def test_1d_A_2d_n(self):
A = np.array([7,8,9])
n = np.array([[2],[3], [0]])
B1 = rldecode(A, n, axis=0)
assert np.array_equal(B1, np.array([7, 7, 8, 8, 8]))
# A only has one axis, so axis=1 does not make sense
with pytest.raises(ValueError):
B2 = rldecode(A, n, axis=1)
def getCellNoFaces(G):
"""
Get a list of all half faces, accounting for possible NNC.
Synopsis:
cellNo, cellFaces, isNNC = getCellNoFaces(G)
Description:
This utility function is used to produce a listing of all half faces in
a grid along with the respective cells they belong to. While relatively
trivial for most grids, this function specifically accounts for
non-neighboring connections / NNC.
Arguments:
G (Grid):
Grid structure with optional .nnc.cells attribute.
Returns:
cellNo (ndarray):
Column array with shape (M,1) where M is the number of geometric
half-faces + 2 * number of NNC, where each entry corresponds to
cell index of that half face.
cellFaces (ndarray):
Column array with shape (M,1) with M as above, where each entry is
the connection index. For the first entries, this is simply the
face number. Otherwise, it is the entry of the NNC connection.
See also:
prst.utils.rldecode
"""
import prst.utils as utils # circular import
cellNo = utils.rldecode(np.arange(G.cells.num),
np.diff(G.cells.facePos, axis=0))[:, np.newaxis]
cellFaces = G.cells.faces[:, 0][:, np.newaxis]
# Mapping to show which entries in cellNo/cellFaces are resulting from
# NNC and not actual geometric faces.
isNNC = np.zeros((len(cellNo), 1), dtype=np.bool)
# If NNC is present, we add these extra connections to cellNo
# and cellFaces to allow consisten treatment.
if hasattr(G, 'nnc') and hasattr(G.nnc, "cells"):
prst.warning(
"getCellNoFaces is untested for grids with NNC. Compare results with MRST."
)
# Stack columns into a single column
nnc_cells = np.r_[G.nnc.cells[:, 0], G.nnc.cells[:, 1]][:, np.newaxis]
# NNC is located at the end after the regular faces
nnc_faceno = G.faces.num + np.arange(G.nnc.cells.shape[0])[:,
np.newaxis]
cellNo = np.r_[cellNo, nnc_cells] # Stack as 2d column
cellFaces = np.r_[cellFaces, nnc_faceno, nnc_faceno] # Stack as column
# Added connections are NNC
isNNC = np.r_[isNNC, np.ones((len(nnc_cells), 1), dtype=np.bool)]
return cellNo, cellFaces, isNNC
def getCellNoFaces(G):
"""
Get a list of all half faces, accounting for possible NNC.
Synopsis:
cellNo, cellFaces, isNNC = getCellNoFaces(G)
Description:
This utility function is used to produce a listing of all half faces in
a grid along with the respective cells they belong to. While relatively
trivial for most grids, this function specifically accounts for
non-neighboring connections / NNC.
Arguments:
G (Grid):
Grid structure with optional .nnc.cells attribute.
Returns:
cellNo (ndarray):
Column array with shape (M,1) where M is the number of geometric
half-faces + 2 * number of NNC, where each entry corresponds to
cell index of that half face.
cellFaces (ndarray):
Column array with shape (M,1) with M as above, where each entry is
the connection index. For the first entries, this is simply the
face number. Otherwise, it is the entry of the NNC connection.
See also:
prst.utils.rldecode
"""
import prst.utils as utils # circular import
cellNo = utils.rldecode(np.arange(G.cells.num), np.diff(G.cells.facePos,axis=0))[:,np.newaxis]
cellFaces = G.cells.faces[:,0][:,np.newaxis]
# Mapping to show which entries in cellNo/cellFaces are resulting from
# NNC and not actual geometric faces.
isNNC = np.zeros((len(cellNo), 1), dtype=np.bool)
# If NNC is present, we add these extra connections to cellNo
# and cellFaces to allow consisten treatment.
if hasattr(G, 'nnc') and hasattr(G.nnc, "cells"):
prst.warning("getCellNoFaces is untested for grids with NNC. Compare results with MRST.")
# Stack columns into a single column
nnc_cells = np.r_[G.nnc.cells[:,0], G.nnc.cells[:,1]][:,np.newaxis]
# NNC is located at the end after the regular faces
nnc_faceno = G.faces.num + np.arange(G.nnc.cells.shape[0])[:,np.newaxis]
cellNo = np.r_[cellNo, nnc_cells] # Stack as 2d column
cellFaces = np.r_[cellFaces, nnc_faceno, nnc_faceno] # Stack as column
# Added connections are NNC
isNNC = np.r_[isNNC, np.ones((len(nnc_cells),1), dtype=np.bool)]
return cellNo, cellFaces, isNNC
def _grav_pressure(G, omega):
"""Computes innerproduct cf (face_centroid - cell_centroid) * g for each face"""
g_vec = prst.gravity
if np.linalg.norm(g_vec[:G.gridDim]) > 0:
dim = G.gridDim
assert 1 <= dim <= 3, "Wrong grid dimension"
cellno = utils.rldecode(np.arange(G.cells.num), np.diff(G.cells.facePos, axis=0))
cvec = G.faces.centroids[G.cells.faces[:,0],:] - G.cells.centroids[cellno,:]
ff = omega[cellno] * np.dot(cvec, g_vec[:dim].reshape([3,1]))
else:
ff = np.zeros([G.cells.faces.shape[0], 1])
return ff
def computeGeometry(G, findNeighbors=False, hingenodes=None):
"""
Compute and add geometry attributes to grid object.
Synopsis:
G = computeGeometry(G)
Arguments:
G (Grid): Grid object. Input argument is mutated.
findNeighbors (Optional[bool]):
Force finding the neighbors array even if it exists. Defaults to
False.
Returns:
G - Grid object with added attributes:
- cells
- volumes -- An array with size G.cells.num of cell volumes.
- centroids -- An array with shape (G.cells.num, G.gridDim)
of approximate cell centroids.
- faces
- areas -- An array with size G.faces.num of face areas.
- normals -- An array with shape (G.faces.num, G.gridDim)
of face normals
- centroids -- An array with shape (G.faces.num, G.griddim) of
approximate face centroids.
Individual face normals have length (i.e. Euclidean norm) equal to the
corresponding face areas. In other words, subject to numerical round-off,
the identity
np.linalg.norm(G.faces.normals[i,:], 2) == G.faces.areas[i]
holds for all faces i in range(0, G.faces.num) .
In three space dimensions, i.e. when G.gridDim == 3, the function
`computeGeometry` assumes that the nodes on a given face `f` are ordered
such that the face normal on `f` is directed from cell
`G.faces.neighbors[f,0]` to cell `G.faces.neighbors[f,1]`.
"""
## Setup
assert hingenodes is None or G.gridDim == 3,\
"Hinge nodes are only supported for 3D grids"
numCells = G.cells.num
numFaces = G.faces.num
## Possibly find neighbors
if findNeighbors:
G.faces.neighbors = _findNeighbors(G)
G = _findNormalDirections(G)
else:
if not hasattr(G.faces, "neighbors"):
import prst
prst.log.warn("No field faces.neighbors found. "
+ "Adding plausible values... proceed with caution!")
G.faces.neighbors = _findNeighbors(G)
G = _findNormalDirections(G)
## Main part
if G.gridDim == 3:
## 3D grid
assert G.nodes.coords.shape[1] == 3
faceNumbers = utils.rldecode(np.arange(G.faces.num), np.diff(G.faces.nodePos,axis=0))
nodePos = G.faces.nodePos;
nextNode = np.arange(1, G.faces.nodes.size+1)
nextNode[nodePos[1:,0]-1] = nodePos[:-1,0]
# Divide each face into sub-triangles all having one node as pCenter =
# sum(nodes) / numNodes. Compute area-weighted normals, and add to
# obtain approx face-normals. Compute resulting areas and centroids.
import prst
prst.log.info("Computing normals, areas and centroids...")
# Construct a sparse matrix with zeros and ones.
localEdge2Face = scipy.sparse.csc_matrix((
np.ones(G.faces.nodes.size),
(np.arange(G.faces.nodes.size), faceNumbers)
))
# Divide each row in the matrix product by the numbers in the final
# array elementwise
pCenters = (localEdge2Face.transpose().dot(
G.nodes.coords[G.faces.nodes[:,0]]
)[None,:] / np.diff(G.faces.nodePos,axis=0))[0]
pCenters = localEdge2Face.dot(pCenters)
if hingenodes:
raise NotImplementedError("hingenodes are not yet supported in PRST")
subNormals = np.cross(
G.nodes.coords[G.faces.nodes[nextNode,0],:]
- G.nodes.coords[G.faces.nodes[:,0],:],
pCenters - G.nodes.coords[G.faces.nodes[:,0],:]) / 2
subAreas = np.linalg.norm(subNormals, axis=1)
subCentroids = (G.nodes.coords[G.faces.nodes[:,0],:]
+ G.nodes.coords[G.faces.nodes[nextNode,0],:] + pCenters) / 3
faceNormals = localEdge2Face.transpose().dot(subNormals)
faceAreas = localEdge2Face.transpose().dot(subAreas)
subNormalSigns = np.sign(np.sum(
subNormals * (localEdge2Face * faceNormals), axis=1))
faceCentroids = localEdge2Face.transpose().dot(
subAreas[:,np.newaxis] * subCentroids
) / faceAreas[:,np.newaxis]
# Computation above does not make sense for faces with zero area
zeroAreaIndices = np.where(faceAreas <= 0)
if np.any(zeroAreaIndices):
import prst
prst.log.warning("Faces with zero area detected. Such faces should be"
+ "removed before calling computeGeometry")
# Divide each cell into sub-tetrahedra according to sub-triangles above,
# all having one node as cCenter = sum(faceCentroids) / #faceCentroids
import prst
prst.log.info("Computing cell volumes and centroids")
cellVolumes = np.zeros(numCells)
cellCentroids = np.zeros([numCells, 3])
lastIndex = 0
for cell in range(numCells):
# Number of faces for the current cell
cellNumFaces = G.cells.facePos[cell+1] - G.cells.facePos[cell]
indexes = np.arange(cellNumFaces) + lastIndex
# The indices to the faces for the current cell
cellFaces = G.cells.faces[indexes,0]
# triE are the row indices of the non-zero elements in the matrix, while
# triF are the col indices of the same elements.
# Original code based on MRST:
#
# tmp = localEdge2Face[:,cellFaces]
# triEa, triFa = tmp.nonzero()
#
# Was very slow, so a custom function for extracting columns for a
# csc_matrix was created. It is not fully tested, but is 4x faster.
triF, triE = _csc_columns_nonzero(localEdge2Face.indptr,
localEdge2Face.indices, cellFaces)
cellFaceCentroids = faceCentroids[cellFaces,:]
cellCenter = np.sum(cellFaceCentroids, axis=0) / cellNumFaces
relSubC = subCentroids[triE,:] - cellCenter[np.newaxis,:]
# The normal of a face f is directed from cell G.faces.neighbors[f,0]
# to cell G.faces.neighbors[f,1]. If cell c is in the second column
# for face f, then the normal must be multiplied by -1 to be an outer
# normal.
orientation = 2 * (G.faces.neighbors[G.cells.faces[indexes,0], 0] == cell) - 1
outNormals = subNormals[triE,:] * (
(subNormalSigns[triE] * orientation[triF])[:,np.newaxis]
)
tetraVolumes = (1/3) * np.sum(relSubC * outNormals, axis=1)
tetraCentroids = (3/4) * relSubC;
cellVolume = np.sum(tetraVolumes)
# Warning: This expression can be very close to zero, and often differs from
# the same calculation in MATLAB.
relCentroid = (tetraVolumes.dot(tetraCentroids)) / cellVolume
cellCentroid = relCentroid + cellCenter
cellVolumes[cell] = cellVolume
cellCentroids[cell,:] = cellCentroid
lastIndex += cellNumFaces
elif G.gridDim == 2 and G.nodes.coords.shape[1] == 2:
# Sometimes G.cells.faces has a second column with face directions.
# So we retrieve the index column only.
cellFaces = G.cells.faces[:,0]
## 2D grid in 2D space
import prst
prst.log.info("Computing normals, areas and centroids")
edges = G.faces.nodes.reshape([-1,2], order="C")
# Distance between edge nodes as a vector. "Length" is misleading.
edgeLength = G.nodes.coords[edges[:,1],:] \
- G.nodes.coords[edges[:,0],:]
# Since this is 2D, these are actually lengths
faceAreas = np.linalg.norm(edgeLength, axis=1)
faceCentroids = np.average(G.nodes.coords[edges], axis=1)
faceNormals = np.column_stack([edgeLength[:,1], -edgeLength[:,0]])
import prst
prst.log.info("Computing cell volumes and centroids")
numFaces = np.diff(G.cells.facePos, axis=0)[:,0]
cellNumbers = prst.utils.rldecode(np.arange(G.cells.num), numFaces)
cellEdges = edges[cellFaces,:]
r = G.faces.neighbors[cellFaces, 1] == cellNumbers
# swap the two columns
cellEdges[r, 0], cellEdges[r, 1] = cellEdges[r, 1], cellEdges[r, 0]
cCenter = np.zeros([G.cells.num, 2])
# npg.aggregate is similar to accumarray in MATLAB
cCenter[:,0] = aggregate(cellNumbers,
faceCentroids[cellFaces, 0]) / numFaces
cCenter[:,1] = aggregate(cellNumbers,
faceCentroids[cellFaces, 1]) / numFaces
a = G.nodes.coords[cellEdges[:,0],:] - cCenter[cellNumbers,:]
b = G.nodes.coords[cellEdges[:,1],:] - cCenter[cellNumbers,:]
subArea = 0.5 * (a[:,0]*b[:,1] - a[:,1] * b[:,0])
subCentroid = ( cCenter[cellNumbers,:]
+ 2*faceCentroids[cellFaces,:])/3
cellVolumes = aggregate(cellNumbers, subArea)
cellCentroids = np.zeros([G.cells.num, 2], dtype=np.float64)
cellCentroids[:,0] = aggregate(
cellNumbers, subArea * subCentroid[:,0]) / cellVolumes
cellCentroids[:,1] = aggregate(
cellNumbers, subArea * subCentroid[:,1]) / cellVolumes
elif G.gridDim == 2 and G.nodes.coords.shape[1] == 3:
## 2D grid in 3D space
raise NotImplementedError(
"computeGeometry not yet implemented for surface grids")
else:
raise ValueError("gridDim or nodes.coords have invalid values")
## Update grid
G.faces.areas = faceAreas[:,np.newaxis]
G.faces.normals = faceNormals
G.faces.centroids = faceCentroids
G.cells.volumes = cellVolumes[:,np.newaxis]
G.cells.centroids = cellCentroids
if not hasattr(G, "gridType"):
import prst
prst.log.warning("Input grid has no type")
G.gridType = []
G.gridType.append("computeGeometry")
return G
def computeTrans(G, rock, K_system="xyz", cellCenters=None, cellFaceCenters=None,
verbose=False):
"""
Compute transmissibilities for a grid.
Synopsis:
T = computeTrans(G, rock)
T = computeTrans(G, rock, **kwargs)
Arguments:
G (Grid):
prst.gridprocessing.Grid instance.
rock (Rock):
prst.params.rock.Rock instance with `perm` attribute. The
permeability is assumed to be in units of metres squared (m^2).
Use constant `darcy` from prst.utils.units to convert to m^2, e.g.,
from prst.utils.units import *
perm = convert(perm, from_=milli*darcy, to=meter**2)
if the permeability is provided in units of millidarcies.
The field rock.perm may have ONE column for a scalar permeability in each cell,
TWO/THREE columns for a diagonal permeability in each cell (in 2/D
D) and THREE/SIX columns for a symmetric full tensor permeability.
In the latter case, each cell gets the permability tensor.
K_i = [ k1 k2 ] in two space dimensions
[ k2 k3 ]
K_i = [ k1 k2 k3 ] in three space dimensions
[ k2 k4 k5 ]
[ k3 k5 k6 ]
K_system (Optional[str]):
The system permeability. Valid values are "xyz" and "loc_xyz".
cellCenters (Optional[ndarray]):
Compute transmissibilities based on supplied cellCenters rather
than default G.cells.centroids. Must have shape (n,2) for 2D and
(n,3) for 3D.
cellFaceCenters (Optional[ndarray]):
Compute transmissibilities based on supplied cellFaceCenters rather
than default `G.faces.centroids[G.cells.faces[:,0], :]`.
Returns:
T: Half-transmissibilities for each local face of each grid cell in the
grid. The number of half-transmissibilities equals the number of rows
in `G.cells.faces`. 2D column array.
Comments:
PLEASE NOTE: Face normals are assumed to have length equal to the
corresponding face areas. This property is guaranteed by function
`computeGeometry`.
See also:
computeGeometry, computeMimeticIP (MRST), darcy, permTensor, Rock
"""
if K_system not in ["xyz", "loc_xyz"]:
raise TypeError(
"Specified permeability coordinate system must be a 'xyz' or 'loc_xyz'")
if verbose:
print("Computing one-sided transmissibilites.")
# Vectors from cell centroids to face centroids
assert G.cells.facePos.ndim == 2, "facePos has wrong dimensions"
cellNo = rldecode(np.arange(G.cells.num), np.diff(G.cells.facePos, axis=0))
if cellCenters is None:
C = G.cells.centroids
else:
C = cellCenters
if cellFaceCenters is None:
C = G.faces.centroids[G.cells.faces[:,0],:] - C[cellNo,:]
else:
C = cellFaceCenters - C[cellNo,:]
# Normal vectors
sgn = 2*(cellNo == G.faces.neighbors[G.cells.faces[:,0], 0]) - 1
N = sgn[:,np.newaxis] * G.faces.normals[G.cells.faces[:,0],:]
if K_system == "xyz":
K, i, j = permTensor(rock, G.gridDim, rowcols=True)
assert K.shape[0] == G.cells.num, \
"Permeability must be defined in active cells only.\n"+\
"Got {} tensors, expected {} (== num cells)".format(K.shape[0], G.cells.num)
# Compute T = C'*K*N / C'*C. Loop based to limit memory use.
T = np.zeros(cellNo.size)
for k in range(i.size):
tmp = C[:,i[k]] * K[cellNo,k] * N[:,j[k]]
# Handle both 1d and 2d array.
if tmp.ndim == 1:
T += tmp
else:
T += np.sum(tmp, axis=1)
T = T / np.sum(C*C, axis=1)
elif K_system == "loc_xyz":
if rock.perm.shape[1] == 1:
rock.perm = np.tile(rock.perm, (1, G.gridDim))
if rock.perm.shape[1] != G.cartDims.size:
raise ValueError(
"Permeability coordinate system `loc_xyz` is only "+\
"valid for diagonal tensor.")
assert rock.perm.shape[0] == G.cells.num,\
"Permeability must be defined in active cells only. "+\
"Got {} tensors, expected {} == (num cells)".format(rock.perm.shape[0], G.cells.num)
dim = np.ceil(G.cells.faces[:,1] / 2)
raise NotImplementedError("Function not finished for K_system='loc_xyz'")
# See MRST, solvers/computeTrans.m
else:
raise ValueError("Unknown permeability coordinate system {}.".format(K_system))
is_neg = T < 0
if np.any(is_neg):
if verbose:
prst.log.warn("Warning: {} negative transmissibilities. ".format(np.sum(is_neg))+
"Replaced by absolute values...")
T[is_neg] = -T[is_neg]
return np.atleast_2d(T).transpose()
def computeTrans(G,
rock,
K_system="xyz",
cellCenters=None,
cellFaceCenters=None,
verbose=False):
"""
Compute transmissibilities for a grid.
Synopsis:
T = computeTrans(G, rock)
T = computeTrans(G, rock, **kwargs)
Arguments:
G (Grid):
prst.gridprocessing.Grid instance.
rock (Rock):
prst.params.rock.Rock instance with `perm` attribute. The
permeability is assumed to be in units of metres squared (m^2).
Use constant `darcy` from prst.utils.units to convert to m^2, e.g.,
from prst.utils.units import *
perm = convert(perm, from_=milli*darcy, to=meter**2)
if the permeability is provided in units of millidarcies.
The field rock.perm may have ONE column for a scalar permeability in each cell,
TWO/THREE columns for a diagonal permeability in each cell (in 2/D
D) and THREE/SIX columns for a symmetric full tensor permeability.
In the latter case, each cell gets the permability tensor.
K_i = [ k1 k2 ] in two space dimensions
[ k2 k3 ]
K_i = [ k1 k2 k3 ] in three space dimensions
[ k2 k4 k5 ]
[ k3 k5 k6 ]
K_system (Optional[str]):
The system permeability. Valid values are "xyz" and "loc_xyz".
cellCenters (Optional[ndarray]):
Compute transmissibilities based on supplied cellCenters rather
than default G.cells.centroids. Must have shape (n,2) for 2D and
(n,3) for 3D.
cellFaceCenters (Optional[ndarray]):
Compute transmissibilities based on supplied cellFaceCenters rather
than default `G.faces.centroids[G.cells.faces[:,0], :]`.
Returns:
T: Half-transmissibilities for each local face of each grid cell in the
grid. The number of half-transmissibilities equals the number of rows
in `G.cells.faces`. 2D column array.
Comments:
PLEASE NOTE: Face normals are assumed to have length equal to the
corresponding face areas. This property is guaranteed by function
`computeGeometry`.
See also:
computeGeometry, computeMimeticIP (MRST), darcy, permTensor, Rock
"""
if K_system not in ["xyz", "loc_xyz"]:
raise TypeError(
"Specified permeability coordinate system must be a 'xyz' or 'loc_xyz'"
)
if verbose:
print("Computing one-sided transmissibilites.")
# Vectors from cell centroids to face centroids
assert G.cells.facePos.ndim == 2, "facePos has wrong dimensions"
cellNo = rldecode(np.arange(G.cells.num), np.diff(G.cells.facePos, axis=0))
if cellCenters is None:
C = G.cells.centroids
else:
C = cellCenters
if cellFaceCenters is None:
C = G.faces.centroids[G.cells.faces[:, 0], :] - C[cellNo, :]
else:
C = cellFaceCenters - C[cellNo, :]
# Normal vectors
sgn = 2 * (cellNo == G.faces.neighbors[G.cells.faces[:, 0], 0]) - 1
N = sgn[:, np.newaxis] * G.faces.normals[G.cells.faces[:, 0], :]
if K_system == "xyz":
K, i, j = permTensor(rock, G.gridDim, rowcols=True)
assert K.shape[0] == G.cells.num, \
"Permeability must be defined in active cells only.\n"+\
"Got {} tensors, expected {} (== num cells)".format(K.shape[0], G.cells.num)
# Compute T = C'*K*N / C'*C. Loop based to limit memory use.
T = np.zeros(cellNo.size)
for k in range(i.size):
tmp = C[:, i[k]] * K[cellNo, k] * N[:, j[k]]
# Handle both 1d and 2d array.
if tmp.ndim == 1:
T += tmp
else:
T += np.sum(tmp, axis=1)
T = T / np.sum(C * C, axis=1)
elif K_system == "loc_xyz":
if rock.perm.shape[1] == 1:
rock.perm = np.tile(rock.perm, (1, G.gridDim))
if rock.perm.shape[1] != G.cartDims.size:
raise ValueError(
"Permeability coordinate system `loc_xyz` is only "+\
"valid for diagonal tensor.")
assert rock.perm.shape[0] == G.cells.num,\
"Permeability must be defined in active cells only. "+\
"Got {} tensors, expected {} == (num cells)".format(rock.perm.shape[0], G.cells.num)
dim = np.ceil(G.cells.faces[:, 1] / 2)
raise NotImplementedError(
"Function not finished for K_system='loc_xyz'")
# See MRST, solvers/computeTrans.m
else:
raise ValueError(
"Unknown permeability coordinate system {}.".format(K_system))
is_neg = T < 0
if np.any(is_neg):
if verbose:
prst.log.warn("Warning: {} negative transmissibilities. ".format(
np.sum(is_neg)) + "Replaced by absolute values...")
T[is_neg] = -T[is_neg]
return np.atleast_2d(T).transpose()
