/* nag_zgebal (f08nvc) Example Program. * * Copyright 2001 Numerical Algorithms Group. * * Mark 7, 2001. */ #include #include #include #include #include int main(int argc, char *argv[]) { FILE *fpin, *fpout; char *outfile = 0; /* Scalars */ Integer i, ihi, ilo, j, m, n, pda, pdh, pdvr; Integer scale_len, tau_len, w_len; Integer exit_status = 0; NagError fail; Nag_OrderType order; /* Arrays */ Complex *a = 0, *h = 0, *tau = 0, *vl = 0, *vr = 0, *w = 0; double *scale = 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); /* Check for command-line IO options */ fpin = nag_example_file_io(argc, argv, "-data", NULL); fpout = nag_example_file_io(argc, argv, "-results", NULL); (void) nag_example_file_io(argc, argv, "-nag_write", &outfile); fprintf(fpout, "nag_zgebal (f08nvc) Example Program Results\n\n"); /* Skip heading in data file */ fscanf(fpin, "%*[^\n] "); fscanf(fpin, "%ld%*[^\n] ", &n); pda = n; pdh = n; pdvr = n; scale_len = n; tau_len = n; w_len = n; /* Allocate memory */ if (!(a = NAG_ALLOC(n * n, Complex)) || !(h = NAG_ALLOC(n * n, Complex)) || !(scale = NAG_ALLOC(scale_len, double)) || !(tau = NAG_ALLOC(tau_len, Complex)) || !(vl = NAG_ALLOC(1 * 1, Complex)) || !(vr = NAG_ALLOC(n * n, Complex)) || !(w = NAG_ALLOC(w_len, Complex)) || !(select = NAG_ALLOC(1, Nag_Boolean))) { fprintf(fpout, "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) fscanf(fpin, " ( %lf , %lf )", &A(i, j).re, &A(i, j).im); } fscanf(fpin, "%*[^\n] "); /* Balance A */ /* nag_zgebal (f08nvc). * Balance complex general matrix */ nag_zgebal(order, Nag_DoBoth, n, a, pda, &ilo, &ihi, scale, &fail); if (fail.code != NE_NOERROR) { fprintf(fpout, "Error from nag_zgebal (f08nvc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Reduce A to upper Hessenberg form H = (Q**H)*A*Q */ /* nag_zgehrd (f08nsc). * Unitary reduction of complex general matrix to upper * Hessenberg form */ nag_zgehrd(order, n, ilo, ihi, a, pda, tau, &fail); if (fail.code != NE_NOERROR) { fprintf(fpout, "Error from nag_zgehrd (f08nsc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Copy A to H and VR */ 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; VR(i, j).re = A(i, j).re; VR(i, j).im = A(i, j).im; } } /* Form Q explicitly, storing the result in VR */ /* nag_zunghr (f08ntc). * Generate unitary transformation matrix from reduction to * Hessenberg form determined by nag_zgehrd (f08nsc) */ nag_zunghr(order, n, 1, n, vr, pdvr, tau, &fail); if (fail.code != NE_NOERROR) { fprintf(fpout, "Error from nag_zunghr (f08ntc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Calculate the eigenvalues and Schur factorization of A */ /* 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, ilo, ihi, h, pdh, w, vr, pdvr, &fail); if (fail.code != NE_NOERROR) { fprintf(fpout, "Error from nag_zhseqr (f08psc).\n%s\n", fail.message); exit_status = 1; goto END; } fprintf(fpout, " Eigenvalues\n"); for (i = 0; i < n; ++i) fprintf(fpout, " (%7.4f,%7.4f)", w[i].re, w[i].im); fprintf(fpout, "\n"); /* Calculate the eigenvectors of A, storing the result in VR */ /* nag_ztrevc (f08qxc). * Left and right eigenvectors of complex upper triangular * matrix */ nag_ztrevc(order, Nag_RightSide, Nag_BackTransform, select, n, h, pdh, vl, 1, vr, pdvr, n, &m, &fail); if (fail.code != NE_NOERROR) { fprintf(fpout, "Error from nag_ztrevc (f08qxc).\n%s\n", fail.message); exit_status = 1; goto END; } /* nag_zgebak (f08nwc). * Transform eigenvectors of complex balanced matrix to * those of original matrix supplied to nag_zgebal (f08nvc) */ nag_zgebak(order, Nag_DoBoth, Nag_RightSide, n, ilo, ihi, scale, m, vr, pdvr, &fail); if (fail.code != NE_NOERROR) { fprintf(fpout, "Error from nag_zgebak (f08nwc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Print eigenvectors */ fprintf(fpout, "\n"); /* nag_gen_complx_mat_print_comp (x04dbc). * Print complex general matrix (comprehensive) */ if (outfile) fclose(fpout); 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, outfile, &fail); if (outfile && !(fpout = fopen(outfile, "a"))) { exit_status = 2; goto END; } if (fail.code != NE_NOERROR) { fprintf(fpout, "Error from nag_gen_complx_mat_print_comp (x04dbc).\n%s\n", fail.message); exit_status = 1; goto END; } END: if (fpin != stdin) fclose(fpin); if (fpout != stdout) fclose(fpout); if (a) NAG_FREE(a); if (h) NAG_FREE(h); if (scale) NAG_FREE(scale); if (tau) NAG_FREE(tau); if (vl) NAG_FREE(vl); if (vr) NAG_FREE(vr); if (w) NAG_FREE(w); if (select) NAG_FREE(select); return exit_status; }