def createLaplacianMat(self):
'''create a PETSc.Mat() for discrete Laplacian.
TODO: more than dim 3; more than second order; different dx,dy,dz'''
dim = self.Dim
dx = (self.hGrid,)*dim
ll = np.array(self.ll) + self.hGrid/2
pt = self.getCoordinates()
# find the sub index of itself
subItself = findGridInterpBasePt(pt,dx,ll,0)
if dim == 2:
offsets = np.array([[0,0,1,0,-1],
[0,1,0,-1,0]])
weight = np.array([-4.,1.,1.,1.,1.]) / self.hGrid**2
elif dim == 3:
offsets = np.array([[0,0,0,1,0,0,-1],
[0,0,1,0,0,-1,0],
[0,1,0,0,-1,0,0]])
weight = np.array([-6.,1.,1.,1.,1.,1.,1.]) / self.hGrid**2
sub = ( subItself[...,np.newaxis] + offsets[np.newaxis,...] ).transpose((1,0,2))
# Convert sub indices to global PETSc indices
ind = self.subToPetscInd(sub)
weights = np.tile(weight,(ind.shape[0],1))
L = self.createMat((self.gvec.sizes,self.gvec.sizes),ind,weights,(2*dim+1,dim))
return L
def build_interp_matrix(int_band, cp, dx, p, ll, shape):
dim = len(shape)
offsets = np.mgrid[tuple(slice(p + 1) for _ in xrange(dim))].reshape((dim, -1))
Ei = np.tile(np.arange(cp.shape[0])[:, np.newaxis], (p + 1) ** dim)
Ej = np.zeros_like(Ei)
Es = np.zeros_like(Ei, dtype=np.float)
base_points = findGridInterpBasePt(cp, dx, ll, p)
weights = buildInterpWeights(base_points * dx + ll, cp, dx, p + 1)
Ej = np.ravel_multi_index(
(base_points[..., np.newaxis] + offsets[np.newaxis, ...]).transpose((0, 2, 1)).reshape((-1, dim)).T, shape
)
Es = weights
E = coo_matrix((Es.ravel(), (Ei.ravel(), Ej.ravel())), (cp.shape[0], reduce(mul, shape))).tocsr()
return E[:, np.ravel_multi_index(int_band.T, shape)]
def findIndForIntpl(self,cp):
'''find the indices of interpolation points'''
dim = self.Dim
dx = (self.hGrid,)*dim
p = self.interpDegree
M = self.M
m = self.m
ll = np.array(self.ll) + self.hGrid/2;
#find base point first
subBasept = findGridInterpBasePt(cp, dx, ll, p)
offsets = np.mgrid[(slice(p+1),)*dim].reshape((dim, -1))
# x = np.arange((p+1)**dim)
# offsets = np.column_stack(np.unravel_index(x,(p+1,)*dim,order='F')).T
sub = ( subBasept[...,np.newaxis] + offsets[np.newaxis,...] ).transpose((1,0,2))
ind = self.subToPetscInd(sub)
basept = subBasept*dx + ll
return basept,ind
def createExtensionMat(self, p = None, cp = None):
'''create a PETSc.Mat() for the closest point extension'''
if p is None: p = self.interpDegree
if cp is None:
wvecsizes = self.wvec.sizes
cp = self.cp
else:
wvecsizes = (cp.shape[0],PETSc.DECIDE)
gvec = self.gvec
dim = self.Dim
dx = (self.hGrid,)*dim
M = self.M
m = self.m
# The lower left grid point 'll' is at the center of the lower left element 'self.ll'
ll = np.array(self.ll) + self.hGrid/2;
# find the sub-indices of the base points, 'subBasept' is a N*dim array (N:number of base-points).
subBasept = findGridInterpBasePt(cp, dx, ll, p)
# offsets is the sub-indices of the interpolation stencil, a dim*STENCIL array (STENCIL=(p+1)^dim).
# If in 'C' order, should be the following line:
offsets = np.mgrid[(slice(p+1),)*dim].reshape((dim, -1))
# or equivalently the following two lines:
# x = np.arange((p+1)**dim)
# offsets = np.column_stack(np.unravel_index(x,(p+1,)*dim,order='C')).T
#If in the structure branch, it should be 'Fortran' order:
# x = np.arange((p+1)**dim)
# offsets = np.column_stack(np.unravel_index(x,(p+1,)*dim,order='F')).T
# The sub indices of the whole interpolation stencil with Fortran order, a dim*N*STENCIL array.
sub = ( subBasept[...,np.newaxis] + offsets[np.newaxis,...] ).transpose((1,0,2))
# Convert sub indices to global PETSc indices
ind = self.subToPetscInd(sub)
basept = subBasept*dx + ll
weights = buildInterpWeights(basept,cp,dx,p+1)
E = self.createMat((wvecsizes,gvec.sizes),ind,weights)
return E
