/* nag_dorgtr (f08ffc) Example Program. * * Copyright 2001 Numerical Algorithms Group. * * Mark 7, 2001. */ #include #include #include #include #include int main(void) { /* Scalars */ Integer i, j, n, pda, pdz, d_len, e_len, tau_len; Integer exit_status=0; NagError fail; Nag_UploType uplo; Nag_OrderType order; /* Arrays */ char uplo_char[2]; double *a=0, *d=0, *e=0, *tau=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_dorgtr (f08ffc) 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; d_len = n; e_len = n-1; /* Allocate memory */ if ( !(a = NAG_ALLOC(n * n, double)) || !(d = NAG_ALLOC(d_len, double)) || !(e = NAG_ALLOC(e_len, double)) || !(tau = NAG_ALLOC(tau_len, double)) || !(z = NAG_ALLOC(n * n, double)) ) { Vprintf("Allocation failure\n"); exit_status = -1; goto END; } /* Read A from data file */ Vscanf(" ' %1s '%*[^\n] ", uplo_char); if (*(unsigned char *)uplo_char == 'L') uplo = Nag_Lower; else if (*(unsigned char *)uplo_char == 'U') uplo = Nag_Upper; else { Vprintf("Unrecognised character for Nag_UploType type\n"); exit_status = -1; goto END; } if (uplo == Nag_Upper) { for (i = 1; i <= n; ++i) { for (j = i; j <= n; ++j) Vscanf("%lf", &A(i,j)); } Vscanf("%*[^\n] "); } else { for (i = 1; i <= n; ++i) { for (j = 1; j <= i; ++j) Vscanf("%lf", &A(i,j)); } Vscanf("%*[^\n] "); } /* Reduce A to tridiagonal form T = (Q**T)*A*Q */ /* nag_dsytrd (f08fec). * Orthogonal reduction of real symmetric matrix to * symmetric tridiagonal form */ nag_dsytrd(order, uplo, n, a, pda, d, e, tau, &fail); if (fail.code != NE_NOERROR) { Vprintf("Error from nag_dsytrd (f08fec).\n%s\n", fail.message); exit_status = 1; } /* Copy A into Z */ if (uplo == Nag_Upper) { for (i = 1; i <= n; ++i) { for (j = i; j <= n; ++j) Z(i,j) = A(i,j); } } else { for (i = 1; i <= n; ++i) { for (j = 1; j <= i; ++j) Z(i,j) = A(i,j); } } /* Form Q explicitly, storing the result in Z */ /* nag_dorgtr (f08ffc). * Generate orthogonal transformation matrix from reduction * to tridiagonal form determined by nag_dsytrd (f08fec) */ nag_dorgtr(order, uplo, n, z, pdz, tau, &fail); if (fail.code != NE_NOERROR) { Vprintf("Error from nag_dorgtr (f08ffc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Calculate all the eigenvalues and eigenvectors of A */ /* nag_dsteqr (f08jec). * All eigenvalues and eigenvectors of real symmetric * tridiagonal matrix, reduced from real symmetric matrix * using implicit QL or QR */ nag_dsteqr(order, Nag_UpdateZ, n, d, e, z, pdz, &fail); if (fail.code != NE_NOERROR) { Vprintf("Error from nag_dsteqr (f08jec).\n%s\n", fail.message); exit_status = 1; goto END; } /* Print eigenvalues and eigenvectors */ Vprintf("Eigenvalues\n"); for (i = 1; i <= n; ++i) Vprintf("%8.4f%s", d[i-1], i%8==0 ?"\n":" "); Vprintf("\n\n"); /* 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, z, pdz, "Eigenvectors", 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 (d) NAG_FREE(d); if (e) NAG_FREE(e); if (tau) NAG_FREE(tau); if (z) NAG_FREE(z); return exit_status; }