Azure CI commit ref 8d780d2db08987c824a7498eb77a55e95696d4c4

Author: simpeg-bot

en/latest

@@ -1 +1 @@
-v0.11.0
+v0.11.1

en/v0.11.1/.buildinfo

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+# Sphinx build info version 1
+# This file records the configuration used when building these files. When it is not found, a full rebuild will be done.
+config: 03fcd7c1152a1a651a3bc079a15e6708
+tags: 645f666f9bcd5a90fca523b33c5a78b7

en/v0.11.1/_downloads/005789fc4d07d603b5f8ac849b9d13b3/discretize-TensorMesh-stencil_cell_gradient_z-1_01_00.pdf

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+# Here we compute the values of a scalar function on the z-faces. We then create
+# an averaging operator to approximate the function at cell centers. We choose
+# to define a scalar function that is strongly discontinuous in some places to
+# demonstrate how the averaging operator will smooth out discontinuities.
+#
+# We start by importing the necessary packages and defining a mesh.
+#
+from discretize import TensorMesh
+import numpy as np
+import matplotlib.pyplot as plt
+#
+h = np.ones(40)
+mesh = TensorMesh([h, h, h], x0="CCC")
+#
+# Create a scalar variable on z-faces
+#
+phi_z = np.zeros(mesh.nFz)
+xyz = mesh.faces_z
+phi_z[(xyz[:, 2] > 0)] = 25.0
+phi_z[(xyz[:, 2] < -10.0) & (xyz[:, 0] > -10.0) & (xyz[:, 0] < 10.0)] = 50.0
+#
+# Next, we construct the averaging operator and apply it to
+# the discrete scalar quantity to approximate the value at cell centers.
+# We plot the original scalar and its average at cell centers for a
+# slice at y=0.
+#
+Azc = mesh.average_face_z_to_cell
+phi_c = Azc @ phi_z
+#
+# And plot the results:
+#
+fig = plt.figure(figsize=(11, 5))
+ax1 = fig.add_subplot(121)
+v = np.r_[np.zeros(mesh.nFx+mesh.nFy), phi_z]  # create vector for plotting
+mesh.plot_slice(v, ax=ax1, normal='Y', slice_loc=0, v_type="Fz")
+ax1.set_title("Variable at z-faces", fontsize=16)
+ax2 = fig.add_subplot(122)
+mesh.plot_image(phi_c, ax=ax2, normal='Y', slice_loc=0, v_type="CC")
+ax2.set_title("Averaged to cell centers", fontsize=16)
+plt.show()
+#
+# Below, we show a spy plot illustrating the sparsity and mapping
+# of the operator
+#
+fig = plt.figure(figsize=(9, 9))
+ax1 = fig.add_subplot(111)
+ax1.spy(Azc, ms=1)
+ax1.set_title("Z-Face Index", fontsize=12, pad=5)
+ax1.set_ylabel("Cell Index", fontsize=12)
+plt.show()

en/v0.11.1/_downloads/00703114884c34134968315009dc1fb7/discretize-base-BaseRectangularMesh-average_node_to_cell-1_00_00.png

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+# Here, we construct a 4 by 3 cell 2D tensor mesh and return the indices
+# of the x and y-boundary faces. In this case there are 3 x-faces on each
+# x-boundary, and there are 4 y-faces on each y-boundary.
+#
+from discretize import TensorMesh
+import numpy as np
+import matplotlib.pyplot as plt
+#
+hx = [1, 1, 1, 1]
+hy = [2, 2, 2]
+mesh = TensorMesh([hx, hy])
+ind_Bx1, ind_Bx2, ind_By1, ind_By2 = mesh.face_boundary_indices
+#
+ax = plt.subplot(111)
+mesh.plot_grid(ax=ax)
+ax.scatter(*mesh.faces_x[ind_Bx1].T)
+plt.show()

en/v0.11.1/_downloads/00972b6fe8d2afd4a5bbe6b217d60537/discretize-operators-DiffOperators-face_x_divergence-1_01_00.pdf

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+# Here we compute the values of a scalar function on the x-edges. We then create
+# an averaging operator to approximate the function at cell centers. We choose
+# to define a scalar function that is strongly discontinuous in some places to
+# demonstrate how the averaging operator will smooth out discontinuities.
+#
+# We start by importing the necessary packages and defining a mesh.
+#
+from discretize import TensorMesh
+import numpy as np
+import matplotlib.pyplot as plt
+h = np.ones(40)
+mesh = TensorMesh([h, h], x0="CC")
+#
+# Then we create a scalar variable on x-edges,
+#
+phi_x = np.zeros(mesh.nEx)
+xy = mesh.edges_x
+phi_x[(xy[:, 1] > 0)] = 25.0
+phi_x[(xy[:, 1] < -10.0) & (xy[:, 0] > -10.0) & (xy[:, 0] < 10.0)] = 50.0
+#
+# Next, we construct the averaging operator and apply it to
+# the discrete scalar quantity to approximate the value at cell centers.
+#
+Axc = mesh.average_edge_x_to_cell
+phi_c = Axc @ phi_x
+#
+# And plot the results,
+#
+fig = plt.figure(figsize=(11, 5))
+ax1 = fig.add_subplot(121)
+v = np.r_[phi_x, np.zeros(mesh.nEy)]  # create vector for plotting function
+mesh.plot_image(v, ax=ax1, v_type="Ex")
+ax1.set_title("Variable at x-edges", fontsize=16)
+ax2 = fig.add_subplot(122)
+mesh.plot_image(phi_c, ax=ax2, v_type="CC")
+ax2.set_title("Averaged to cell centers", fontsize=16)
+plt.show()
+#
+# Below, we show a spy plot illustrating the sparsity and mapping
+# of the operator
+#
+fig = plt.figure(figsize=(9, 9))
+ax1 = fig.add_subplot(111)
+ax1.spy(Axc, ms=1)
+ax1.set_title("X-Edge Index", fontsize=12, pad=5)
+ax1.set_ylabel("Cell Index", fontsize=12)
+plt.show()

en/v0.11.1/_downloads/00a125aeea8e7e004754bebfced6fee4/discretize-CurvilinearMesh-get_edge_inner_product_deriv-1_01_00.png

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+# We create a simple mesh and refine the TreeMesh such that all cells that
+# intersect the line segment path are at the given levels.
+#
+import discretize
+import matplotlib.pyplot as plt
+import matplotlib.patches as patches
+mesh = discretize.TreeMesh([32, 32, 32])
+mesh.max_level
+# Expected:
+## 5
+#
+# Next we define the bottom points of the prism, its heights, and the level we
+# want to refine to, then refine the mesh.
+#
+triangle = [[0.14, 0.31, 0.21], [0.32, 0.96, 0.34], [0.87, 0.23, 0.12]]
+height = 0.35
+levels = 5
+mesh.refine_vertical_trianglular_prism(triangle, height, levels)
+#
+# Now lets look at the mesh.
+#
+v = mesh.cell_levels_by_index(np.arange(mesh.n_cells))
+fig, axs = plt.subplots(1, 3, figsize=(12,4))
+mesh.plot_slice(v, ax=axs[0], normal='x', grid=True, clim=[2, 5])
+mesh.plot_slice(v, ax=axs[1], normal='y', grid=True, clim=[2, 5])
+mesh.plot_slice(v, ax=axs[2], normal='z', grid=True, clim=[2, 5])
+plt.show()

en/v0.11.1/_downloads/00de1867302800446136e7f6e8a82203/discretize-base-BaseTensorMesh-average_edge_to_cell-1_01_00.pdf

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+# Here we compute the values of a vector function discretized to the edges.
+# We then create an averaging operator to approximate the function at cell centers.
+#
+# We start by importing the necessary packages and defining a mesh.
+#
+from discretize import TensorMesh
+import numpy as np
+import matplotlib.pyplot as plt
+h = 0.5 * np.ones(40)
+mesh = TensorMesh([h, h], x0="CC")
+#
+# Then we create a discrete vector on mesh edges
+#
+edges_x = mesh.edges_x
+edges_y = mesh.edges_y
+u_ex = -(edges_x[:, 1] / np.sqrt(np.sum(edges_x ** 2, axis=1))) * np.exp(
+    -(edges_x[:, 0] ** 2 + edges_x[:, 1] ** 2) / 6 ** 2
+)
+u_ey = (edges_y[:, 0] / np.sqrt(np.sum(edges_y ** 2, axis=1))) * np.exp(
+    -(edges_y[:, 0] ** 2 + edges_y[:, 1] ** 2) / 6 ** 2
+)
+u_e = np.r_[u_ex, u_ey]
+#
+# Next, we construct the averaging operator and apply it to
+# the discrete vector quantity to approximate the value at cell centers.
+#
+Aec = mesh.average_edge_to_cell_vector
+u_c = Aec @ u_e
+#
+# And plot the results:
+#
+fig = plt.figure(figsize=(11, 5))
+ax1 = fig.add_subplot(121)
+mesh.plot_image(u_e, ax=ax1, v_type="E", view='vec')
+ax1.set_title("Variable at edges", fontsize=16)
+ax2 = fig.add_subplot(122)
+mesh.plot_image(u_c, ax=ax2, v_type="CCv", view='vec')
+ax2.set_title("Averaged to cell centers", fontsize=16)
+plt.show()
+#
+# Below, we show a spy plot illustrating the sparsity and mapping
+# of the operator
+#
+fig = plt.figure(figsize=(9, 9))
+ax1 = fig.add_subplot(111)
+ax1.spy(Aec, ms=1)
+ax1.set_title("Edge Index", fontsize=12, pad=5)
+ax1.set_ylabel("Cell Vector Index", fontsize=12)
+plt.show()

en/v0.11.1/_downloads/00eec92f5aa995bddf3caca93103192e/discretize-CylindricalMesh-average_face_z_to_cell-1.py

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+# Here we compute the values of a scalar function on the nodes. We then create
+# an averaging operator to approximate the function at the edges. We choose
+# to define a scalar function that is strongly discontinuous in some places to
+# demonstrate how the averaging operator will smooth out discontinuities.
+#
+# We start by importing the necessary packages and defining a mesh.
+#
+from discretize import TensorMesh
+import numpy as np
+import matplotlib.pyplot as plt
+h = np.ones(40)
+mesh = TensorMesh([h, h], x0="CC")
+#
+# Then we create a scalar variable on nodes,
+#
+phi_n = np.zeros(mesh.nN)
+xy = mesh.nodes
+phi_n[(xy[:, 1] > 0)] = 25.0
+phi_n[(xy[:, 1] < -10.0) & (xy[:, 0] > -10.0) & (xy[:, 0] < 10.0)] = 50.0
+#
+# Next, we construct the averaging operator and apply it to
+# the discrete scalar quantity to approximate the value on the edges.
+#
+Ane = mesh.average_node_to_edge
+phi_e = Ane @ phi_n
+#
+# Plot the results,
+#
+fig = plt.figure(figsize=(11, 5))
+ax1 = fig.add_subplot(121)
+mesh.plot_image(phi_n, ax=ax1, v_type="N")
+ax1.set_title("Variable at nodes")
+ax2 = fig.add_subplot(122)
+mesh.plot_image(phi_e, ax=ax2, v_type="E")
+ax2.set_title("Averaged to edges")
+plt.show()
+#
+# Below, we show a spy plot illustrating the sparsity and mapping
+# of the operator
+#
+fig = plt.figure(figsize=(9, 9))
+ax1 = fig.add_subplot(111)
+ax1.spy(Ane, ms=1)
+ax1.set_title("Node Index", fontsize=12, pad=5)
+ax1.set_ylabel("Edge Index", fontsize=12)
+plt.show()

en/v0.11.1/_downloads/01052d519ac9db44bbd1653a41d5f035/discretize-CurvilinearMesh-average_face_to_cell_vector-1_00_00.png

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+# For the 4 classifications allowable (scalar, isotropic, anistropic and tensor),
+# we construct and compare the property tensor on a small 2D mesh. For this
+# example, note the following:
+#
+#     - The dimensions for all property tensors are the same
+#     - All property tensors, except in the case of full anisotropy are diagonal
+#       sparse matrices
+#     - For the scalar case, the non-zero elements are equal
+#     - For the isotropic case, the non-zero elements repreat in order for the x, y
+#       (and z) components
+#     - For the anisotropic case (diagonal anisotropy), the non-zero elements do not
+#       repeat
+#     - For the tensor caes (full anisotropy), there are off-diagonal components
+#
+from discretize.utils import make_property_tensor
+from discretize import TensorMesh
+import numpy as np
+import matplotlib.pyplot as plt
+import matplotlib as mpl
+rng = np.random.default_rng(421)
+#
+# Define a 2D tensor mesh
+#
+h = [1., 1., 1.]
+mesh = TensorMesh([h, h], origin='00')
+#
+# Define a physical property for all cases (2D)
+#
+sigma_scalar = 4.
+sigma_isotropic = rng.integers(1, 10, mesh.nC)
+sigma_anisotropic = rng.integers(1, 10, (mesh.nC, 2))
+sigma_tensor = rng.integers(1, 10, (mesh.nC, 3))
+#
+# Construct the property tensor in each case
+#
+M_scalar = make_property_tensor(mesh, sigma_scalar)
+M_isotropic = make_property_tensor(mesh, sigma_isotropic)
+M_anisotropic = make_property_tensor(mesh, sigma_anisotropic)
+M_tensor = make_property_tensor(mesh, sigma_tensor)
+#
+# Plot the property tensors.
+#
+M_list = [M_scalar, M_isotropic, M_anisotropic, M_tensor]
+case_list = ['Scalar', 'Isotropic', 'Anisotropic', 'Full Tensor']
+ax1 = 4*[None]
+fig = plt.figure(figsize=(15, 4))
+for ii in range(0, 4):
+    ax1[ii] = fig.add_axes([0.05+0.22*ii, 0.05, 0.18, 0.9])
+    ax1[ii].imshow(
+        M_list[ii].todense(), interpolation='none', cmap='binary', vmax=10.
+    )
+    ax1[ii].set_title(case_list[ii], fontsize=24)
+ax2 = fig.add_axes([0.92, 0.15, 0.01, 0.7])
+norm = mpl.colors.Normalize(vmin=0., vmax=10.)
+cbar = mpl.colorbar.ColorbarBase(
+    ax2, norm=norm, orientation="vertical", cmap=mpl.cm.binary
+)
+plt.show()

en/v0.11.1/_downloads/010850f2a2c66f99069cda7e03fd34af/discretize-CurvilinearMesh-get_interpolation_matrix-1_00_00.png

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+# Create two meshes with the same extent, but different divisions (the meshes
+# do not have to be the same extent).
+#
+import numpy as np
+from discretize import TensorMesh
+rng = np.random.default_rng(853)
+h1 = np.ones(32)
+h2 = np.ones(16)*2
+mesh_in = TensorMesh([h1, h1])
+mesh_out = TensorMesh([h2, h2])
+#
+# Create a random model defined on the input mesh, and use volume averaging to
+# interpolate it to the output mesh.
+#
+from discretize.utils import volume_average
+model1 = rng.random(mesh_in.nC)
+model2 = volume_average(mesh_in, mesh_out, model1)
+#
+# Because these two meshes' cells are perfectly aligned, but the output mesh
+# has 1 cell for each 4 of the input cells, this operation should effectively
+# look like averaging each of those cells values
+#
+import matplotlib.pyplot as plt
+plt.figure(figsize=(6, 3))
+ax1 = plt.subplot(121)
+mesh_in.plot_image(model1, ax=ax1)
+ax2 = plt.subplot(122)
+mesh_out.plot_image(model2, ax=ax2)
+plt.show()