/* nag_dorghr (f08nfc) Example Program. * * Copyright 2001 Numerical Algorithms Group. * * Mark 7, 2001. * Mark 7b revised, 2004. */ #include #include #include #include #include int main(void) { /* Scalars */ Integer i, j, n, pda, pdz, tau_len, wi_len; Integer exit_status=0; NagError fail; Nag_OrderType order; /* Arrays */ double *a=0, *tau=0, *wi=0, *wr=0, *z=0; #ifdef NAG_COLUMN_MAJOR #define A(I,J) a[(J-1)*pda + 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 Z(I,J) z[(I-1)*pdz + J - 1] order = Nag_RowMajor; #endif INIT_FAIL(fail); Vprintf("nag_dorghr (f08nfc) Example Program Results\n\n"); /* Skip heading in data file */ Vscanf("%*[^\n] "); Vscanf("%ld%*[^\n] ", &n); #ifdef NAG_COLUMN_MAJOR pda = n; pdz = n; #else pda = n; pdz = n; #endif tau_len = n - 1; wi_len = n; /* Allocate memory */ if ( !(a = NAG_ALLOC(n * n, double)) || !(tau = NAG_ALLOC(tau_len, double)) || !(wi = NAG_ALLOC(wi_len, double)) || !(wr = NAG_ALLOC(wi_len, double)) || !(z = NAG_ALLOC(n * n, double)) ) { Vprintf("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) Vscanf("%lf", &A(i,j)); } Vscanf("%*[^\n] "); /* Reduce A to upper Hessenberg form H = (Q**T)*A*Q */ /* 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) { Vprintf("Error from nag_dgehrd (f08nec).\n%s\n", fail.message); exit_status = 1; goto END; } /* Copy A into Z */ for (i = 1; i <= n; ++i) { for (j = 1; j <= n; ++j) Z(i,j) = A(i,j); } /* Form Q explicitly, storing the result in Z */ /* nag_dorghr (f08nfc). * Generate orthogonal transformation matrix from reduction * to Hessenberg form determined by nag_dgehrd (f08nec) */ nag_dorghr(order, n, 1, n, z, pdz, tau, &fail); if (fail.code != NE_NOERROR) { Vprintf("Error from nag_dorghr (f08nfc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Calculate the Schur factorization of H = Y*T*(Y**T) and form */ /* Q*Y explicitly, storing the result in Z */ /* Note that A = Z*T*(Z**T), where Z = Q*Y */ /* nag_dhseqr (f08pec). * Eigenvalues and Schur factorization of real upper * Hessenberg matrix reduced from real general matrix */ nag_dhseqr(order, Nag_Schur, Nag_UpdateZ, n, 1, n, a, pda, wr, wi, z, pdz, &fail); if (fail.code != NE_NOERROR) { Vprintf("Error from nag_dhseqr (f08pec).\n%s\n", fail.message); exit_status = 1; goto END; } /* Print Schur form */ /* nag_gen_real_mat_print (x04cac). * Print real general matrix (easy-to-use) */ nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, a, pda, "Schur form", 0, &fail); if (fail.code != NE_NOERROR) { Vprintf("Error from nag_gen_real_mat_print (x04cac).\n%s\n", fail.message); exit_status = 1; goto END; } /* Print Schur vectors */ Vprintf("\n"); /* nag_gen_real_mat_print (x04cac), see above. */ nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, z, pdz, "Schur vectors of A", 0, &fail); if (fail.code != NE_NOERROR) { Vprintf("Error from nag_gen_real_mat_print (x04cac).\n%s\n", fail.message); exit_status = 1; goto END; } END: if (a) NAG_FREE(a); if (tau) NAG_FREE(tau); if (wi) NAG_FREE(wi); if (wr) NAG_FREE(wr); if (z) NAG_FREE(z); return exit_status; }