/* nag_dtrsen (f08qgc) Example Program. * * Copyright 2001 Numerical Algorithms Group. * * Mark 7, 2001. */ #include #include #include #include #include #include #include #include int main(void) { /* Scalars */ Integer i, j, m, n, pda, pdc, pdq, pdt, select_len, w_len; Integer exit_status = 0; double alpha, beta, norm, s, sep; NagError fail; Nag_OrderType order; /* Arrays */ double *a = 0, *c = 0, *q = 0, *t = 0, *wi = 0, *wr = 0; char nag_enum_arg[40]; Nag_Boolean *select = 0; #ifdef NAG_COLUMN_MAJOR #define T(I, J) t[(J-1)*pdt + I - 1] #define Q(I, J) q[(J-1)*pdq + I - 1] order = Nag_ColMajor; #else #define T(I, J) t[(I-1)*pdt + J - 1] #define Q(I, J) q[(I-1)*pdq + J - 1] order = Nag_RowMajor; #endif INIT_FAIL(fail); printf("nag_dtrsen (f08qgc) Example Program Results\n\n"); /* Skip heading in data file */ scanf("%*[^\n] "); scanf("%ld%*[^\n] ", &n); #ifdef NAG_COLUMN_MAJOR pda = n; pdc = n; pdq = n; pdt = n; #else pda = n; pdc = n; pdq = n; pdt = n; #endif w_len = n; select_len = n; /* Allocate memory */ if (!(a = NAG_ALLOC(n * n, double)) || !(c = NAG_ALLOC(n * n, double)) || !(q = NAG_ALLOC(n * n, double)) || !(wi = NAG_ALLOC(w_len, double)) || !(wr = NAG_ALLOC(w_len, double)) || !(select = NAG_ALLOC(select_len, Nag_Boolean)) || !(t = NAG_ALLOC(n * n, double))) { printf("Allocation failure\n"); exit_status = -1; goto END; } /* Read T and Q from data file */ for (i = 1; i <= n; ++i) { for (j = 1; j <= n; ++j) scanf("%lf", &T(i, j)); } scanf("%*[^\n] "); for (i = 1; i <= n; ++i) { for (j = 1; j <= n; ++j) scanf("%lf", &Q(i, j)); } scanf("%*[^\n] "); for (i = 0; i < n; ++i) { scanf("%39s", nag_enum_arg); /* nag_enum_name_to_value (x04nac). * Converts NAG enum member name to value */ select[i] = (Nag_Boolean) nag_enum_name_to_value(nag_enum_arg); } scanf("%*[^\n] "); /* nag_dgemm (f16yac): Compute Q*T*QT and store in matrix A */ 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) { printf("Error from nag_dgemm (f16yac).\n%s\n", fail.message); exit_status = 1; goto END; } nag_dgemm(order, Nag_NoTrans, Nag_Trans, n, n, n, alpha, c, pdc, q, pdq, beta, a, pda, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dgemm (f16yac).\n%s\n", fail.message); exit_status = 1; goto END; } /* nag_gen_real_mat_print (x04cac): Print Matrix A. */ fflush(stdout); nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, a, pda, "Matrix A", 0, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_gen_real_mat_print (x04cac).\n%s\n", fail.message); exit_status = 1; goto END; } printf("\n"); /* Reorder the Schur factorization T */ /* nag_dtrsen (f08qgc). * Reorder Schur factorization of real matrix, form * orthonormal basis of right invariant subspace for * selected eigenvalues, with estimates of sensitivities */ nag_dtrsen(order, Nag_DoBoth, Nag_UpdateSchur, select, n, t, pdt, q, pdq, wr, wi, &m, &s, &sep, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dtrsen (f08qgc).\n%s\n", fail.message); exit_status = 1; goto END; } /* nag_dgemm (f16yac): Compute A = Q*T*Q^T - Qt*Tt*Qt^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) { printf("Error from nag_dgemm (f16yac).\n%s\n", fail.message); exit_status = 1; goto END; } alpha = -1.0; beta = 1.0; nag_dgemm(order, Nag_NoTrans, Nag_Trans, n, n, n, alpha, c, pdc, q, pdq, beta, a, pda, &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 A and print warning if */ /* it is too large */ nag_dge_norm(order, Nag_OneNorm, n, n, a, pda, &norm, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dge_norm (f16rac).\n%s\n", fail.message); exit_status = 1; goto END; } if (norm>pow(x02ajc(),0.8)) { printf("%s\n%s\n","Norm of Q*T*Q^H - (Qt*Tt*Qt^H) is much greater than 0.", "Schur factorization has failed."); } else { /* Print condition number estimates */ printf(" Condition number estimate of the selected cluster of" " eigenvalues = %11.2e\n", 1.0/s); printf("\n Condition number estimate of the specified invariant" " subspace = %11.2e\n", 1.0/sep); } END: NAG_FREE(a); NAG_FREE(c); NAG_FREE(q); NAG_FREE(t); NAG_FREE(wi); NAG_FREE(wr); NAG_FREE(select); return exit_status; }