/* nag_zunmhr (f08nuc) Example Program. * * Copyright 2001 Numerical Algorithms Group. * * Mark 7, 2001. * Mark 7b revised, 2004. */ #include #include #include #include #include #include int main(void) { /* Scalars */ Integer i, j, m, n, pda, pdh, pdvl, pdvr, pdz; Integer tau_len, ifaill_len, select_len, w_len; Integer exit_status = 0; double thresh; NagError fail; Nag_OrderType order; /* Arrays */ Complex *a = 0, *h = 0, *vl = 0, *vr = 0, *z = 0, *w = 0, *tau = 0; Integer *ifaill = 0, *ifailr = 0; Nag_Boolean *select = 0; #ifdef NAG_COLUMN_MAJOR #define A(I, J) a[(J - 1) * pda + I - 1] #define H(I, J) h[(J - 1) * pdh + I - 1] #define VR(I, J) vr[(J - 1) * pdvr + I - 1] order = Nag_ColMajor; #else #define A(I, J) a[(I - 1) * pda + J - 1] #define H(I, J) h[(I - 1) * pdh + J - 1] #define VR(I, J) vr[(I - 1) * pdvr + J - 1] order = Nag_RowMajor; #endif INIT_FAIL(fail); printf("nag_zunmhr (f08nuc) Example Program Results\n\n"); /* Skip heading in data file */ scanf("%*[^\n] "); scanf("%ld%*[^\n] ", &n); pda = n; pdh = n; pdvl = n; pdvr = n; pdz = 1; tau_len = n; w_len = n; ifaill_len = n; select_len = n; /* Allocate memory */ if (!(a = NAG_ALLOC(n * n, Complex)) || !(h = NAG_ALLOC(n * n, Complex)) || !(vl = NAG_ALLOC(n * n, Complex)) || !(vr = NAG_ALLOC(n * n, Complex)) || !(z = NAG_ALLOC(1 * 1, Complex)) || !(w = NAG_ALLOC(w_len, Complex)) || !(ifaill = NAG_ALLOC(ifaill_len, Integer)) || !(ifailr = NAG_ALLOC(ifaill_len, Integer)) || !(select = NAG_ALLOC(select_len, Nag_Boolean)) || !(tau = NAG_ALLOC(tau_len, 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] "); scanf("%lf%*[^\n] ", &thresh); /* Reduce A to upper Hessenberg form */ /* 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 to H */ for (i = 1; i <= n; ++i) { for (j = 1; j <= n; ++j) { H(i, j).re = A(i, j).re; H(i, j).im = A(i, j).im; } } /* Calculate the eigenvalues of H (same as A) */ /* nag_zhseqr (f08psc). * Eigenvalues and Schur factorization of complex upper * Hessenberg matrix reduced from complex general matrix */ nag_zhseqr(order, Nag_EigVals, Nag_NotZ, 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; } /* Print eigenvalues */ printf(" Eigenvalues\n"); for (i = 0; i < n; ++i) printf(" (%7.4f,%7.4f)", w[i].re, w[i].im); printf("\n"); for (i = 0; i < n; ++i) select[i] = w[i].re < thresh?Nag_TRUE:Nag_FALSE; /* Calculate the eigenvectors of H (as specified by SELECT), */ /* storing the result in VR */ /* nag_zhsein (f08pxc). * Selected right and/or left eigenvectors of complex upper * Hessenberg matrix by inverse iteration */ nag_zhsein(order, Nag_RightSide, Nag_HSEQRSource, Nag_NoVec, select, n, a, pda, w, vl, pdvl, vr, pdvr, n, &m, ifaill, ifailr, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_zhsein (f08pxc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Calculate the eigenvectors of A = Q * VR */ /* nag_zunmhr (f08nuc). * Apply unitary transformation matrix from reduction to * Hessenberg form determined by nag_zgehrd (f08nsc) */ nag_zunmhr(order, Nag_LeftSide, Nag_NoTrans, n, m, 1, n, a, pda, tau, vr, pdvr, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_zunmhr (f08nuc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Normalize the eigenvectors */ for(j=1; j<=m; j++) { for(i=n; i>=1; i--) { VR(i, j) = nag_complex_divide(VR(i, j), VR(1,j)); } } /* Print Eigenvectors */ printf("\n"); /* nag_gen_complx_mat_print_comp (x04dbc). * Print complex general matrix (comprehensive) */ fflush(stdout); nag_gen_complx_mat_print_comp(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, m, vr, pdvr, Nag_BracketForm, "%7.4f", "Contents of array VR", Nag_IntegerLabels, 0, Nag_IntegerLabels, 0, 80, 0, 0, &fail); 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; } END: if (a) NAG_FREE(a); if (h) NAG_FREE(h); if (vl) NAG_FREE(vl); if (vr) NAG_FREE(vr); if (z) NAG_FREE(z); if (w) NAG_FREE(w); if (ifaill) NAG_FREE(ifaill); if (ifailr) NAG_FREE(ifailr); if (select) NAG_FREE(select); if (tau) NAG_FREE(tau); return exit_status; }