/* nag_zhseqr (f08psc) Example Program. * * Copyright 2001 Numerical Algorithms Group. * * Mark 7, 2001. */ #include #include #include #include #include #include #include #include int main(void) { /* Scalars */ Complex alpha, beta; double norm; Integer i, j, n, pdc, pdd, pdh, pdz, w_len; Integer exit_status = 0; NagError fail; Nag_OrderType order; /* Arrays */ Complex *c = 0, *d = 0, *h = 0, *w = 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_zhseqr (f08psc) 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 w_len = n; /* Allocate memory */ if (!(c = NAG_ALLOC(n * n, Complex)) || !(d = NAG_ALLOC(n * n, Complex)) || !(h = NAG_ALLOC(n * n, Complex)) || !(w = NAG_ALLOC(w_len, Complex)) || !(z = NAG_ALLOC(n * n, Complex))) { 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 , %lf )", &H(i, j).re, &H(i, j).im); } scanf("%*[^\n] "); /* Copy H into D */ for (i = 1; i <= n; ++i) { for (j = 1; j <= n; ++j) { D(i, j).re = H(i, j).re; D(i, j).im = H(i, j).im; } } /* nag_gen_complx_mat_print_comp (x04dbc): Print matrix H */ fflush(stdout); nag_gen_complx_mat_print_comp(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, h, pdh, Nag_BracketForm, "%7.4f", "Matrix H", 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; } /* Calculate the eigenvalues and Schur factorization of H */ /* nag_zhseqr (f08psc). * Eigenvalues and Schur factorization of complex upper * Hessenberg matrix reduced from complex general matrix */ nag_zhseqr(order, Nag_Schur, Nag_InitZ, n, 1, n, h, pdh, w, z, pdz, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_zhseqr (f08psc).\n%s\n", fail.message); exit_status = 1; goto END; } /* nag_zgemm (f16zac): Compute A - Z*T*Z^H from the factorization of */ /* A and store in matrix D*/ alpha.re = 1.0; alpha.im = 0.0; beta.re = 0.0; beta.im = 0.0; nag_zgemm(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_zgemm (f16zac).\n%s\n", fail.message); exit_status = 1; goto END; } alpha.re = -1.0; beta.re = 1.0; nag_zgemm(order, Nag_NoTrans, Nag_ConjTrans, n, n, n, alpha, c, pdc, z, pdz, 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; } /* nag_zge_norm (f16uac): Find norm of matrix D and print warning if */ /* it is too large */ nag_zge_norm(order, Nag_OneNorm, n, 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; } if (norm>pow(x02ajc(),0.8)) { printf("%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("(%7.4f,%7.4f) ", w[i-1].re, w[i-1].im); printf("\n\n"); } END: if (c) NAG_FREE(c); if (d) NAG_FREE(d); if (h) NAG_FREE(h); if (w) NAG_FREE(w); if (z) NAG_FREE(z); return exit_status; }