/* nag_dhgeqz (f08xec) Example Program. * * Copyright 2001 Numerical Algorithms Group. * * Mark 7, 2001. */ #include #include #include #include #include int main(void) { /* Scalars */ Integer i, ihi, ilo, irows, j, n, pda, pdb; Integer alpha_len, beta_len, scale_len, tau_len; Integer exit_status = 0; NagError fail; Nag_OrderType order; /* Arrays */ double *a = 0, *alphai = 0, *alphar = 0, *b = 0, *beta = 0; double *lscale = 0, *q = 0, *rscale = 0, *tau = 0, *z = 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] order = Nag_ColMajor; #else #define A(I, J) a[(I-1)*pda + J - 1] #define B(I, J) b[(I-1)*pdb + J - 1] order = Nag_RowMajor; #endif INIT_FAIL(fail); printf("nag_dhgeqz (f08xec) Example Program Results\n\n"); /* Skip heading in data file */ scanf("%*[^\n] "); scanf("%ld%*[^\n] ", &n); pda = n; pdb = n; alpha_len = n; beta_len = n; scale_len = n; tau_len = n; /* Allocate memory */ if (!(a = NAG_ALLOC(n * n, double)) || !(alphai = NAG_ALLOC(alpha_len, double)) || !(alphar = NAG_ALLOC(alpha_len, double)) || !(b = NAG_ALLOC(n * n, double)) || !(beta = NAG_ALLOC(beta_len, double)) || !(lscale = NAG_ALLOC(scale_len, double)) || !(q = NAG_ALLOC(1 * 1, double)) || !(rscale = NAG_ALLOC(scale_len, double)) || !(tau = NAG_ALLOC(tau_len, double)) || !(z = NAG_ALLOC(1 * 1, double))) { printf("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) scanf("%lf", &A(i, j)); } scanf("%*[^\n] "); /* READ matrix B from data file */ for (i = 1; i <= n; ++i) { for (j = 1; j <= n; ++j) scanf("%lf", &B(i, j)); } scanf("%*[^\n] "); /* Balance matrix pair (A,B) */ /* nag_dggbal (f08whc). * Balance a pair of real general matrices */ nag_dggbal(order, Nag_DoBoth, n, a, pda, b, pdb, &ilo, &ihi, lscale, rscale, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dggbal (f08whc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Matrix A after balancing */ /* nag_gen_real_mat_print (x04cac). * Print real general matrix (easy-to-use) */ fflush(stdout); nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, a, pda, "Matrix A after balancing", 0, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_gen_real_mat_print (x04cac).\n%s\n", fail.message); exit_status = 1; goto END; } printf("\n"); /* Matrix B after balancing */ /* nag_gen_real_mat_print (x04cac), see above. */ fflush(stdout); nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, b, pdb, "Matrix B after balancing", 0, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_gen_real_mat_print (x04cac).\n%s\n", fail.message); exit_status = 1; goto END; } printf("\n"); /* Reduce B to triangular form using QR */ irows = ihi + 1 - ilo; /* nag_dgeqrf (f08aec). * QR factorization of real general rectangular matrix */ nag_dgeqrf(order, irows, irows, &B(ilo, ilo), pdb, tau, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dgeqrf (f08aec).\n%s\n", fail.message); exit_status = 1; goto END; } /* Apply the orthogonal transformation to matrix A */ /* nag_dormqr (f08agc). * Apply orthogonal transformation determined by nag_dgeqrf * (f08aec) or nag_dgeqpf (f08bec) */ nag_dormqr(order, Nag_LeftSide, Nag_Trans, irows, irows, irows, &B(ilo, ilo), pdb, tau, &A(ilo, ilo), pda, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dormqr (f08agc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Compute the generalized Hessenberg form of (A,B) */ /* nag_dgghrd (f08wec). * Orthogonal reduction of a pair of real general matrices * to generalized upper Hessenberg form */ nag_dgghrd(order, Nag_NotQ, Nag_NotZ, irows, 1, irows, &A(ilo, ilo), pda, &B(ilo, ilo), pdb, q, 1, z, 1, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dgghrd (f08wec).\n%s\n", fail.message); exit_status = 1; goto END; } /* Matrix A in generalized Hessenberg form */ /* nag_gen_real_mat_print (x04cac), see above. */ fflush(stdout); nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, a, pda, "Matrix A in Hessenberg form", 0, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_gen_real_mat_print (x04cac).\n%s\n", fail.message); exit_status = 1; goto END; } printf("\n"); /* Matrix B in generalized Hessenberg form */ /* nag_gen_real_mat_print (x04cac), see above. */ fflush(stdout); nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, b, pdb, "Matrix B is triangular", 0, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_gen_real_mat_print (x04cac).\n%s\n", fail.message); exit_status = 1; goto END; } /* Compute the generalized Schur form */ /* nag_dhgeqz (f08xec). * Eigenvalues and generalized Schur factorization of real * generalized upper Hessenberg form reduced from a pair of * real general matrices */ nag_dhgeqz(order, Nag_EigVals, Nag_NotQ, Nag_NotZ, n, ilo, ihi, a, pda, b, pdb, alphar, alphai, beta, q, 1, z, 1, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dhgeqz (f08xec).\n%s\n", fail.message); exit_status = 1; goto END; } /* Print the generalized eigenvalues */ printf("\n Generalized eigenvalues\n"); for (i = 1; i <= n; ++i) { if (beta[i-1] != 0.0) { printf(" %4ld (%7.3f,%7.3f)\n", i, alphar[i-1]/beta[i-1], alphai[i-1]/beta[i-1]); } else printf(" %4ldEigenvalue is infinite\n", i); } END: if (a) NAG_FREE(a); if (alphai) NAG_FREE(alphai); if (alphar) NAG_FREE(alphar); 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); return exit_status; }