/* nag_dormhr (f08ngc) Example Program. * * Copyright 2001 Numerical Algorithms Group. * * Mark 7, 2001. * Mark 7b revised, 2004. */ #include #include #include #include #include #include int main(void) { /* Scalars */ Integer i, j, k, m, n, pda, pdh, pdvl, pdvr, pdz; Integer tau_len, ifaill_len, select_len, w_len; Integer exit_status = 0; double thresh; Complex eig, eig1; /* Arrays */ double *a = 0, *h = 0, *vl = 0, *vr = 0, *z = 0, *wi = 0, *wr = 0; double *tau = 0; Integer *ifaill = 0, *ifailr = 0; /* Nag Types */ NagError fail; Nag_OrderType order; Nag_Boolean *select = 0; #ifdef NAG_COLUMN_MAJOR #define A(I, J) a[(J - 1) * pda + I - 1] #define H(I, J) h[(J - 1) * pdh + 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 H(I, J) h[(I - 1) * pdh + J - 1] #define VR(I, J) vr[(I - 1) * pdvr + J - 1] order = Nag_RowMajor; #endif INIT_FAIL(fail); printf("nag_dormhr (f08ngc) Example Program Results\n\n"); /* Skip heading in data file */ scanf("%*[^\n] "); scanf("%ld%*[^\n] ", &n); pda = n; pdh = n; pdvl = n; pdvr = n; pdz = 1; tau_len = n; w_len = n; ifaill_len = n; select_len = n; /* Allocate memory */ if (!(a = NAG_ALLOC(n * n, double)) || !(h = NAG_ALLOC(n * n, double)) || !(vl = NAG_ALLOC(n * n, double)) || !(vr = NAG_ALLOC(n * n, double)) || !(z = NAG_ALLOC(1 * 1, double)) || !(wi = NAG_ALLOC(w_len, double)) || !(wr = NAG_ALLOC(w_len, double)) || !(ifaill = NAG_ALLOC(ifaill_len, Integer)) || !(ifailr = NAG_ALLOC(ifaill_len, Integer)) || !(select = NAG_ALLOC(select_len, Nag_Boolean)) || !(tau = NAG_ALLOC(tau_len, double))) { printf("Allocation failure\n"); exit_status = -1; goto END; } /* Read A from data file */ for (i = 1; i <= n; ++i) for (j = 1; j <= n; ++j) scanf("%lf", &A(i, j)); scanf("%*[^\n]"); scanf("%lf%*[^\n]", &thresh); /* Reduce A to upper Hessenberg form */ /* nag_dgehrd (f08nec). * Orthogonal reduction of real general matrix to upper * Hessenberg form */ nag_dgehrd(order, n, 1, n, a, pda, tau, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dgehrd (f08nec).\n%s\n", fail.message); exit_status = 1; goto END; } /* Copy A to H */ for (i = 1; i <= n; ++i) for (j = 1; j <= n; ++j) H(i, j) = A(i, j); /* Calculate the eigenvalues of H (same as A) */ /* nag_dhseqr (f08pec). * Eigenvalues and Schur factorization of real upper * Hessenberg matrix reduced from real general matrix */ nag_dhseqr(order, Nag_EigVals, Nag_NotZ, n, 1, n, h, pdh, wr, wi, z, pdz, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dhseqr (f08pec).\n%s\n", fail.message); exit_status = 1; goto END; } /* Print eigenvalues */ printf(" Eigenvalues\n"); for (i = 0; i < n; ++i) printf(" (%8.4f,%8.4f)\n", wr[i], wi[i]); printf("\n"); for (i = 0; i < n; ++i) select[i] = wr[i] < thresh?Nag_TRUE:Nag_FALSE; /* Calculate the eigenvectors of H (as specified by SELECT), */ /* storing the result in VR */ /* nag_dhsein (f08pkc). * Selected right and/or left eigenvectors of real upper * Hessenberg matrix by inverse iteration */ nag_dhsein(order, Nag_RightSide, Nag_HSEQRSource, Nag_NoVec, select, n, a, pda, wr, wi, vl, pdvl, vr, pdvr, n, &m, ifaill, ifailr, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dhsein (f08pkc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Calculate the eigenvectors of A = Q * VR */ /* nag_dormhr (f08ngc). * Apply orthogonal transformation matrix from reduction to * Hessenberg form determined by nag_dgehrd (f08nec) */ nag_dormhr(order, Nag_LeftSide, Nag_NoTrans, n, m, 1, n, a, pda, tau, vr, pdvr, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dormhr (f08ngc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Scale selected eigenvectors */ j = 0; for(k=0; k