discretize.base.BaseTensorMesh¶

class discretize.base.BaseTensorMesh(h, origin=None, **kwargs)¶

Bases: discretize.base.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.

Attributes

axis_u: Deprecated since version 0.7.0.
axis_v: Deprecated since version 0.7.0.
axis_w: Deprecated since version 0.7.0.
boundary_edges: Boundary edge locations
boundary_face_outward_normals: Outward directed normal vectors for the boundary faces
boundary_faces: Boundary face locations
boundary_nodes: Boundary node locations
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: Edge grid
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: Face grid
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_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
orientation
origin: Origin of the mesh
reference_is_rotated: True if the axes are rotated from the traditional <X,Y,Z> system
reference_system: The type of coordinate reference frame.
rotation_matrix: Builds a rotation matrix to transform coordinates from their coordinate system into a conventional cartesian system.
shape_cells: The number of cells in each direction
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
`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.
`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
`validate`()	Every object will be valid upon initialization

deserialize
equals
serialize
to_dict

Attributes¶

BaseTensorMesh.axis_u¶

Deprecated since version 0.7.0: axis_u will be removed in discretize 1.0.0, it is replaced by mesh.orientation for better mesh orientation validation.

See also

orientation

BaseTensorMesh.boundary_edges¶

Boundary edge locations

Returns

np.ndarray of float: location array of shape (mesh.n_boundary_edges, dim)

BaseTensorMesh.boundary_face_outward_normals¶

Outward directed normal vectors for the boundary faces

Returns

np.ndarray of float: Array of vectors of shape (mesh.n_boundary_faces, dim)

BaseTensorMesh.boundary_faces¶

Boundary face locations

Returns

np.ndarray of float: location array of shape (mesh.n_boundary_faces, dim)

BaseTensorMesh.boundary_nodes¶

Boundary node locations

Returns

np.ndarray of float: location array of shape (mesh.n_boundary_nodes, dim)

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¶: Edge grid

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¶: Face grid

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¶

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.orientation¶

BaseTensorMesh.origin¶: Origin of the mesh

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¶: The type of coordinate reference frame. Can take on the values

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 relationship 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.shape_cells¶

The number of cells in each direction

Returns

tuple of ints

Notes

Also accessible as vnC.

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(items, **kwargs)¶

BaseTensorMesh.equals(other)¶

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.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()¶

BaseTensorMesh.to_dict()¶

BaseTensorMesh.validate()¶: Every object will be valid upon initialization

discretize.base.BaseTensorMesh¶

Examples using discretize.base.BaseTensorMesh¶

Attributes¶

Methods¶

Examples using `discretize.base.BaseTensorMesh`¶