributedArray]: + y = self.args[0].matvec(x) + if y is not None: + y *= self.args[1] + return y + + def _rmatvec(self, x: Union[DistributedArray, StackedDistributedArray]) -> Union[DistributedArray, StackedDistributedArray]: + y = self.args[0].rmatvec(x) + if y is not None: + y *= np.conj(self.args[1]) + return y + + def _adjoint(self) -> MPIStackedLinearOperator: + A, alpha = self.args + return A.H * np.conj(alpha) + + +class _SumStackedLinearOperator(MPIStackedLinearOperator): + """Sum of MPI StackedLinearOperators + """ + + def __init__(self, A: MPIStackedLinearOperator, B: MPIStackedLinearOperator): + if not isinstance(A, MPIStackedLinearOperator) or not isinstance(B, MPIStackedLinearOperator): + raise ValueError('both operands have to be a MPIStackedLinearOperator') + if type(A) != type(B): # noqa: E721 + raise ValueError(f'both operands have to be of same type, {A} != {B}') + if A.shape != B.shape: + raise ValueError("cannot add %r and %r: shape mismatch" % (A, B)) + self.args = (A, B) + super().__init__(shape=A.shape, dtype=A.dtype, base_comm=MPI.COMM_WORLD) + + def _matvec(self, x: Union[DistributedArray, StackedDistributedArray]) -> Union[DistributedArray, StackedDistributedArray]: + arr1 = self.args[0].matvec(x) + arr2 = self.args[1].matvec(x) + return arr1 + arr2 + + def _rmatvec(self, x: Union[DistributedArray, StackedDistributedArray]) -> Union[DistributedArray, StackedDistributedArray]: + arr1 = self.args[0].rmatvec(x) + arr2 = self.args[1].rmatvec(x) + return arr1 + arr2 + + def _adjoint(self) -> MPIStackedLinearOperator: + A, B = self.args + return A.H + B.H + + +class _PowerLinearOperator(MPIStackedLinearOperator): + """Power of MPI StackedLinearOperator + """ + + def __init__(self, A: MPIStackedLinearOperator, p: int) -> None: + if not isinstance(A, MPIStackedLinearOperator): + raise ValueError("MPIStackedLinearOperator expected as A") + if A.shape[0] != A.shape[1]: + raise ValueError("square MPIStackedLinearOperator expected, got %r" % A) + if not isintlike(p) or p < 0: + raise ValueError("non-negative integer expected as p") + + super(_PowerLinearOperator, self).__init__(shape=A.shape, dtype=A.dtype, base_comm=A.base_comm) + self.args = (A, p) + + def _power(self, fun: Callable, x: Union[StackedDistributedArray, DistributedArray]) -> Union[StackedDistributedArray, DistributedArray]: + res = x.copy() + for _ in range(self.args[1]): + res[:] = fun(res)[:] + return res + + def _matvec(self, x: Union[DistributedArray, StackedDistributedArray]) -> Union[DistributedArray, StackedDistributedArray]: + return self._power(self.args[0].matvec, x) + + def _rmatvec(self, x: Union[DistributedArray, StackedDistributedArray]) -> Union[DistributedArray, StackedDistributedArray]: + return self._power(self.args[0].rmatvec, x) + + +class _ConjLinearOperator(MPIStackedLinearOperator): + """Complex conjugate MPI StackedLinearOperator + """ + + def __init__(self, A: MPIStackedLinearOperator): + if not isinstance(A, MPIStackedLinearOperator): + raise TypeError('A must be a MPIStackedLinearOperator') + self.A = A + super().__init__(shape=A.shape, dtype=A.dtype, base_comm=MPI.COMM_WORLD) + + def _matvec(self, x: Union[DistributedArray, StackedDistributedArray]) -> Union[DistributedArray, StackedDistributedArray]: + x = x.conj() + y = self.A.matvec(x) + if y is not None: + y = y.conj() + return y + + def _rmatvec(self, x: Union[DistributedArray, StackedDistributedArray]) -> Union[DistributedArray, StackedDistributedArray]: + x = x.conj() + y = self.A.rmatvec(x) + if y is not None: + y = y.conj() + return y + + def _adjoint(self) -> MPIStackedLinearOperator: + return _ConjLinearOperator(self.A.H) +
      + +
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      + + \ No newline at end of file diff --git a/_modules/pylops_mpi/basicoperators/BlockDiag.html b/_modules/pylops_mpi/basicoperators/BlockDiag.html index d0bd9582..4a1cc80d 100644 --- a/_modules/pylops_mpi/basicoperators/BlockDiag.html +++ b/_modules/pylops_mpi/basicoperators/BlockDiag.html @@ -21,15 +21,15 @@ - - - + + + - - - - + + + + @@ -41,9 +41,9 @@ - - - + + + @@ -63,10 +63,9 @@ - +
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      pylops_mpi.MPIStackedLinearOperator#

      +
      +
      +class pylops_mpi.MPIStackedLinearOperator(shape=None, dtype=None, base_comm=<mpi4py.MPI.Intracomm object>)[source]#
      +

      Common interface for performing matrix-vector products in distributed fashion +for StackedLinearOperators.

      +

      This class provides methods to perform matrix-vector product and adjoint matrix-vector +products on a stack of MPILinearOperator objects.

      +
      +

      Note

      +

      End users of pylops-mpi should not use this class directly but simply

      +
      +

      use operators that are already implemented. This class is meant for +developers only, it has to be used as the parent class of any new operator +developed within pylops-mpi.

      +
      +
      Parameters:
      +
      +
      shapetuple(int, int), optional

      Shape of the MPIStackedLinearOperator. Defaults to None.

      +
      +
      dtypestr, optional

      Type of elements in input array. Defaults to None.

      +
      +
      base_commmpi4py.MPI.Comm, optional

      MPI Base Communicator. Defaults to mpi4py.MPI.COMM_WORLD.

      +
      +
      +
      +
      +

      Methods

      + + + + + + + + + + + + + + + + + + + + + + + + +

      __init__([shape, dtype, base_comm])

      adjoint()

      Adjoint MPIStackedLinearOperator

      conj()

      Complex conjugate operator

      dot(x)

      Matrix Vector Multiplication

      matvec(x)

      rmatvec(x)

      transpose()

      Transposition of MPIStackedLinearOperator

      +
      + +
      +

      Examples using pylops_mpi.MPIStackedLinearOperator#

      +
      +

      Stacked Array

      +
      Stacked Array
      +
      +

      Post Stack Inversion - 3D

      +
      Post Stack Inversion - 3D
      +
      +
      + + +
      + + + + + + + +
      + + + + + + +
      +
      + +
      + +
      +
      +
      + + + + + +
      + + +
      + + \ No newline at end of file diff --git a/api/generated/pylops_mpi.Partition.html b/api/generated/pylops_mpi.Partition.html index b8ee4b53..3fa1d418 100644 --- a/api/generated/pylops_mpi.Partition.html +++ b/api/generated/pylops_mpi.Partition.html @@ -22,15 +22,15 @@ - - - + + + - - - - + + + + @@ -42,9 +42,9 @@ - - - + + + @@ -66,10 +66,9 @@ - +
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      + + + + + +
      + +
      +

      pylops_mpi.StackedDistributedArray#

      +
      +
      +class pylops_mpi.StackedDistributedArray(distarrays)[source]#
      +

      Stacked DistributedArrays

      +

      Stack DistributedArray objects and power them with basic mathematical operations. +This class allows one to work with a series of distributed arrays to avoid having to create +a single distributed array with some special internal sorting.

      +
      +
      Parameters:
      +
      +
      distarrayslist

      List of pylops_mpi.DistributedArray objects.

      +
      +
      +
      +
      +

      Methods

      + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

      __init__(distarrays)

      add(stacked_array)

      Stacked Distributed Addition of arrays

      asarray()

      Global view of the array

      conj()

      Distributed conj() method

      copy()

      Creates a copy of the DistributedArray

      dot(stacked_array)

      iadd(stacked_array)

      Stacked Distributed In-Place Addition of arrays

      multiply(stacked_array)

      norm([ord])

      numpy.linalg.norm method on stacked Distributed arrays

      +
      + +
      +

      Examples using pylops_mpi.StackedDistributedArray#

      +
      +

      Stacked Array

      +
      Stacked Array
      +
      +

      Post Stack Inversion - 3D

      +
      Post Stack Inversion - 3D
      +
      +
      + + +
      + + + + + + + +
      + + + + + + +
      +
      + +
      + +
      +
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      + + + + + +
      + + +
      + + \ No newline at end of file diff --git a/api/generated/pylops_mpi.asmpilinearoperator.html b/api/generated/pylops_mpi.asmpilinearoperator.html index 1d1649a5..b92f77cf 100644 --- a/api/generated/pylops_mpi.asmpilinearoperator.html +++ b/api/generated/pylops_mpi.asmpilinearoperator.html @@ -22,15 +22,15 @@ - - - + + + - - - - + + + + @@ -42,9 +42,9 @@ - - - + + + @@ -54,7 +54,7 @@ - + @@ -66,10 +66,9 @@ - +
      - + + + + + + + + +
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      pylops_mpi.basicoperators.MPIStackedBlockDiag#

      +
      +
      +class pylops_mpi.basicoperators.MPIStackedBlockDiag(ops, base_comm=<mpi4py.MPI.Intracomm object>, dtype=None)[source]#
      +

      MPI Stacked BlockDiag Operator

      +

      Create a diagonal stack of pylops_mpi.MPILinearOperator operators.

      +
      +
      Parameters:
      +
      +
      opslist

      One or more pylops_mpi.MPILinearOperator to be stacked.

      +
      +
      +
      +
      +

      Notes

      +

      A MPIStackedBlockDiag is composed of N :class:pylops_mpi.MPILinearOperator instances stacked along the diagonal. +These MPI operators will be applied sequentially, with distributed computations +performed within each operator.

      +
      +
      Attributes:
      +
      +
      shapetuple

      Operator shape

      +
      +
      +
      +
      +

      Methods

      + + + + + + + + + + + + + + + + + + + + + + + + +

      __init__(ops[, base_comm, dtype])

      adjoint()

      Adjoint MPIStackedLinearOperator

      conj()

      Complex conjugate operator

      dot(x)

      Matrix Vector Multiplication

      matvec(x)

      rmatvec(x)

      transpose()

      Transposition of MPIStackedLinearOperator

      +
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      + + \ No newline at end of file diff --git a/api/generated/pylops_mpi.basicoperators.MPIStackedVStack.html b/api/generated/pylops_mpi.basicoperators.MPIStackedVStack.html new file mode 100644 index 00000000..997055a6 --- /dev/null +++ b/api/generated/pylops_mpi.basicoperators.MPIStackedVStack.html @@ -0,0 +1,659 @@ + + + + + + + + + + + + + pylops_mpi.basicoperators.MPIStackedVStack — PyLops-MPI + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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      pylops_mpi.basicoperators.MPIStackedVStack#

      +
      +
      +class pylops_mpi.basicoperators.MPIStackedVStack(ops, base_comm=<mpi4py.MPI.Intracomm object>, dtype=None)[source]#
      +

      MPI Stacked VStack Operator

      +

      Create a vertical stack of pylops_mpi.MPILinearOperator operators.

      +
      +
      Parameters:
      +
      +
      opslist

      One or more pylops_mpi.MPILinearOperator to be vertically stacked.

      +
      +
      +
      +
      Raises:
      +
      +
      ValueError

      If ops have different number of columns

      +
      +
      +
      +
      +

      Notes

      +

      An MPIStackedVStack is composed of N pylops_mpi.MPILinearOperator stacked +vertically. These MPI operators will be applied sequentially, however distributed +computations will be performed within each operator.

      +
      +
      Attributes:
      +
      +
      shapetuple

      Operator shape

      +
      +
      +
      +
      +

      Methods

      + + + + + + + + + + + + + + + + + + + + + + + + +

      __init__(ops[, base_comm, dtype])

      adjoint()

      Adjoint MPIStackedLinearOperator

      conj()

      Complex conjugate operator

      dot(x)

      Matrix Vector Multiplication

      matvec(x)

      rmatvec(x)

      transpose()

      Transposition of MPIStackedLinearOperator

      +
      + +
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      + + + + + + + +
      + + + +
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      + + + + + +
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      + + \ No newline at end of file diff --git a/api/generated/pylops_mpi.basicoperators.MPIVStack.html b/api/generated/pylops_mpi.basicoperators.MPIVStack.html index ad03f48b..1be5409c 100644 --- a/api/generated/pylops_mpi.basicoperators.MPIVStack.html +++ b/api/generated/pylops_mpi.basicoperators.MPIVStack.html @@ -22,15 +22,15 @@ - - - + + + - - - - + + + + @@ -42,9 +42,9 @@ - - - + + + @@ -56,8 +56,8 @@ - - + + @@ -68,10 +68,9 @@ - +
      - + + + + + + + + +
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      + + + + +
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      + + + + + + + + + + + + + +
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      +

      Stacked Array#

      +

      This example shows how to use the pylops_mpi.StackedDistributedArray. +This class provides a way to combine and act on multiple pylops_mpi.DistributedArray +within the same program. This is very useful in scenarios where an array can be logically +divided in subarrays and each of them lends naturally to distribution across multiple processes in +a parallel computing environment.

      +
      from matplotlib import pyplot as plt
      +import numpy as np
      +from mpi4py import MPI
      +
      +import pylops
      +import pylops_mpi
      +
      +plt.close("all")
      +np.random.seed(42)
      +rank = MPI.COMM_WORLD.Get_rank()
      +size = MPI.COMM_WORLD.Get_size()
      +
      +
      +

      Let’s start by defining two distributed array

      +
      subarr1 = pylops_mpi.DistributedArray(global_shape=size * 10,
      +                                      partition=pylops_mpi.Partition.SCATTER,
      +                                      axis=0)
      +subarr2 = pylops_mpi.DistributedArray(global_shape=size * 4,
      +                                      partition=pylops_mpi.Partition.SCATTER,
      +                                      axis=0)
      +# Filling the local arrays
      +subarr1[:], subarr2[:] = 1, 2
      +
      +
      +

      We combine them into a single +pylops_mpi.StackedDistributedArray object.

      +
      arr1 = pylops_mpi.StackedDistributedArray([subarr1, subarr2])
      +if rank == 0:
      +    print('Stacked array:', arr1)
      +
      +# Extract and print full array
      +full_arr1 = arr1.asarray()
      +if rank == 0:
      +    print('Full array:', full_arr1)
      +
      +# Modify the part of the first array in rank0
      +if rank == 0:
      +    arr1[0][:] = 10
      +full_arr1 = arr1.asarray()
      +if rank == 0:
      +    print('Modified full array:', full_arr1)
      +
      +
      +
      Stacked array: <StackedDistributedArray with 2 distributed arrays:
      +<DistributedArray with global shape=(10,), local shape=(10,), dtype=<class 'numpy.float64'>, processes=[0])>
      +<DistributedArray with global shape=(4,), local shape=(4,), dtype=<class 'numpy.float64'>, processes=[0])>
      +Full array: [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 2. 2. 2. 2.]
      +Modified full array: [10. 10. 10. 10. 10. 10. 10. 10. 10. 10.  2.  2.  2.  2.]
      +
      +
      +

      Let’s now create a second pylops_mpi.StackedDistributedArray object +and perform different mathematical operations on those two objects.

      +
      subarr1_ = pylops_mpi.DistributedArray(global_shape=size * 10,
      +                                       partition=pylops_mpi.Partition.SCATTER,
      +                                       axis=0)
      +subarr2_ = pylops_mpi.DistributedArray(global_shape=size * 4,
      +                                       partition=pylops_mpi.Partition.SCATTER,
      +                                       axis=0)
      +# Filling the local arrays
      +subarr1_[:], subarr2_[:] = 5, 6
      +arr2 = pylops_mpi.StackedDistributedArray([subarr1_, subarr2_])
      +if rank == 0:
      +    print('Stacked array 2:', arr2)
      +
      +full_arr2 = arr2.asarray()
      +if rank == 0:
      +    print('Full array2:', full_arr2)
      +
      +
      +
      Stacked array 2: <StackedDistributedArray with 2 distributed arrays:
      +<DistributedArray with global shape=(10,), local shape=(10,), dtype=<class 'numpy.float64'>, processes=[0])>
      +<DistributedArray with global shape=(4,), local shape=(4,), dtype=<class 'numpy.float64'>, processes=[0])>
      +Full array2: [5. 5. 5. 5. 5. 5. 5. 5. 5. 5. 6. 6. 6. 6.]
      +
      +
      +

      Negation

      +
      neg_arr = -arr1
      +full_neg_arr = neg_arr.asarray()
      +if rank == 0:
      +    print('Negated full array:', full_neg_arr)
      +
      +
      +
      Negated full array: [-10. -10. -10. -10. -10. -10. -10. -10. -10. -10.  -2.  -2.  -2.  -2.]
      +
      +
      +

      Element-wise Addition

      +
      sum_arr = arr1 + arr2
      +full_sum_arr = sum_arr.asarray()
      +if rank == 0:
      +    print('Summed full array:', full_sum_arr)
      +
      +
      +
      Summed full array: [15. 15. 15. 15. 15. 15. 15. 15. 15. 15.  8.  8.  8.  8.]
      +
      +
      +

      Element-wise Subtraction

      +
      sub_arr = arr1 - arr2
      +full_sub_arr = sub_arr.asarray()
      +if rank == 0:
      +    print('Subtracted full array:', full_sub_arr)
      +
      +
      +
      Subtracted full array: [ 5.  5.  5.  5.  5.  5.  5.  5.  5.  5. -4. -4. -4. -4.]
      +
      +
      +

      Multiplication

      +
      mult_arr = arr1 * arr2
      +full_mult_arr = mult_arr.asarray()
      +if rank == 0:
      +    print('Multipled full array:', full_mult_arr)
      +
      +
      +
      Multipled full array: [50. 50. 50. 50. 50. 50. 50. 50. 50. 50. 12. 12. 12. 12.]
      +
      +
      +

      Dot-product

      +
      dot_arr = arr1.dot(arr2)
      +if rank == 0:
      +    print('Dot-product:', dot_arr)
      +    print('Dot-product (np):', np.dot(full_arr1, full_arr2))
      +
      +
      +
      Dot-product: 548.0
      +Dot-product (np): 548.0
      +
      +
      +

      Norms

      +
      l0norm = arr1.norm(0)
      +l1norm = arr1.norm(1)
      +l2norm = arr1.norm(2)
      +linfnorm = arr1.norm(np.inf)
      +
      +if rank == 0:
      +    print('L0 norm', l0norm, np.linalg.norm(full_arr1, 0))
      +    print('L1 norm', l1norm, np.linalg.norm(full_arr1, 1))
      +    print('L2 norm', l2norm, np.linalg.norm(full_arr1, 2))
      +    print('Linf norm', linfnorm, np.linalg.norm(full_arr1, np.inf))
      +
      +
      +
      L0 norm 14.0 14.0
      +L1 norm 108.0 108.0
      +L2 norm 31.874754901018456 31.874754901018456
      +Linf norm 10.0 10.0
      +
      +
      +

      Now that we have a way to stack multiple pylops_mpi.StackedDistributedArray objects, +let’s see how we can apply operators to them. More specifically this can be +done using the pylops_mpi.MPIStackedVStack operator that takes multiple +pylops_mpi.MPILinearOperator objects, each acting on one specific +distributed array

      +
      x = pylops_mpi.DistributedArray(global_shape=size * 10,
      +                                partition=pylops_mpi.Partition.SCATTER,
      +                                axis=0)
      +# Filling the local arrays
      +x[:] = 1.
      +
      +# Make stacked operator
      +mop1 = pylops_mpi.MPIBlockDiag([pylops.MatrixMult(np.ones((5, 10))), ])
      +mop2 = pylops_mpi.MPIBlockDiag([pylops.MatrixMult(2 * np.ones((8, 10))), ])
      +mop = pylops_mpi.MPIStackedVStack([mop1, mop2])
      +
      +y = mop.matvec(x)
      +y_arr = y.asarray()
      +xadj = mop.rmatvec(y)
      +xadj_arr = xadj.asarray()
      +
      +if rank == 0:
      +    print('StackedVStack y', y, y_arr, y_arr.shape)
      +    print('StackedVStack xadj', xadj, xadj_arr, xadj_arr.shape)
      +
      +
      +
      StackedVStack y <StackedDistributedArray with 2 distributed arrays:
      +<DistributedArray with global shape=(5,), local shape=(5,), dtype=float64, processes=[0])>
      +<DistributedArray with global shape=(8,), local shape=(8,), dtype=float64, processes=[0])>  [10. 10. 10. 10. 10. 20. 20. 20. 20. 20. 20. 20. 20.] (13,)
      +StackedVStack xadj <DistributedArray with global shape=(10,), local shape=(10,), dtype=float64, processes=[0])>  [370. 370. 370. 370. 370. 370. 370. 370. 370. 370.] (10,)
      +
      +
      +

      Finally, let’s solve now an inverse problem using stacked arrays instead +of distributed arrays

      +
      x0 = x.copy()
      +x0[:] = 0.
      +xinv = pylops_mpi.cgls(mop, y, x0=x0, niter=15, tol=1e-10, show=False)[0]
      +xinv_array = xinv.asarray()
      +
      +if rank == 0:
      +    print('xinv_array', xinv_array)
      +
      +
      +
      xinv_array [1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]
      +
      +
      +

      Total running time of the script: (0 minutes 0.015 seconds)

      + +

      Gallery generated by Sphinx-Gallery

      +
      + + +
      + + + + + + + +
      + + + +
      + + +
      +
      + +
      + +
      +
      +
      + + + + + +
      + + +
      + + \ No newline at end of file diff --git a/gallery/plot_stacking.html b/gallery/plot_stacking.html index 32b151dd..e7cfdc2c 100644 --- a/gallery/plot_stacking.html +++ b/gallery/plot_stacking.html @@ -22,15 +22,15 @@ - - - + + + - - - - + + + + @@ -42,9 +42,9 @@ - - - + + + @@ -57,7 +57,7 @@ - + @@ -68,10 +68,9 @@ - +
      -

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