def makeDowndate(I_up, normalize=True, verb=0):
timer = Timer('AMG downdate formation')
Debug.msg3(verb, 'Forming downdate operator')
I_down = I_up.transpose(copy=True).tolil()
if normalize:
for r in range(I_down.shape[0]):
row = I_down.getrowview(r)
nrm = row.sum()
row /= nrm
Debug.msg3(verb, 'Done forming downdate operator')
return I_down.tocsr()
def smoothUpdate(A, C, verb=0):
'''
Create an update operator from a coarse mesh to a fine mesh, based on
a matrix A and a set of coarse-mesh nodes C
'''
tab0 = Tab()
timer = Timer('AMG update formation')
Debug.msg3(verb, tab0, 'forming update operator')
Debug.msg3(verb, tab0, 'C=', C)
if not sp.isspmatrix_csr(A):
raise ValueError('makeUpdate() expected a CSR matrix as input')
M = A.shape[0]
if A.shape[1] != A.shape[0]:
raise ValueError('Non-square matrix in makeUpdate(): size is %d by %d' %
(A.shape[0], A.shape[1]))
c_to_f, f_to_c = makeIndexMaps(C)
Debug.msg3(verb, tab0, 'f2c map is ', f_to_c)
I_up = sp.dok_matrix((M,len(C)))
ip = A.indptr
allVals = A.data
allCols = A.indices
tab1 = Tab()
tab2 = Tab()
tab3 = Tab()
tab4 = Tab()
tab5 = Tab()
# Main loop over rows
for i in range(M):
Debug.msg3(verb, tab0, 'row %d' % i)
# If the current index is in the coarse mesh, take its value directly
# from the fine mesh
if i in C:
I_up[i, f_to_c[i]] = 1.0
Debug.msg3(verb, tab1, 'coarse-coarse connection, entry is 1')
continue
Debug.msg3(verb, tab1, 'interpolating value for fine row ', i)
# Get arrays of column indices and values for this row
cols_i = allCols[ip[i] : ip[i+1]]
vals_i = allVals[ip[i] : ip[i+1]]
# Find diagonal
diag = vals_i[np.where(cols_i==i)]
Debug.msg3(verb, tab1, 'diagonal is %g' % diag)
# Diagonal must be nonzero!
if diag == 0.0:
raise ValueError('zero diagonal detected in row %d' % i)
# build interpolation matrix
for j, a_ij in zip(cols_i, vals_i):
if j==i:
continue
if j not in C:
continue
Debug.msg3(verb, tab2, 'contrib from coarse node f=%d, c=%d' % (j, f_to_c[j]))
w_ij = a_ij
Debug.msg3(verb, tab2, 'direct connection: (%d,%d)=%g' % (i,j,w_ij))
Debug.msg3(verb, tab2, 'finding indirect contributions')
Debug.msg3(verb, tab2, 'looking at neighbors ', cols_i)
for m, a_im in zip(cols_i, vals_i):
if m==i: # <--- I forgot this on first pass!
continue
if m not in C: # Approximate values on F by averaging
Debug.msg3(verb, tab3, 'approximating fine node m=%d' % m)
cols_m = allCols[ip[m] : ip[m+1]]
vals_m = allVals[ip[m] : ip[m+1]]
denom = 0.0
num = 0.0
Debug.msg3(verb, tab3, 'neighbors of m=%d are ' % m, cols_m)
count = 0
for k,a_mk in zip(cols_m, vals_m):
if k in C and k in cols_i:
Debug.msg3(verb, tab4, 'indirect contribution from coarse node k=', k)
denom += a_mk
count += 1
if k==j:
num = a_im * a_mk
Debug.msg3(verb, tab4, 'numerator=%g, denominator=%g' % (num,denom))
if count>0:
if denom==0.0:
raise ValueError('zero denominator detected in (%d,%d)' %(i,j))
Debug.msg3(verb, tab3, 'indirect connection through fine node %d: %g' % (m,num/denom))
w_ij += num/denom
else: # No need to approximate coarse node values
Debug.msg3(verb, tab3, 'no need to approximate value at coarse node m=', m)
continue
Debug.msg3(verb, tab2, '(%d,%d), val=%g' %(i,j,w_ij))
I_up[i, f_to_c[j]] = -w_ij/diag
# end second pass through row i
# end loop over rows
Debug.msg3(verb, tab0, 'done forming update operator')
return I_up.tocsr()
