/* nag_ztgsja (f08ysc) Example Program. * * Copyright 2011 Numerical Algorithms Group. * * Mark 23, 2011. */ #include #include #include #include #include #include #include int main(void) { /* Scalars */ double eps, norma, normb, tola, tolb; Integer i, irank, j, k, l, m, n, ncycle, p, pda, pdb, pdu, pdv; Integer pdq, printq, printr, printu, printv, vsize; Integer exit_status = 0; /* Arrays */ Complex *a = 0, *b = 0, *q = 0, *u = 0, *v = 0; double *alpha = 0, *beta = 0; char nag_enum_arg[40]; /* Nag Types */ NagError fail; Nag_OrderType order; Nag_ComputeUType jobu; Nag_ComputeVType jobv; Nag_ComputeQType jobq; Nag_MatrixType genmat = Nag_GeneralMatrix, upmat = Nag_UpperMatrix; Nag_DiagType diag = Nag_NonUnitDiag; Nag_LabelType intlab = Nag_IntegerLabels; Nag_ComplexFormType brac = Nag_BracketForm; #ifdef NAG_COLUMN_MAJOR #define A(I, J) a[(J-1)*pda + I - 1] #define B(I, J) b[(J-1)*pdb + I - 1] order = Nag_ColMajor; #else #define A(I, J) a[(I-1)*pda + J - 1] #define B(I, J) b[(I-1)*pdb + J - 1] order = Nag_RowMajor; #endif INIT_FAIL(fail); printf("nag_ztgsja (f08ysc) Example Program Results\n\n"); /* Skip heading in data file */ scanf("%*[^\n]"); scanf("%ld%ld%ld%*[^\n]", &m, &n, &p); if (m < 0 || n < 0 || p < 0) { printf("Invalid m, n or p\n"); exit_status = 1; goto END; } scanf(" %39s%*[^\n]", nag_enum_arg); /* nag_enum_name_to_value (x04nac). * Converts NAG enum member name to value */ jobu = (Nag_ComputeUType) nag_enum_name_to_value(nag_enum_arg); scanf(" %39s%*[^\n]", nag_enum_arg); jobv = (Nag_ComputeVType) nag_enum_name_to_value(nag_enum_arg); scanf(" %39s%*[^\n]", nag_enum_arg); jobq = (Nag_ComputeQType) nag_enum_name_to_value(nag_enum_arg); pdu = (jobu!=Nag_NotU?m:1); pdv = (jobv!=Nag_NotV?p:1); pdq = (jobq!=Nag_NotQ?n:1); vsize = (jobv!=Nag_NotV?p*m:1); #ifdef NAG_COLUMN_MAJOR pda = m; pdb = p; #else pda = n; pdb = n; #endif /* Read in 0s or 1s to determine whether matrices U, V, Q or R are to be * printed. */ scanf("%ld%ld%ld%ld%*[^\n]", &printu, &printv, &printq, &printr); /* Allocate memory */ if (!(a = NAG_ALLOC(m*n, Complex)) || !(b = NAG_ALLOC(p*n, Complex)) || !(alpha = NAG_ALLOC(n, double)) || !(beta = NAG_ALLOC(n, double)) || !(q = NAG_ALLOC(pdq*pdq, Complex)) || !(u = NAG_ALLOC(pdu*pdu, Complex)) || !(v = NAG_ALLOC(vsize, Complex))) { printf("Allocation failure\n"); exit_status = -1; goto END; } /* Read the m by n matrix A and p by n matrix B from data file */ for (i = 1; i <= m; ++i) for (j = 1; j <= n; ++j) scanf(" ( %lf , %lf )", &A(i, j).re, &A(i, j).im); scanf("%*[^\n]"); for (i = 1; i <= p; ++i) for (j = 1; j <= n; ++j) scanf(" ( %lf , %lf )", &B(i, j).re, &B(i, j).im); scanf("%*[^\n]"); /* Compute tola and tolb as */ /* tola = max(m,n)*norm(A)*macheps */ /* tolb = max(p,n)*norm(B)*macheps */ nag_zge_norm(order, Nag_OneNorm, m, n, a, pda, &norma, &fail); nag_zge_norm(order, Nag_OneNorm, p, n, b, pdb, &normb, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_zge_norm (f16uac).\n%s\n", fail.message); exit_status = 1; goto END; } /* Compute tola and tolb using nag_machine_precision (x02ajc) */ eps = nag_machine_precision; tola = MAX(m, n) * norma * eps; tolb = MAX(p, n) * normb * eps; /* Preprocess step: * compute transformations to reduce (A, B) to upper triangular form * (A = U1*S*(Q1^H), B = V1*T*(Q1^H)) * using nag_zggsvp (f08vsc). */ nag_zggsvp(order, jobu, jobv, jobq, m, p, n, a, pda, b, pdb, tola, tolb, &k, &l, u, pdu, v, pdv, q, pdq, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_zggsvp (f08vsc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Compute the generalized singular value decomposition of preprocessed (A, B) * (A = U*D1*(0 R)*(Q**H), B = V*D2*(0 R)*(Q**H)) * using nag_ztgsja (f08ysc). */ nag_ztgsja(order, jobu, jobv, jobq, m, p, n, k, l, a, pda, b, pdb, tola, tolb, alpha, beta, u, pdu, v, pdv, q, pdq, &ncycle, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_ztgsja (f08ysc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Print the generalized singular value pairs alpha, beta */ irank = MIN(k + l,m); printf("Number of infinite generalized singular values (k): %5ld\n", k); printf("Number of finite generalized singular values (l): %5ld\n", l); printf("Effective Numerical rank of (A^H B^HT)^H (k+l): %5ld\n", irank); printf("\nFinite generalized singular values:\n"); for (j = k; j < irank; ++j) printf("%45s%12.4e\n", "", alpha[j]/beta[j]); printf("\nNumber of cycles of the Kogbetliantz method: %12ld\n\n", ncycle); if (printu && jobu!=Nag_NotU) { fflush(stdout); nag_gen_complx_mat_print_comp(order, genmat, diag, m, m, u, pdu, brac, "%13.4e", "Orthogonal matrix U", intlab, NULL, intlab, NULL, 80, 0, NULL, &fail); if (fail.code != NE_NOERROR) goto PRINTERR; } if (printv && jobv!=Nag_NotV) { printf("\n"); fflush(stdout); nag_gen_complx_mat_print_comp(order, genmat, diag, p, p, v, pdv, brac, "%13.4e", "Orthogonal matrix V", intlab, NULL, intlab, NULL, 80, 0, NULL, &fail); if (fail.code != NE_NOERROR) goto PRINTERR; } if (printq && jobq!=Nag_NotQ) { printf("\n"); fflush(stdout); nag_gen_complx_mat_print_comp(order, genmat, diag, n, n, q, pdq, brac, "%13.4e", "Orthogonal matrix Q", intlab, NULL, intlab, NULL, 80, 0, NULL, &fail); if (fail.code != NE_NOERROR) goto PRINTERR; } if (printr) { printf("\n"); fflush(stdout); nag_gen_complx_mat_print_comp(order, upmat, diag, irank, irank, &A(1, n - irank + 1), pda, brac, "%13.4e", "Non singular upper triangular matrix R", intlab, NULL, intlab, NULL, 80, 0, NULL, &fail); } PRINTERR: if (fail.code != NE_NOERROR) { printf("Error from nag_gen_real_mat_print_comp (x04cbc).\n%s\n", fail.message); exit_status = 1; } END: NAG_FREE(a); NAG_FREE(b); NAG_FREE(alpha); NAG_FREE(beta); NAG_FREE(q); NAG_FREE(u); NAG_FREE(v); return exit_status; }