/* nag_zunghr (f08ntc) 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, pda, pdc, pdd, pdz, tau_len, w_len; Integer exit_status = 0; NagError fail; Nag_OrderType order; /* Arrays */ Complex *a = 0, *c = 0, *d = 0, *tau = 0, *w = 0, *z = 0; #ifdef NAG_COLUMN_MAJOR #define A(I, J) a[(J - 1) * pda + I - 1] #define D(I, J) d[(J - 1) * pdd + I - 1] #define Z(I, J) z[(J - 1) * pdz + I - 1] order = Nag_ColMajor; #else #define A(I, J) a[(I - 1) * pda + J - 1] #define D(I, J) d[(I - 1) * pdd + J - 1] #define Z(I, J) z[(I - 1) * pdz + J - 1] order = Nag_RowMajor; #endif INIT_FAIL(fail); printf("nag_zunghr (f08ntc) Example Program Results\n\n"); /* Skip heading in data file */ scanf("%*[^\n] "); scanf("%ld%*[^\n] ", &n); #ifdef NAG_COLUMN_MAJOR pda = n; pdc = n; pdd = n; pdz = n; #else pda = n; pdc = n; pdd = n; pdz = n; #endif tau_len = n - 1; w_len = n; /* Allocate memory */ if (!(a = NAG_ALLOC(n * n, Complex)) || !(c = NAG_ALLOC(n * n, Complex)) || !(d = NAG_ALLOC(n * n, Complex)) || !(tau = NAG_ALLOC(tau_len, Complex)) || !(w = NAG_ALLOC(w_len, Complex)) || !(z = NAG_ALLOC(n * n, Complex))) { printf("Allocation failure\n"); exit_status = -1; goto END; } /* Read A from data file */ for (i = 1; i <= n; ++i) { for (j = 1; j <= n; ++j) scanf(" ( %lf , %lf )", &A(i, j).re, &A(i, j).im); } scanf("%*[^\n] "); /* Copy A into D */ for (i = 1; i <= n; ++i) { for (j = 1; j <= n; ++j) { D(i, j).re = A(i, j).re; D(i, j).im = A(i, j).im; } } /* nag_gen_complx_mat_print_comp (x04dbc): Print matrix A */ fflush(stdout); nag_gen_complx_mat_print_comp(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, a, pda, Nag_BracketForm, "%7.4f", "Matrix A", 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; } /* Reduce A to upper Hessenberg form H = (Q**T)*A*Q */ /* nag_zgehrd (f08nsc). * Unitary reduction of complex general matrix to upper * Hessenberg form */ nag_zgehrd(order, n, 1, n, a, pda, tau, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_zgehrd (f08nsc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Copy A into Z */ for (i = 1; i <= n; ++i) { for (j = 1; j <= n; ++j) { Z(i, j).re = A(i, j).re; Z(i, j).im = A(i, j).im; } } /* Form Q explicitly, storing the result in Z */ /* nag_zunghr (f08ntc). * Generate unitary transformation matrix from reduction to * Hessenberg form determined by nag_zgehrd (f08nsc) */ nag_zunghr(order, n, 1, n, z, pdz, tau, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_zunghr (f08ntc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Calculate the Schur factorization of H = Y*T*(Y**T) and form */ /* Q*Y explicitly, storing the result in Z */ /* Note that A = Z*T*(Z**T), where Z = Q*Y */ /* nag_zhseqr (f08psc). * Eigenvalues and Schur factorization of complex upper * Hessenberg matrix reduced from complex general matrix */ nag_zhseqr(order, Nag_Schur, Nag_UpdateZ, n, 1, n, a, pda, 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, a, pda, 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 A-(Z*T*Z^H) is much greater than 0.", "Schur factorization has failed."); } END: NAG_FREE(a); NAG_FREE(c); NAG_FREE(d); NAG_FREE(tau); NAG_FREE(w); NAG_FREE(z); return exit_status; }