/* nag_dggevx (f08wbc) Example Program. * * Copyright 2011 Numerical Algorithms Group. * * Mark 23, 2011. */ #include #include #include #include #include #include #include int main(void) { /* Scalars */ Complex eig, eigl, eigr; double abnorm, abnrm, bbnrm, eps, sign, small, tol; Integer i, ihi, ilo, j, k, n, pda, pdb, pdvl, pdvr; Integer exit_status = 0; /* Arrays */ double *a = 0, *alphai = 0, *alphar = 0, *b = 0, *beta = 0; double *lscale = 0, *rconde = 0, *rcondv = 0, *rscale = 0; double *vl = 0, *vr = 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] #define VL(I, J) vl[(J-1)*pdvl + 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 B(I, J) b[(I-1)*pdb + J - 1] #define VL(I, J) vl[(I-1)*pdvl + J - 1] #define VR(I, J) vr[(I-1)*pdvr + J - 1] order = Nag_RowMajor; #endif INIT_FAIL(fail); printf("nag_dggevx (f08wbc) 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(" %s%*[^\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(" %s%*[^\n]", nag_enum_arg); jobvr = (Nag_RightVecsType) nag_enum_name_to_value(nag_enum_arg); scanf(" %s%*[^\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, double)) || !(alphai = NAG_ALLOC(n, double)) || !(alphar = NAG_ALLOC(n, double)) || !(b = NAG_ALLOC(n*n, double)) || !(beta = NAG_ALLOC(n, double)) || !(lscale = NAG_ALLOC(n, double)) || !(rconde = NAG_ALLOC(n, double)) || !(rcondv = NAG_ALLOC(n, double)) || !(rscale = NAG_ALLOC(n, double)) || !(vl = NAG_ALLOC(pdvl*pdvl, double)) || !(vr = NAG_ALLOC(pdvr*pdvr, 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", &A(i, j)); scanf("%*[^\n]"); for (i = 1; i <= n; ++i) for (j = 1; j <= n; ++j) scanf("%lf", &B(i, j)); scanf("%*[^\n]"); /* Solve the generalized eigenvalue problem using nag_dggevx (f08wbc). */ nag_dggevx(order, Nag_BalanceBoth, jobvl, jobvr, sense, n, a, pda, b, pdb, alphar, alphai, beta, vl, pdvl, vr, pdvr, &ilo, &ihi, lscale, rscale, &abnrm, &bbnrm, rconde, rcondv, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dggevx (f08wbc).\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 vectors and associated condition * number and bounds. */ for (j = 0; j < n; ++j) { /* Print out information on the jth eigenvalue */ printf("\n"); if ((fabs(alphar[j]) + fabs(alphai[j])) * small >= fabs(beta[j])) { printf("Eigenvalue %2ld is numerically infinite or " "undetermined\n", j+1); printf("alpha = (%13.4e, %13.4e), beta = %13.4e\n", alphar[j], alphai[j], beta[j]); } else if (alphai[j] == 0.0) { printf("Eigenvalue %2ld = %13.4e\n", j+1, alphar[j]/beta[j]); } else { eig.re = alphar[j]/beta[j], eig.im = alphai[j]/beta[j]; printf("Eigenvalue %2ld = (%11.4e, %11.4e)\n", j+1, eig.re, eig.im); } if (sense==Nag_RCondEigVals || sense==Nag_RCondBoth) { printf("\n Reciprocal condition number = %10.1e\n", rconde[j]); if ( rconde[j] > 0.0) printf(" Error bound = %10.1e\n", tol/rconde[j]); else printf(" Error bound is infinite\n"); } printf("\n\n"); /* Normalize and print out information on the jth eigenvector(s) */ if (jobvl==Nag_LeftVecs) printf("%21s%8s", "Left Eigenvector", ""); if (jobvr==Nag_RightVecs) printf("%21s", "Right Eigenvector"); printf(" %2ld\n", j+1); if (alphai[j] == 0.0) for (i = 1; i <= n; ++i) { if (jobvl==Nag_LeftVecs) printf("%7s%11.4e%12s", "", VL(i, j+1)/VL(n, j+1), ""); if (jobvr==Nag_RightVecs) printf("%7s%11.4e", "", VR(i, j+1)/VR(n, j+1)); printf("\n"); } else { k = (alphai[j]>0.0?j+1:j); sign = (alphai[j]>0.0?1.0:-1.0); if (jobvl==Nag_LeftVecs) eigl = nag_complex(VL(n,k), VL(n,k+1)); if (jobvr==Nag_RightVecs) eigr = nag_complex(VR(n,k), VR(n,k+1)); for (i = 1; i <= n; ++i) { if (jobvl==Nag_LeftVecs) { eig = nag_complex_divide(nag_complex(VL(i,k), VL(i,k+1)), eigl); printf(" (%11.4e,%11.4e) ", eig.re, sign*eig.im); } if (jobvr==Nag_RightVecs) { eig = nag_complex_divide(nag_complex(VR(i,k), VR(i,k+1)), eigr); printf(" (%11.4e,%11.4e)", eig.re, sign*eig.im); } printf("\n"); } } if (sense==Nag_RCondEigVecs || sense==Nag_RCondBoth) { printf("\n Reciprocal condition number = %10.1e\n", rcondv[j]); if (rcondv[j] > 0.0) printf(" Error bound = %10.1e\n\n", tol/rcondv[j]); else printf(" Error bound is infinite\n\n"); } } 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 (rconde) NAG_FREE(rconde); if (rcondv) NAG_FREE(rcondv); if (rscale) NAG_FREE(rscale); if (vl) NAG_FREE(vl); if (vr) NAG_FREE(vr); return exit_status; }