def assert_problem(self, prob, m, n, nnz, sym, sym_nnz, norm):
self.assertEquals (m, prob.A.m)
self.assertEquals (n, prob.A.n)
self.assertEquals (nnz, prob.A.p [n])
self.assertEquals (sym, prob.sym)
self.assertEquals (sym_nnz, prob.C.p [n] if sym != 0 else 0)
self.assertEquals (norm, cs.cs_norm (prob.C), 1e-2)
def assert_problem(self, prob, m, n, nnz, sym, sym_nnz, norm):
self.assertEquals(m, prob.A.m)
self.assertEquals(n, prob.A.n)
self.assertEquals(nnz, prob.A.p[n])
self.assertEquals(sym, prob.sym)
self.assertEquals(sym_nnz, prob.C.p[n] if sym != 0 else 0)
self.assertEquals(norm, cs.cs_norm(prob.C), 1e-2)
def get_problem(self, inp, tol, base=0):
"""Reads a problem from a file.
@param fileName: file name
@param tol: drop tolerance
@param base: file index base
@return: problem
"""
prob = Problem()
T = cs.cs_load (inp, base) # load triplet matrix T from a file
prob.A = A = cs.cs_compress (T) # A = compressed-column form of T
if not cs.cs_dupl (A): return None # sum up duplicates
prob.sym = sym = self.is_sym (A) # determine if A is symmetric
m = A.m ; n = A.n
mn = max (m, n)
nz1 = A.p [n]
if tol > 0: cs.cs_dropzeros (A) # drop zero entries
nz2 = A.p [n]
if tol > 0: cs.cs_droptol (A, tol) # drop tiny entries (just to test)
prob.C = C = self.make_sym(A) if sym != 0 else A # C = A + triu(A,1)', or C=A
if C == None: return None
print ("\n--- Matrix: %d-by-%d, nnz: %d (sym: %d: nnz %d), norm: %8.2e\n" %
(m, n, A.p [n], sym, C.p [n] if sym != 0 else 0, cs.cs_norm (C)))
prob.dropped_zeros = nz1 - nz2
if nz1 != nz2: print "zero entries dropped: %d\n" % nz1 - nz2
prob.dropped_tiny = nz2 - A.p [n]
if nz2 != A.p [n]: print "tiny entries dropped: %d\n" % nz2 - A.p [n]
prob.b = [0.0]*mn
prob.x = [0.0]*mn
prob.resid = [0.0]*mn
return prob
def get_problem(self, inp, tol, base=0):
"""Reads a problem from a file.
@param fileName: file name
@param tol: drop tolerance
@param base: file index base
@return: problem
"""
prob = Problem()
T = cs.cs_load(inp, base) # load triplet matrix T from a file
prob.A = A = cs.cs_compress(T) # A = compressed-column form of T
if not cs.cs_dupl(A): return None # sum up duplicates
prob.sym = sym = self.is_sym(A) # determine if A is symmetric
m = A.m
n = A.n
mn = max(m, n)
nz1 = A.p[n]
if tol > 0: cs.cs_dropzeros(A) # drop zero entries
nz2 = A.p[n]
if tol > 0: cs.cs_droptol(A, tol) # drop tiny entries (just to test)
prob.C = C = self.make_sym(
A) if sym != 0 else A # C = A + triu(A,1)', or C=A
if C == None: return None
print(
"\n--- Matrix: %d-by-%d, nnz: %d (sym: %d: nnz %d), norm: %8.2e\n"
% (m, n, A.p[n], sym, C.p[n] if sym != 0 else 0, cs.cs_norm(C)))
prob.dropped_zeros = nz1 - nz2
if nz1 != nz2: print "zero entries dropped: %d\n" % nz1 - nz2
prob.dropped_tiny = nz2 - A.p[n]
if nz2 != A.p[n]: print "tiny entries dropped: %d\n" % nz2 - A.p[n]
prob.b = [0.0] * mn
prob.x = [0.0] * mn
prob.resid = [0.0] * mn
return prob
def assert_dimensions(self, A, m, n, nzmax, nnz, norm1=None, delta=1e-3):
self.assertEquals (m, A.m)
self.assertEquals (n, A.n)
# self.assertEquals (nzmax, A.nzmax)
nz = A.p [A.n] if (A.nz < 0) else A.nz
self.assertEquals (nnz, nz)
if norm1 is not None:
self.assertAlmostEquals (norm1, cs.cs_norm (A), delta=delta)
def assert_dimensions(self, A, m, n, nzmax, nnz, norm1=None, delta=1e-3):
self.assertEquals(m, A.m)
self.assertEquals(n, A.n)
# self.assertEquals (nzmax, A.nzmax)
nz = A.p[A.n] if (A.nz < 0) else A.nz
self.assertEquals(nnz, nz)
if norm1 is not None:
self.assertAlmostEquals(norm1, cs.cs_norm(A), delta=delta)
def multiply_add(self, A, AT):
m = A.m if A != None else 0 # m = # of rows of A
T = cs.cs_spalloc (m, m, m, True, True) # create triplet identity matrix
for i in range(m): cs.cs_entry (T, i, i, 1)
Eye = cs.cs_compress (T) # Eye = speye (m)
C = cs.cs_multiply (A, AT) # C = A*A'
D = cs.cs_add(C, Eye, 1, cs.cs_norm (C)) # D = C + Eye*norm (C,1)
# print "D:"
# cs.cs_print(D, False) # print D
return D
def multiply_add(self, A, AT):
m = A.m if A != None else 0 # m = # of rows of A
T = cs.cs_spalloc(m, m, m, True,
True) # create triplet identity matrix
for i in range(m):
cs.cs_entry(T, i, i, 1)
Eye = cs.cs_compress(T) # Eye = speye (m)
C = cs.cs_multiply(A, AT) # C = A*A'
D = cs.cs_add(C, Eye, 1, cs.cs_norm(C)) # D = C + Eye*norm (C,1)
# print "D:"
# cs.cs_print(D, False) # print D
return D
def print_resid(self, ok, A, x, b, resid, prob):
"""compute residual, norm(A*x-b,inf) / (norm(A,1)*norm(x,inf) + norm(b,inf))
"""
if not ok:
print " (failed)\n"
return
m = A.m; n = A.n
for i in range(m):
resid[i] = -b[i] # resid = -b
cs.cs_gaxpy (A, x, resid) # resid = resid + A*x
r = self.norm (resid, m) / (1 if (n == 0) else (cs.cs_norm (A) * self.norm (x, n) + self.norm (b, m)))
print "resid: %8.2e" % r
nrm = self.norm (x, n) ;
print " (norm: %8.4f, %8.4f)\n" % (nrm, self.norm (b, m))
prob.norms.append (nrm)
def print_resid(self, ok, A, x, b, resid, prob):
"""compute residual, norm(A*x-b,inf) / (norm(A,1)*norm(x,inf) + norm(b,inf))
"""
if not ok:
print " (failed)\n"
return
m = A.m
n = A.n
for i in range(m):
resid[i] = -b[i] # resid = -b
cs.cs_gaxpy(A, x, resid) # resid = resid + A*x
r = self.norm(
resid, m) / (1 if (n == 0) else
(cs.cs_norm(A) * self.norm(x, n) + self.norm(b, m)))
print "resid: %8.2e" % r
nrm = self.norm(x, n)
print " (norm: %8.4f, %8.4f)\n" % (nrm, self.norm(b, m))
prob.norms.append(nrm)
