/* nag_dtgexc (f08yfc) 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, norma, normb, norms, normt; Integer i, ifst, ilst, j, n, pda, pdb, pdc, pdq, pds; Integer pdt, pdz, exit_status = 0; /* Arrays */ double *a = 0, *b = 0, *c = 0, *q = 0, *s = 0, *t = 0, *z = 0; char nag_enum_arg[40]; /* Nag Types */ NagError fail; Nag_OrderType order; Nag_Boolean wantq, wantz; #ifdef NAG_COLUMN_MAJOR #define S(I, J) s[(J-1)*pds + I - 1] #define T(I, J) t[(J-1)*pdt + I - 1] order = Nag_ColMajor; #else #define S(I, J) s[(I-1)*pds + J - 1] #define T(I, J) t[(I-1)*pdt + J - 1] order = Nag_RowMajor; #endif INIT_FAIL(fail); printf("nag_dtgexc (f08yfc) Example Program Results\n\n"); /* Skip heading in data file */ scanf("%*[^\n]"); scanf("%ld%*[^\n]", &n); if (n < 0) { printf("Invalid n\n"); exit_status = 1; goto END; } scanf(" %s%*[^\n]", nag_enum_arg); /* nag_enum_name_to_value(x04nac). * Converts NAG enum member name to value */ wantq = (Nag_Boolean) nag_enum_name_to_value(nag_enum_arg); scanf(" %s%*[^\n]", nag_enum_arg); wantz = (Nag_Boolean) nag_enum_name_to_value(nag_enum_arg); pds = n; pdt = n; pdq = (wantq?n:1); pdz = (wantz?n:1); pda = (wantq && wantz?n:1); pdb = pda; pdc = pda; /* Allocate memory */ if (!(s = NAG_ALLOC(n*n, double)) || !(t = NAG_ALLOC(n*n, double)) || !(a = NAG_ALLOC(pda*pda, double)) || !(b = NAG_ALLOC(pdb*pdb, double)) || !(c = NAG_ALLOC(pdc*pdc, double)) || !(q = NAG_ALLOC(pdq*pdq, double)) || !(z = NAG_ALLOC(pdz*pdz, double))) { printf("Allocation failure\n"); exit_status = -1; goto END; } /* Read S and T from data file */ for (i = 1; i <= n; ++i) for (j = 1; j <= n; ++j) scanf("%lf", &S(i, j)); scanf("%*[^\n]"); for (i = 1; i <= n; ++i) for (j = 1; j <= n; ++j) scanf("%lf", &T(i, j)); scanf("%*[^\n]"); /* Compute norm of matrices S and T using nag_dge_norm (f16rac). */ nag_dge_norm(order, Nag_OneNorm, n, n, s, pds, &norms, &fail); nag_dge_norm(order, Nag_OneNorm, n, n, t, pdt, &normt, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dge_norm (f16rac).\n%s\n", fail.message); exit_status = 1; goto END; } norms = sqrt(norms*norms + normt*normt); /* Copy matrices S and T to matrices A and B using nag_dge_copy (f16qfc), * real valued general matrix copy. * The copies will be used as comparison against reconstructed matrices. */ if (wantq && wantz) { nag_dge_copy(order, Nag_NoTrans, n, n, s, pds, a, pda, &fail); nag_dge_copy(order, Nag_NoTrans, n, n, t, pdt, b, pdb, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dge_copy (f16qfc).\n%s\n", fail.message); exit_status = 1; goto END; } } /* Initialize Q an Z to identity matrices using nag_dge_load (f16qhc). */ alpha = 0.0; beta = 1.0; if (wantq) nag_dge_load(order, n, n, alpha, beta, q, pdq, &fail); if (wantz) nag_dge_load(order, n, n, alpha, beta, z, pdz, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dge_load (f16qhc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Read the row indices of diagonal elements or blocks to be swapped. */ scanf("%ld%ld%*[^\n]", &ifst, &ilst); /* nag_gen_real_mat_print (x04cac): Print Matrix S and Matrix T. */ fflush(stdout); nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, s, pds, "Matrix S", 0, &fail); printf("\n"); if (fail.code != NE_NOERROR) goto PRERR; fflush(stdout); nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, t, pdt, "Matrix T", 0, &fail); printf("\n"); if (fail.code != NE_NOERROR) goto PRERR; /* Reorder S and T */ nag_dtgexc(order, wantq, wantz, n, s, pds, t, pdt, q, pdq, z, pdz, &ifst, &ilst, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dtgexc (f08yfc).\n%s\n", fail.message); exit_status = 1; goto END; } /* nag_gen_real_mat_print (x04cac): Print reordered S and T. */ fflush(stdout); nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, s, pds, "Reordered matrix S", 0, &fail); printf("\n"); if (fail.code != NE_NOERROR) goto PRERR; fflush(stdout); nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, t, pdt, "Reordered matrix T", 0, &fail); printf("\n"); PRERR: if (fail.code != NE_NOERROR) { printf("Error from nag_gen_real_mat_print (x04cac).\n%s\n", fail.message); exit_status = 1; goto END; } if (wantq && wantz) { /* Reconstruct original S and T by applying orthogonal transformations: * e.g. S = Q^T S' Z, and subtract from original S and T using * nag_dgemm (f16yac), twice each. */ alpha = 1.0; beta = 0.0; nag_dgemm(order, Nag_NoTrans, Nag_NoTrans, n, n, n, alpha, q, pdq, s, pds, beta, c, pdc, &fail); if (fail.code != NE_NOERROR) goto DGEMMERR; beta = -1.0; nag_dgemm(order, Nag_NoTrans, Nag_Trans, n, n, n, alpha, c, pdc, z, pdz, beta, a, pda, &fail); if (fail.code != NE_NOERROR) goto DGEMMERR; /* nag_dgemm (f16yac): Compute B - Qt*Tt*Zt^T */ alpha = 1.0; beta = 0.0; nag_dgemm(order, Nag_NoTrans, Nag_NoTrans, n, n, n, alpha, q, pdq, t, pdt, beta, c, pdc, &fail); if (fail.code != NE_NOERROR) goto DGEMMERR; beta = -1.0; nag_dgemm(order, Nag_NoTrans, Nag_Trans, n, n, n, alpha, c, pdc, z, pdz, beta, b, pdb, &fail); DGEMMERR: if (fail.code != NE_NOERROR) { printf("Error from nag_dgemm (f16yac).\n%s\n", fail.message); exit_status = 1; goto END; } /* Compute norm of difference matrices using nag_dge_norm (f16rac). */ nag_dge_norm(order, Nag_OneNorm, n, n, a, pda, &norma, &fail); nag_dge_norm(order, Nag_OneNorm, n, n, b, pdb, &normb, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dge_norm (f16rac).\n%s\n", fail.message); exit_status = 1; goto END; } norma = sqrt(norma*norma + normb*normb); /* nag_machine_precision (x02ajc) */ eps = nag_machine_precision; if (norma > pow(eps,0.8)*norms) { printf("The norm of the error in the reconstructed matrices is greater " "than expected.\nThe Schur factorization has failed.\n"); exit_status = 1; goto END; } } END: if (a) NAG_FREE(a); if (b) NAG_FREE(b); if (c) NAG_FREE(c); if (q) NAG_FREE(q); if (s) NAG_FREE(s); if (t) NAG_FREE(t); if (z) NAG_FREE(z); return exit_status; }