/* nag_ztgevc (f08yxc) Example Program. * * Copyright 2001 Numerical Algorithms Group. * * Mark 7, 2001. */ #include #include #include #include #include #include #include #include #include static Integer normalize_vectors(Nag_OrderType order, Integer n, Complex qz[], const char* title); int main(void) { /* Scalars */ Integer i, icols, ihi, ilo, irows, j, m, n, pda, pdb, pdq, pdz; Integer exit_status = 0; Complex e, one, zero; 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; #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); printf("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; zero = nag_complex(0.0,0.0); one = nag_complex(1.0,0.0); /* Skip heading in data file and read matrix size.*/ scanf("%*[^\n] "); scanf("%ld%*[^\n] ", &n); pda = n; pdb = n; pdq = n; pdz = n; /* Allocate memory */ if ( !(a = NAG_ALLOC(n * n, Complex)) || !(b = NAG_ALLOC(n * n, Complex)) || !(q = NAG_ALLOC(n * n, Complex)) || !(z = NAG_ALLOC(n * n, Complex)) || !(alpha = NAG_ALLOC(n, Complex)) || !(beta = NAG_ALLOC(n, Complex)) || !(tau = NAG_ALLOC(n, Complex)) || !(lscale = NAG_ALLOC(n, double)) || !(rscale = NAG_ALLOC(n, 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 , %lf )", &A(i, j).re, &A(i, j).im); scanf("%*[^\n] "); /* READ matrix B from data file */ for (i = 1; i <= n; ++i) for (j = 1; j <= n; ++j) scanf(" ( %lf , %lf )", &B(i, j).re, &B(i, j).im); scanf("%*[^\n] "); /* Balance pair (A,B) of complex general matrices using * nag_zggbal (f08wvc). */ nag_zggbal(order, Nag_DoBoth, n, a, pda, b, pdb, &ilo, &ihi, lscale, rscale, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_zggbal (f08wvc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Print complex general matrices A and B after balancing using * nag_gen_complx_mat_print_comp (x04dbc). */ fflush(stdout); 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, 0, &fail); if (fail.code == NE_NOERROR) { fflush(stdout); 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, 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; } printf("\n"); /* Reduce B to triangular form using QR and premultiply A by Q^H. */ irows = ihi + 1 - ilo; icols = n + 1 - ilo; /* nag_zgeqrf (f08asc). * QR factorization of complex general rectangular matrix B. */ nag_zgeqrf(order, irows, icols, &B(ilo, ilo), pdb, tau, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_zgeqrf (f08asc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Apply the orthogonal transformation Q^H to matrix A using * nag_zunmqr (f08auc). */ 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) { printf("Error from nag_zunmqr (f08auc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Initialize Q (if left eigenvectors are required) */ if (ileft) { /* Q = I */ nag_zge_load(order, n, n, zero, one, q, pdq, &fail); /* Q = B using nag_zge_copy (f16tfc). */ nag_zge_copy(order, Nag_NoTrans, irows-1, irows-1, &B(ilo+1,ilo), pdb, &Q(ilo+1,ilo), pdq, &fail); /* Form Q from QR factorization using nag_zungqr (f08atc). */ nag_zungqr(order, irows, irows, irows, &Q(ilo, ilo), pdq, tau, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_zungqr (f08atc).\n%s\n", fail.message); exit_status = 1; goto END; } } if (iright) { /* Z = I. */ nag_zge_load(order, n, n, zero, one, z, pdz, &fail); } /* Compute the generalized Hessenberg form of (A,B) by Unitary reduction * using nag_zgghrd (f08wsc). */ nag_zgghrd(order, Nag_UpdateSchur, Nag_UpdateZ, n, ilo, ihi, a, pda, b, pdb, q, pdq, z, pdz, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_zgghrd (f08wsc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Print generalized Hessenberg form of (A,B) using * nag_gen_complx_mat_print_comp (x04dbc). */ fflush(stdout); 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, 0, &fail); if (fail.code == NE_NOERROR) { printf("\n"); fflush(stdout); 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, 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; } /* 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) { printf("Error from nag_zhgeqz (f08xsc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Print the generalized eigenvalue parameters */ printf("\n Generalized eigenvalues\n"); for (i = 0; i < n; ++i) { if (beta[i].re != 0.0 || beta[i].im != 0.0) { /* nag_complex_divide (a02cdc) - Quotient of two complex numbers. */ e = nag_complex_divide(alpha[i], beta[i]); printf(" %4ld (%7.3f,%7.3f)\n", i+1, e.re, e.im); } else printf(" %4ldEigenvalue is infinite\n", i+1); } printf("\n"); /* nag_ztgevc (f08yxc). * Left and right eigenvectors of a pair of complex upper * triangular matrices */ nag_ztgevc(order, Nag_BothSides, Nag_BackTransform, NULL, n, a, pda, b, pdb, q, pdq, z, pdz, n, &m, &fail); if (fail.code != NE_NOERROR) { printf("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) { printf("Error from nag_zggbak (f08wwc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Normalize and print the right eigenvectors */ exit_status = normalize_vectors(order, n, z, "Right eigenvectors"); printf("\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) { printf("Error from nag_zggbak (f08wwc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Normalize and print the left eigenvectors */ exit_status = normalize_vectors(order, n, q, "Left eigenvectors"); } END: NAG_FREE(a); NAG_FREE(b); NAG_FREE(q); NAG_FREE(z); NAG_FREE(alpha); NAG_FREE(beta); NAG_FREE(tau); NAG_FREE(lscale); NAG_FREE(rscale); return exit_status; } static Integer normalize_vectors(Nag_OrderType order, Integer n, Complex qz[], const char* title) { /* Each complex eigenvector z[] is normalized so that the element of largest * magnitude is scaled to be (1.0,0.0). */ double r; Integer colinc, rowinc, j, k, indqz, errors=0; Complex alpha, beta, x[1]; NagError fail; INIT_FAIL(fail); if (order==Nag_ColMajor) { rowinc = 1; colinc = n; } else { rowinc = n; colinc = 1; } indqz = 0; for (j=0; j