/* nag_dhseqr (f08pec) Example Program. * * Copyright 2001 Numerical Algorithms Group. * * Mark 7, 2001. */ #include #include #include #include #include #include #include #include int main(void) { /* Scalars */ double alpha, beta, norm; Integer i, j, n, pdc, pdd, pdh, pdz, wi_len, wr_len; Integer exit_status = 0; NagError fail; Nag_OrderType order; /* Arrays */ double *c = 0, *d = 0, *h = 0, *wi = 0, *wr = 0, *z = 0; #ifdef NAG_COLUMN_MAJOR #define H(I, J) h[(J-1)*pdh + I - 1] #define D(I, J) d[(J-1)*pdd + I - 1] order = Nag_ColMajor; #else #define H(I, J) h[(I-1)*pdh + J - 1] #define D(I, J) d[(I-1)*pdd + J - 1] order = Nag_RowMajor; #endif INIT_FAIL(fail); printf("nag_dhseqr (f08pec) Example Program Results\n\n"); /* Skip heading in data file */ scanf("%*[^\n] "); scanf("%ld%*[^\n] ", &n); #ifdef NAG_COLUMN_MAJOR pdc = n; pdd = n; pdh = n; pdz = n; #else pdc = n; pdd = n; pdh = n; pdz = n; #endif wr_len = n; wi_len = n; /* Allocate memory */ if (!(c = NAG_ALLOC(n * n, double)) || !(d = NAG_ALLOC(n * n, double)) || !(h = NAG_ALLOC(n * n, double)) || !(wi = NAG_ALLOC(wi_len, double)) || !(wr = NAG_ALLOC(wr_len, double)) || !(z = NAG_ALLOC(n * n, double))) { printf("Allocation failure\n"); exit_status = -1; goto END; } /* Read H from data file */ for (i = 1; i <= n; ++i) { for (j = 1; j <= n; ++j) scanf("%lf", &H(i, j)); } scanf("%*[^\n] "); /* Copy H into D */ for (i = 1; i <= n; ++i) { for (j = 1; j <= n; ++j) D(i, j) = H(i, j); } /* nag_gen_real_mat_print (x04cac): Print Matrix H. */ fflush(stdout); nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, h, pdh, "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; } /* Calculate the eigenvalues and Schur factorization of H */ /* nag_dhseqr (f08pec). * Eigenvalues and Schur factorization of real upper * Hessenberg matrix reduced from real general matrix */ nag_dhseqr(order, Nag_Schur, Nag_InitZ, n, 1, n, h, pdh, wr, wi, z, pdz, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dhseqr (f08pec).\n%s\n", fail.message); exit_status = 1; goto END; } /* nag_dgemm (f16yac): Compute H - Z*T*Z^T from the factorization of */ /* H and store in matrix D*/ alpha = 1.0; beta = 0.0; nag_dgemm(order, Nag_NoTrans, Nag_NoTrans, n, n, n, alpha, z, pdz, h, pdh, 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, z, pdz, 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, n, 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; } if (norm>pow(x02ajc(),0.8)) { printf("\n%s\n%s\n","Norm of H-(Z*T*Z^H) is much greater than 0.", "Schur factorization has failed."); } else { printf(" Eigenvalues\n"); for (i = 1; i <= n; ++i) printf(" (%8.4f,%8.4f)", wr[i-1], wi[i-1]); printf("\n"); } END: NAG_FREE(c); NAG_FREE(d); NAG_FREE(h); NAG_FREE(wi); NAG_FREE(wr); NAG_FREE(z); return exit_status; }