def _calcValueIn(self, N, M, ids, orientations, volumes):
val = self._getArray().copy()
inline._runIterateElementInline(self.modIn + """
ITEM(val, i, vec) = 0.;
int k;
for (k = 0; k < M; k++) {
int id = ITEM(ids, i, &k);
ITEM(val, i, vec) += ITEM(orientations, i, &k) * ITEM(areaProj, id, vec) * ITEM(faceValues, id, NULL);
}
ITEM(val, i, vec) /= ITEM(volumes, i, NULL);
ITEM(val, i, vec) = mod(ITEM(val, i, vec) * gridSpacing[vec[0]]) / gridSpacing[vec[0]];
""",val = val,
ids = numerix.array(ids),
orientations = numerix.array(orientations),
volumes = numerix.array(volumes),
areaProj = numerix.array(self.mesh._getAreaProjections()),
faceValues = numerix.array(self.var.getArithmeticFaceValue()),
M = M,
ni = N,
gridSpacing = numerix.array(self.mesh._getMeshSpacing()),
shape=numerix.array(numerix.shape(val)))
return self._makeValue(value = val)
def _calcValueIn(self, N, M, ids, orientations, volumes):
val = self._getArray().copy()
inline._runIterateElementInline(
"""
ITEM(val, i, vec) = 0.;
int k;
for (k = 0; k < M; k++) {
int id = ITEM(ids, i, &k);
ITEM(val, i, vec) += ITEM(orientations, i, &k) * ITEM(areaProj, id, vec) * ITEM(faceValues, id, NULL);
}
ITEM(val, i, vec) /= ITEM(volumes, i, NULL);
""",
val=val,
ids=numerix.array(numerix.MA.filled(ids, 0)),
orientations=numerix.array(numerix.MA.filled(orientations, 0)),
volumes=numerix.array(volumes),
areaProj=numerix.array(self.mesh._getAreaProjections()),
faceValues=numerix.array(self.var.getArithmeticFaceValue()),
M=M,
ni=N,
shape=numerix.array(numerix.shape(val)),
)
return self._makeValue(value=val)
def __mul__(self, factor):
if numerix.shape(factor) is ():
factor = numerix.resize(factor, (2, 1))
return UniformGrid2D(dx=self.args['dx'] * numerix.array(factor[0]), nx=self.args['nx'],
dy=self.args['dy'] * numerix.array(factor[1]), ny=self.args['ny'],
origin=numerix.array(self.args['origin']) * factor, overlap=self.args['overlap'])
def __setitem__(self, index, value):
N = self.mesh.numberOfCells
for i, var in enumerate(self.vars):
if numerix.shape(value) == ():
var[index] = value
else:
var[index] = value[i * N:(i + 1) * N]
def __setitem__(self, index, value):
N = self.mesh.numberOfCells
for i, var in enumerate(self.vars):
if numerix.shape(value) == ():
var[index] = value
else:
var[index] = value[i * N:(i + 1) * N]
def _calcValueInline(self, N, M, ids, orientations, volumes):
val = self._array.copy()
inline._runIterateElementInline(
self.modIn + """
ITEM(val, i, vec) = 0.;
int k;
for (k = 0; k < M; k++) {
int id = ITEM(ids, i, &k);
ITEM(val, i, vec) += ITEM(orientations, i, &k) * ITEM(areaProj, id, vec) * ITEM(faceValues, id, NULL);
}
ITEM(val, i, vec) /= ITEM(volumes, i, NULL);
ITEM(val, i, vec) = mod(ITEM(val, i, vec) * gridSpacing[vec[0]]) / gridSpacing[vec[0]];
""",
val=val,
ids=numerix.array(ids),
orientations=numerix.array(orientations),
volumes=numerix.array(volumes),
areaProj=numerix.array(self.mesh._areaProjections),
faceValues=numerix.array(self.var.arithmeticFaceValue),
M=M,
ni=N,
gridSpacing=numerix.array(self.mesh._meshSpacing),
shape=numerix.array(numerix.shape(val)))
return self._makeValue(value=val)
def _calcValue_(self, alpha, id1, id2):
val = self._array.copy()
inline._runIterateElementInline("""
int ID1 = ITEM(id1, i, NULL);
int ID2 = ITEM(id2, i, NULL);
double cell1 = ITEM(var, ID1, vec);
double cell2 = ITEM(var, ID2, vec);
double cell1Xcell2 = cell1 * cell2;
double tmp = ((cell2 - cell1) * ITEM(alpha, i, NULL) + cell1);
if (tmp != 0 && cell1Xcell2 > 0.) {
ITEM(val, i, vec) = cell1Xcell2 / tmp;
} else {
ITEM(val, i, vec) = 0.;
}
""",
var=self.var.numericValue,
val=val,
alpha=alpha,
id1=id1,
id2=id2,
shape=numerix.array(
numerix.shape(val)),
ni=self.mesh.numberOfFaces)
return self._makeValue(value=val)
def __mul__(self, other):
"""
Multiply a sparse matrix by another sparse matrix
>>> L1 = _PETScMatrixFromShape(rows=3, cols=3, bandwidth=2)
>>> L1.put([3.,10.,numerix.pi,2.5], [0,0,1,2], [2,1,1,0])
>>> L2 = _PETScIdentityMatrix(size=3, bandwidth=3)
>>> L2.put([4.38], [2], [1])
>>> L2.put([4.38,12357.2,1.1], [2,1,0], [1,0,2])
>>> tmp = numerix.array(((1.23572000e+05, 2.31400000e+01, 3.00000000e+00),
... (3.88212887e+04, 3.14159265e+00, 0.00000000e+00),
... (2.50000000e+00, 0.00000000e+00, 2.75000000e+00)))
>>> numerix.allclose((L1 * L2).numpyArray, tmp)
1
or a sparse matrix by a vector
>>> tmp = numerix.array((29., 6.28318531, 2.5))
>>> numerix.allclose(L1 * numerix.array((1,2,3),'d'), tmp)
1
or a vector by a sparse matrix
>>> tmp = numerix.array((7.5, 16.28318531, 3.))
>>> numerix.allclose(numerix.array((1,2,3),'d') * L1, tmp) ## The multiplication is broken. Numpy is calling __rmul__ for every element instead of with the whole array.
1
"""
N = self._shape[1]
self.matrix.assemblyBegin()
self.matrix.assemblyEnd()
if isinstance(other, _PETScMatrix):
other.matrix.assemblyBegin()
other.matrix.assemblyEnd()
copy = self.copy()
copy.matrix = self.matrix.matMult(other.matrix)
return copy
elif isinstance(other, PETSc.Vec):
y = other.duplicate()
self.matrix.mult(other, y)
return y
else:
shape = numerix.shape(other)
if shape == ():
result = self.copy()
result.matrix = self.matrix * other
return result
elif shape == (N, ):
y = PETSc.Vec().createWithArray(other, comm=self.matrix.comm)
result = y.duplicate()
self.matrix.mult(y, result)
return result
else:
raise TypeError
def __mul__(self, other):
"""Multiply a sparse matrix by another sparse matrix
>>> L1 = _PETScMatrixFromShape(rows=3, cols=3, bandwidth=2)
>>> L1.put([3.,10.,numerix.pi,2.5], [0,0,1,2], [2,1,1,0])
>>> L2 = _PETScIdentityMatrix(size=3, bandwidth=3)
>>> L2.put([4.38], [2], [1])
>>> L2.put([4.38,12357.2,1.1], [2,1,0], [1,0,2])
>>> tmp = numerix.array(((1.23572000e+05, 2.31400000e+01, 3.00000000e+00),
... (3.88212887e+04, 3.14159265e+00, 0.00000000e+00),
... (2.50000000e+00, 0.00000000e+00, 2.75000000e+00)))
>>> numerix.allclose((L1 * L2).numpyArray, tmp)
1
or a sparse matrix by a vector
>>> tmp = numerix.array((29., 6.28318531, 2.5))
>>> vec = L1 * numerix.array((1,2,3),'d')
>>> numerix.allclose(vec, tmp)
1
>>> _ = vec.destroy()
or a vector by a sparse matrix
>>> tmp = numerix.array((7.5, 16.28318531, 3.))
>>> numerix.allclose(numerix.array((1,2,3),'d') * L1, tmp)
1
(The multiplication is broken. Numpy is calling __rmul__ for every
element instead of with the whole array.)
"""
N = self._shape[1]
self.matrix.assemble()
if isinstance(other, (_PETScMatrix, PETSc.Vec)):
return _PETScMatrixFromShape.__mul__(self, other=other)
else:
shape = numerix.shape(other)
if shape == ():
result = self.copy()
result.matrix = self.matrix * other
return result
else:
x = other[self._m2m.localNonOverlappingColIDs]
x = PETSc.Vec().createWithArray(x, comm=self.matrix.comm)
y = PETSc.Vec().createGhost(
ghosts=self._m2m.ghosts.astype('int32'),
size=(len(self._m2m.localNonOverlappingColIDs), None),
comm=self.matrix.comm)
self.matrix.mult(x, y)
arr = self._petsc2fipyGhost(vec=y)
x.destroy()
y.destroy()
return arr
def __getitem__(self, index):
self.matrix.assemblyBegin()
self.matrix.assemblyEnd()
m = self.matrix[index]
if numerix.shape(m) == ():
return m
else:
return _PETScMatrix(matrix=m)
def _calcValueInline(self):
id1, id2 = self.mesh._adjacentCellIDs
tangents1 = self.mesh._faceTangents1
tangents2 = self.mesh._faceTangents2
val = self._array.copy()
faceNormals = self.mesh._orientedFaceNormals
if numerix.MA.isMaskedArray(faceNormals):
faceNormals = faceNormals.filled()
inline._runIterateElementInline(
"""
int j;
double t1grad1, t1grad2, t2grad1, t2grad2, N, N2;
int ID1 = ITEM(id1, i, NULL);
int ID2 = ITEM(id2, i, NULL);
if ITEM(exteriorFaces, i, NULL) {
N2 = ITEM(facevar, i, NULL);
} else {
N2 = ITEM(var, ID2, NULL);
}
N = (N2 - ITEM(var, ID1, NULL)) / ITEM(dAP, i, NULL);
t1grad1 = t1grad2 = t2grad1 = t2grad2 = 0.;
t1grad1 += ITEM(tangents1, i, vec) * ITEM(cellGrad, ID1, vec);
t1grad2 += ITEM(tangents1, i, vec) * ITEM(cellGrad, ID2, vec);
t2grad1 += ITEM(tangents2, i, vec) * ITEM(cellGrad, ID1, vec);
t2grad2 += ITEM(tangents2, i, vec) * ITEM(cellGrad, ID2, vec);
ITEM(val, i, vec) = ITEM(normals, i, vec) * N;
ITEM(val, i, vec) += ITEM(tangents1, i, vec) * (t1grad1 + t1grad2) / 2.;
ITEM(val, i, vec) += ITEM(tangents2, i, vec) * (t2grad1 + t2grad2) / 2.;
""",
tangents1=tangents1,
tangents2=tangents2,
cellGrad=self.var.grad.numericValue,
normals=faceNormals,
id1=id1,
id2=id2,
dAP=numerix.array(self.mesh._cellDistances),
var=self.var.numericValue,
facevar=self.var.faceValue.numericValue,
exteriorFaces=self.mesh.exteriorFaces.numericValue,
val=val,
ni=tangents1.shape[1],
shape=numerix.array(numerix.shape(tangents1)))
return self._makeValue(value=val)
def _calcValueInline(self):
id1, id2 = self.mesh._adjacentCellIDs
tangents1 = self.mesh._faceTangents1
tangents2 = self.mesh._faceTangents2
val = self._array.copy()
faceNormals = self.mesh._orientedFaceNormals
if numerix.MA.isMaskedArray(faceNormals):
faceNormals = faceNormals.filled()
inline._runIterateElementInline("""
int j;
double t1grad1, t1grad2, t2grad1, t2grad2, N, N2;
int ID1 = ITEM(id1, i, NULL);
int ID2 = ITEM(id2, i, NULL);
if ITEM(exteriorFaces, i, NULL) {
N2 = ITEM(facevar, i, NULL);
} else {
N2 = ITEM(var, ID2, NULL);
}
N = (N2 - ITEM(var, ID1, NULL)) / ITEM(dAP, i, NULL);
t1grad1 = t1grad2 = t2grad1 = t2grad2 = 0.;
t1grad1 += ITEM(tangents1, i, vec) * ITEM(cellGrad, ID1, vec);
t1grad2 += ITEM(tangents1, i, vec) * ITEM(cellGrad, ID2, vec);
t2grad1 += ITEM(tangents2, i, vec) * ITEM(cellGrad, ID1, vec);
t2grad2 += ITEM(tangents2, i, vec) * ITEM(cellGrad, ID2, vec);
ITEM(val, i, vec) = ITEM(normals, i, vec) * N;
ITEM(val, i, vec) += ITEM(tangents1, i, vec) * (t1grad1 + t1grad2) / 2.;
ITEM(val, i, vec) += ITEM(tangents2, i, vec) * (t2grad1 + t2grad2) / 2.;
""", tangents1 = tangents1,
tangents2 = tangents2,
cellGrad = self.var.grad.numericValue,
normals = faceNormals,
id1 = id1,
id2 = id2,
dAP = numerix.array(self.mesh._cellDistances),
var = self.var.numericValue,
facevar = self.var.faceValue.numericValue,
exteriorFaces = self.mesh.exteriorFaces.numericValue,
val = val,
ni = tangents1.shape[1],
shape=numerix.array(numerix.shape(tangents1)))
return self._makeValue(value = val)
def _dsUniformLen(self):
"""
Return True if all entries in `self.ds` are the same length, False
otherwise.
Exists to get around the fact that `_calcPhysicalShape` and
`_calcMeshSpacing` don't work for cylindrical grids.
"""
# if the first entry in `ds` is non-scalar
if numerix.shape(self.ds[0]) != ():
lenDs = len(self.ds[0])
for d in self.ds[1:]:
if numerix.shape(d) == () or len(d) != lenDs:
return False
# if any other entry in `ds` is non-scalar and first isn't
elif True in [numerix.shape(d) != () for d in self.ds[1:]]:
return False
return True
def _dsUniformLen(self):
"""
Return True if all entries in `self.ds` are the same length, False
otherwise.
Exists to get around the fact that `_calcPhysicalShape` and
`_calcMeshSpacing` don't work for cylindrical grids.
"""
# if the first entry in `ds` is non-scalar
if numerix.shape(self.ds[0]) != ():
lenDs = len(self.ds[0])
for d in self.ds[1:]:
if numerix.shape(d) == () or len(d) != lenDs:
return False
# if any other entry in `ds` is non-scalar and first isn't
elif True in [numerix.shape(d) != () for d in self.ds[1:]]:
return False
return True
def _buildMatrix(self, var, SparseMatrix, boundaryConditions=(), dt=1., equation=None):
L , b = self.term._buildMatrix(var,
SparseMatrix,
boundaryConditions=boundaryConditions,
dt=dt,
equation=equation)
if len(numerix.shape(self.coeff)) == 0:
matcoeff = float(self.coeff)
else:
matcoeff = SparseMatrix(size=len(var), bandwidth=1)
matcoeff.addAtDiagonal(self.coeff)
return (matcoeff * L, self.coeff * b)
def _calcFaceCenters(self):
maskedFaceVertexIDs = MA.filled(self.faceVertexIDs, 0)
faceVertexCoords = numerix.take(self.vertexCoords, maskedFaceVertexIDs, axis=1)
if MA.getmask(self.faceVertexIDs) is False:
faceVertexCoordsMask = numerix.zeros(numerix.shape(faceVertexCoords), 'l')
else:
faceVertexCoordsMask = \
numerix.repeat(MA.getmaskarray(self.faceVertexIDs)[numerix.newaxis,...],
self.dim, axis=0)
faceVertexCoords = MA.array(data=faceVertexCoords, mask=faceVertexCoordsMask)
return MA.filled(MA.average(faceVertexCoords, axis=1))
def __mul__(self, other):
"""
Multiply a sparse matrix by another sparse matrix
>>> L1 = _PysparseMatrixFromShape(rows=3, cols=3)
>>> L1.put([3.,10.,numerix.pi,2.5], [0,0,1,2], [2,1,1,0])
>>> L2 = _PysparseIdentityMatrix(size=3)
>>> L2.put([4.38,12357.2,1.1], [2,1,0], [1,0,2])
>>> tmp = numerix.array(((1.23572000e+05, 2.31400000e+01, 3.00000000e+00),
... (3.88212887e+04, 3.14159265e+00, 0.00000000e+00),
... (2.50000000e+00, 0.00000000e+00, 2.75000000e+00)))
>>> numerix.allclose((L1 * L2).numpyArray, tmp)
1
or a sparse matrix by a vector
>>> tmp = numerix.array((29., 6.28318531, 2.5))
>>> numerix.allclose(L1 * numerix.array((1,2,3),'d'), tmp)
1
or a vector by a sparse matrix
>>> tmp = numerix.array((7.5, 16.28318531, 3.))
>>> numerix.allclose(numerix.array((1,2,3),'d') * L1, tmp) ## The multiplication is broken. Numpy is calling __rmul__ for every element instead of with the whole array.
1
"""
N = self.matrix.shape[1]
if isinstance(other, _PysparseMatrix):
return _PysparseMatrix(
matrix=spmatrix.matrixmultiply(self.matrix, other.matrix))
else:
shape = numerix.shape(other)
if shape == ():
L = spmatrix.ll_mat(N, N, N)
L.put(other * numerix.ones(N, 'l'))
return _PysparseMatrix(
matrix=spmatrix.matrixmultiply(self.matrix, L))
elif shape == (N, ):
y = numerix.empty((self.matrix.shape[0], ))
self.matrix.matvec(other, y)
return y
else:
raise TypeError
def __mul__(self, other):
"""
Multiply a sparse matrix by another sparse matrix
>>> L1 = _PysparseMatrix(size = 3)
>>> L1.put([3.,10.,numerix.pi,2.5], [0,0,1,2], [2,1,1,0])
>>> L2 = _PysparseIdentityMatrix(size = 3)
>>> L2.put([4.38,12357.2,1.1], [2,1,0], [1,0,2])
>>> tmp = numerix.array(((1.23572000e+05, 2.31400000e+01, 3.00000000e+00),
... (3.88212887e+04, 3.14159265e+00, 0.00000000e+00),
... (2.50000000e+00, 0.00000000e+00, 2.75000000e+00)))
>>> numerix.allclose((L1 * L2).getNumpyArray(), tmp)
1
or a sparse matrix by a vector
>>> tmp = numerix.array((29., 6.28318531, 2.5))
>>> numerix.allclose(L1 * numerix.array((1,2,3),'d'), tmp)
1
or a vector by a sparse matrix
>>> tmp = numerix.array((7.5, 16.28318531, 3.))
>>> numerix.allclose(numerix.array((1,2,3),'d') * L1, tmp) ## The multiplication is broken. Numpy is calling __rmul__ for every element instead of with the whole array.
1
"""
N = self.matrix.shape[0]
if isinstance(other, _PysparseMatrix):
return _PysparseMatrix(matrix = spmatrix.matrixmultiply(self.matrix, other._getMatrix()))
else:
shape = numerix.shape(other)
if shape == ():
L = spmatrix.ll_mat(N, N, N)
L.put(other * numerix.ones(N))
return _PysparseMatrix(matrix = spmatrix.matrixmultiply(self.matrix, L))
elif shape == (N,):
y = other.copy()
self.matrix.matvec(other, y)
return y
else:
raise TypeError
def _calcValue_(self, alpha, id1, id2):
val = self._array.copy()
inline._runIterateElementInline("""
int ID1 = ITEM(id1, i, NULL);
int ID2 = ITEM(id2, i, NULL);
double cell1 = ITEM(var, ID1, vec);
double cell2 = ITEM(var, ID2, vec);
ITEM(val, i, vec) = (cell2 - cell1) * ITEM(alpha, i, NULL) + cell1;
""",
var = self.var.numericValue,
val = val,
alpha = alpha,
id1 = id1, id2 = id2,
shape=numerix.array(numerix.shape(val)),
ni = self.mesh.numberOfFaces)
return self._makeValue(value = val)
def _calcValue(self):
id1, id2 = self.mesh._adjacentCellIDs
tangents1 = self.mesh._faceTangents1
tangents2 = self.mesh._faceTangents2
val = self._array.copy()
inline._runIterateElementInline(
self.modIn + """
int j;
double t1grad1, t1grad2, t2grad1, t2grad2, N;
int ID1 = ITEM(id1, i, NULL);
int ID2 = ITEM(id2, i, NULL);
N = mod(ITEM(var, ID2, NULL) - ITEM(var, ID1, NULL)) / ITEM(dAP, i, NULL);
t1grad1 = t1grad2 = t2grad1 = t2grad2 = 0.;
t1grad1 += ITEM(tangents1, i, vec) * ITEM(cellGrad, ID1, vec);
t1grad2 += ITEM(tangents1, i, vec) * ITEM(cellGrad, ID2, vec);
t2grad1 += ITEM(tangents2, i, vec) * ITEM(cellGrad, ID1, vec);
t2grad2 += ITEM(tangents2, i, vec) * ITEM(cellGrad, ID2, vec);
ITEM(val, i, vec) = ITEM(normals, i, vec) * N;
ITEM(val, i, vec) += ITEM(tangents1, i, vec) * (t1grad1 + t1grad2) / 2.;
ITEM(val, i, vec) += ITEM(tangents2, i, vec) * (t2grad1 + t2grad2) / 2.;
""",
tangents1=tangents1,
tangents2=tangents2,
cellGrad=self.var.grad.numericValue,
normals=numerix.array(self.mesh._orientedFaceNormals),
id1=numerix.array(id1),
id2=numerix.array(id2),
dAP=numerix.array(self.mesh._cellDistances),
var=self.var.numericValue,
val=val,
ni=tangents1.shape[1],
shape=numerix.array(numerix.shape(val)))
return self._makeValue(value=val)
def _calcValueInline(self):
id1, id2 = self.mesh._getAdjacentCellIDs()
tangents1 = self.mesh._getFaceTangents1()
tangents2 = self.mesh._getFaceTangents2()
val = self._getArray().copy()
inline._runIterateElementInline("""
int j;
double t1grad1, t1grad2, t2grad1, t2grad2, N;
int ID1 = ITEM(id1, i, NULL);
int ID2 = ITEM(id2, i, NULL);
N = (ITEM(var, ID2, NULL) - ITEM(var, ID1, NULL)) / ITEM(dAP, i, NULL);
t1grad1 = t1grad2 = t2grad1 = t2grad2 = 0.;
t1grad1 += ITEM(tangents1, i, vec) * ITEM(cellGrad, ID1, vec);
t1grad2 += ITEM(tangents1, i, vec) * ITEM(cellGrad, ID2, vec);
t2grad1 += ITEM(tangents2, i, vec) * ITEM(cellGrad, ID1, vec);
t2grad2 += ITEM(tangents2, i, vec) * ITEM(cellGrad, ID2, vec);
ITEM(val, i, vec) = ITEM(normals, i, vec) * N;
ITEM(val, i, vec) += ITEM(tangents1, i, vec) * (t1grad1 + t1grad2) / 2.;
ITEM(val, i, vec) += ITEM(tangents2, i, vec) * (t2grad1 + t2grad2) / 2.;
""",tangents1 = tangents1,
tangents2 = tangents2,
cellGrad = self.var.getGrad().getNumericValue(),
normals = self.mesh._getOrientedFaceNormals(),
id1 = id1,
id2 = id2,
dAP = numerix.array(self.mesh._getCellDistances()),
var = self.var.getNumericValue(),
val = val,
ni = tangents1.shape[1],
shape=numerix.array(numerix.shape(tangents1)))
return self._makeValue(value = val)
def __mul__(self, other):
"""
Multiply a sparse matrix by another sparse matrix
>>> L1 = _ScipyMatrixFromShape(size=3)
>>> L1.put([3.,10.,numerix.pi,2.5], [0,0,1,2], [2,1,1,0])
>>> L2 = _ScipyIdentityMatrix(size=3)
>>> L2.put([4.38,12357.2,1.1], [2,1,0], [1,0,2])
>>> tmp = numerix.array(((1.23572000e+05, 2.31400000e+01, 3.00000000e+00),
... (3.88212887e+04, 3.14159265e+00, 0.00000000e+00),
... (2.50000000e+00, 0.00000000e+00, 2.75000000e+00)))
>>> numerix.allclose((L1 * L2).numpyArray, tmp)
1
or a sparse matrix by a vector
>>> tmp = numerix.array((29., 6.28318531, 2.5))
>>> numerix.allclose(L1 * numerix.array((1,2,3),'d'), tmp)
1
or a vector by a sparse matrix
>>> tmp = numerix.array((7.5, 16.28318531, 3.))
>>> numerix.allclose(numerix.array((1,2,3),'d') * L1, tmp) ## The multiplication is broken. Numpy is calling __rmul__ for every element instead of with the whole array.
1
"""
N = self.matrix.shape[0]
if isinstance(other, _ScipyMatrix):
return _ScipyMatrix(matrix=(self.matrix * other.matrix))
else:
shape = numerix.shape(other)
if shape == ():
return _ScipyMatrix(matrix=(self.matrix * other))
elif shape == (N,):
return self.matrix * other
else:
raise TypeError
def _calcValue(self):
id1, id2 = self.mesh._adjacentCellIDs
tangents1 = self.mesh._faceTangents1
tangents2 = self.mesh._faceTangents2
val = self._array.copy()
inline._runIterateElementInline(self.modIn + """
int j;
double t1grad1, t1grad2, t2grad1, t2grad2, N;
int ID1 = ITEM(id1, i, NULL);
int ID2 = ITEM(id2, i, NULL);
N = mod(ITEM(var, ID2, NULL) - ITEM(var, ID1, NULL)) / ITEM(dAP, i, NULL);
t1grad1 = t1grad2 = t2grad1 = t2grad2 = 0.;
t1grad1 += ITEM(tangents1, i, vec) * ITEM(cellGrad, ID1, vec);
t1grad2 += ITEM(tangents1, i, vec) * ITEM(cellGrad, ID2, vec);
t2grad1 += ITEM(tangents2, i, vec) * ITEM(cellGrad, ID1, vec);
t2grad2 += ITEM(tangents2, i, vec) * ITEM(cellGrad, ID2, vec);
ITEM(val, i, vec) = ITEM(normals, i, vec) * N;
ITEM(val, i, vec) += ITEM(tangents1, i, vec) * (t1grad1 + t1grad2) / 2.;
ITEM(val, i, vec) += ITEM(tangents2, i, vec) * (t2grad1 + t2grad2) / 2.;
""",tangents1 = tangents1,
tangents2 = tangents2,
cellGrad = self.var.grad.numericValue,
normals = numerix.array(self.mesh._orientedFaceNormals),
id1 = numerix.array(id1),
id2 = numerix.array(id2),
dAP = numerix.array(self.mesh._cellDistances),
var = self.var.numericValue,
val = val,
ni = tangents1.shape[1],
shape=numerix.array(numerix.shape(val)))
return self._makeValue(value = val)
def _calcValueIn(self, alpha, id1, id2):
val = self._getArray().copy()
inline._runIterateElementInline("""
int ID1 = ITEM(id1, i, NULL);
int ID2 = ITEM(id2, i, NULL);
double cell1 = ITEM(var, ID1, vec);
double cell2 = ITEM(var, ID2, vec);
double cell1Xcell2 = cell1 * cell2;
double tmp = ((cell2 - cell1) * ITEM(alpha, i, NULL) + cell1);
if (tmp != 0 && cell1Xcell2 > 0.) {
ITEM(val, i, vec) = cell1Xcell2 / tmp;
} else {
ITEM(val, i, vec) = 0.;
}
""",
var = self.var.getNumericValue(),
val = val,
alpha = alpha,
id1 = id1, id2 = id2,
shape=numerix.array(numerix.shape(val)),
ni = self.mesh._getNumberOfFaces())
return self._makeValue(value = val)
def _calcNumPts(d, n = None, axis = "x"):
"""
Calculate the number of cells along the specified axis, based
on either the specified number or on the number elements in the
cell `d` spacings.
Used by the `Grid` meshes.
This tests a bug that was occurring with PeriodicGrid1D when
using a numpy float as the argument for the grid spacing.
>>> from fipy.meshes.periodicGrid1D import PeriodicGrid1D
>>> PeriodicGrid1D(nx=2, dx=numerix.float32(1.))
PeriodicGrid1D(dx=1.0, nx=2)
"""
if type(d) in [int, float] or numerix.shape(d) == ():
n = int(n or 1)
else:
n = int(n or len(d))
if n != len(d) and len(d) != 1:
raise IndexError("n%s != len(d%s)" % (axis, axis))
return n
def __mul__(self, other):
"""
Multiply a sparse matrix by another sparse matrix.
>>> L1 = _TrilinosMatrix(size=3)
>>> L1.addAt((3,10,numerix.pi,2.5), (0,0,1,2), (2,1,1,0))
>>> L2 = _TrilinosIdentityMatrix(size=3)
>>> L2.addAt((4.38,12357.2,1.1), (2,1,0), (1,0,2))
>>> tmp = numerix.array(((1.23572000e+05, 2.31400000e+01, 3.00000000e+00),
... (3.88212887e+04, 3.14159265e+00, 0.00000000e+00),
... (2.50000000e+00, 0.00000000e+00, 2.75000000e+00)))
>>> for i in range(0,3):
... for j in range(0,3):
... numerix.allclose(((L1*L2)[i,j],), tmp[i,j])
True
True
True
True
True
True
True
True
True
or a sparse matrix by a vector
>>> tmp = numerix.array((29., 6.28318531, 2.5))
>>> numerix.allclose(L1 * numerix.array((1,2,3),'d'), tmp)
1
or a vector by a sparse matrix
>>> tmp = numerix.array((7.5, 16.28318531, 3.))
>>> numerix.allclose(numerix.array((1,2,3),'d') * L1, tmp)
1
"""
N = self._getMatrix().NumMyCols()
if isinstance(other, _TrilinosMatrixBase):
if isinstance(other._getMatrix(), Epetra.RowMatrix):
if not self._getMatrix().Filled():
self._getMatrix().FillComplete()
if not other._getMatrix().Filled():
other._getMatrix().FillComplete()
result = Epetra.CrsMatrix(Epetra.Copy, self.nonOverlappingMap, 0)
EpetraExt.Multiply(self._getMatrix(), False, other._getMatrix(), False, result)
copy = self.copy()
copy.matrix = result
return copy
else:
raise TypeError
else:
shape = numerix.shape(other)
if shape == ():
result = self.copy()
result._getMatrix().Scale(other)
return result
elif shape == (N,):
if not self._getMatrix().Filled():
self._getMatrix().FillComplete()
y = _numpyToTrilinosVector(other, self.nonOverlappingMap)
result = Epetra.Vector(self.nonOverlappingMap)
self._getMatrix().Multiply(False, y, result)
return _trilinosToNumpyVector(result)
else:
raise TypeError
def plot(self, matrix, RHSvector, log='auto'):
import tempfile
import os
if "print" in os.environ['FIPY_DISPLAY_MATRIX'].lower().split():
print("-" * 75)
print(self.title)
print("-" * 75)
print("L:")
print(matrix)
print("b:", RHSvector)
(f, mtxName) = tempfile.mkstemp(suffix='.mtx')
matrix.exportMmf(mtxName)
mtx = mmio.mmread(mtxName)
os.remove(mtxName)
pyplot.ion()
c = mtx.tocoo()
y = c.row
x = c.col
z = c.data
N = matrix._shape[0]
b = RHSvector
if numerix.shape(b) == ():
b = numerix.zeros((N, ), 'l')
if len(z) == 0:
y = numerix.zeros((1, ), 'l')
x = numerix.zeros((1, ), 'l')
z = numerix.zeros((1, ), 'l')
def signed_to_logs(v):
return (numerix.where(v > 0, numerix.log10(v), numerix.nan),
numerix.where(v < 0, numerix.log10(-v), numerix.nan))
def logs_to_signed(v, plus, minus):
v = numerix.where(v > 0, plus, -minus)
v = numerix.where(numerix.isnan(v), 0., v)
return v
zPlus, zMinus = signed_to_logs(z)
bPlus, bMinus = signed_to_logs(b)
logs = (zPlus, zMinus, bPlus, bMinus)
log = ((log == True)
or (log == 'auto' and
(numerix.nanmax(numerix.concatenate(logs)) -
numerix.nanmin(numerix.concatenate(logs)) > 2)))
if log:
zMin = numerix.nanmin(numerix.concatenate(logs))
zMax = numerix.nanmax(numerix.concatenate(logs))
zMin -= 0.5
numdec = numerix.floor(zMax) - numerix.ceil(zMin)
if numdec < 0:
zMax += 0.5
for v in logs:
v -= zMin
zRange = zMax - zMin
if zRange == 0:
zRange = numerix.nanmax(zPlus) + 1
z = logs_to_signed(z, zPlus, zMinus)
b = logs_to_signed(b, bPlus, bMinus)
fmt = SignedLogFormatter(threshold=zMin)
loc = SignedLogLocator(threshold=zMin)
else:
zRange = max(abs(numerix.concatenate((z, b))))
if zRange == 0:
zRange = 1
fmt = None
loc = None
pyplot.ioff()
fig = pyplot.figure(self.id)
fig.clf()
usetex = rcParams['text.usetex']
rcParams['text.usetex'] = False
cmap = cm.RdBu
norm = Normalize(vmin=-zRange, vmax=zRange)
x0 = self.margin
L_ax = fig.add_axes([
x0 / self.aspect, self.margin, self.L_width / self.aspect,
self.L_width
])
L_ax.text(0.5,
-0.1,
"L",
transform=L_ax.transAxes,
horizontalalignment='center',
verticalalignment='baseline')
x0 += self.L_width + self.buffer
c_ax = fig.add_axes([
x0 / self.aspect, self.margin, self.c_width / self.aspect,
self.L_width
])
x0 += self.c_width + self.buffer
b_ax = fig.add_axes([
x0 / self.aspect, self.margin, self.b_width / self.aspect,
self.L_width
],
sharey=L_ax)
b_ax.text(0.5,
-0.1,
"b",
transform=b_ax.transAxes,
horizontalalignment='center',
verticalalignment='baseline')
def scatterRectangles(x, y, z, norm=None, cmap=None):
patches = [
Rectangle(numerix.array([X - 0.5, Y - 0.5]),
1.,
1.,
edgecolor='none') for X, Y in zip(x, y)
]
collection = PatchCollection(patches,
norm=norm,
cmap=cmap,
edgecolors='none')
collection.set_array(z)
return collection
L_ax.add_collection(
scatterRectangles(x=x, y=y, z=z, norm=norm, cmap=cmap))
b_ax.add_collection(
scatterRectangles(x=numerix.zeros((N, ), 'l'),
y=numerix.arange(N),
z=b,
norm=norm,
cmap=cmap))
ColorbarBase(ax=c_ax,
cmap=cmap,
norm=norm,
orientation='vertical',
format=fmt,
ticks=loc)
pyplot.setp((b_ax.get_xticklabels(), b_ax.get_yticklabels(),
b_ax.get_xticklines(), b_ax.get_yticklines()),
visible=False)
L_ax.set_xlim(xmin=-0.5, xmax=N - 0.5)
L_ax.set_ylim(ymax=-0.5, ymin=N - 0.5)
b_ax.set_xlim(xmin=-0.5, xmax=0.5)
b_ax.set_ylim(ymax=-0.5, ymin=N - 0.5)
fig.suptitle(self.title, x=0.5, y=0.95, fontsize=14)
pyplot.draw()
rcParams['text.usetex'] = usetex
def constrain(self, value, where=None):
r"""
Constrains the `CellVariable` to `value` at a location specified by `where`.
>>> from fipy import *
>>> m = Grid1D(nx=3)
>>> v = CellVariable(mesh=m, value=m.cellCenters[0])
>>> v.constrain(0., where=m.facesLeft)
>>> v.faceGrad.constrain([1.], where=m.facesRight)
>>> print v.faceGrad
[[ 1. 1. 1. 1.]]
>>> print v.faceValue
[ 0. 1. 2. 2.5]
Changing the constraint changes the dependencies
>>> v.constrain(1., where=m.facesLeft)
>>> print v.faceGrad
[[-1. 1. 1. 1.]]
>>> print v.faceValue
[ 1. 1. 2. 2.5]
Constraints can be `Variable`
>>> c = Variable(0.)
>>> v.constrain(c, where=m.facesLeft)
>>> print v.faceGrad
[[ 1. 1. 1. 1.]]
>>> print v.faceValue
[ 0. 1. 2. 2.5]
>>> c.value = 1.
>>> print v.faceGrad
[[-1. 1. 1. 1.]]
>>> print v.faceValue
[ 1. 1. 2. 2.5]
Constraints can have a `Variable` mask.
>>> v = CellVariable(mesh=m)
>>> mask = FaceVariable(mesh=m, value=m.facesLeft)
>>> v.constrain(1., where=mask)
>>> print v.faceValue
[ 1. 0. 0. 0.]
>>> mask[:] = mask | m.facesRight
>>> print v.faceValue
[ 1. 0. 0. 1.]
"""
from fipy.boundaryConditions.constraint import Constraint
if not isinstance(value, Constraint):
value = Constraint(value=value, where=where)
if numerix.shape(value.where)[-1] == self.mesh.numberOfFaces:
if not hasattr(self, 'faceConstraints'):
self.faceConstraints = []
self.faceConstraints.append(value)
self._requires(value.value)
# self._requires(value.where) ???
self._markStale()
else:
## _MeshVariable.constrain(value, where)
super(CellVariable, self).constrain(value, where)
def __mul__(self, other):
"""
Multiply a sparse matrix by another sparse matrix.
>>> L1 = _TrilinosMatrix(size=3)
>>> L1.addAt((3,10,numerix.pi,2.5), (0,0,1,2), (2,1,1,0))
>>> L2 = _TrilinosIdentityMatrix(size=3)
>>> L2.addAt((4.38,12357.2,1.1), (2,1,0), (1,0,2))
>>> tmp = numerix.array(((1.23572000e+05, 2.31400000e+01, 3.00000000e+00),
... (3.88212887e+04, 3.14159265e+00, 0.00000000e+00),
... (2.50000000e+00, 0.00000000e+00, 2.75000000e+00)))
>>> for i in range(0,3):
... for j in range(0,3):
... numerix.allclose(((L1*L2)[i,j],), tmp[i,j])
True
True
True
True
True
True
True
True
True
or a sparse matrix by a vector
>>> tmp = numerix.array((29., 6.28318531, 2.5))
>>> numerix.allclose(L1 * numerix.array((1,2,3),'d'), tmp)
1
or a vector by a sparse matrix
>>> tmp = numerix.array((7.5, 16.28318531, 3.))
>>> numerix.allclose(numerix.array((1,2,3),'d') * L1, tmp)
1
"""
if not self._getMatrix().Filled():
self._getMatrix().FillComplete()
N = self._getMatrix().NumMyCols()
if isinstance(other, _TrilinosMatrixBase):
return _TrilinosMatrix.__mul__(self, other=other)
else:
shape = numerix.shape(other)
if shape == ():
result = self.copy()
result._getMatrix().Scale(other)
return result
else:
if isinstance(other, Epetra.Vector):
other_map = other.Map()
else:
other_map = self.overlappingMap
if other_map.SameAs(self.overlappingMap):
localNonOverlappingCellIDs = self.mesh._getLocalNonOverlappingCellIDs()
other = Epetra.Vector(self.nonOverlappingMap,
other[localNonOverlappingCellIDs])
if other.Map().SameAs(self.matrix.RowMap()):
nonoverlapping_result = Epetra.Vector(self.nonOverlappingMap)
self._getMatrix().Multiply(False, other, nonoverlapping_result)
if other_map.SameAs(self.overlappingMap):
overlapping_result = Epetra.Vector(self.overlappingMap)
overlapping_result.Import(nonoverlapping_result,
Epetra.Import(self.overlappingMap,
self.nonOverlappingMap),
Epetra.Insert)
return overlapping_result
else:
return nonoverlapping_result
else:
raise TypeError("%s: %s != (%d,)" % (self.__class__, str(shape), N))
# Calculate H-field for uniaxial anisotropy
HuniaxBase = HeffUniaxialAnisotropyKM(gridCoor, uAxis, Ku2, Msat)
HeffBase = HuniaxBase
TuniaxBase = calculateDampingTerm(gridCoor / numerix.linalg.norm(gridCoor), HeffBase)
TuniaxBase = numerix.multiply(TuniaxBase, alphaDamping)
TuniaxBase = TuniaxBase + calculatePrecessionTerm(gridCoor / numerix.linalg.norm(gridCoor), HeffBase)
TuniaxBase = numerix.multiply(TuniaxBase, (-1.0 * gamFac))
TeffBase = TuniaxBase
Teff = CellVariable(mesh=mesh, value=TeffBase)
#phi = CellVariable(name=r"$\Phi$", mesh=mesh) # doctest: +GMSH
phi = CellVariable(mesh=mesh, value=0.25 / numerix.pi)
print(numerix.shape(TeffBase))
print(max(numerix.linalg.norm(TeffBase,axis=0)))
if __name__ == "__main__":
try:
print("\n done") #Intermediate Print Statement
viewer = VTKViewer(vars=phi,datamin=0., datamax=1.) #Changed Statement
print("\n Daemon file") #Intermediate Print Statement
except (NameError,ImportError,SystemError,TypeError):
viewer = VTKViewer(vars=phi,datamin=0., datamax=1.) #Changed Statement
viewer.plot(filename="trial.vtk") #It will only save the final vtk file. You can change the name
eqI = (TransientTerm()
== DiffusionTerm(coeff=D)
def constrain(self, value, where=None):
r"""
Constrains the `CellVariable` to `value` at a location specified by `where`.
>>> from fipy import *
>>> m = Grid1D(nx=3)
>>> v = CellVariable(mesh=m, value=m.cellCenters[0])
>>> v.constrain(0., where=m.facesLeft)
>>> v.faceGrad.constrain([1.], where=m.facesRight)
>>> print v.faceGrad
[[ 1. 1. 1. 1.]]
>>> print v.faceValue
[ 0. 1. 2. 2.5]
Changing the constraint changes the dependencies
>>> v.constrain(1., where=m.facesLeft)
>>> print v.faceGrad
[[-1. 1. 1. 1.]]
>>> print v.faceValue
[ 1. 1. 2. 2.5]
Constraints can be `Variable`
>>> c = Variable(0.)
>>> v.constrain(c, where=m.facesLeft)
>>> print v.faceGrad
[[ 1. 1. 1. 1.]]
>>> print v.faceValue
[ 0. 1. 2. 2.5]
>>> c.value = 1.
>>> print v.faceGrad
[[-1. 1. 1. 1.]]
>>> print v.faceValue
[ 1. 1. 2. 2.5]
Constraints can have a `Variable` mask.
>>> v = CellVariable(mesh=m)
>>> mask = FaceVariable(mesh=m, value=m.facesLeft)
>>> v.constrain(1., where=mask)
>>> print v.faceValue
[ 1. 0. 0. 0.]
>>> mask[:] = mask | m.facesRight
>>> print v.faceValue
[ 1. 0. 0. 1.]
"""
from fipy.boundaryConditions.constraint import Constraint
if not isinstance(value, Constraint):
value = Constraint(value=value, where=where)
if numerix.shape(value.where)[-1] == self.mesh.numberOfFaces:
if not hasattr(self, 'faceConstraints'):
self.faceConstraints = []
self.faceConstraints.append(value)
self._requires(value.value)
# self._requires(value.where) ???
self._markStale()
else:
## _MeshVariable.constrain(value, where)
super(CellVariable, self).constrain(value, where)
def __init__(self, mesh, name='', value=0., rank=None, elementshape=None,
unit=None, cached=1):
"""
:Parameters:
- `mesh`: the mesh that defines the geometry of this `Variable`
- `name`: the user-readable name of the `Variable`
- `value`: the initial value
- `rank`: the rank (number of dimensions) of each element of this
`Variable`. Default: 0
- `elementshape`: the shape of each element of this variable
Default: `rank * (mesh.getDim(),)`
- `unit`: the physical units of the `Variable`
"""
from fipy.tools import debug
if isinstance(value, (list, tuple)):
value = numerix.array(value)
if isinstance(value, _MeshVariable):
if mesh is None:
mesh = value.mesh
elif mesh != value.mesh:
raise ValueError, "The new 'Variable' must use the same mesh as the supplied value"
self.mesh = mesh
value = self._globalToLocalValue(value)
if value is None:
array = None
elif not isinstance(value, _Constant) and isinstance(value, Variable):
name = name or value.name
unit = None
if isinstance(value, _MeshVariable):
if not isinstance(value, self._getVariableClass()):
raise TypeError, "A '%s' cannot be cast to a '%s'" % (value._getVariableClass().__name__,
self._getVariableClass().__name__)
if elementshape is not None and elementshape != value.shape[:-1]:
raise ValueError, "'elementshape' != shape of elements of 'value'"
if rank is not None and rank != value.getRank():
raise ValueError, "'rank' != rank of 'value'"
elementshape = value.shape[:-1]
array = None
# value = value._copyValue()
if elementshape is None:
valueShape = numerix.getShape(value)
if valueShape != () and valueShape[-1] == self._getShapeFromMesh(mesh)[-1]:
if elementshape is not None and elementshape != valueShape[:-1]:
raise ValueError, "'elementshape' != shape of elements of 'value'"
if rank is not None and rank != len(valueShape[:-1]):
raise ValueError, "'rank' != rank of 'value'"
elementshape = valueShape[:-1]
elif rank is None and elementshape is None:
elementshape = valueShape
if rank is None:
if elementshape is None:
elementshape = ()
elif elementshape is None:
elementshape = rank * (mesh.getDim(),)
elif len(elementshape) != rank:
raise ValueError, 'len(elementshape) != rank'
self.elementshape = elementshape
if not locals().has_key("array"):
if numerix._isPhysical(value):
dtype = numerix.obj2sctype(value.value)
else:
dtype = numerix.obj2sctype(value)
array = numerix.zeros(self.elementshape
+ self._getShapeFromMesh(mesh),
dtype)
if numerix._broadcastShape(array.shape, numerix.shape(value)) is None:
if not isinstance(value, Variable):
value = _Constant(value)
value = value[..., numerix.newaxis]
Variable.__init__(self, name=name, value=value, unit=unit,
array=array, cached=cached)
def __mul__(self, other):
"""
Multiply a sparse matrix by another sparse matrix.
>>> L1 = _TrilinosMatrixFromShape(rows=3, cols=3)
>>> L1.addAt((3, 10, numerix.pi, 2.5), (0, 0, 1, 2), (2, 1, 1, 0))
>>> L2 = _TrilinosIdentityMatrix(size=3)
>>> L2.addAt((4.38, 12357.2, 1.1), (2, 1, 0), (1, 0, 2))
>>> tmp = numerix.array(((1.23572000e+05, 2.31400000e+01, 3.00000000e+00),
... (3.88212887e+04, 3.14159265e+00, 0.00000000e+00),
... (2.50000000e+00, 0.00000000e+00, 2.75000000e+00)))
>>> L = (L1 * L2).numpyArray
>>> print(numerix.allclose(tmp, L))
True
or a sparse matrix by a vector
>>> tmp = numerix.array((29., 6.28318531, 2.5))
>>> print(numerix.allclose(L1 * numerix.array((1, 2, 3), 'd'), tmp)) # doctest: +SERIAL
True
or a vector by a sparse matrix
>>> tmp = numerix.array((7.5, 16.28318531, 3.))
>>> numerix.allclose(numerix.array((1, 2, 3), 'd') * L1, tmp) # doctest: +SERIAL
True
Should be able to multiply an overlapping value obtained from a
`CellVariable`. This is required to make the `--no-pysparse` flag
work correctly.
>>> from fipy import *
>>> m = Grid1D(nx=6)
>>> v0 = CellVariable(mesh=m, value=numerix.arange(m.globalNumberOfCells, dtype=float))
>>> v1 = CellVariable(mesh=m, value=_TrilinosIdentityMeshMatrix(mesh=m) * v0.value)
>>> print(numerix.allclose(v0, v1))
True
"""
self.fillComplete()
N = self.matrix.NumMyCols()
if isinstance(other, _TrilinosMatrix):
return super(_TrilinosMeshMatrix, self).__mul__(other=other)
else:
shape = numerix.shape(other)
if shape == ():
result = self.copy()
result.matrix.Scale(other)
return result
else:
if isinstance(other, Epetra.Vector):
other_map = other.Map()
else:
other_map = self.colMap
if other_map.SameAs(self.colMap):
localNonOverlappingColIDs = self._m2m.localNonOverlappingColIDs
other = Epetra.Vector(self.domainMap,
other[localNonOverlappingColIDs])
if other.Map().SameAs(self.matrix.DomainMap()):
nonoverlapping_result = Epetra.Vector(self.rangeMap)
self.matrix.Multiply(False, other, nonoverlapping_result)
if other_map.SameAs(self.colMap):
overlapping_result = Epetra.Vector(self.colMap)
overlapping_result.Import(
nonoverlapping_result,
Epetra.Import(self.colMap, self.domainMap),
Epetra.Insert)
return overlapping_result
else:
return nonoverlapping_result
else:
raise TypeError("%s: %s != (%d,)" %
(self.__class__, str(shape), N))
def __mul__(self, other):
"""
Multiply a sparse matrix by another sparse matrix.
>>> L1 = _TrilinosMatrix(size=3)
>>> L1.addAt((3,10,numerix.pi,2.5), (0,0,1,2), (2,1,1,0))
>>> L2 = _TrilinosIdentityMatrix(size=3)
>>> L2.addAt((4.38,12357.2,1.1), (2,1,0), (1,0,2))
>>> tmp = numerix.array(((1.23572000e+05, 2.31400000e+01, 3.00000000e+00),
... (3.88212887e+04, 3.14159265e+00, 0.00000000e+00),
... (2.50000000e+00, 0.00000000e+00, 2.75000000e+00)))
>>> for i in range(0,3):
... for j in range(0,3):
... numerix.allclose(((L1*L2)[i,j],), tmp[i,j])
True
True
True
True
True
True
True
True
True
or a sparse matrix by a vector
>>> tmp = numerix.array((29., 6.28318531, 2.5))
>>> numerix.allclose(L1 * numerix.array((1,2,3),'d'), tmp)
1
or a vector by a sparse matrix
>>> tmp = numerix.array((7.5, 16.28318531, 3.))
>>> numerix.allclose(numerix.array((1,2,3),'d') * L1, tmp)
1
"""
if not self._getMatrix().Filled():
self._getMatrix().FillComplete()
N = self._getMatrix().NumMyCols()
if isinstance(other, _TrilinosMatrixBase):
return _TrilinosMatrix.__mul__(self, other=other)
else:
shape = numerix.shape(other)
if shape == ():
result = self.copy()
result._getMatrix().Scale(other)
return result
else:
if isinstance(other, Epetra.Vector):
other_map = other.Map()
else:
other_map = self.overlappingMap
if other_map.SameAs(self.overlappingMap):
localNonOverlappingCellIDs = self.mesh._getLocalNonOverlappingCellIDs()
other = Epetra.Vector(self.nonOverlappingMap,
other[localNonOverlappingCellIDs])
if other.Map().SameAs(self.matrix.RowMap()):
nonoverlapping_result = Epetra.Vector(self.nonOverlappingMap)
self._getMatrix().Multiply(False, other, nonoverlapping_result)
if other_map.SameAs(self.overlappingMap):
overlapping_result = Epetra.Vector(self.overlappingMap)
overlapping_result.Import(nonoverlapping_result,
Epetra.Import(self.overlappingMap,
self.nonOverlappingMap),
Epetra.Insert)
return overlapping_result
else:
return nonoverlapping_result
else:
raise TypeError("%s: %s != (%d,)" % (self.__class__, str(shape), N))
def __mul__(self, other):
"""
Multiply a sparse matrix by another sparse matrix.
>>> L1 = _TrilinosMatrixFromShape(rows=3, cols=3)
>>> L1.addAt((3, 10, numerix.pi, 2.5), (0, 0, 1, 2), (2, 1, 1, 0))
>>> L2 = _TrilinosIdentityMatrix(size=3)
>>> L2.addAt((4.38, 12357.2, 1.1), (2, 1, 0), (1, 0, 2))
>>> tmp = numerix.array(((1.23572000e+05, 2.31400000e+01, 3.00000000e+00),
... (3.88212887e+04, 3.14159265e+00, 0.00000000e+00),
... (2.50000000e+00, 0.00000000e+00, 2.75000000e+00)))
>>> L = (L1 * L2).numpyArray
>>> print(numerix.allclose(tmp, L)) # doctest: +SERIAL
True
or a sparse matrix by a vector
>>> tmp = numerix.array((29., 6.28318531, 2.5))
>>> print(numerix.allclose(L1 * numerix.array((1, 2, 3), 'd'), tmp)) # doctest: +SERIAL
True
or a vector by a sparse matrix
>>> tmp = numerix.array((7.5, 16.28318531, 3.))
>>> print(numerix.allclose(numerix.array((1, 2, 3), 'd') * L1, tmp)) # doctest: +SERIAL
True
"""
N = self.matrix.NumMyCols()
if isinstance(other, _TrilinosMatrix):
if isinstance(other.matrix, Epetra.RowMatrix):
self.fillComplete()
other.fillComplete()
result = Epetra.CrsMatrix(Epetra.Copy, self.rowMap, 0)
EpetraExt.Multiply(self.matrix, False, other.matrix, False,
result)
copy = self.copy()
copy.matrix = result
return copy
else:
raise TypeError
else:
shape = numerix.shape(other)
if shape == ():
result = self.copy()
result.matrix.Scale(other)
return result
elif shape == (N, ):
self.fillComplete()
y = Epetra.Vector(self.domainMap, other)
result = Epetra.Vector(self.rangeMap)
self.matrix.Multiply(False, y, result)
return numerix.array(result)
else:
raise TypeError
def __mul__(self, other):
"""
Multiply a sparse matrix by another sparse matrix.
>>> L1 = _TrilinosMatrix(size=3)
>>> L1.addAt((3,10,numerix.pi,2.5), (0,0,1,2), (2,1,1,0))
>>> L2 = _TrilinosIdentityMatrix(size=3)
>>> L2.addAt((4.38,12357.2,1.1), (2,1,0), (1,0,2))
>>> tmp = numerix.array(((1.23572000e+05, 2.31400000e+01, 3.00000000e+00),
... (3.88212887e+04, 3.14159265e+00, 0.00000000e+00),
... (2.50000000e+00, 0.00000000e+00, 2.75000000e+00)))
>>> for i in range(0,3):
... for j in range(0,3):
... numerix.allclose(((L1*L2)[i,j],), tmp[i,j])
True
True
True
True
True
True
True
True
True
or a sparse matrix by a vector
>>> tmp = numerix.array((29., 6.28318531, 2.5))
>>> numerix.allclose(L1 * numerix.array((1,2,3),'d'), tmp)
1
or a vector by a sparse matrix
>>> tmp = numerix.array((7.5, 16.28318531, 3.))
>>> numerix.allclose(numerix.array((1,2,3),'d') * L1, tmp)
1
"""
N = self._getMatrix().NumMyCols()
if isinstance(other, _TrilinosMatrixBase):
if isinstance(other._getMatrix(), Epetra.RowMatrix):
if not self._getMatrix().Filled():
self._getMatrix().FillComplete()
if not other._getMatrix().Filled():
other._getMatrix().FillComplete()
result = Epetra.CrsMatrix(Epetra.Copy, self.nonOverlappingMap, 0)
EpetraExt.Multiply(self._getMatrix(), False, other._getMatrix(), False, result)
copy = self.copy()
copy.matrix = result
return copy
else:
raise TypeError
else:
shape = numerix.shape(other)
if shape == ():
result = self.copy()
result._getMatrix().Scale(other)
return result
elif shape == (N,):
if not self._getMatrix().Filled():
self._getMatrix().FillComplete()
y = _numpyToTrilinosVector(other, self.nonOverlappingMap)
result = Epetra.Vector(self.nonOverlappingMap)
self._getMatrix().Multiply(False, y, result)
return _trilinosToNumpyVector(result)
else:
raise TypeError
def __getitem__(self, index):
self.matrix.assemble()
m = self.matrix[index]
if numerix.shape(m) != ():
m = _PETScMatrix(matrix=m)
return m
def plot(self, matrix, RHSvector, log='auto'):
import tempfile
import os
if "print" in os.environ['FIPY_DISPLAY_MATRIX'].lower().split():
print("-"*75)
print(self.title)
print("-"*75)
print("L:")
print(matrix)
print("b:", RHSvector)
(f, mtxName) = tempfile.mkstemp(suffix='.mtx')
matrix.exportMmf(mtxName)
mtx = mmio.mmread(mtxName)
os.remove(mtxName)
pyplot.ion()
c = mtx.tocoo()
y = c.row
x = c.col
z = c.data
N = matrix._shape[0]
b = RHSvector
if numerix.shape(b) == ():
b = numerix.zeros((N,), 'l')
if len(z) == 0:
y = numerix.zeros((1,), 'l')
x = numerix.zeros((1,), 'l')
z = numerix.zeros((1,), 'l')
def signed_to_logs(v):
return (numerix.where(v > 0, numerix.log10(v), numerix.nan),
numerix.where(v < 0, numerix.log10(-v), numerix.nan))
def logs_to_signed(v, plus, minus):
v = numerix.where(v > 0, plus, -minus)
v = numerix.where(numerix.isnan(v), 0., v)
return v
zPlus, zMinus = signed_to_logs(z)
bPlus, bMinus = signed_to_logs(b)
logs = (zPlus, zMinus, bPlus, bMinus)
log = ((log == True)
or (log == 'auto'
and (numerix.nanmax(numerix.concatenate(logs))
- numerix.nanmin(numerix.concatenate(logs)) > 2)))
if log:
zMin = numerix.nanmin(numerix.concatenate(logs))
zMax = numerix.nanmax(numerix.concatenate(logs))
zMin -= 0.5
numdec = numerix.floor(zMax) - numerix.ceil(zMin)
if numdec < 0:
zMax += 0.5
for v in logs:
v -= zMin
zRange = zMax - zMin
if zRange == 0:
zRange = numerix.nanmax(zPlus) + 1
z = logs_to_signed(z, zPlus, zMinus)
b = logs_to_signed(b, bPlus, bMinus)
fmt = SignedLogFormatter(threshold=zMin)
loc = SignedLogLocator(threshold=zMin)
else:
zRange = max(abs(numerix.concatenate((z, b))))
if zRange == 0:
zRange = 1
fmt = None
loc = None
pyplot.ioff()
fig = pyplot.figure(self.id)
fig.clf()
usetex = rcParams['text.usetex']
rcParams['text.usetex'] = False
cmap = cm.RdBu
norm = Normalize(vmin=-zRange, vmax=zRange)
x0 = self.margin
L_ax = fig.add_axes([x0 / self.aspect, self.margin, self.L_width / self.aspect, self.L_width])
L_ax.text(0.5, -0.1, "L",
transform=L_ax.transAxes, horizontalalignment='center', verticalalignment='baseline')
x0 += self.L_width + self.buffer
c_ax = fig.add_axes([x0 / self.aspect, self.margin, self.c_width / self.aspect, self.L_width])
x0 += self.c_width + self.buffer
b_ax = fig.add_axes([x0 / self.aspect, self.margin, self.b_width / self.aspect, self.L_width],
sharey=L_ax)
b_ax.text(0.5, -0.1, "b",
transform=b_ax.transAxes, horizontalalignment='center', verticalalignment='baseline')
def scatterRectangles(x, y, z, norm=None, cmap=None):
patches = [Rectangle(numerix.array([X - 0.5, Y - 0.5]), 1., 1.,
edgecolor='none') for X, Y in zip(x, y)]
collection = PatchCollection(patches, norm=norm, cmap=cmap,
edgecolors='none')
collection.set_array(z)
return collection
L_ax.add_collection(scatterRectangles(x=x, y=y, z=z,
norm=norm, cmap=cmap))
b_ax.add_collection(scatterRectangles(x=numerix.zeros((N,), 'l'), y=numerix.arange(N), z=b,
norm=norm, cmap=cmap))
ColorbarBase(ax=c_ax, cmap=cmap, norm=norm, orientation='vertical',
format=fmt, ticks=loc)
pyplot.setp((b_ax.get_xticklabels(),
b_ax.get_yticklabels(),
b_ax.get_xticklines(),
b_ax.get_yticklines()), visible=False)
L_ax.set_xlim(xmin=-0.5, xmax=N-0.5)
L_ax.set_ylim(ymax=-0.5, ymin=N-0.5)
b_ax.set_xlim(xmin=-0.5, xmax=0.5)
b_ax.set_ylim(ymax=-0.5, ymin=N-0.5)
fig.suptitle(self.title, x=0.5, y=0.95, fontsize=14)
pyplot.draw()
rcParams['text.usetex'] = usetex
def __init__(self,
mesh,
name='',
value=0.,
rank=None,
elementshape=None,
unit=None,
cached=1):
"""
:Parameters:
- `mesh`: the mesh that defines the geometry of this `Variable`
- `name`: the user-readable name of the `Variable`
- `value`: the initial value
- `rank`: the rank (number of dimensions) of each element of this
`Variable`. Default: 0
- `elementshape`: the shape of each element of this variable
Default: `rank * (mesh.dim,)`
- `unit`: the physical units of the `Variable`
"""
if isinstance(value, (list, tuple)):
value = numerix.array(value)
if isinstance(value, _MeshVariable):
if mesh is None:
mesh = value.mesh
elif mesh != value.mesh:
raise ValueError, "The new 'Variable' must use the same mesh as the supplied value"
self.mesh = mesh
value = self._globalToLocalValue(value)
if value is None:
array = None
elif not isinstance(value, _Constant) and isinstance(value, Variable):
name = name or value.name
unit = None
if isinstance(value, _MeshVariable):
if not isinstance(value, self._variableClass):
raise TypeError, "A '%s' cannot be cast to a '%s'" % (
value._variableClass.__name__,
self._variableClass.__name__)
if elementshape is not None and elementshape != value.shape[:
-1]:
raise ValueError, "'elementshape' != shape of elements of 'value'"
if rank is not None and rank != value.rank:
raise ValueError, "'rank' != rank of 'value'"
elementshape = value.shape[:-1]
array = None
# value = value._copyValue()
if elementshape is None:
valueShape = numerix.getShape(value)
if valueShape != () and valueShape[-1] == self._getShapeFromMesh(
mesh)[-1]:
if elementshape is not None and elementshape != valueShape[:-1]:
raise ValueError, "'elementshape' != shape of elements of 'value'"
if rank is not None and rank != len(valueShape[:-1]):
raise ValueError, "'rank' != rank of 'value'"
elementshape = valueShape[:-1]
elif rank is None and elementshape is None:
elementshape = valueShape
if rank is None:
if elementshape is None:
elementshape = ()
elif elementshape is None:
elementshape = rank * (mesh.dim, )
elif len(elementshape) != rank:
raise ValueError, 'len(elementshape) != rank'
self.elementshape = elementshape
if not "array" in locals():
if numerix._isPhysical(value):
dtype = numerix.obj2sctype(value.value)
else:
dtype = numerix.obj2sctype(value)
#print "meshvariable elshape: ",self.elementshape
#print "meshvariable _getShapeFromMesh: ",self._getShapeFromMesh(mesh)
array = numerix.zeros(
self.elementshape + self._getShapeFromMesh(mesh), dtype)
if numerix._broadcastShape(array.shape,
numerix.shape(value)) is None:
if not isinstance(value, Variable):
value = _Constant(value)
value = value[..., numerix.newaxis]
Variable.__init__(self,
name=name,
value=value,
unit=unit,
array=array,
cached=cached)
# ### Load mesh details from a saved file
# In[411]:
mesh = pickle.load(
open("mesh_details_cellsize_0pt008_extrude_1pt00001.p", "rb"))
gridCoor = mesh.cellCenters
mUnit = gridCoor
mNorm = numerix.linalg.norm(mUnit, axis=0)
print('max mNorm=' + str(max(mNorm)))
print('min mNorm=' + str(min(mNorm)))
mAllCell = mUnit / mNorm
# In[412]:
msize = numerix.shape(mAllCell)
number_of_cells = msize[1]
print(number_of_cells)
# ### Loading phi values from a saved file
# In[413]:
phi_value = get_phi_tuple(
number_of_cells) # get phi values from a previous .vtk file
phi = CellVariable(name=r"$\Phi$", mesh=mesh, value=phi_value)
# ### To convert into numpy array, save it in numpy file and again store it in a variable
# In[414]:
