/* nag_zgesvd (f08kpc) Example Program. * * Copyright 2011 Numerical Algorithms Group. * * Mark 23, 2011. */ #include #include #include #include #include #include #include #include #include int main(void) { /* Scalars */ Complex alpha, beta; double eps, norm, serrbd; Integer exit_status = 0, i, j, m, n, pda, pdd, pdu, pdvt; /* Arrays */ Complex *a = 0, *d = 0, *u = 0, *vt = 0; double *rcondu = 0, *rcondv = 0, *s = 0, *uerrbd = 0, *verrbd = 0; double *rwork = 0; /* Nag Types */ NagError fail; Nag_OrderType order; #ifdef NAG_COLUMN_MAJOR #define A(I, J) a[(J - 1) * pda + I - 1] order = Nag_ColMajor; #else #define A(I, J) a[(I - 1) * pda + J - 1] order = Nag_RowMajor; #endif INIT_FAIL(fail); printf("nag_zgesvd (f08kpc) Example Program Results\n\n"); /* Skip heading in data file */ scanf("%*[^\n]"); scanf("%ld%ld%*[^\n]", &m, &n); if (m < 0 || n < 0) { printf("Invalid m or n\n"); exit_status = 1; goto END; } /* Allocate memory: these assume that A is overwritten by U, and * all of VT is required. */ if (!(a = NAG_ALLOC(m * n, Complex)) || !(d = NAG_ALLOC(m * n, Complex)) || !(u = NAG_ALLOC(1, Complex)) || !(vt = NAG_ALLOC(MIN(m, n) * n, Complex)) || !(rcondu = NAG_ALLOC(MIN(m, n), double)) || !(rcondv = NAG_ALLOC(MIN(m, n), double)) || !(s = NAG_ALLOC(MIN(m, n), double)) || !(uerrbd = NAG_ALLOC(MIN(m, n), double)) || !(verrbd = NAG_ALLOC(MIN(m, n), double)) || !(rwork = NAG_ALLOC(MIN(m, n), double))) { printf("Allocation failure\n"); exit_status = -1; goto END; } #ifdef NAG_COLUMN_MAJOR pda = m; #else pda = n; #endif pdu = 1; pdvt = n; pdd = pda; /* Read the m by n matrix A 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]"); /* Copy A to D: nag_zge_copy (f16tfc), * Complex valued general matrix copy. */ nag_zge_copy(order, Nag_NoTrans, m, n, a, pda, d, pdd, &fail); /* nag_gen_complx_mat_print_comp (x04dbc): Print matrix A */ fflush(stdout); nag_gen_complx_mat_print_comp(order, Nag_GeneralMatrix, Nag_NonUnitDiag, m, n, a, pda, Nag_BracketForm, "%7.4f", "Matrix A", Nag_IntegerLabels, 0, Nag_IntegerLabels, 0, 80, 0, 0, &fail); printf("\n"); if (fail.code != NE_NOERROR) { printf("Error from nag_gen_complx_mat_print_comp (x04dbc).\n%s\n", fail.message); exit_status = 1; goto END; } /* nag_zgesvd (f08kpc) * Compute the singular values and left and right singular vectors * of A (A = U*S*(V**H), m.ge.n) */ nag_zgesvd(order, Nag_Overwrite, Nag_AllVT, m, n, a, pda, s, u, pdu, vt, pdvt, rwork, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_zgesvd (f08kpc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Reconstruct A from its decomposition and subtract from original A: * first, A <- U(A)*S, then D <- D - U*S*V^H using * nag_zgemm (f16zac). */ for(i = 1; i <= m; i++) for(j = 1; j <= MIN(m,n); j++) A(i, j).re *= s[j-1], A(i, j).im *= s[j-1]; alpha = nag_complex(-1.0,0.0); beta = nag_complex(1.0,0.0); nag_zgemm(order, Nag_NoTrans, Nag_NoTrans, m, n, n, alpha, a, pda, vt, pdvt, beta, d, pdd, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_zgemm (f16zac).\n%s\n", fail.message); exit_status = 1; goto END; } /* Find norm of difference matrix D and print warning if it is too large: * nag_zge_norm (f16uac) using one-norm. */ nag_zge_norm(order, Nag_OneNorm, m, n, d, pdd, &norm, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_zge_norm (f16uac).\n%s\n", fail.message); exit_status = 1; goto END; } /* Get the machine precision, using nag_machine_precision (x02ajc) */ eps = nag_machine_precision; if (norm>pow(eps,0.8)) { printf("Norm of A-(U*S*V^H) is much greater than 0.\n" " Schur factorization has failed.\n"); exit_status = 1; goto END; } /* Print singular values and error estimates on values and vectors. */ printf("\nSingular values\n"); for (i = 0; i < n; ++i) printf("%10.4f%s", s[i], i%8 == 7?"\n":" "); printf("\n\n"); /* Approximate error bound for the computed singular values. * Note that for the 2-norm, s[0] = norm(A). */ serrbd = eps * s[0]; /* Call nag_ddisna (f08flc) to estimate reciprocal condition numbers for the * singular vectors. */ nag_ddisna(Nag_LeftSingVecs, m, n, s, rcondu, &fail); nag_ddisna(Nag_RightSingVecs, m, n, s, rcondv, &fail); /* Compute the error estimates for the singular vectors */ for (i = 0; i < n; ++i) { uerrbd[i] = serrbd / rcondu[i]; verrbd[i] = serrbd / rcondv[i]; } printf("Error estimate for the singular values\n%11.1e\n", serrbd); printf("\nError estimates for the left singular vectors\n"); for (i = 0; i < n; ++i) printf(" %10.1e%s", uerrbd[i], i%6 == 5?"\n":""); printf("\n\nError estimates for the right singular vectors\n"); for (i = 0; i < n; ++i) printf(" %10.1e%s", verrbd[i], i%6 == 5?"\n":""); printf("\n"); END: NAG_FREE(a); NAG_FREE(d); NAG_FREE(u); NAG_FREE(vt); NAG_FREE(rcondu); NAG_FREE(rcondv); NAG_FREE(s); NAG_FREE(uerrbd); NAG_FREE(verrbd); NAG_FREE(rwork); return exit_status; } #undef A