/* nag_dggsvd (f08vac) Example Program. * * Copyright 2004 Numerical Algorithms Group. * * Mark 9, 2009. */ #include #include #include #include #include #include #include int main(void) { /* Scalars */ double d, eps, rcond, serrbd; Integer exit_status = 0, i, irank, j, k, l, m, n, p, pda, pdb, pdq, pdu, pdv; NagError fail; Nag_OrderType order; /* Arrays */ double *a = 0, *alpha = 0, *b = 0, *beta = 0, *q = 0, *u = 0, *v = 0; Integer *iwork = 0; #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_dggsvd (f08vac) Example Program Results\n\n"); /* Skip heading in data file */ scanf("%*[^\n] "); scanf("%ld%ld%ld%*[^\n] ", &m, &n, &p); if (m <= 10 && n <= 10 && p <= 10) { /* Allocate memory */ if (!(a = NAG_ALLOC(m*n, double)) || !(alpha = NAG_ALLOC(n, double)) || !(b = NAG_ALLOC(p*n, double)) || !(beta = NAG_ALLOC(n, double)) || !(q = NAG_ALLOC(n*n, double)) || !(u = NAG_ALLOC(m*m, double)) || !(v = NAG_ALLOC(p*p, double)) || !(iwork = NAG_ALLOC(n, Integer)) ) { printf("Allocation failure\n"); exit_status = -1; goto END; } #ifdef NAG_COLUMN_MAJOR pda = m; pdb = p; pdq = n; pdu = m; pdv = p; #else pda = n; pdb = n; pdq = n; pdu = m; pdv = p; #endif } else { printf("m and/or n too small\n"); 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", &A(i, j)); scanf("%*[^\n] "); for (i = 1; i <= p; ++i) for (j = 1; j <= n; ++j) scanf("%lf", &B(i, j)); scanf("%*[^\n] "); /* nag_dggsvd (f08vac) * Compute the generalized singular value decomposition of (A, B) * (A = U*D1*(0 R)*(Q**T), B = V*D2*(0 R)*(Q**T), m.ge.n) */ nag_dggsvd(order, Nag_AllU, Nag_ComputeV, Nag_ComputeQ, m, n, p, &k, &l, a, pda, b, pdb, alpha, beta, u, pdu, v, pdv, q, pdq, iwork, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dggsvd (f08vac).\n%s\n", fail.message); exit_status = 1; goto END; } /* Print solution */ irank = k + l; printf("Number of infinite generalized singular values (K)\n"); printf("%5ld\n", k); printf("\nNumber of finite generalized singular values (L)\n"); printf("%5ld\n", l); printf("Numerical rank of (A**T B**T)**T (K+L)\n"); printf("%5ld\n", irank); printf("\nFinite generalized singular values\n"); for (j = k; j < irank; ++j) { d = alpha[j] / beta[j]; printf("%13.4e%s", d, (j+1)%8 == 0 || (j+1) == irank?"\n":" "); } printf("\n"); fflush(stdout); nag_gen_real_mat_print_comp(order, Nag_GeneralMatrix, Nag_NonUnitDiag, m, m, u, pdu, "%13.4e", "Orthogonal matrix U", Nag_IntegerLabels, 0, Nag_IntegerLabels, 0, 80, 0, 0, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_gen_real_mat_print_comp (x04cbc).\n%s\n", fail.message); exit_status = 1; goto END; } printf("\n"); fflush(stdout); nag_gen_real_mat_print_comp(order, Nag_GeneralMatrix, Nag_NonUnitDiag, p, p, v, pdv, "%13.4e", "Orthogonal matrix V", Nag_IntegerLabels, 0, Nag_IntegerLabels, 0, 80, 0, 0, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_gen_real_mat_print_comp (x04cbc).\n%s\n", fail.message); exit_status = 1; goto END; } printf("\n"); fflush(stdout); nag_gen_real_mat_print_comp(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, q, pdq, "%13.4e", "Orthogonal matrix Q", Nag_IntegerLabels, 0, Nag_IntegerLabels, 0, 80, 0, 0, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_gen_real_mat_print_comp (x04cbc).\n%s\n", fail.message); exit_status = 1; goto END; } printf("\n"); fflush(stdout); nag_gen_real_mat_print_comp(order, Nag_UpperMatrix, Nag_NonUnitDiag, irank, irank, &A(1, n - irank + 1), pda, "%13.4e", "Non singular upper triangular matrix R", Nag_IntegerLabels, 0, Nag_IntegerLabels, 0, 80, 0, 0, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_gen_real_mat_print_comp (x04cbc).\n%s\n", fail.message); exit_status = 1; goto END; } /* nag_dtrcon (f07tgc) * estimate the reciprocal condition number of R */ nag_dtrcon(order, Nag_InfNorm, Nag_Upper, Nag_NonUnitDiag, irank, &A(1, n - irank + 1), pda, &rcond, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dtrcon (f07tgc).\n%s\n", fail.message); exit_status = 1; goto END; } printf("\nEstimate of reciprocal condition number for R\n"); printf("%11.1e\n\n", rcond); /* So long as irank = n, get the machine precision, eps, and compute the * approximate error bound for the computed generalized singular values */ if (irank == n) { eps = nag_machine_precision; serrbd = eps / rcond; printf("Error estimate for the generalized singular values"); printf("\n%11.1e\n", serrbd); } else { printf("(A**T B**T)**T is not of full rank\n"); } END: if (a) NAG_FREE(a); if (alpha) NAG_FREE(alpha); if (b) NAG_FREE(b); if (beta) NAG_FREE(beta); if (q) NAG_FREE(q); if (u) NAG_FREE(u); if (v) NAG_FREE(v); if (iwork) NAG_FREE(iwork); return exit_status; } #undef B #undef A