discretize.TreeMesh¶

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

Bases: discretize._extensions.tree_ext._TreeMesh, discretize.base.base_tensor_mesh.BaseTensorMesh, discretize.operators.inner_products.InnerProducts, discretize.base.mesh_io.TreeMeshIO

TreeMesh is a class for adaptive QuadTree (2D) and OcTree (3D) meshes.

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

area: area has been deprecated. See face_areas for documentation
areaFx: areaFx has been deprecated. See face_x_areas for documentation
areaFy: areaFy has been deprecated. See face_y_areas for documentation
areaFz: areaFz has been deprecated. See face_z_areas for documentation
average_cell_to_face: Construct the averaging operator on cell centers to cell faces.
average_cell_to_face_x: Construct the averaging operator on cell centers to cell x-faces.
average_cell_to_face_y: Construct the averaging operator on cell centers to cell y-faces.
average_cell_to_face_z: Construct the averaging operator on cell centers to cell z-faces.
average_cell_vector_to_face: Construct the averaging operator on cell centers to cell faces.
average_edge_to_cell: Construct the averaging operator on cell edges to cell centers.
average_edge_to_cell_vector: Construct the averaging operator on cell edges to cell centers.
average_edge_x_to_cell: Construct the averaging operator on cell edges in the x direction to cell centers.
average_edge_y_to_cell: Construct the averaging operator on cell edges in the y direction to cell centers.
average_edge_z_to_cell: Construct the averaging operator on cell edges in the z direction to cell centers.
average_face_to_cell: Construct the averaging operator on cell faces to cell centers.
average_face_to_cell_vector: Construct the averaging operator on cell faces to cell centers.
average_face_x_to_cell: Construct the averaging operator on cell faces in the x direction to cell centers.
average_face_y_to_cell: Construct the averaging operator on cell faces in the y direction to cell centers.
average_face_z_to_cell: Construct the averaging operator on cell faces in the z direction to cell centers.
average_node_to_cell: Construct the averaging operator on cell nodes to cell centers.
average_node_to_edge: Construct the averaging operator on cell nodes to cell edges, keeping each dimension separate.
average_node_to_edge_x: Averaging operator on cell nodes to x-edges
average_node_to_edge_y: Averaging operator on cell nodes to y-edges
average_node_to_edge_z: Averaging operator on cell nodes to z-edges
average_node_to_face: Construct the averaging operator on cell nodes to cell edges, keeping each dimension separate.
average_node_to_face_x: Averaging operator on cell nodes to x-faces
average_node_to_face_y: Averaging operator on cell nodes to y-faces
average_node_to_face_z: Averaging operator on cell nodes to z-faces
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
cellBoundaryInd: cellBoundaryInd has been deprecated. See cell_boundary_indices for documentation
cellGrad: cellGrad has been deprecated. See cell_gradient for documentation
cellGradStencil: cellGradStencil has been deprecated. See cell_gradient_stencil for documentation
cellGradx: cellGradx has been deprecated. See cell_gradient_x for documentation
cellGrady: cellGrady has been deprecated. See cell_gradient_y for documentation
cellGradz: cellGradz has been deprecated. See cell_gradient_z for documentation
cell_boundary_indices: Returns a tuple of arrays of indexes for boundary cells in each direction
cell_centers: Returns a numpy arrayof shape (n_cells, dim) with the center locations of all cells in order.
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.
cell_gradient: Cell centered Gradient operator built off of the faceDiv operator.
cell_gradient_x: Cell centered Gradient operator in x-direction (Gradx)
cell_gradient_y: Cell centered Gradient operator in y-direction (Grady)
cell_gradient_z: Cell centered Gradient operator in z-direction (Gradz)
cell_nodes: The index of nodes for each cell.
cell_volumes: Returns a numpy array of length n_cells with the volumes (areas in 2D) of all cells in order.
dim: The dimension of the mesh (1, 2, or 3).
edge: edge has been deprecated. See edge_lengths for documentation
edgeCurl: edgeCurl has been deprecated. See edge_curl for documentation
edgeEx: edgeEx has been deprecated. See edge_x_lengths for documentation
edgeEy: edgeEy has been deprecated. See edge_y_lengths for documentation
edgeEz: edgeEz has been deprecated. See edge_z_lengths for documentation
edge_curl: Construct the 3D curl operator.
edge_lengths: Returns a numpy array of length n_edges with the length of all edges ordered by x, then y, then z.
edge_nodes: The index of nodes for every edge.
edge_tangents: Edge Tangents
edges_x: Returns a numpy array of shape (n_edges_x, dim) with the centers of all non-hanging edges along the first dimension in order.
edges_y: Returns a numpy array of shape (n_edges_y, dim) with the centers of all non-hanging edges along the second dimension in order.
edges_z: Returns a numpy array of shape (n_edges_z, dim) with the centers of all non-hanging edges along the third dimension in order.
faceBoundaryInd: faceBoundaryInd has been deprecated. See face_boundary_indices for documentation
faceDiv: faceDiv has been deprecated. See face_divergence for documentation
faceDivx: faceDivx has been deprecated. See face_x_divergence for documentation
faceDivy: faceDivy has been deprecated. See face_y_divergence for documentation
faceDivz: faceDivz has been deprecated. See face_z_divergence for documentation
face_areas: Returns a numpy array of length n_faces with the area (length in 2D) of all faces ordered by x, then y, then z.
face_boundary_indices: Returns a tuple of arrays of indexes for boundary faces in each direction
face_divergence: Construct divergence operator (face-stg to cell-centres).
face_normals: Face Normals
face_x_divergence
face_y_divergence
face_z_divergence
faces_x: Returns a numpy array of shape (n_faces_x, dim) with the centers of all non-hanging faces along the first dimension in order.
faces_y: Returns a numpy array of shape (n_faces_y, dim) with the centers of all non-hanging faces along the second dimension in order.
faces_z: Returns a numpy array of shape (n_faces_z, dim) with the centers of all non-hanging faces along the third dimension in order.
fill: How filled is the mesh compared to a TensorMesh? As a fraction: [0, 1].
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 (n_cells, dim) numpy array with the widths of all cells in order
hanging_edges_x: Returns a numpy array of shape (n_hanging_edges_x, dim) with the centers of all hanging edges along the first dimension in order.
hanging_edges_y: Returns a numpy array of shape (n_hanging_edges_y, dim) with the centers of all hanging edges along the second dimension in order.
hanging_edges_z: Returns a numpy array of shape (n_hanging_edges_z, dim) with the centers of all hanging edges along the third dimension in order.
hanging_faces_x: Returns a numpy array of shape (n_hanging_faces_x, dim) with the centers of all hanging faces along the first dimension in order.
hanging_faces_y: Returns a numpy array of shape (n_hanging_faces_y, dim) with the centers of all hanging faces along the second dimension in order.
hanging_faces_z: Returns a numpy array of shape (n_hanging_faces_z, dim) with the centers of all hanging faces along the third dimension in order.
hanging_nodes: Returns a numpy array of shape (n_nodes, dim) with the locations of all hanging nodes 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
maxLevel: maxLevel has been deprecated. See max_used_level for documentation
max_level: The maximum possible level for a cell on this mesh
max_used_level: The maximum level used, which may be less than max_level.
n_cells: Number of cells
n_edges: Total number of non-hanging edges amongst all dimensions
n_edges_per_direction: The number of edges in each direction
n_edges_x: Number of non-hanging edges oriented along the first dimension
n_edges_y: Number of non-hanging edges oriented along the second dimension
n_edges_z: Number of non-hanging edges oriented along the third dimension
n_faces: Total number of non-hanging faces amongst all dimensions
n_faces_per_direction: The number of faces in each direction
n_faces_x: Number of non-hanging faces oriented along the first dimension
n_faces_y: Number of non-hanging faces oriented along the second dimension
n_faces_z: Number of non-hanging faces oriented along the third dimension
n_hanging_edges: Total number of hanging edges amongst all dimensions
n_hanging_edges_x: Number of hanging edges oriented along the first dimension
n_hanging_edges_y: Number of hanging edges oriented along the second dimension
n_hanging_edges_z: Number of hanging edges oriented along the third dimension
n_hanging_faces: Total number of hanging faces amongst all dimensions
n_hanging_faces_x: Number of hanging faces oriented along the first dimension
n_hanging_faces_y: Number of hanging faces oriented along the second dimension
n_hanging_faces_z: Number of hanging faces oriented along the third dimension
n_hanging_nodes: Number of hanging nodes
n_nodes: Number of non-hanging nodes
n_total_edges: Total number of non-hanging and hanging edges amongst all dimensions
n_total_edges_x: Number of non-hanging and hanging edges oriented along the first dimension
n_total_edges_y: Number of non-hanging and hanging edges oriented along the second dimension
n_total_edges_z: Number of non-hanging and hanging edges oriented along the third dimension
n_total_faces: Total number of hanging and non-hanging faces amongst all dimensions
n_total_faces_x: Number of non-hanging and hanging faces oriented along the first dimension
n_total_faces_y: Number of non-hanging and hanging faces oriented along the second dimension
n_total_faces_z: Number of non-hanging and hanging faces oriented along the third dimension
n_total_nodes: Number of non-hanging and hanging nodes
nodalGrad: nodalGrad has been deprecated. See nodal_gradient for documentation
nodalLaplacian: nodalLaplacian has been deprecated. See nodal_laplacian for documentation
nodal_gradient: Construct gradient operator (nodes to edges).
nodal_laplacian
nodes: Returns a numpy array of shape (n_nodes, dim) with the locations of all non-hanging nodes in order.
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 (*)
permuteCC: permuteCC has been deprecated. See permute_cells for documentation
permuteE: permuteE has been deprecated. See permute_edges for documentation
permuteF: permuteF has been deprecated. See permute_faces for documentation
permute_cells: Permutation matrix re-ordering of cells sorted by x, then y, then z
permute_edges: Permutation matrix re-ordering of edges sorted by x, then y, then z
permute_faces: Permutation matrix re-ordering of faces sorted by x, then y, then z
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.
stencil_cell_gradient
stencil_cell_gradient_x: Cell gradient stencil matrix to total (including hanging) x faces
stencil_cell_gradient_y: Cell gradient stencil matrix to total (including hanging) y faces
stencil_cell_gradient_z: Cell gradient stencil matrix to total (including hanging) z faces
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
vntE: Total number of hanging and non-hanging edges in a [nx,ny,nz] form
vntF: Total number of hanging and non-hanging faces in a [nx,ny,nz] form
vol: vol has been deprecated. See cell_volumes for documentation
x0

Methods

`average_cell_to_total_face_x`(self)	Average matrix for cell center to total (including hanging) x faces
`average_cell_to_total_face_y`(self)	Average matrix for cell center to total (including hanging) y faces
`average_cell_to_total_face_z`(self)	Average matrix for cell center to total (including hanging) z faces
`cell_levels_by_index`(indices)	Fast function to return a list of levels for the given cell indices
`copy`()	Make a copy of the current mesh
`deserialize`(serial)	Creates HasProperties instance from serialized dictionary
`equal`(other)	Determine if two HasProperties instances are equivalent
`finalize`(self)	Finalize the TreeMesh Called after finished cronstruction of the mesh.
`from_omf`(element)	Convert an OMF element to it’s proper `discretize` type.
`getEdgeInnerProduct`(args, *kwargs)	getEdgeInnerProduct has been deprecated.
`getEdgeInnerProductDeriv`(args, *kwargs)	getEdgeInnerProductDeriv has been deprecated.
`getFaceInnerProduct`(args, *kwargs)	getFaceInnerProduct has been deprecated.
`getFaceInnerProductDeriv`(args, *kwargs)	getFaceInnerProductDeriv has been deprecated.
`getInterpolationMat`(args, *kwargs)	getInterpolationMat has been deprecated.
`getTensor`(args, *kwargs)	getTensor has been deprecated.
`get_boundary_cells`(self[, active_ind, direction])	Returns the indices of boundary cells in a given direction given an active index array.
`get_cells_along_line`(self, x0, x1)	Finds the cells along a line segment defined by two points
`get_edge_inner_product`([model, …])	Generate the edge inner product matrix
`get_edge_inner_product_deriv`(model[, …])	Parameters
`get_face_inner_product`([model, …])	Generate the face inner product matrix
`get_face_inner_product_deriv`(model[, …])	Parameters
`get_interpolation_matrix`(locs[, …])	Produces interpolation matrix
`get_overlapping_cells`(self, rectangle)
`get_tensor`(key)	Returns a tensor list.
`insert_cells`(self, points, levels[, finalize])	Insert cells into the TreeMesh that contain given points
`isInside`(args, *kwargs)	isInside has been deprecated.
`is_inside`(pts[, location_type])	Determines if a set of points are inside a mesh.
`number`(self)	Number the cells, nodes, faces, and edges of the TreeMesh
`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.
`point2index`(locs)	Finds cells that contain the given points.
`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.
`readModelUBC`(args, *kwargs)	readModelUBC has been deprecated.
`readUBC`(file_name[, directory])
`read_UBC`(meshFile[, directory])	Read UBC 3D OcTree mesh file Input: :param str meshFile: path to the UBC GIF OcTree mesh file to read :rtype: discretize.TreeMesh :return: The octree mesh
`read_model_UBC`(file_name)	Read UBC OcTree model and get vector :param string file_name: path to the UBC GIF model file to read :rtype: numpy.ndarray :return: OcTree model
`refine`(self, function[, finalize])	Refine a TreeMesh using a user supplied function.
`refine_ball`(self, points, radii, levels[, …])	Refines the TreeMesh around points with the given radii
`refine_box`(self, x0s, x1s, levels[, finalize])	Refines the TreeMesh within the axis aligned boxes to the desired level
`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`()	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
`writeModelUBC`(args, *kwargs)	writeModelUBC has been deprecated.
`writeUBC`(args, *kwargs)	writeUBC has been deprecated.
`writeVTK`(file_name[, models, directory])	Makes and saves a VTK object from this mesh and given models
`write_UBC`(file_name[, models, directory])	Write UBC ocTree mesh and model files from a octree mesh and model.
`write_model_UBC`(file_name, model[, directory])	Writes a model associated with a TreeMesh to a UBC-GIF format model file.
`write_vtk`(file_name[, models, directory])	Makes and saves a VTK object from this mesh and given models

Examples using `discretize.TreeMesh`¶

Basic: PlotImage¶

QuadTree: FaceDiv¶

QuadTree: Hanging Nodes¶

Overview of Mesh Types¶

Tree Meshes¶

Differential Operators¶

Attributes¶

TreeMesh.area¶: area has been deprecated. See face_areas for documentation

TreeMesh.areaFx¶: areaFx has been deprecated. See face_x_areas for documentation

TreeMesh.areaFy¶: areaFy has been deprecated. See face_y_areas for documentation

TreeMesh.areaFz¶: areaFz has been deprecated. See face_z_areas for documentation

TreeMesh.average_cell_to_face¶: Construct the averaging operator on cell centers to cell faces.

TreeMesh.average_cell_to_face_x¶: Construct the averaging operator on cell centers to cell x-faces.

TreeMesh.average_cell_to_face_y¶: Construct the averaging operator on cell centers to cell y-faces.

TreeMesh.average_cell_to_face_z¶: Construct the averaging operator on cell centers to cell z-faces.

TreeMesh.average_cell_vector_to_face¶: Construct the averaging operator on cell centers to cell faces.

TreeMesh.average_edge_to_cell¶: Construct the averaging operator on cell edges to cell centers.

TreeMesh.average_edge_to_cell_vector¶: Construct the averaging operator on cell edges to cell centers.

TreeMesh.average_edge_x_to_cell¶: Construct the averaging operator on cell edges in the x direction to cell centers.

TreeMesh.average_edge_y_to_cell¶: Construct the averaging operator on cell edges in the y direction to cell centers.

TreeMesh.average_edge_z_to_cell¶: Construct the averaging operator on cell edges in the z direction to cell centers.

TreeMesh.average_face_to_cell¶: Construct the averaging operator on cell faces to cell centers.

TreeMesh.average_face_to_cell_vector¶: Construct the averaging operator on cell faces to cell centers.

TreeMesh.average_face_x_to_cell¶: Construct the averaging operator on cell faces in the x direction to cell centers.

TreeMesh.average_face_y_to_cell¶: Construct the averaging operator on cell faces in the y direction to cell centers.

TreeMesh.average_face_z_to_cell¶: Construct the averaging operator on cell faces in the z direction to cell centers.

TreeMesh.average_node_to_cell¶: Construct the averaging operator on cell nodes to cell centers.

TreeMesh.average_node_to_edge¶: Construct the averaging operator on cell nodes to cell edges, keeping each dimension separate.

TreeMesh.average_node_to_edge_x¶: Averaging operator on cell nodes to x-edges

TreeMesh.average_node_to_edge_y¶: Averaging operator on cell nodes to y-edges

TreeMesh.average_node_to_edge_z¶: Averaging operator on cell nodes to z-edges

TreeMesh.average_node_to_face¶: Construct the averaging operator on cell nodes to cell edges, keeping each dimension separate.

TreeMesh.average_node_to_face_x¶: Averaging operator on cell nodes to x-faces

TreeMesh.average_node_to_face_y¶: Averaging operator on cell nodes to y-faces

TreeMesh.average_node_to_face_z¶: Averaging operator on cell nodes to z-faces

TreeMesh.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

TreeMesh.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

TreeMesh.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

TreeMesh.cellBoundaryInd¶: cellBoundaryInd has been deprecated. See cell_boundary_indices for documentation

TreeMesh.cellGrad¶: cellGrad has been deprecated. See cell_gradient for documentation

TreeMesh.cellGradStencil¶: cellGradStencil has been deprecated. See cell_gradient_stencil for documentation

TreeMesh.cellGradx¶: cellGradx has been deprecated. See cell_gradient_x for documentation

TreeMesh.cellGrady¶: cellGrady has been deprecated. See cell_gradient_y for documentation

TreeMesh.cellGradz¶: cellGradz has been deprecated. See cell_gradient_z for documentation

TreeMesh.cell_boundary_indices¶: Returns a tuple of arrays of indexes for boundary cells in each direction xdown, xup, ydown, yup, zdown, zup

TreeMesh.cell_centers¶: Returns a numpy arrayof shape (n_cells, dim) with the center locations of all cells in order.

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

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

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

TreeMesh.cell_gradient¶: Cell centered Gradient operator built off of the faceDiv operator. Grad = - (Mf)^{-1} * Div * diag (volume)

TreeMesh.cell_gradient_x¶: Cell centered Gradient operator in x-direction (Gradx) Grad = sp.vstack((Gradx, Grady, Gradz))

TreeMesh.cell_gradient_y¶: Cell centered Gradient operator in y-direction (Grady) Grad = sp.vstack((Gradx, Grady, Gradz))

TreeMesh.cell_gradient_z¶: Cell centered Gradient operator in z-direction (Gradz) Grad = sp.vstack((Gradx, Grady, Gradz))

TreeMesh.cell_nodes¶

The index of nodes for each cell.

Returns

numpy.ndarray of ints: Index array of shape (n_cells, 4) if 2D, or (n_cells, 6) if 3D

Notes

These indices will also point to hanging nodes.

TreeMesh.cell_volumes¶: Returns a numpy array of length n_cells with the volumes (areas in 2D) of all cells in order.

TreeMesh.dim¶

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

Returns

int: dimension of the mesh

TreeMesh.edge¶: edge has been deprecated. See edge_lengths for documentation

TreeMesh.edgeCurl¶: edgeCurl has been deprecated. See edge_curl for documentation

TreeMesh.edgeEx¶: edgeEx has been deprecated. See edge_x_lengths for documentation

TreeMesh.edgeEy¶: edgeEy has been deprecated. See edge_y_lengths for documentation

TreeMesh.edgeEz¶: edgeEz has been deprecated. See edge_z_lengths for documentation

TreeMesh.edge_curl¶: Construct the 3D curl operator.

TreeMesh.edge_lengths¶: Returns a numpy array of length n_edges with the length of all edges ordered by x, then y, then z.

TreeMesh.edge_nodes¶

The index of nodes for every edge.

The index of the nodes at each end of every (including hanging) edge.

Returns

tuple of numpy.ndarray of ints: One numpy array for each edge type (x, y, (z)) for this mesh.

Notes

These arrays will also index into the hanging nodes.

TreeMesh.edge_tangents¶

Edge Tangents

Returns

numpy.ndarray: normals, (n_edges, dim)

TreeMesh.edges_x¶: Returns a numpy array of shape (n_edges_x, dim) with the centers of all non-hanging edges along the first dimension in order.

TreeMesh.edges_y¶: Returns a numpy array of shape (n_edges_y, dim) with the centers of all non-hanging edges along the second dimension in order.

TreeMesh.edges_z¶: Returns a numpy array of shape (n_edges_z, dim) with the centers of all non-hanging edges along the third dimension in order.

TreeMesh.faceBoundaryInd¶: faceBoundaryInd has been deprecated. See face_boundary_indices for documentation

TreeMesh.faceDiv¶: faceDiv has been deprecated. See face_divergence for documentation

TreeMesh.faceDivx¶: faceDivx has been deprecated. See face_x_divergence for documentation

TreeMesh.faceDivy¶: faceDivy has been deprecated. See face_y_divergence for documentation

TreeMesh.faceDivz¶: faceDivz has been deprecated. See face_z_divergence for documentation

TreeMesh.face_areas¶: Returns a numpy array of length n_faces with the area (length in 2D) of all faces ordered by x, then y, then z.

TreeMesh.face_boundary_indices¶: Returns a tuple of arrays of indexes for boundary faces in each direction xdown, xup, ydown, yup, zdown, zup

TreeMesh.face_divergence¶: Construct divergence operator (face-stg to cell-centres).

TreeMesh.face_normals¶

Face Normals

Returns

numpy.ndarray: normals, (n_faces, dim)

TreeMesh.face_x_divergence¶

TreeMesh.face_y_divergence¶

TreeMesh.face_z_divergence¶

TreeMesh.faces_x¶: Returns a numpy array of shape (n_faces_x, dim) with the centers of all non-hanging faces along the first dimension in order.

TreeMesh.faces_y¶: Returns a numpy array of shape (n_faces_y, dim) with the centers of all non-hanging faces along the second dimension in order.

TreeMesh.faces_z¶: Returns a numpy array of shape (n_faces_z, dim) with the centers of all non-hanging faces along the third dimension in order.

TreeMesh.fill¶: How filled is the mesh compared to a TensorMesh? As a fraction: [0, 1].

TreeMesh.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

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

TreeMesh.hanging_edges_x¶: Returns a numpy array of shape (n_hanging_edges_x, dim) with the centers of all hanging edges along the first dimension in order.

TreeMesh.hanging_edges_y¶: Returns a numpy array of shape (n_hanging_edges_y, dim) with the centers of all hanging edges along the second dimension in order.

TreeMesh.hanging_edges_z¶: Returns a numpy array of shape (n_hanging_edges_z, dim) with the centers of all hanging edges along the third dimension in order.

TreeMesh.hanging_faces_x¶: Returns a numpy array of shape (n_hanging_faces_x, dim) with the centers of all hanging faces along the first dimension in order.

TreeMesh.hanging_faces_y¶: Returns a numpy array of shape (n_hanging_faces_y, dim) with the centers of all hanging faces along the second dimension in order.

TreeMesh.hanging_faces_z¶: Returns a numpy array of shape (n_hanging_faces_z, dim) with the centers of all hanging faces along the third dimension in order.

TreeMesh.hanging_nodes¶: Returns a numpy array of shape (n_nodes, dim) with the locations of all hanging nodes in order.

TreeMesh.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].

TreeMesh.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].

TreeMesh.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].

TreeMesh.maxLevel¶: maxLevel has been deprecated. See max_used_level for documentation

TreeMesh.max_level¶: The maximum possible level for a cell on this mesh

TreeMesh.max_used_level¶: The maximum level used, which may be less than max_level.

TreeMesh.n_cells¶: Number of cells

TreeMesh.n_edges¶: Total number of non-hanging edges amongst all dimensions

TreeMesh.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)

TreeMesh.n_edges_x¶: Number of non-hanging edges oriented along the first dimension

TreeMesh.n_edges_y¶: Number of non-hanging edges oriented along the second dimension

TreeMesh.n_edges_z¶: Number of non-hanging edges oriented along the third dimension

TreeMesh.n_faces¶: Total number of non-hanging faces amongst all dimensions

TreeMesh.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)

TreeMesh.n_faces_x¶: Number of non-hanging faces oriented along the first dimension

TreeMesh.n_faces_y¶: Number of non-hanging faces oriented along the second dimension

TreeMesh.n_faces_z¶: Number of non-hanging faces oriented along the third dimension

TreeMesh.n_hanging_edges¶: Total number of hanging edges amongst all dimensions

TreeMesh.n_hanging_edges_x¶: Number of hanging edges oriented along the first dimension

TreeMesh.n_hanging_edges_y¶: Number of hanging edges oriented along the second dimension

TreeMesh.n_hanging_edges_z¶: Number of hanging edges oriented along the third dimension

TreeMesh.n_hanging_faces¶: Total number of hanging faces amongst all dimensions

TreeMesh.n_hanging_faces_x¶: Number of hanging faces oriented along the first dimension

TreeMesh.n_hanging_faces_y¶: Number of hanging faces oriented along the second dimension

TreeMesh.n_hanging_faces_z¶: Number of hanging faces oriented along the third dimension

TreeMesh.n_hanging_nodes¶: Number of hanging nodes

TreeMesh.n_nodes¶: Number of non-hanging nodes

TreeMesh.n_total_edges¶: Total number of non-hanging and hanging edges amongst all dimensions

TreeMesh.n_total_edges_x¶: Number of non-hanging and hanging edges oriented along the first dimension

TreeMesh.n_total_edges_y¶: Number of non-hanging and hanging edges oriented along the second dimension

TreeMesh.n_total_edges_z¶: Number of non-hanging and hanging edges oriented along the third dimension

TreeMesh.n_total_faces¶: Total number of hanging and non-hanging faces amongst all dimensions

TreeMesh.n_total_faces_x¶: Number of non-hanging and hanging faces oriented along the first dimension

TreeMesh.n_total_faces_y¶: Number of non-hanging and hanging faces oriented along the second dimension

TreeMesh.n_total_faces_z¶: Number of non-hanging and hanging faces oriented along the third dimension

TreeMesh.n_total_nodes¶: Number of non-hanging and hanging nodes

TreeMesh.nodalGrad¶: nodalGrad has been deprecated. See nodal_gradient for documentation

TreeMesh.nodalLaplacian¶: nodalLaplacian has been deprecated. See nodal_laplacian for documentation

TreeMesh.nodal_gradient¶: Construct gradient operator (nodes to edges).

TreeMesh.nodal_laplacian¶

TreeMesh.nodes¶: Returns a numpy array of shape (n_nodes, dim) with the locations of all non-hanging nodes in order.

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

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

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

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

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

TreeMesh.permuteCC¶: permuteCC has been deprecated. See permute_cells for documentation

TreeMesh.permuteE¶: permuteE has been deprecated. See permute_edges for documentation

TreeMesh.permuteF¶: permuteF has been deprecated. See permute_faces for documentation

TreeMesh.permute_cells¶: Permutation matrix re-ordering of cells sorted by x, then y, then z

TreeMesh.permute_edges¶: Permutation matrix re-ordering of edges sorted by x, then y, then z

TreeMesh.permute_faces¶: Permutation matrix re-ordering of faces sorted by x, then y, then z

TreeMesh.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 \((0,0,1)\)

TreeMesh.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

TreeMesh.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.

TreeMesh.stencil_cell_gradient¶

TreeMesh.stencil_cell_gradient_x¶: Cell gradient stencil matrix to total (including hanging) x faces

TreeMesh.stencil_cell_gradient_y¶: Cell gradient stencil matrix to total (including hanging) y faces

TreeMesh.stencil_cell_gradient_z¶: Cell gradient stencil matrix to total (including hanging) z faces

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

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

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

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

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

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

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

TreeMesh.vntE¶: Total number of hanging and non-hanging edges in a [nx,ny,nz] form

TreeMesh.vntF¶: Total number of hanging and non-hanging faces in a [nx,ny,nz] form

TreeMesh.vol¶: vol has been deprecated. See cell_volumes for documentation

TreeMesh.x0¶

Methods¶

TreeMesh.average_cell_to_total_face_x(self)¶: Average matrix for cell center to total (including hanging) x faces

TreeMesh.average_cell_to_total_face_y(self)¶: Average matrix for cell center to total (including hanging) y faces

TreeMesh.average_cell_to_total_face_z(self)¶: Average matrix for cell center to total (including hanging) z faces

TreeMesh.cell_levels_by_index(indices)[source]¶

Fast function to return a list of levels for the given cell indices

Parameters

index: array_like of length (N): Cell indexes to query

Returns

numpy.array of length (N): Levels for the cells.

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

classmethod TreeMesh.deserialize(serial)[source]¶

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.

TreeMesh.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.

TreeMesh.finalize(self)¶: Finalize the TreeMesh Called after finished cronstruction of the mesh. Can only be called once. After finalize is called, all other attributes and functions are valid.

static TreeMesh.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.

TreeMesh.getEdgeInnerProduct(*args, **kwargs)¶: getEdgeInnerProduct has been deprecated. See get_edge_inner_product for documentation

TreeMesh.getEdgeInnerProductDeriv(*args, **kwargs)¶: getEdgeInnerProductDeriv has been deprecated. See get_edge_inner_product_deriv for documentation

TreeMesh.getFaceInnerProduct(*args, **kwargs)¶: getFaceInnerProduct has been deprecated. See get_face_inner_product for documentation

TreeMesh.getFaceInnerProductDeriv(*args, **kwargs)¶: getFaceInnerProductDeriv has been deprecated. See get_face_inner_product_deriv for documentation

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

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

TreeMesh.get_boundary_cells(self, active_ind=None, direction='zu')¶

Returns the indices of boundary cells in a given direction given an active index array.

Parameters

active_indarray_like of bool, optional: If not None, then this must show which cells are active
direction: str, optional: must be one of (‘zu’, ‘zd’, ‘xu’, ‘xd’, ‘yu’, ‘yd’)

Returns

numpy.array: Array of indices for the boundary cells in the requested direction

TreeMesh.get_cells_along_line(self, x0, x1)¶

Finds the cells along a line segment defined by two points

Parameters

x0,x1array_like of length (dim): Begining and ending point of the line segment.

Returns

list of ints: Indexes for cells that contain the a line defined by the two input points, ordered in the direction of the line.

TreeMesh.get_edge_inner_product(model=None, invert_model=False, invert_matrix=False, do_fast=True, **kwargs)¶

Generate the edge inner product matrix

Parameters

modelnumpy.ndarray: material property (tensor properties are possible) at each cell center (nC, (1, 3, or 6))
invert_modelbool: inverts the material property
invert_matrixbool: inverts the matrix
do_fastbool: do a faster implementation if available.

Returns

scipy.sparse.csr_matrix: M, the inner product matrix (nE, nE)

TreeMesh.get_edge_inner_product_deriv(model, do_fast=True, invert_model=False, invert_matrix=False, **kwargs)¶

Parameters

modelnumpy.ndarray: material property (tensor properties are possible) at each cell center (nC, (1, 3, or 6))
do_fastbool: do a faster implementation if available.
invert_modelbool: inverts the material property
invert_matrixbool: inverts the matrix

Returns

scipy.sparse.csr_matrix: dMdm, the derivative of the inner product matrix (nE, nC*nA)

TreeMesh.get_face_inner_product(model=None, invert_model=False, invert_matrix=False, do_fast=True, **kwargs)¶

Generate the face inner product matrix

Parameters

modelnumpy.ndarray: material property (tensor properties are possible) at each cell center (nC, (1, 3, or 6))
invert_modelbool: inverts the material property
invert_matrixbool: inverts the matrix
do_fastbool: do a faster implementation if available.

Returns

scipy.sparse.csr_matrix: M, the inner product matrix (nF, nF)

TreeMesh.get_face_inner_product_deriv(model, do_fast=True, invert_model=False, invert_matrix=False, **kwargs)¶

Parameters

modelnumpy.ndarray: material property (tensor properties are possible) at each cell center (nC, (1, 3, or 6))
do_fast :: bool do a faster implementation if available.
invert_modelbool: inverts the material property
invert_matrixbool: inverts the matrix

Returns

scipy.sparse.csr_matrix: dMdmu(u), the derivative of the inner product matrix for a certain u

TreeMesh.get_interpolation_matrix(locs, location_type='CC', zeros_outside=False, **kwargs)[source]¶

Produces interpolation matrix

Parameters

locnumpy.ndarray

Location of points to interpolate to

location_type: str

What to interpolate

location_type can be:

'Ex'    -> x-component of field defined on edges
'Ey'    -> y-component of field defined on edges
'Ez'    -> z-component of field defined on edges
'Fx'    -> x-component of field defined on faces
'Fy'    -> y-component of field defined on faces
'Fz'    -> z-component of field defined on faces
'N'     -> scalar field defined on nodes
'CC'    -> scalar field defined on cell centers

Returns

scipy.sparse.csr_matrix: M, the interpolation matrix

TreeMesh.get_overlapping_cells(self, rectangle)¶

TreeMesh.get_tensor(key)¶

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.

TreeMesh.insert_cells(self, points, levels, finalize=True)¶

Insert cells into the TreeMesh that contain given points

Insert cell(s) into the TreeMesh that contain the given point(s) at the assigned level(s).

Parameters

pointsarray_like with shape (N, dim)
levelsarray_like of integers with shape (N)
finalizebool, optional: Whether to finalize after inserting point(s)

Examples

>>> from discretize import TreeMesh
>>> mesh = TreeMesh([32,32])
>>> mesh.insert_cells([0.5, 0.5], mesh.max_level)
>>> print(mesh)
---- QuadTreeMesh ----
 origin: 0.00, 0.00
 hx: 32*0.03,
 hy: 32*0.03,
n_cells: 40
Fill: 3.91%

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

TreeMesh.is_inside(pts, location_type='nodes', **kwargs)¶

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

TreeMesh.number(self)¶: Number the cells, nodes, faces, and edges of the TreeMesh

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

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

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

TreeMesh.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.

TreeMesh.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-TreeMesh-3_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-TreeMesh-3_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-TreeMesh-3_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-TreeMesh-3_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-TreeMesh-3_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-TreeMesh-3_05_00.png

TreeMesh.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-TreeMesh-4_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-TreeMesh-4_01_00.png

TreeMesh.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-TreeMesh-5_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-TreeMesh-5_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-TreeMesh-5_02_00.png

TreeMesh.point2index(locs)[source]¶

Finds cells that contain the given points. Returns an array of index values of the cells that contain the given points

Parameters

locs: array_like of shape (N, dim): points to search for the location of

Returns

numpy.array of integers of length(N): Cell indices that contain the points

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

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

TreeMesh.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, )

TreeMesh.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, )

TreeMesh.readModelUBC(*args, **kwargs)¶: readModelUBC has been deprecated. See read_model_UBC for documentation

classmethod TreeMesh.readUBC(file_name, directory='')¶

classmethod TreeMesh.read_UBC(meshFile, directory='')¶: Read UBC 3D OcTree mesh file Input: :param str meshFile: path to the UBC GIF OcTree mesh file to read :rtype: discretize.TreeMesh :return: The octree mesh

TreeMesh.read_model_UBC(file_name)¶: Read UBC OcTree model and get vector :param string file_name: path to the UBC GIF model file to read :rtype: numpy.ndarray :return: OcTree model

TreeMesh.refine(self, function, finalize=True)¶

Refine a TreeMesh using a user supplied function.

Refines the TreeMesh using a function that is recursively called on each cell of the mesh. It must accept an object of type discretize.TreeMesh.Cell and return an integer like object defining the desired level. The function can also simply be an integer, which will then cause all cells to be at least that level.

Parameters

functioncallable | int: a function describing the desired level, or an integer to refine all cells to at least that level.
finalizebool, optional: Whether to finalize the mesh

discretize.TreeMesh¶

Examples using discretize.TreeMesh¶

Attributes¶

Methods¶

Examples using `discretize.TreeMesh`¶