discretize.TreeMesh¶

class
discretize.
TreeMesh
(h=None, x0=None, **kwargs)[source]¶ Bases:
discretize.tree_ext._TreeMesh
,discretize.base.base_tensor_mesh.BaseTensorMesh
,discretize.InnerProducts.InnerProducts
,discretize.MeshIO.TreeMeshIO
TreeMesh is a class for adaptive QuadTree (2D) and OcTree (3D) meshes.Required Properties:
 axis_u (
Vector3
): Vector orientation of udirection. For more details see the docs for therotation_matrix
property., a 3D Vector of <class ‘float’> with shape (3), Default: X  axis_v (
Vector3
): Vector orientation of vdirection. For more details see the docs for therotation_matrix
property., a 3D Vector of <class ‘float’> with shape (3), Default: Y  axis_w (
Vector3
): Vector orientation of wdirection. For more details see the docs for therotation_matrix
property., a 3D Vector of <class ‘float’> with shape (3), Default: Z  h (a list of
Array
): h is a list containing the cell widths of the tensor mesh in each dimension., a list (each item is a list or numpy array of <class ‘float’> with shape (*)) with length between 0 and 3  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  x0 (
Array
): origin of the mesh (dim, ), a list or numpy array of <class ‘float’>, <class ‘int’> with shape (*)
Attributes: area
Returns a numpy array of length nF with the area (length in 2D) of all faces ordered by x, then y, then z.
aveCC2F
Construct the averaging operator on cell centers to cell faces.
aveCC2Fx
Construct the averaging operator on cell centers to cell xfaces.
aveCC2Fy
Construct the averaging operator on cell centers to cell yfaces.
aveCC2Fz
Construct the averaging operator on cell centers to cell zfaces.
aveCCV2F
Construct the averaging operator on cell centers to cell faces.
aveE2CC
Construct the averaging operator on cell edges to cell centers.
aveE2CCV
Construct the averaging operator on cell edges to cell centers.
aveEx2CC
Construct the averaging operator on cell edges in the x direction to cell centers.
aveEy2CC
Construct the averaging operator on cell edges in the y direction to cell centers.
aveEz2CC
Construct the averaging operator on cell edges in the z direction to cell centers.
aveF2CC
Construct the averaging operator on cell faces to cell centers.
aveF2CCV
Construct the averaging operator on cell faces to cell centers.
aveFx2CC
Construct the averaging operator on cell faces in the x direction to cell centers.
aveFy2CC
Construct the averaging operator on cell faces in the y direction to cell centers.
aveFz2CC
Construct the averaging operator on cell faces in the z direction to cell centers.
aveN2CC
Construct the averaging operator on cell nodes to cell centers.
aveN2E
Construct the averaging operator on cell nodes to cell edges, keeping each dimension separate.
aveN2Ex
Averaging operator on cell nodes to xedges
aveN2Ey
Averaging operator on cell nodes to yedges
aveN2Ez
Averaging operator on cell nodes to zedges
aveN2F
Construct the averaging operator on cell nodes to cell edges, keeping each dimension separate.
aveN2Fx
Averaging operator on cell nodes to xfaces
aveN2Fy
Averaging operator on cell nodes to yfaces
aveN2Fz
Averaging operator on cell nodes to zfaces
axis_u
axis_u (
Vector3
): Vector orientation of udirection. For more details see the docs for therotation_matrix
property., a 3D Vector of <class ‘float’> with shape (3), Default: Xaxis_v
axis_v (
Vector3
): Vector orientation of vdirection. For more details see the docs for therotation_matrix
property., a 3D Vector of <class ‘float’> with shape (3), Default: Yaxis_w
axis_w (
Vector3
): Vector orientation of wdirection. For more details see the docs for therotation_matrix
property., a 3D Vector of <class ‘float’> with shape (3), Default: ZcellBoundaryInd
Returns a tuple of arrays of indexes for boundary cells in each direction
cellGrad
Cell centered Gradient operator built off of the faceDiv operator.
 cellGradStencil
cellGradx
Cell centered Gradient operator in xdirection (Gradx)
cellGrady
Cell centered Gradient operator in ydirection (Grady)
cellGradz
Cell centered Gradient operator in zdirection (Gradz)
dim
The dimension of the mesh (1, 2, or 3).
edge
Returns a numpy array of length nE with the length of all edges ordered by x, then y, then z.
edgeCurl
Construct the 3D curl operator.
faceBoundaryInd
Returns a tuple of arrays of indexes for boundary faces in each direction
faceDiv
Construct divergence operator (facestg to cellcentres).
 faceDivx
 faceDivy
 faceDivz
fill
How filled is the mesh compared to a TensorMesh? As a fraction: [0, 1].
gridCC
Returns a numpy arrayof shape (nC, dim) with the center locations of all cells in order.
gridEx
Returns a numpy array of shape (nEx, dim) with the centers of all nonhanging edges along the first dimension in order.
gridEy
Returns a numpy array of shape (nEy, dim) with the centers of all nonhanging edges along the second dimension in order.
gridEz
Returns a numpy array of shape (nEz, dim) with the centers of all nonhanging edges along the third dimension in order.
gridFx
Returns a numpy array of shape (nFx, dim) with the centers of all nonhanging faces along the first dimension in order.
gridFy
Returns a numpy array of shape (nFy, dim) with the centers of all nonhanging faces along the second dimension in order.
gridFz
Returns a numpy array of shape (nFz, dim) with the centers of all nonhanging faces along the third dimension in order.
gridN
Returns a numpy array of shape (nN, dim) with the locations of all nonhanging nodes in order.
gridhEx
Returns a numpy array of shape (nhEx, dim) with the centers of all hanging edges along the first dimension in order.
gridhEy
Returns a numpy array of shape (nhEy, dim) with the centers of all hanging edges along the second dimension in order.
gridhEz
Returns a numpy array of shape (nhEz, dim) with the centers of all hanging edges along the third dimension in order.
gridhFx
Returns a numpy array of shape (nhFx, dim) with the centers of all hanging faces along the first dimension in order.
gridhFy
Returns a numpy array of shape (nhFy, dim) with the centers of all hanging faces along the second dimension in order.
gridhFz
Returns a numpy array of shape (nhFz, dim) with the centers of all hanging faces along the third dimension in order.
gridhN
Returns a numpy array of shape (nN, dim) with the locations of all hanging nodes in order.
h
h (a list of
Array
): h is a list containing the cell widths of the tensor mesh in each dimension., a list (each item is a list or numpy array of <class ‘float’> with shape (*)) with length between 0 and 3h_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
maxLevel
The maximum level used, which may be less than levels or max_level.
max_level
The maximum possible level for a cell on this mesh
nC
Number of cells
nE
Total number of nonhanging edges amongst all dimensions
nEx
Number of nonhanging edges oriented along the first dimension
nEy
Number of nonhanging edges oriented along the second dimension
nEz
Number of nonhanging edges oriented along the third dimension
nF
Total number of nonhanging faces amongst all dimensions
nFx
Number of nonhanging faces oriented along the first dimension
nFy
Number of nonhanging faces oriented along the second dimension
nFz
Number of nonhanging faces oriented along the third dimension
nN
Number of nonhanging nodes
nhE
Total number of hanging edges amongst all dimensions
nhEx
Number of hanging edges oriented along the first dimension
nhEy
Number of hanging edges oriented along the second dimension
nhEz
Number of hanging edges oriented along the third dimension
nhF
Total number of hanging faces amongst all dimensions
nhFx
Number of hanging faces oriented along the first dimension
nhFy
Number of hanging faces oriented along the second dimension
nhFz
Number of hanging faces oriented along the third dimension
nhN
Number of hanging nodes
nodalGrad
Construct gradient operator (nodes to edges).
 nodalLaplacian
normals
Face Normals
ntE
Total number of nonhanging and hanging edges amongst all dimensions
ntEx
Number of nonhanging and hanging edges oriented along the first dimension
ntEy
Number of nonhanging and hanging edges oriented along the second dimension
ntEz
Number of nonhanging and hanging edges oriented along the third dimension
ntF
Total number of hanging and nonhanging faces amongst all dimensions
ntFx
Number of nonhanging and hanging faces oriented along the first dimension
ntFy
Number of nonhanging and hanging faces oriented along the second dimension
ntFz
Number of nonhanging and hanging faces oriented along the third dimension
ntN
Number of nonhanging and hanging nodes
permuteCC
Permutation matrix reordering of cells sorted by x, then y, then z
permuteE
Permutation matrix reordering of edges sorted by x, then y, then z
permuteF
Permutation matrix reordering 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: cartesianrotation_matrix
Builds a rotation matrix to transform coordinates from their coordinate system into a conventional cartesian system.
tangents
Edge Tangents
vectorCCx
Cellcentered grid vector (1D) in the x direction.
vectorCCy
Cellcentered grid vector (1D) in the y direction.
vectorCCz
Cellcentered grid vector (1D) in the z direction.
vectorNx
Nodal grid vector (1D) in the x direction.
vectorNy
Nodal grid vector (1D) in the y direction.
vectorNz
Nodal grid vector (1D) in the z direction.
vnE
Total number of edges in each direction
vnF
Total number of faces in each direction
vntE
Total number of hanging and nonhanging edges in a [nx,ny,nz] form
vntF
Total number of hanging and nonhanging faces in a [nx,ny,nz] form
vol
Returns a numpy array of length nC with the volumes (areas in 2D) of all cells in order.
x0
x0 (
Array
): origin of the mesh (dim, ), a list or numpy array of <class ‘float’>, <class ‘int’> with shape (*)
Methods
load plotSlice  axis_u (
Attributes¶

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

TreeMesh.
aveCC2F
¶ Construct the averaging operator on cell centers to cell faces.

TreeMesh.
aveCC2Fx
¶ Construct the averaging operator on cell centers to cell xfaces.

TreeMesh.
aveCC2Fy
¶ Construct the averaging operator on cell centers to cell yfaces.

TreeMesh.
aveCC2Fz
¶ Construct the averaging operator on cell centers to cell zfaces.

TreeMesh.
aveCCV2F
¶ Construct the averaging operator on cell centers to cell faces.

TreeMesh.
aveE2CC
¶ Construct the averaging operator on cell edges to cell centers.

TreeMesh.
aveE2CCV
¶ Construct the averaging operator on cell edges to cell centers.

TreeMesh.
aveEx2CC
¶ Construct the averaging operator on cell edges in the x direction to cell centers.

TreeMesh.
aveEy2CC
¶ Construct the averaging operator on cell edges in the y direction to cell centers.

TreeMesh.
aveEz2CC
¶ Construct the averaging operator on cell edges in the z direction to cell centers.

TreeMesh.
aveF2CC
¶ Construct the averaging operator on cell faces to cell centers.

TreeMesh.
aveF2CCV
¶ Construct the averaging operator on cell faces to cell centers.

TreeMesh.
aveFx2CC
¶ Construct the averaging operator on cell faces in the x direction to cell centers.

TreeMesh.
aveFy2CC
¶ Construct the averaging operator on cell faces in the y direction to cell centers.

TreeMesh.
aveFz2CC
¶ Construct the averaging operator on cell faces in the z direction to cell centers.

TreeMesh.
aveN2CC
¶ Construct the averaging operator on cell nodes to cell centers.

TreeMesh.
aveN2E
¶ Construct the averaging operator on cell nodes to cell edges, keeping each dimension separate.

TreeMesh.
aveN2Ex
¶ Averaging operator on cell nodes to xedges

TreeMesh.
aveN2Ey
¶ Averaging operator on cell nodes to yedges

TreeMesh.
aveN2Ez
¶ Averaging operator on cell nodes to zedges

TreeMesh.
aveN2F
¶ Construct the averaging operator on cell nodes to cell edges, keeping each dimension separate.

TreeMesh.
aveN2Fx
¶ Averaging operator on cell nodes to xfaces

TreeMesh.
aveN2Fy
¶ Averaging operator on cell nodes to yfaces

TreeMesh.
aveN2Fz
¶ Averaging operator on cell nodes to zfaces

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

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

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

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

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

TreeMesh.
cellGradStencil
¶

TreeMesh.
cellGradx
¶ Cell centered Gradient operator in xdirection (Gradx) Grad = sp.vstack((Gradx, Grady, Gradz))

TreeMesh.
cellGrady
¶ Cell centered Gradient operator in ydirection (Grady) Grad = sp.vstack((Gradx, Grady, Gradz))

TreeMesh.
cellGradz
¶ Cell centered Gradient operator in zdirection (Gradz) Grad = sp.vstack((Gradx, Grady, Gradz))

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

TreeMesh.
edgeCurl
¶ Construct the 3D curl operator.

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

TreeMesh.
faceDiv
¶ Construct divergence operator (facestg to cellcentres).

TreeMesh.
faceDivx
¶

TreeMesh.
faceDivy
¶

TreeMesh.
faceDivz
¶

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

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

TreeMesh.
gridEx
¶ Returns a numpy array of shape (nEx, dim) with the centers of all nonhanging edges along the first dimension in order.

TreeMesh.
gridEy
¶ Returns a numpy array of shape (nEy, dim) with the centers of all nonhanging edges along the second dimension in order.

TreeMesh.
gridEz
¶ Returns a numpy array of shape (nEz, dim) with the centers of all nonhanging edges along the third dimension in order.

TreeMesh.
gridFx
¶ Returns a numpy array of shape (nFx, dim) with the centers of all nonhanging faces along the first dimension in order.

TreeMesh.
gridFy
¶ Returns a numpy array of shape (nFy, dim) with the centers of all nonhanging faces along the second dimension in order.

TreeMesh.
gridFz
¶ Returns a numpy array of shape (nFz, dim) with the centers of all nonhanging faces along the third dimension in order.

TreeMesh.
gridN
¶ Returns a numpy array of shape (nN, dim) with the locations of all nonhanging nodes in order.

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

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

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

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

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

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

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

TreeMesh.
h
¶ h is a list containing the cell widths of the tensor mesh in each dimension., a list (each item is a list or numpy array of <class ‘float’> with shape (*)) with length between 0 and 3
Type: h (a list of Array
)

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

TreeMesh.
hx
¶ Width of cells in the x direction

TreeMesh.
hy
¶ Width of cells in the y direction

TreeMesh.
hz
¶ Width of cells in the z direction

TreeMesh.
maxLevel
¶ The maximum level used, which may be less than levels or max_level.

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

TreeMesh.
nC
¶ Number of cells

TreeMesh.
nE
¶ Total number of nonhanging edges amongst all dimensions

TreeMesh.
nEx
¶ Number of nonhanging edges oriented along the first dimension

TreeMesh.
nEy
¶ Number of nonhanging edges oriented along the second dimension

TreeMesh.
nEz
¶ Number of nonhanging edges oriented along the third dimension

TreeMesh.
nF
¶ Total number of nonhanging faces amongst all dimensions

TreeMesh.
nFx
¶ Number of nonhanging faces oriented along the first dimension

TreeMesh.
nFy
¶ Number of nonhanging faces oriented along the second dimension

TreeMesh.
nFz
¶ Number of nonhanging faces oriented along the third dimension

TreeMesh.
nN
¶ Number of nonhanging nodes

TreeMesh.
nhE
¶ Total number of hanging edges amongst all dimensions

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

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

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

TreeMesh.
nhF
¶ Total number of hanging faces amongst all dimensions

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

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

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

TreeMesh.
nhN
¶ Number of hanging nodes

TreeMesh.
nodalGrad
¶ Construct gradient operator (nodes to edges).

TreeMesh.
nodalLaplacian
¶

TreeMesh.
normals
¶ Face Normals
Return type: numpy.ndarray Returns: normals, (sum(nF), dim)

TreeMesh.
ntE
¶ Total number of nonhanging and hanging edges amongst all dimensions

TreeMesh.
ntEx
¶ Number of nonhanging and hanging edges oriented along the first dimension

TreeMesh.
ntEy
¶ Number of nonhanging and hanging edges oriented along the second dimension

TreeMesh.
ntEz
¶ Number of nonhanging and hanging edges oriented along the third dimension

TreeMesh.
ntF
¶ Total number of hanging and nonhanging faces amongst all dimensions

TreeMesh.
ntFx
¶ Number of nonhanging and hanging faces oriented along the first dimension

TreeMesh.
ntFy
¶ Number of nonhanging and hanging faces oriented along the second dimension

TreeMesh.
ntFz
¶ Number of nonhanging and hanging faces oriented along the third dimension

TreeMesh.
ntN
¶ Number of nonhanging and hanging nodes

TreeMesh.
permuteCC
¶ Permutation matrix reordering of cells sorted by x, then y, then z

TreeMesh.
permuteE
¶ Permutation matrix reordering of edges sorted by x, then y, then z

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

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.
tangents
¶ Edge Tangents
Return type: numpy.ndarray Returns: normals, (sum(nE), dim)

TreeMesh.
vectorCCx
¶ Cellcentered grid vector (1D) in the x direction.

TreeMesh.
vectorCCy
¶ Cellcentered grid vector (1D) in the y direction.

TreeMesh.
vectorCCz
¶ Cellcentered grid vector (1D) in the z direction.

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

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

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

TreeMesh.
vnE
¶ Total number of edges in each direction
Returns:  vnE (numpy.ndarray = [nEx, nEy, nEz], (dim, ))
 .. plot:: – :includesource:
import discretize import numpy as np M = discretize.TensorMesh([np.ones(n) for n in [2,3]]) M.plotGrid(edges=True, showIt=True)

TreeMesh.
vnF
¶ Total number of faces in each direction
Return type: numpy.ndarray Returns: [nFx, nFy, nFz], (dim, ) import discretize import numpy as np M = discretize.TensorMesh([np.ones(n) for n in [2,3]]) M.plotGrid(faces=True, showIt=True)
(Source code, png, hires.png, pdf)

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

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

TreeMesh.
vol
¶ Returns a numpy array of length nC with the volumes (areas in 2D) of all cells in order.
Methods¶

TreeMesh.
cell_levels_by_index
(self, 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: Levels for the cells. Return type: numpy.array of length (N)

classmethod
TreeMesh.
deserialize
(serial)[source]¶ Creates HasProperties instance from serialized dictionary
This uses the Property deserializers to deserialize all JSONcompatible 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
(self, 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
()¶ 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
(self, prop=None, invProp=False, invMat=False, doFast=True)¶ Generate the edge inner product matrix
Parameters:  prop (numpy.ndarray) – material property (tensor properties are possible) at each cell center (nC, (1, 3, or 6))
 invProp (bool) – inverts the material property
 invMat (bool) – inverts the matrix
 doFast (bool) – do a faster implementation if available.
Returns: M, the inner product matrix (nE, nE)
Return type:

TreeMesh.
getEdgeInnerProductDeriv
(self, prop, doFast=True, invProp=False, invMat=False)¶ Parameters:  prop (numpy.ndarray) – material property (tensor properties are possible) at each cell center (nC, (1, 3, or 6))
 doFast (bool) – do a faster implementation if available.
 invProp (bool) – inverts the material property
 invMat (bool) – inverts the matrix
Returns: dMdm, the derivative of the inner product matrix (nE, nC*nA)
Return type:

TreeMesh.
getFaceInnerProduct
(self, prop=None, invProp=False, invMat=False, doFast=True)¶ Generate the face inner product matrix
Parameters:  prop (numpy.ndarray) – material property (tensor properties are possible) at each cell center (nC, (1, 3, or 6))
 invProp (bool) – inverts the material property
 invMat (bool) – inverts the matrix
 doFast (bool) – do a faster implementation if available.
Returns: M, the inner product matrix (nF, nF)
Return type:

TreeMesh.
getFaceInnerProductDeriv
(self, prop, doFast=True, invProp=False, invMat=False)¶ Parameters:  prop (numpy.ndarray) – material property (tensor properties are possible) at each cell center (nC, (1, 3, or 6))
 doFast – bool do a faster implementation if available.
 invProp (bool) – inverts the material property
 invMat (bool) – inverts the matrix
Returns: dMdmu(u), the derivative of the inner product matrix for a certain u
Return type:

TreeMesh.
getInterpolationMat
(self, locs, locType, zerosOutside=False)[source]¶ Produces interpolation matrix
Parameters:  loc (numpy.ndarray) – Location of points to interpolate to
 locType (str) –
What to interpolate
locType can be:
'Ex' > xcomponent of field defined on edges 'Ey' > ycomponent of field defined on edges 'Ez' > zcomponent of field defined on edges 'Fx' > xcomponent of field defined on faces 'Fy' > ycomponent of field defined on faces 'Fz' > zcomponent of field defined on faces 'N' > scalar field defined on nodes 'CC' > scalar field defined on cell centers
Returns: M, the interpolation matrix
Return type:

TreeMesh.
getTensor
(self, key)¶ Returns a tensor list.
Parameters: key (str) – Which tensor (see below)
key can be:
'CC' > scalar field defined on cell centers 'N' > scalar field defined on nodes 'Fx' > xcomponent of field defined on faces 'Fy' > ycomponent of field defined on faces 'Fz' > zcomponent of field defined on faces 'Ex' > xcomponent of field defined on edges 'Ey' > ycomponent of field defined on edges 'Ez' > zcomponent of field defined on edges
Returns: list of the tensors that make up the mesh. Return type: list

TreeMesh.
get_boundary_cells
()¶ Returns the indices of boundary cells in a given direction given an active index array.
Parameters:  active_ind (array_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: Array of indices for the boundary cells in the requested direction
Return type: numpy.array

TreeMesh.
get_cells_along_line
()¶ Finds the cells along a line segment defined by two points
Parameters: x0,x1 (array_like of length (dim)) – Begining and ending point of the line segment. Returns: Indexes for cells that contain the a line defined by the two input points, ordered in the direction of the line. Return type: list of ints

TreeMesh.
insert_cells
()¶ 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:  points (array_like with shape (N, dim)) –
 levels (array_like of integers with shape (N)) –
 finalize (bool, 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  x0: 0.00 y0: 0.00 hx: 32*0.03, hy: 32*0.03, nC: 40 Fill: 3.91%

TreeMesh.
isInside
(self, pts, locType='N')¶ 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
()¶ Number the cells, nodes, faces, and edges of the TreeMesh

TreeMesh.
plotGrid
()¶ Plot the nodel, cellcentered, and staggered grids for 2 and 3 dimensions Plots the mesh grid in either 2D or 3D of the TreeMesh
Parameters:  ax (matplotlib.axes.Axes or None, optional) – The axes handle to plot on
 nodes (bool, optional) – Plot the nodal points
 faces (bool, optional) – Plot the center points of the faces
 centers (bool, optional) – Plot the center points of the cells
 edges (bool, optional) – Plot the center points of the edges
 lines (bool, optional) – Plot the lines connecting the nodes
 cell_line (bool, optional) – Plot the line through the cell centers in order
 faces_y, faces_z (faces_x,) – Plot the center points of the x, y, or z faces
 edges_y, edges_z (edges_x,) – Plot the center points of the x, y, or z edges
 showIt (bool, optional) – whether to call plt.show() within the codes
 color (Color or str, optional) – if lines=True, the color of the lines, defaults to first color.
 linewidth (float, optional) – if lines=True, the linewidth for the lines.
Returns: Axes handle for the plot
Return type:

TreeMesh.
plotImage
()¶ Plots an image of values defined on the TreeMesh If 3D, this function plots a default slice of the TreeMesh
Parameters:  v (array_like) – Array containing the values to plot
 vType (str, optional) – type of value in v one of ‘CC’, ‘N’, ‘Fx’, ‘Fy’, ‘Fz’, ‘Ex’, ‘Ey’, or ‘Ez’
 grid (bool, optional) – plot the grid lines
 view (['real', 'imag', 'abs'], optional) – The values to plot from v
 ax (matplotlib.axes.Axes or None, optional) – The axes handle
 clim (array_like of length 2, or None, optional) – A pair of [min, max] for the Colorbar
 pcolorOpts (dict, or None) – options to be passed on to pcolormesh
 gridOpt (dict, or None) – options for the plotting the grid
 range_y (range_x,) – pairs of [min, max] values for the x and y ranges

TreeMesh.
plotSlice
(self, v, vType='CC', normal='Z', ind=None, grid=False, view='real', ax=None, clim=None, showIt=False, pcolorOpts=None, streamOpts=None, gridOpts=None, range_x=None, range_y=None)[source]¶

TreeMesh.
point2index
(self, 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: Cell indices that contain the points Return type: numpy.array of integers of length(N)

TreeMesh.
projectEdgeVector
(self, eV)¶ Given a vector, eV, in cartesian coordinates, this will project it onto the mesh using the tangents
Parameters: eV (numpy.ndarray) – edge vector with shape (nE, dim) Return type: numpy.ndarray Returns: projected edge vector, (nE, )

TreeMesh.
projectFaceVector
(self, fV)¶ Given a vector, fV, in cartesian coordinates, this will project it onto the mesh using the normals
Parameters: fV (numpy.ndarray) – face vector with shape (nF, dim) Return type: numpy.ndarray Returns: projected face vector, (nF, )

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

classmethod
TreeMesh.
readUBC
(meshFile)¶ 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.
refine
()¶ 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:  function (callable  int) – a function describing the desired level, or an integer to refine all cells to at least that level.
 finalize (bool, optional) – Whether to finalize the mesh
Examples
>>> from discretize import TreeMesh >>> mesh = TreeMesh([32,32]) >>> def func(cell): >>> r = np.linalg.norm(cell.center0.5) >>> return mesh.max_level if r<0.2 else mesh.max_level1 >>> mesh.refine(func) >>> mesh  QuadTreeMesh  x0: 0.00 y0: 0.00 hx: 32*0.03, hy: 32*0.03, nC: 352 Fill: 34.38%
See also
discretize.TreeMesh.TreeCell()
 a description of the TreeCell object

TreeMesh.
save
(self, filename='mesh.json', verbose=False)¶ Save the mesh to json :param str file: filename for saving the casing properties :param str directory: working directory for saving the file

TreeMesh.
serialize
(self)[source]¶ Serializes a HasProperties instance to dictionary
This uses the Property serializers to serialize all Property values to a JSONcompatible 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.
 include_class  If True (the default), the name of the class
will also be saved to the serialized dictionary under key

TreeMesh.
toVTK
(mesh, 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: models (dict(numpy.ndarray)) – Name(‘s) and array(‘s). Match number of cells

TreeMesh.
to_omf
(mesh, 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: models (dict(numpy.ndarray)) – Name(‘s) and array(‘s). Match number of cells

TreeMesh.
to_vtk
(mesh, 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: models (dict(numpy.ndarray)) – Name(‘s) and array(‘s). Match number of cells

TreeMesh.
validate
(self)¶ 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.

TreeMesh.
writeUBC
(mesh, fileName, models=None)¶ Write UBC ocTree mesh and model files from a octree mesh and model. :param string fileName: File to write to :param dict models: Models in a dict, where each key is the filename

TreeMesh.
writeVTK
(mesh, filename, models=None, directory='')¶ Makes and saves a VTK object from this mesh and given models
Parameters:

TreeMesh.
write_vtk
(mesh, filename, models=None, directory='')¶ Makes and saves a VTK object from this mesh and given models
Parameters: