/* nag_zggevx (f08wpc) Example Program. * * Copyright 2011 Numerical Algorithms Group. * * Mark 23, 2011. */ #include #include #include #include #include #include #include int main(void) { /* Scalars */ Complex z; double abnorm, abnrm, bbnrm, eps, small, tol; Integer i, ihi, ilo, j, n, pda, pdb, pdvl, pdvr; Integer exit_status = 0; /* Arrays */ Complex *a = 0, *alpha = 0, *b = 0, *beta = 0, *vl = 0, *vr = 0; double *lscale = 0, *rconde = 0, *rcondv = 0, *rscale = 0; char nag_enum_arg[40]; /* Nag Types */ NagError fail; Nag_OrderType order; Nag_LeftVecsType jobvl; Nag_RightVecsType jobvr; Nag_RCondType sense; #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_zggevx (f08wpc) Example Program Results\n"); /* Skip heading in data file */ scanf("%*[^\n]"); scanf("%ld%*[^\n]", &n); if (n < 0) { printf("Invalid n\n"); exit_status = 1; goto END; } scanf(" %39s%*[^\n]", nag_enum_arg); /* nag_enum_name_to_value (x04nac). * Converts NAG enum member name to value */ jobvl = (Nag_LeftVecsType) nag_enum_name_to_value(nag_enum_arg); scanf(" %39s%*[^\n]", nag_enum_arg); jobvr = (Nag_RightVecsType) nag_enum_name_to_value(nag_enum_arg); scanf(" %39s%*[^\n]", nag_enum_arg); sense = (Nag_RCondType) nag_enum_name_to_value(nag_enum_arg); pda = n; pdb = n; pdvl = (jobvl==Nag_LeftVecs?n:1); pdvr = (jobvr==Nag_RightVecs?n:1); /* Allocate memory */ if (!(a = NAG_ALLOC(n*n, Complex)) || !(b = NAG_ALLOC(n*n, Complex)) || !(alpha = NAG_ALLOC(n, Complex)) || !(beta = NAG_ALLOC(n, Complex)) || !(vl = NAG_ALLOC(pdvl*pdvl, Complex)) || !(vr = NAG_ALLOC(pdvr*pdvr, Complex)) || !(lscale = NAG_ALLOC(n, double)) || !(rconde = NAG_ALLOC(n, double)) || !(rcondv = NAG_ALLOC(n, double)) || !(rscale = NAG_ALLOC(n, double))) { printf("Allocation failure\n"); exit_status = -1; goto END; } /* Read in the matrices A and B */ 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]"); 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]"); /* Solve the generalized eigenvalue problem using nag_zggevx (f08wpc). */ nag_zggevx(order, Nag_BalanceBoth, jobvl, jobvr, sense, n, a, pda, b, pdb, alpha, beta, vl, pdvl, vr, pdvr, &ilo, &ihi, lscale, rscale, &abnrm, &bbnrm, rconde, rcondv, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_zggevx (f08wpc).\n%s\n", fail.message); exit_status = 1; goto END; } /* nag_real_safe_small_number (x02amc), nag_machine_precision (x02ajc) */ eps = nag_machine_precision; small = nag_real_safe_small_number; if (abnrm == 0.0) abnorm = ABS(bbnrm); else if (bbnrm == 0.0) abnorm = ABS(abnrm); else if (ABS(abnrm) >= ABS(bbnrm)) abnorm = ABS(abnrm)*sqrt(1.0+(bbnrm/abnrm)*(bbnrm/abnrm)); else abnorm = ABS(bbnrm)*sqrt(1.0+(abnrm/bbnrm)*(abnrm/bbnrm)); tol = eps * abnorm; /* Print out eigenvalues and associated condition number and bounds */ if (sense!=Nag_NotRCond) printf("\n R = Reciprocal condition number, E = Error bound\n\n"); printf("%22s","Eigenvalues"); if (sense==Nag_RCondEigVals || sense==Nag_RCondBoth) printf("%15s%10s","R","E"); printf("\n"); for (j = 0; j < n; ++j) { /* Print out information on the jth eigenvalue */ if (nag_complex_abs(alpha[j])*small >= nag_complex_abs(beta[j])) { printf("%2ld is numerically infinite or undetermined\n", j+1); printf(" alpha = (%9.4f, %9.4f), beta = (%9.4f, %9.4f)\n", alpha[j].re, alpha[j].im, beta[j].re, beta[j].im); } else { z = nag_complex_divide(alpha[j], beta[j]); printf("%2ld (%13.4e, %13.4e)", j+1, z.re, z.im); if (sense==Nag_RCondEigVals || sense==Nag_RCondBoth) { printf(" %10.1e", rconde[j]); if (rconde[j] > 0.0) printf(" %9.1e", tol/rconde[j]); else printf(" infinite"); } printf("\n"); } } /* Print out information on the eigenvectors as requested */ if (jobvl==Nag_LeftVecs) { printf("\n"); /* Print left eigenvectors using nag_gen_complx_mat_print (x04dac). */ fflush(stdout); nag_gen_complx_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, vl, pdvl, " Left eigenvectors (columns)", 0, &fail); } if ( jobvr==Nag_RightVecs && fail.code == NE_NOERROR) { printf("\n"); /* Print rightt eigenvectors using nag_gen_complx_mat_print (x04dac). */ fflush(stdout); nag_gen_complx_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, vr, pdvr, " Right eigenvectors (columns)", 0, &fail); } if (fail.code != NE_NOERROR) { printf("Error from nag_gen_complx_mat_print (x04dac).\n%s\n", fail.message); exit_status = 1; goto END; } if (sense==Nag_RCondEigVecs || sense==Nag_RCondBoth) { printf("%2s","R"); for (j = 0; j < n; ++j) printf(" %8.1e", rcondv[j]); printf("\n%2s","E"); for (j = 0; j < n; ++j) { if (rcondv[j] > 0.0) printf(" %8.1e", tol/rcondv[j]); else printf(" infinite"); } printf("\n"); } END: NAG_FREE(a); NAG_FREE(b); NAG_FREE(alpha); NAG_FREE(beta); NAG_FREE(vl); NAG_FREE(vr); NAG_FREE(lscale); NAG_FREE(rconde); NAG_FREE(rcondv); NAG_FREE(rscale); return exit_status; }