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)