/* nag_ztgevc (f08yxc) Example Program. * * Copyright 2001 Numerical Algorithms Group. * * Mark 7, 2001. */ #include #include #include #include #include #include int main(int argc, char *argv[]) { FILE *fpin, *fpout; char *outfile = 0; /* Scalars */ Integer i, icols, ihi, ilo, irows, j, m, n, pda, pdb, pdq, pdz; Integer alpha_len, beta_len, scale_len, tau_len, select_len; Integer exit_status = 0; Complex e; Nag_Boolean ileft, iright; NagError fail; Nag_OrderType order; /* Arrays */ Complex *a = 0, *alpha = 0, *b = 0, *beta = 0, *q = 0, *tau = 0; Complex *z = 0; double *lscale = 0, *rscale = 0; Nag_Boolean *select = 0; #ifdef NAG_COLUMN_MAJOR #define A(I, J) a[(J-1)*pda + I - 1] #define B(I, J) b[(J-1)*pdb + I - 1] #define Q(I, J) q[(J-1)*pdq + 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 B(I, J) b[(I-1)*pdb + J - 1] #define Q(I, J) q[(I-1)*pdq + J - 1] #define Z(I, J) z[(I-1)*pdz + 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_ztgevc (f08yxc) Example Program Results\n\n"); /* ILEFT is TRUE if left eigenvectors are required */ /* IRIGHT is TRUE if right eigenvectors are required */ ileft = Nag_TRUE; iright = Nag_TRUE; /* Skip heading in data file */ fscanf(fpin, "%*[^\n] "); fscanf(fpin, "%ld%*[^\n] ", &n); pda = n; pdb = n; pdq = n; pdz = n; alpha_len = n; beta_len = n; scale_len = n; tau_len = n; select_len = n; /* Allocate memory */ if ( !(a = NAG_ALLOC(n * n, Complex)) || !(alpha = NAG_ALLOC(alpha_len, Complex)) || !(b = NAG_ALLOC(n * n, Complex)) || !(beta = NAG_ALLOC(beta_len, Complex)) || !(lscale = NAG_ALLOC(scale_len, double)) || !(rscale = NAG_ALLOC(scale_len, double)) || !(q = NAG_ALLOC(n * n, Complex)) || !(tau = NAG_ALLOC(tau_len, Complex)) || !(z = NAG_ALLOC(n * n, Complex)) || !(select = NAG_ALLOC(select_len, Nag_Boolean))) { fprintf(fpout, "Allocation failure\n"); exit_status = -1; goto END; } /* READ matrix 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] "); /* READ matrix B from data file */ for (i = 1; i <= n; ++i) { for (j = 1; j <= n; ++j) fscanf(fpin, " ( %lf , %lf )", &B(i, j).re, &B(i, j).im); } fscanf(fpin, "%*[^\n] "); /* Balance matrix pair (A,B) */ /* nag_zggbal (f08wvc). * Balance a pair of complex general matrices */ nag_zggbal(order, Nag_DoBoth, n, a, pda, b, pdb, &ilo, &ihi, lscale, rscale, &fail); if (fail.code != NE_NOERROR) { fprintf(fpout, "Error from nag_zggbal (f08wvc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Matrix A after balancing */ /* 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, n, a, pda, Nag_BracketForm, "%7.4f", "Matrix A after balancing", 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; } /* Matrix B after balancing */ /* nag_gen_complx_mat_print_comp (x04dbc), see above. */ if (outfile) fclose(fpout); nag_gen_complx_mat_print_comp(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, b, pdb, Nag_BracketForm, "%7.4f", "Matrix B after balancing", 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; } fprintf(fpout, "\n"); /* Reduce B to triangular form using QR */ irows = ihi + 1 - ilo; icols = n + 1 - ilo; /* nag_zgeqrf (f08asc). * QR factorization of complex general rectangular matrix */ nag_zgeqrf(order, irows, icols, &B(ilo, ilo), pdb, tau, &fail); if (fail.code != NE_NOERROR) { fprintf(fpout, "Error from nag_zgeqrf (f08asc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Apply the orthogonal transformation to matrix A */ /* nag_zunmqr (f08auc). * Apply unitary transformation determined by nag_zgeqrf * (f08asc) or nag_zgeqpf (f08bsc) */ nag_zunmqr(order, Nag_LeftSide, Nag_ConjTrans, irows, icols, irows, &B(ilo, ilo), pdb, tau, &A(ilo, ilo), pda, &fail); if (fail.code != NE_NOERROR) { fprintf(fpout, "Error from nag_zunmqr (f08auc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Initialize Q (if left eigenvectors are required) */ if (ileft) { for (i = 1; i <= n; ++i) { for (j = 1; j <= n; ++j) { Q(i, j).re = 0.0; Q(i, j).im = 0.0; } Q(i, i).re = 1.0; } for (i = ilo+1; i <= ilo+irows-1; ++i) { for (j = ilo; j <= MIN(i, ilo+irows-2); ++j) { Q(i, j).re = B(i, j).re; Q(i, j).im = B(i, j).im; } } /* nag_zungqr (f08atc). * Form all or part of unitary Q from QR factorization * determined by nag_zgeqrf (f08asc) or nag_zgeqpf (f08bsc) */ nag_zungqr(order, irows, irows, irows, &Q(ilo, ilo), pdq, tau, &fail); if (fail.code != NE_NOERROR) { fprintf(fpout, "Error from nag_zungqr (f08atc).\n%s\n", fail.message); exit_status = 1; goto END; } } /* Initialize Z (if right eigenvectors are required) */ if (iright) { for (i = 1; i <= n; ++i) { for (j = 1; j <= n; ++j) { Z(i, j).re = 0.0; Z(i, j).im = 0.0; } Z(i, i).re = 1.0; } } /* Compute the generalized Hessenberg form of (A,B) */ /* nag_zgghrd (f08wsc). * Unitary reduction of a pair of complex general matrices * to generalized upper Hessenberg form */ nag_zgghrd(order, Nag_UpdateSchur, Nag_UpdateZ, n, ilo, ihi, a, pda, b, pdb, q, pdq, z, pdz, &fail); if (fail.code != NE_NOERROR) { fprintf(fpout, "Error from nag_zgghrd (f08wsc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Matrix A in generalized Hessenberg form */ /* nag_gen_complx_mat_print_comp (x04dbc), see above. */ if (outfile) fclose(fpout); nag_gen_complx_mat_print_comp(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, a, pda, Nag_BracketForm, "%7.3f", "Matrix A in Hessenberg form", 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; } fprintf(fpout, "\n"); /* Matrix B in generalized Hessenberg form */ /* nag_gen_complx_mat_print_comp (x04dbc), see above. */ if (outfile) fclose(fpout); nag_gen_complx_mat_print_comp(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, b, pdb, Nag_BracketForm, "%7.3f", "Matrix B in Hessenberg form", 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; } /* Compute the generalized Schur form - nag_zhgeqz (f08xsc). * Eigenvalues and generalized Schur factorization of * complex generalized upper Hessenberg form reduced from a * pair of complex general matrices */ nag_zhgeqz(order, Nag_Schur, Nag_AccumulateQ, Nag_AccumulateZ, n, ilo, ihi, a, pda, b, pdb, alpha, beta, q, pdq, z, pdz, &fail); if (fail.code != NE_NOERROR) { fprintf(fpout, "Error from nag_zhgeqz (f08xsc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Print the generalized eigenvalue parameters */ fprintf(fpout, "\n Generalized eigenvalues\n"); for (i = 1; i <= n; ++i) { if (beta[i-1].re != 0.0 || beta[i-1].im != 0.0) { /* nag_complex_divide (a02cdc). * Quotient of two complex numbers */ e = nag_complex_divide(alpha[i - 1], beta[i - 1]); fprintf(fpout, " %4ld (%7.3f,%7.3f)\n", i, e.re, e.im); } else fprintf(fpout, " %4ldEigenvalue is infinite\n", i); } fprintf(fpout, "\n"); /* nag_ztgevc (f08yxc). * Left and right eigenvectors of a pair of complex upper * triangular matrices */ nag_ztgevc(order, Nag_BothSides, Nag_BackTransform, select, n, a, pda, b, pdb, q, pdq, z, pdz, n, &m, &fail); if (fail.code != NE_NOERROR) { fprintf(fpout, "Error from nag_ztgevc (f08yxc).\n%s\n", fail.message); exit_status = 1; goto END; } if (iright) { /* nag_zggbak (f08wwc). * Transform eigenvectors of a pair of complex balanced * matrices to those of original matrix pair supplied to * nag_zggbal (f08wvc) */ nag_zggbak(order, Nag_DoBoth, Nag_RightSide, n, ilo, ihi, lscale, rscale, n, z, pdz, &fail); if (fail.code != NE_NOERROR) { fprintf(fpout, "Error from nag_zggbak (f08wwc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Print the right eigenvectors */ /* nag_gen_complx_mat_print_comp (x04dbc), see above. */ if (outfile) fclose(fpout); nag_gen_complx_mat_print_comp(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, z, pdz, Nag_BracketForm, "%7.4f", "Right eigenvectors", 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; } fprintf(fpout, "\n"); } /* Compute left eigenvectors of the original matrix */ if (ileft) { /* nag_zggbak (f08wwc), see above. */ nag_zggbak(order, Nag_DoBoth, Nag_LeftSide, n, ilo, ihi, lscale, rscale, n, q, pdq, &fail); if (fail.code != NE_NOERROR) { fprintf(fpout, "Error from nag_zggbak (f08wwc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Print the left eigenvectors */ /* nag_gen_complx_mat_print_comp (x04dbc), see above. */ if (outfile) fclose(fpout); nag_gen_complx_mat_print_comp(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, q, pdq, Nag_BracketForm, "%7.4f", "Left eigenvectors", 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 (alpha) NAG_FREE(alpha); if (b) NAG_FREE(b); if (beta) NAG_FREE(beta); if (lscale) NAG_FREE(lscale); if (q) NAG_FREE(q); if (rscale) NAG_FREE(rscale); if (tau) NAG_FREE(tau); if (z) NAG_FREE(z); if (select) NAG_FREE(select); return exit_status; }