/* nag_dgesvd (f08kbc) Example Program. * * Copyright 2011 Numerical Algorithms Group. * * Mark 23, 2011. */ #include #include #include #include #include #include #include #include int main(void) { /* Scalars */ double alpha, beta, eps, norm, serrbd; Integer exit_status = 0, i, j, m, n, pda, pdd, pdu, pdvt; /* Arrays */ double *a = 0, *d = 0, *rcondu = 0, *rcondv = 0; double *s = 0, *u = 0, *uerrbd = 0, *verrbd = 0, *vt = 0, *work = 0; /* Nag Types */ NagError fail; Nag_OrderType order; #ifdef NAG_COLUMN_MAJOR #define A(I, J) a[(J - 1) * pda + I - 1] #define U(I, J) u[(J - 1) * pdu + I - 1] order = Nag_ColMajor; #else #define A(I, J) a[(I - 1) * pda + J - 1] #define U(I, J) u[(I - 1) * pdu + J - 1] order = Nag_RowMajor; #endif INIT_FAIL(fail); printf("nag_dgesvd (f08kbc) 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 */ if (!(a = NAG_ALLOC(m * n, double)) || !(d = NAG_ALLOC(m * n, double)) || !(rcondu = NAG_ALLOC(n, double)) || !(rcondv = NAG_ALLOC(n, double)) || !(s = NAG_ALLOC(MIN(m, n), double)) || !(u = NAG_ALLOC(m * m, double)) || !(uerrbd = NAG_ALLOC(n, double)) || !(verrbd = NAG_ALLOC(n, double)) || !(vt = NAG_ALLOC(n * n, double)) || !(work = NAG_ALLOC(MIN(m, n), double)) ) { printf("Allocation failure\n"); exit_status = -1; goto END; } pdu = m; pdvt = n; #ifdef NAG_COLUMN_MAJOR pda = m; pdd = m; #else pda = n; pdd = n; #endif /* Read the m by n matrix A from data file */ for (i = 1; i <= m; ++i) for (j = 1; j <= n; ++j) scanf("%lf", &A(i, j)); scanf("%*[^\n]"); /* Copy a into d */ for(i = 0; i < m*n; i++) d[i] = a[i]; /* nag_gen_real_mat_print (x04cac) * Print real general matrix A. */ fflush(stdout); nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, m, n, a, pda, "Matrix A", 0, &fail); printf("\n"); if (fail.code != NE_NOERROR) { printf("Error from nag_gen_real_mat_print (x04cac).\n%s\n", fail.message); exit_status = 1; goto END; } /* nag_dgesvd (f08kbc). * Compute the singular values and left and right singular vectors * of A (A = U*S*(V**T), m.ge.n) */ nag_dgesvd(order, Nag_AllU, Nag_AllVT, m, n, a, pda, s, u, pdu, vt, pdvt, work, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dgesvd (f08kbc).\n%s\n", fail.message); exit_status = 1; goto END; } /* U <- U*S */ for(i = 1; i <= m; i++) for(j = 1; j <= n; j++) U(i, j) *= s[j-1]; /* nag_dgemm (f16yac): * Compute D = D - U*S*V^T from the factorization of A * and store in d */ alpha = -1.0; beta = 1.0; nag_dgemm(order, Nag_NoTrans, Nag_NoTrans, m, n, n, alpha, u, pdu, vt, pdvt, beta, d, pdd, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dgemm (f16yac).\n%s\n", fail.message); exit_status = 1; goto END; } /* nag_dge_norm (f16rac) * Find norm of matrix D and print warning if it is too large. */ nag_dge_norm(order, Nag_OneNorm, m, n, d, pdd, &norm, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dge_norm (f16rac).\n%s\n", fail.message); exit_status = 1; goto END; } /* nag_machine_precision (x02ajc): the machine precision. */ eps = nag_machine_precision; if (norm > pow(eps,0.8)) { printf("\nNorm of A-(U*S*V^T) is much greater than 0.\n" "Schur factorization has failed.\n"); exit_status = 1; goto END; } /* Get the machine precision, eps and compute the approximate * error bound for the computed singular values. * Note that for the 2-norm, s[0] = norm(A). */ serrbd = eps * s[0]; /* Estimate reciprocal condition numbers for the singular vectors using * nag_ddisna (f08flc). */ 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]; } /* Print the approximate error bounds for the singular values and vectors */ 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(rcondu); NAG_FREE(rcondv); NAG_FREE(s); NAG_FREE(u); NAG_FREE(uerrbd); NAG_FREE(verrbd); NAG_FREE(vt); NAG_FREE(work); return exit_status; } #undef A #undef U