discretize.base.BaseTensorMesh¶

class discretize.base.BaseTensorMesh(*args, **kwargs)[source]¶

Bases: discretize.base.base_mesh.BaseMesh

Base class for tensor-product style meshes

This class contains properites and methods that are common to cartesian and cylindrical meshes defined by tensor-produts of vectors describing cell spacings.

Do not use this class directly, instead, inherit it if you plan to develop a tensor-style mesh (e.g. a spherical mesh) or use the discretize.TensorMesh() class to create a cartesian tensor mesh.

Required Properties:

axis_u (Vector3): Vector orientation of u-direction. For more details see the docs for the rotation_matrix property., a 3D Vector of <class ‘float’> with shape (3), Default: X
axis_v (Vector3): Vector orientation of v-direction. For more details see the docs for the rotation_matrix property., a 3D Vector of <class ‘float’> with shape (3), Default: Y
axis_w (Vector3): Vector orientation of w-direction. For more details see the docs for the rotation_matrix property., a 3D Vector of <class ‘float’> with shape (3), Default: Z
h (a tuple of Array): h is a list containing the cell widths of the tensor mesh in each dimension., a tuple (each item is a list or numpy array of <class ‘float’> with shape (*)) with length between 1 and 3
origin (Array): origin of the mesh (dim, ), a list or numpy array of <class ‘float’>, <class ‘int’> with shape (*)
reference_system (String): The type of coordinate reference frame. Can take on the values cartesian, cylindrical, or spherical. Abbreviations of these are allowed., a unicode string, Default: cartesian

Attributes

axis_u: axis_u (Vector3): Vector orientation of u-direction. For more details see the docs for the rotation_matrix property., a 3D Vector of <class ‘float’> with shape (3), Default: X
axis_v: axis_v (Vector3): Vector orientation of v-direction. For more details see the docs for the rotation_matrix property., a 3D Vector of <class ‘float’> with shape (3), Default: Y
axis_w: axis_w (Vector3): Vector orientation of w-direction. For more details see the docs for the rotation_matrix property., a 3D Vector of <class ‘float’> with shape (3), Default: Z
cell_centers: Cell-centered grid.
cell_centers_x: Cell-centered grid vector (1D) in the x direction.
cell_centers_y: Cell-centered grid vector (1D) in the y direction.
cell_centers_z: Cell-centered grid vector (1D) in the z direction.
dim: The dimension of the mesh (1, 2, or 3).
edge_tangents: Edge Tangents
edges_x: Edge staggered grid in the x direction.
edges_y: Edge staggered grid in the y direction.
edges_z: Edge staggered grid in the z direction.
face_normals: Face Normals
faces_x: Face staggered grid in the x direction.
faces_y: Face staggered grid in the y direction.
faces_z: Face staggered grid in the z direction.
h: h (a tuple of Array): h is a list containing the cell widths of the tensor mesh in each dimension., a tuple (each item is a list or numpy array of <class ‘float’> with shape (*)) with length between 1 and 3
h_gridded: Returns an (nC, dim) numpy array with the widths of all cells in order
hx: Width of cells in the x direction
hy: Width of cells in the y direction
hz: Width of cells in the z direction
n_cells: Total number of cells in the mesh.
n_edges: Total number of edges.
n_edges_per_direction: The number of edges in each direction
n_edges_x: Number of x-edges
n_edges_y: Number of y-edges
n_edges_z: Number of z-edges
n_faces: Total number of faces.
n_faces_per_direction: The number of faces in each direction
n_faces_x: Number of x-faces
n_faces_y: Number of y-faces
n_faces_z: Number of z-faces
n_nodes: Total number of nodes
nodes: Nodal grid.
nodes_x: Nodal grid vector (1D) in the x direction.
nodes_y: Nodal grid vector (1D) in the y direction.
nodes_z: Nodal grid vector (1D) in the z direction.
normals: normals has been deprecated. See face_normals for documentation
origin: origin (Array): origin of the mesh (dim, ), a list or numpy array of <class ‘float’>, <class ‘int’> with shape (*)
reference_is_rotated: True if the axes are rotated from the traditional <X,Y,Z> system
reference_system: reference_system (String): The type of coordinate reference frame. Can take on the values cartesian, cylindrical, or spherical. Abbreviations of these are allowed., a unicode string, Default: cartesian
rotation_matrix: Builds a rotation matrix to transform coordinates from their coordinate system into a conventional cartesian system.
tangents: tangents has been deprecated. See edge_tangents for documentation
vectorCCx: vectorCCx has been deprecated. See cell_centers_x for documentation
vectorCCy: vectorCCy has been deprecated. See cell_centers_y for documentation
vectorCCz: vectorCCz has been deprecated. See cell_centers_z for documentation
vectorNx: vectorNx has been deprecated. See nodes_x for documentation
vectorNy: vectorNy has been deprecated. See nodes_y for documentation
vectorNz: vectorNz has been deprecated. See nodes_z for documentation
x0

Methods

`copy`()	Make a copy of the current mesh
`deserialize`(value, **kwargs)	Creates HasProperties instance from serialized dictionary
`equal`(other)	Determine if two HasProperties instances are equivalent
`from_omf`(element)	Convert an OMF element to it’s proper `discretize` type.
`getInterpolationMat`(args, *kwargs)	getInterpolationMat has been deprecated.
`getTensor`(args, *kwargs)	getTensor has been deprecated.
`get_interpolation_matrix`(loc[, …])	Produces linear interpolation matrix
`get_tensor`(key)	Returns a tensor list.
`isInside`(args, *kwargs)	isInside has been deprecated.
`is_inside`(pts[, location_type])	Determines if a set of points are inside a mesh.
`plotGrid`(args, *kwargs)	plotGrid has been deprecated.
`plotImage`(args, *kwargs)	plotImage has been deprecated.
`plotSlice`(args, *kwargs)	plotSlice has been deprecated.
`plot_3d_slicer`(v[, xslice, yslice, zslice, …])	Plot slices of a 3D volume, interactively (scroll wheel).
`plot_grid`([ax, nodes, faces, centers, …])	Plot the nodal, cell-centered and staggered grids.
`plot_image`(v[, v_type, grid, view, ax, …])	Plots fields on the given mesh.
`plot_slice`(v[, v_type, normal, ind, …])	Plots slice of fields on the given 3D mesh.
`projectEdgeVector`(args, *kwargs)	projectEdgeVector has been deprecated.
`projectFaceVector`(args, *kwargs)	projectFaceVector has been deprecated.
`project_edge_vector`(edge_vector)	Project vectors onto the edges of the mesh
`project_face_vector`(face_vector)	Project vectors onto the faces of the mesh.
`save`([file_name, verbose])	Save the mesh to json :param str file: file_name for saving the casing properties :param str directory: working directory for saving the file
`serialize`([include_class, save_dynamic])	Serializes a HasProperties instance to dictionary
`toVTK`([models])	Convert this mesh object to it’s proper VTK or `pyvista` data object with the given model dictionary as the cell data of that dataset.
`to_omf`([models])	Convert this mesh object to it’s proper `omf` data object with the given model dictionary as the cell data of that dataset.
`to_vtk`([models])	Convert this mesh object to it’s proper VTK or `pyvista` data object with the given model dictionary as the cell data of that dataset.
`validate`()	Call all registered class validator methods
`writeVTK`(file_name[, models, directory])	Makes and saves a VTK object from this mesh and given models
`write_vtk`(file_name[, models, directory])	Makes and saves a VTK object from this mesh and given models

Attributes¶

BaseTensorMesh.axis_u¶: axis_u (Vector3): Vector orientation of u-direction. For more details see the docs for the rotation_matrix property., a 3D Vector of <class ‘float’> with shape (3), Default: X

BaseTensorMesh.axis_v¶: axis_v (Vector3): Vector orientation of v-direction. For more details see the docs for the rotation_matrix property., a 3D Vector of <class ‘float’> with shape (3), Default: Y

BaseTensorMesh.axis_w¶: axis_w (Vector3): Vector orientation of w-direction. For more details see the docs for the rotation_matrix property., a 3D Vector of <class ‘float’> with shape (3), Default: Z

BaseTensorMesh.cell_centers¶: Cell-centered grid.

BaseTensorMesh.cell_centers_x¶: Cell-centered grid vector (1D) in the x direction.

BaseTensorMesh.cell_centers_y¶: Cell-centered grid vector (1D) in the y direction.

BaseTensorMesh.cell_centers_z¶: Cell-centered grid vector (1D) in the z direction.

BaseTensorMesh.dim¶

The dimension of the mesh (1, 2, or 3).

Returns

int: dimension of the mesh

BaseTensorMesh.edge_tangents¶

Edge Tangents

Returns

numpy.ndarray: normals, (n_edges, dim)

BaseTensorMesh.edges_x¶: Edge staggered grid in the x direction.

BaseTensorMesh.edges_y¶: Edge staggered grid in the y direction.

BaseTensorMesh.edges_z¶: Edge staggered grid in the z direction.

BaseTensorMesh.face_normals¶

Face Normals

Returns

numpy.ndarray: normals, (n_faces, dim)

BaseTensorMesh.faces_x¶: Face staggered grid in the x direction.

BaseTensorMesh.faces_y¶: Face staggered grid in the y direction.

BaseTensorMesh.faces_z¶: Face staggered grid in the z direction.

BaseTensorMesh.h¶: h (a tuple of Array): h is a list containing the cell widths of the tensor mesh in each dimension., a tuple (each item is a list or numpy array of <class ‘float’> with shape (*)) with length between 1 and 3

BaseTensorMesh.h_gridded¶: Returns an (nC, dim) numpy array with the widths of all cells in order

BaseTensorMesh.hx¶

Width of cells in the x direction

Returns

numpy.ndarray

Deprecated since version 0.5.0: hx will be removed in discretize 1.0.0 to reduce namespace clutter, please use mesh.h[0].

BaseTensorMesh.hy¶

Width of cells in the y direction

Returns

numpy.ndarray or None

Deprecated since version 0.5.0: hy will be removed in discretize 1.0.0 to reduce namespace clutter, please use mesh.h[1].

BaseTensorMesh.hz¶

Width of cells in the z direction

Returns

numpy.ndarray or None

Deprecated since version 0.5.0: hz will be removed in discretize 1.0.0 to reduce namespace clutter, please use mesh.h[2].

BaseTensorMesh.n_cells¶

Total number of cells in the mesh.

Returns

int: number of cells in the mesh

Notes

Also accessible as nC.

Examples

>>> import discretize
>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> mesh = discretize.TensorMesh([np.ones(n) for n in [2,3]])
>>> mesh.plot_grid(centers=True, show_it=True)
>>> print(mesh.n_cells)

(Source code, png, pdf)

../../_images/discretize-base-BaseTensorMesh-1.png

BaseTensorMesh.n_edges¶

Total number of edges.

Returns

int: sum([n_edges_x, n_edges_y, n_edges_z])

Notes

Also accessible as nE.

BaseTensorMesh.n_edges_per_direction¶

The number of edges in each direction

Returns

n_edges_per_directiontuple: [n_edges_x, n_edges_y, n_edges_z], (dim, )

Notes

Also accessible as vnE.

Examples

>>> import discretize
>>> import matplotlib.pyplot as plt
>>> import numpy as np
>>> M = discretize.TensorMesh([np.ones(n) for n in [2,3]])
>>> M.plot_grid(edges=True, show_it=True)

(Source code, png, pdf)

../../_images/discretize-base-BaseTensorMesh-2.png

BaseTensorMesh.n_edges_x¶

Number of x-edges

Returns

int

Notes

Also accessible as nEx.

BaseTensorMesh.n_edges_y¶

Number of y-edges

Returns

int

Notes

Also accessible as nEy.

BaseTensorMesh.n_edges_z¶

Number of z-edges

Returns

int

Notes

Also accessible as nEz.

BaseTensorMesh.n_faces¶

Total number of faces.

Returns

int: sum([n_faces_x, n_faces_y, n_faces_z])

Notes

Also accessible as nF.

BaseTensorMesh.n_faces_per_direction¶

The number of faces in each direction

Returns

n_faces_per_directiontuple: [n_faces_x, n_faces_y, n_faces_z], (dim, )

Notes

Also accessible as vnF.

Examples

>>> import discretize
>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> M = discretize.TensorMesh([np.ones(n) for n in [2,3]])
>>> M.plot_grid(faces=True, show_it=True)

(Source code, png, pdf)

../../_images/discretize-base-BaseTensorMesh-3.png

BaseTensorMesh.n_faces_x¶

Number of x-faces

Returns

int

Notes

Also accessible as nFx.

BaseTensorMesh.n_faces_y¶

Number of y-faces

Returns

int

Notes

Also accessible as nFy.

BaseTensorMesh.n_faces_z¶

Number of z-faces

Returns

int

Notes

Also accessible as nFz.

BaseTensorMesh.n_nodes¶

Total number of nodes

Returns

int: number of nodes in the mesh

Notes

Also accessible as nN.

Examples

>>> import discretize
>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> mesh = discretize.TensorMesh([np.ones(n) for n in [2,3]])
>>> mesh.plot_grid(nodes=True, show_it=True)
>>> print(mesh.n_nodes)

(Source code, png, pdf)

../../_images/discretize-base-BaseTensorMesh-4.png

BaseTensorMesh.nodes¶: Nodal grid.

BaseTensorMesh.nodes_x¶: Nodal grid vector (1D) in the x direction.

BaseTensorMesh.nodes_y¶: Nodal grid vector (1D) in the y direction.

BaseTensorMesh.nodes_z¶: Nodal grid vector (1D) in the z direction.

BaseTensorMesh.normals¶: normals has been deprecated. See face_normals for documentation

BaseTensorMesh.origin¶: origin (Array): origin of the mesh (dim, ), a list or numpy array of <class ‘float’>, <class ‘int’> with shape (*)

BaseTensorMesh.reference_is_rotated¶: True if the axes are rotated from the traditional <X,Y,Z> system with vectors of \((1,0,0)\), \((0,1,0)\), and \((0,0,1)\)

BaseTensorMesh.reference_system¶: reference_system (String): The type of coordinate reference frame. Can take on the values cartesian, cylindrical, or spherical. Abbreviations of these are allowed., a unicode string, Default: cartesian

BaseTensorMesh.rotation_matrix¶

Builds a rotation matrix to transform coordinates from their coordinate system into a conventional cartesian system. This is built off of the three axis_u, axis_v, and axis_w properties; these mapping coordinates use the letters U, V, and W (the three letters preceding X, Y, and Z in the alphabet) to define the projection of the X, Y, and Z durections. These UVW vectors describe the placement and transformation of the mesh’s coordinate sytem assuming at most 3 directions.

Why would you want to use these UVW mapping vectors the this rotation_matrix property? They allow us to define the realationship between local and global coordinate systems and provide a tool for switching between the two while still maintaing the connectivity of the mesh’s cells. For a visual example of this, please see the figure in the docs for the InterfaceVTK.

BaseTensorMesh.tangents¶: tangents has been deprecated. See edge_tangents for documentation

BaseTensorMesh.vectorCCx¶: vectorCCx has been deprecated. See cell_centers_x for documentation

BaseTensorMesh.vectorCCy¶: vectorCCy has been deprecated. See cell_centers_y for documentation

BaseTensorMesh.vectorCCz¶: vectorCCz has been deprecated. See cell_centers_z for documentation

BaseTensorMesh.vectorNx¶: vectorNx has been deprecated. See nodes_x for documentation

BaseTensorMesh.vectorNy¶: vectorNy has been deprecated. See nodes_y for documentation

BaseTensorMesh.vectorNz¶: vectorNz has been deprecated. See nodes_z for documentation

BaseTensorMesh.x0¶

Methods¶

BaseTensorMesh.copy()¶: Make a copy of the current mesh

classmethod BaseTensorMesh.deserialize(value, **kwargs)¶

Creates HasProperties instance from serialized dictionary

This uses the Property deserializers to deserialize all JSON-compatible dictionary values into their corresponding Property values on a new instance of a HasProperties class. Extra keys in the dictionary that do not correspond to Properties will be ignored.

Parameters:

value - Dictionary to deserialize new instance from.
trusted - If True (and if the input dictionary has '__class__' keyword and this class is in the registry), the new HasProperties class will come from the dictionary. If False (the default), only the HasProperties class this method is called on will be constructed.
strict - Requires '__class__', if present on the input dictionary, to match the deserialized instance’s class. Also disallows unused properties in the input dictionary. Default is False.
assert_valid - Require deserialized instance to be valid. Default is False.
Any other keyword arguments will be passed through to the Property deserializers.

BaseTensorMesh.equal(other)¶

Determine if two HasProperties instances are equivalent

Equivalence is determined by checking if all Property values on two instances are equal, using Property.equal.

static BaseTensorMesh.from_omf(element)¶: Convert an OMF element to it’s proper discretize type. Automatically determines the output type. Returns both the mesh and a dictionary of model arrays.

BaseTensorMesh.getInterpolationMat(*args, **kwargs)¶: getInterpolationMat has been deprecated. See get_interpolation_matrix for documentation

BaseTensorMesh.getTensor(*args, **kwargs)¶: getTensor has been deprecated. See get_tensor for documentation

BaseTensorMesh.get_interpolation_matrix(loc, location_type='cell_centers', zeros_outside=False, **kwargs)[source]¶

Produces linear interpolation matrix

Parameters

locnumpy.ndarray

Location of points to interpolate to

location_typestr

What to interpolate (see below)

location_type can be:

'Ex', 'edges_x'           -> x-component of field defined on x edges
'Ey', 'edges_y'           -> y-component of field defined on y edges
'Ez', 'edges_z'           -> z-component of field defined on z edges
'Fx', 'faces_x'           -> x-component of field defined on x faces
'Fy', 'faces_y'           -> y-component of field defined on y faces
'Fz', 'faces_z'           -> z-component of field defined on z faces
'N', 'nodes'              -> scalar field defined on nodes
'CC', 'cell_centers'      -> scalar field defined on cell centers
'CCVx', 'cell_centers_x'  -> x-component of vector field defined on cell centers
'CCVy', 'cell_centers_y'  -> y-component of vector field defined on cell centers
'CCVz', 'cell_centers_z'  -> z-component of vector field defined on cell centers

Returns

scipy.sparse.csr_matrix: M, the interpolation matrix

BaseTensorMesh.get_tensor(key)[source]¶

Returns a tensor list.

Parameters

keystr

Which tensor (see below)

key can be:

'CC', 'cell_centers' -> location of cell centers
'N', 'nodes'         -> location of nodes
'Fx', 'faces_x'      -> location of faces with an x normal
'Fy', 'faces_y'      -> location of faces with an y normal
'Fz', 'faces_z'      -> location of faces with an z normal
'Ex', 'edges_x'      -> location of edges with an x tangent
'Ey', 'edges_y'      -> location of edges with an y tangent
'Ez', 'edges_z'      -> location of edges with an z tangent

Returns

list: list of the tensors that make up the mesh.

BaseTensorMesh.isInside(*args, **kwargs)¶: isInside has been deprecated. See is_inside for documentation

BaseTensorMesh.is_inside(pts, location_type='nodes', **kwargs)[source]¶

Determines if a set of points are inside a mesh.

Parameters: pts (numpy.ndarray) – Location of points to test
Return type: numpy.ndarray
Returns: inside, numpy array of booleans

BaseTensorMesh.plotGrid(*args, **kwargs)¶: plotGrid has been deprecated. See plot_grid for documentation

BaseTensorMesh.plotImage(*args, **kwargs)¶: plotImage has been deprecated. See plot_image for documentation

BaseTensorMesh.plotSlice(*args, **kwargs)¶: plotSlice has been deprecated. See plot_slice for documentation

BaseTensorMesh.plot_3d_slicer(v, xslice=None, yslice=None, zslice=None, v_type='CC', view='real', axis='xy', transparent=None, clim=None, xlim=None, ylim=None, zlim=None, aspect='auto', grid=[2, 2, 1], pcolor_opts=None, fig=None, **kwargs)¶

Plot slices of a 3D volume, interactively (scroll wheel).

If called from a notebook, make sure to set

%matplotlib notebook

See the class discretize.View.Slicer for more information.

It returns nothing. However, if you need the different figure handles you can get it via

fig = plt.gcf()

and subsequently its children via

fig.get_children()

and recursively deeper, e.g.,

fig.get_children()[0].get_children().

One can also provide an existing figure instance, which can be useful for interactive widgets in Notebooks. The provided figure is cleared first.

BaseTensorMesh.plot_grid(ax=None, nodes=False, faces=False, centers=False, edges=False, lines=True, show_it=False, **kwargs)¶

Plot the nodal, cell-centered and staggered grids.

Parameters

axmatplotlib.axes.Axes or None, optional: The axes to draw on. None produces a new Axes.
nodes, faces, centers, edges, linesbool, optional: Whether to plot the corresponding item
show_itbool, optional: whether to call plt.show()
colorColor or str, optional: If lines=True, the color of the lines, defaults to first color.
linewidthfloat, optional: If lines=True, the linewidth for the lines.

Returns

matplotlib.axes.Axes: Axes handle for the plot

Other Parameters

edges_x, edges_y, edges_z, faces_x, faces_y, faces_zbool, optional: When plotting a TreeMesh, these are also options to plot the individual component items.
cell_linebool, optional: When plotting a TreeMesh, you can also plot a line through the cell centers in order.
slice{‘both’, ‘theta’, ‘z’}: When plotting a CylindricalMesh, which dimension to slice over.

Notes

Excess arguments are passed on to plot

Examples

Plotting a 2D TensorMesh grid

>>> from matplotlib import pyplot as plt
>>> import discretize
>>> import numpy as np
>>> h1 = np.linspace(.1, .5, 3)
>>> h2 = np.linspace(.1, .5, 5)
>>> mesh = discretize.TensorMesh([h1, h2])
>>> mesh.plot_grid(nodes=True, faces=True, centers=True, lines=True)
>>> plt.show()

(Source code, png, pdf)

../../_images/discretize-base-BaseTensorMesh-5_00_00.png

Plotting a 3D TensorMesh grid

>>> from matplotlib import pyplot as plt
>>> import discretize
>>> import numpy as np
>>> h1 = np.linspace(.1, .5, 3)
>>> h2 = np.linspace(.1, .5, 5)
>>> h3 = np.linspace(.1, .5, 3)
>>> mesh = discretize.TensorMesh([h1, h2, h3])
>>> mesh.plot_grid(nodes=True, faces=True, centers=True, lines=True)
>>> plt.show()

(png, pdf)

../../_images/discretize-base-BaseTensorMesh-5_01_00.png

Plotting a 2D CurvilinearMesh

>>> from matplotlib import pyplot as plt
>>> import discretize
>>> X, Y = discretize.utils.exampleLrmGrid([10, 10], 'rotate')
>>> M = discretize.CurvilinearMesh([X, Y])
>>> M.plot_grid()
>>> plt.show()

(png, pdf)

../../_images/discretize-base-BaseTensorMesh-5_02_00.png

Plotting a 3D CurvilinearMesh

>>> from matplotlib import pyplot as plt
>>> import discretize
>>> X, Y, Z = discretize.utils.exampleLrmGrid([5, 5, 5], 'rotate')
>>> M = discretize.CurvilinearMesh([X, Y, Z])
>>> M.plot_grid()
>>> plt.show()

(png, pdf)

../../_images/discretize-base-BaseTensorMesh-5_03_00.png

Plotting a 2D TreeMesh

>>> from matplotlib import pyplot as plt
>>> import discretize
>>> M = discretize.TreeMesh([32, 32])
>>> M.insert_cells([[0.25, 0.25]], [4])
>>> M.plot_grid()
>>> plt.show()

(png, pdf)

../../_images/discretize-base-BaseTensorMesh-5_04_00.png

Plotting a 3D TreeMesh

>>> from matplotlib import pyplot as plt
>>> import discretize
>>> M = discretize.TreeMesh([32, 32, 32])
>>> M.insert_cells([[0.3, 0.75, 0.22]], [4])
>>> M.plot_grid()
>>> plt.show()

(png, pdf)

../../_images/discretize-base-BaseTensorMesh-5_05_00.png

BaseTensorMesh.plot_image(v, v_type='CC', grid=False, view='real', ax=None, clim=None, show_it=False, pcolor_opts=None, stream_opts=None, grid_opts=None, range_x=None, range_y=None, sample_grid=None, stream_thickness=None, stream_threshold=None, **kwargs)¶

Plots fields on the given mesh.

Parameters

vnumpy.ndarray: values to plot
v_type{‘CC’,’CCV’, ‘N’, ‘F’, ‘Fx’, ‘Fy’, ‘Fz’, ‘E’, ‘Ex’, ‘Ey’, ‘Ez’}: Where the values of v are defined.
view{‘real’, ‘imag’, ‘abs’, ‘vec’}: How to view the array.
axmatplotlib.axes.Axes, optional: The axes to draw on. None produces a new Axes.
climtuple of float, optional: length 2 tuple of (vmin, vmax) for the color limits
range_x, range_ytuple of float, optional: length 2 tuple of (min, max) for the bounds of the plot axes.
pcolor_optsdict, optional: Arguments passed on to pcolormesh
gridbool, optional: Whether to plot the edges of the mesh cells.
grid_optsdict, optional: If grid is true, arguments passed on to plot for grid
sample_gridtuple of numpy.ndarray, optional: If view == ‘vec’, mesh cell widths (hx, hy) to interpolate onto for vector plotting
stream_optsdict, optional: If view == ‘vec’, arguments passed on to streamplot
stream_thicknessfloat, optional: If view == ‘vec’, linewidth for streamplot
stream_thresholdfloat, optional: If view == ‘vec’, only plots vectors with magnitude above this threshold
show_itbool, optional: Whether to call plt.show()
numberingbool, optional: For 3D TensorMesh only, show the numbering of the slices
annotation_colorColor or str, optional: For 3D TensorMesh only, color of the annotation

Examples

2D TensorMesh plotting

>>> from matplotlib import pyplot as plt
>>> import discretize
>>> import numpy as np
>>> M = discretize.TensorMesh([20, 20])
>>> v = np.sin(M.gridCC[:, 0]*2*np.pi)*np.sin(M.gridCC[:, 1]*2*np.pi)
>>> M.plot_image(v)
>>> plt.show()

(Source code, png, pdf)

../../_images/discretize-base-BaseTensorMesh-6_00_00.png

3D TensorMesh plotting

>>> import discretize
>>> import numpy as np
>>> M = discretize.TensorMesh([20, 20, 20])
>>> v = np.sin(M.gridCC[:, 0]*2*np.pi)*np.sin(M.gridCC[:, 1]*2*np.pi)*np.sin(M.gridCC[:, 2]*2*np.pi)
>>> M.plot_image(v, annotation_color='k')
>>> plt.show()

(png, pdf)

../../_images/discretize-base-BaseTensorMesh-6_01_00.png

BaseTensorMesh.plot_slice(v, v_type='CC', normal='Z', ind=None, slice_loc=None, grid=False, view='real', ax=None, clim=None, show_it=False, pcolor_opts=None, stream_opts=None, grid_opts=None, range_x=None, range_y=None, sample_grid=None, stream_threshold=None, stream_thickness=None, **kwargs)¶

Plots slice of fields on the given 3D mesh.

Parameters

vnumpy.ndarray: values to plot
v_type{‘CC’,’CCV’, ‘N’, ‘F’, ‘Fx’, ‘Fy’, ‘Fz’, ‘E’, ‘Ex’, ‘Ey’, ‘Ez’}, or tuple of these options: Where the values of v are defined.
normal{‘Z’, ‘X’, ‘Y’}: Normal direction of slicing plane.
indNone, optional: index along dimension of slice. Defaults to the center index.
slice_locNone, optional: Value along dimension of slice. Defaults to the center of the mesh.
view{‘real’, ‘imag’, ‘abs’, ‘vec’}: How to view the array.
axmatplotlib.axes.Axes, optional: The axes to draw on. None produces a new Axes. Must be None if v_type is a tuple.
climtuple of float, optional: length 2 tuple of (vmin, vmax) for the color limits
range_x, range_ytuple of float, optional: length 2 tuple of (min, max) for the bounds of the plot axes.
pcolor_optsdict, optional: Arguments passed on to pcolormesh
gridbool, optional: Whether to plot the edges of the mesh cells.
grid_optsdict, optional: If grid is true, arguments passed on to plot for the edges
sample_gridtuple of numpy.ndarray, optional: If view == ‘vec’, mesh cell widths (hx, hy) to interpolate onto for vector plotting
stream_optsdict, optional: If view == ‘vec’, arguments passed on to streamplot
stream_thicknessfloat, optional: If view == ‘vec’, linewidth for streamplot
stream_thresholdfloat, optional: If view == ‘vec’, only plots vectors with magnitude above this threshold
show_itbool, optional: Whether to call plt.show()

Examples

Plot a slice of a 3D TensorMesh solution to a Laplace’s equaiton.

First build the mesh:

>>> from matplotlib import pyplot as plt
>>> import discretize
>>> from pymatsolver import Solver
>>> hx = [(5, 2, -1.3), (2, 4), (5, 2, 1.3)]
>>> hy = [(2, 2, -1.3), (2, 6), (2, 2, 1.3)]
>>> hz = [(2, 2, -1.3), (2, 6), (2, 2, 1.3)]
>>> M = discretize.TensorMesh([hx, hy, hz])

then build the necessary parts of the PDE:

>>> q = np.zeros(M.vnC)
>>> q[[4, 4], [4, 4], [2, 6]]=[-1, 1]
>>> q = discretize.utils.mkvc(q)
>>> A = M.face_divergence * M.cell_gradient
>>> b = Solver(A) * (q)

and finaly, plot the vector values of the result, which are defined on faces

>>> M.plot_slice(M.cell_gradient*b, 'F', view='vec', grid=True, pcolor_opts={'alpha':0.8})
>>> plt.show()

(Source code, png, pdf)

../../_images/discretize-base-BaseTensorMesh-7_00_00.png

We can use the slice_loc kwarg to tell `plot_slice where to slice the mesh. Let’s create a mesh with a random model and plot slice of it. The slice_loc kwarg automatically determines the indices for slicing the mesh along a plane with the given normal.

>>> M = discretize.TensorMesh([32, 32, 32])
>>> v = discretize.utils.random_model(M.vnC, seed=789).reshape(-1, order='F')
>>> x_slice, y_slice, z_slice = 0.75, 0.25, 0.9
>>> plt.figure(figsize=(7.5, 3))
>>> ax = plt.subplot(131)
>>> M.plot_slice(v, normal='X', slice_loc=x_slice, ax=ax)
>>> ax = plt.subplot(132)
>>> M.plot_slice(v, normal='Y', slice_loc=y_slice, ax=ax)
>>> ax = plt.subplot(133)
>>> M.plot_slice(v, normal='Z', slice_loc=z_slice, ax=ax)
>>> plt.tight_layout()
>>> plt.show()

(png, pdf)

../../_images/discretize-base-BaseTensorMesh-7_01_00.png

This also works for TreeMesh. We create a mesh here that is refined within three boxes, along with a base level of refinement.

>>> TM = discretize.TreeMesh([32, 32, 32])
>>> TM.refine(3, finalize=False)
>>> BSW = [[0.25, 0.25, 0.25], [0.15, 0.15, 0.15], [0.1, 0.1, 0.1]]
>>> TNE = [[0.75, 0.75, 0.75], [0.85, 0.85, 0.85], [0.9, 0.9, 0.9]]
>>> levels = [6, 5, 4]
>>> TM.refine_box(BSW, TNE, levels)
>>> v_TM = discretize.utils.volume_average(M, TM, v)
>>> plt.figure(figsize=(7.5, 3))
>>> ax = plt.subplot(131)
>>> TM.plot_slice(v_TM, normal='X', slice_loc=x_slice, ax=ax)
>>> ax = plt.subplot(132)
>>> TM.plot_slice(v_TM, normal='Y', slice_loc=y_slice, ax=ax)
>>> ax = plt.subplot(133)
>>> TM.plot_slice(v_TM, normal='Z', slice_loc=z_slice, ax=ax)
>>> plt.tight_layout()
>>> plt.show()

(png, pdf)

../../_images/discretize-base-BaseTensorMesh-7_02_00.png

BaseTensorMesh.projectEdgeVector(*args, **kwargs)¶: projectEdgeVector has been deprecated. See project_edge_vector for documentation

BaseTensorMesh.projectFaceVector(*args, **kwargs)¶: projectFaceVector has been deprecated. See project_face_vector for documentation

BaseTensorMesh.project_edge_vector(edge_vector)¶

Project vectors onto the edges of the mesh

Given a vector, edge_vector, in cartesian coordinates, this will project it onto the mesh using the tangents

Parameters

edge_vectornumpy.ndarray: edge vector with shape (n_edges, dim)

Returns

numpy.ndarray: projected edge vector, (n_edges, )

BaseTensorMesh.project_face_vector(face_vector)¶

Project vectors onto the faces of the mesh.

Given a vector, face_vector, in cartesian coordinates, this will project it onto the mesh using the normals

Parameters

face_vectornumpy.ndarray: face vector with shape (n_faces, dim)

Returns

numpy.ndarray: projected face vector, (n_faces, )

BaseTensorMesh.save(file_name='mesh.json', verbose=False, **kwargs)¶: Save the mesh to json :param str file: file_name for saving the casing properties :param str directory: working directory for saving the file

BaseTensorMesh.serialize(include_class=True, save_dynamic=False, **kwargs)¶

Serializes a HasProperties instance to dictionary

This uses the Property serializers to serialize all Property values to a JSON-compatible dictionary. Properties that are undefined are not included. If the HasProperties instance contains a reference to itself, a properties.SelfReferenceError will be raised.

Parameters:

include_class - If True (the default), the name of the class will also be saved to the serialized dictionary under key '__class__'
save_dynamic - If True, dynamic properties are written to the serialized dict (default: False).
Any other keyword arguments will be passed through to the Property serializers.

BaseTensorMesh.toVTK(models=None)¶

Convert this mesh object to it’s proper VTK or pyvista data object with the given model dictionary as the cell data of that dataset.

Parameters

modelsdict(numpy.ndarray): Name(‘s) and array(‘s). Match number of cells

BaseTensorMesh.to_omf(models=None)¶

Convert this mesh object to it’s proper omf data object with the given model dictionary as the cell data of that dataset.

Parameters

modelsdict(numpy.ndarray): Name(‘s) and array(‘s). Match number of cells

BaseTensorMesh.to_vtk(models=None)¶

Convert this mesh object to it’s proper VTK or pyvista data object with the given model dictionary as the cell data of that dataset.

Parameters

modelsdict(numpy.ndarray): Name(‘s) and array(‘s). Match number of cells

BaseTensorMesh.validate()¶

Call all registered class validator methods

These are all methods decorated with @properties.validator. Validator methods are expected to raise a ValidationError if they fail.

BaseTensorMesh.writeVTK(file_name, models=None, directory='')¶

Makes and saves a VTK object from this mesh and given models

Parameters

file_namestr: path to the output vtk file or just its name if directory is specified
modelsdict: dictionary of numpy.array - Name(‘s) and array(‘s). Match number of cells
directorystr: directory where the UBC GIF file lives

BaseTensorMesh.write_vtk(file_name, models=None, directory='')¶

Makes and saves a VTK object from this mesh and given models

Parameters

file_namestr: path to the output vtk file or just its name if directory is specified
modelsdict: dictionary of numpy.array - Name(‘s) and array(‘s). Match number of cells
directorystr: directory where the UBC GIF file lives

discretize.base.BaseTensorMesh¶

Examples using discretize.base.BaseTensorMesh¶

Attributes¶

Methods¶

Examples using `discretize.base.BaseTensorMesh`¶