/* nag_dsygst (f08sec) Example Program. * * Copyright 2001 Numerical Algorithms Group. * * Mark 7, 2001. */ #include #include #include #include #include int main(void) { /* Scalars */ Integer i, j, n, pda, pdb, 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, *b=0, *d=0, *e=0, *tau=0; #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); Vprintf("nag_dsygst (f08sec) Example Program Results\n\n"); /* Skip heading in data file */ Vscanf("%*[^\n] "); Vscanf("%ld%*[^\n] ", &n); #ifdef NAG_COLUMN_MAJOR pda = n; pdb = n; #else pda = n; pdb = n; #endif d_len = n; e_len = n-1; tau_len = n-1; /* Allocate memory */ if ( !(a = NAG_ALLOC(n * n, double)) || !(b = NAG_ALLOC(n * n, double)) || !(d = NAG_ALLOC(d_len, double)) || !(e = NAG_ALLOC(e_len, double)) || !(tau = NAG_ALLOC(tau_len, double)) ) { Vprintf("Allocation failure\n"); exit_status = -1; goto END; } /* Read A and B 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] "); for (i = 1; i <= n; ++i) { for (j = i; j <= n; ++j) Vscanf("%lf", &B(i,j)); } Vscanf("%*[^\n] "); } else { for (i = 1; i <= n; ++i) { for (j = 1; j <= i; ++j) Vscanf("%lf", &A(i,j)); } Vscanf("%*[^\n] "); for (i = 1; i <= n; ++i) { for (j = 1; j <= i; ++j) Vscanf("%lf", &B(i,j)); } Vscanf("%*[^\n] "); } /* Compute the Cholesky factorization of B */ /* nag_dpotrf (f07fdc). * Cholesky factorization of real symmetric * positive-definite matrix */ nag_dpotrf(order, uplo, n, b, pdb, &fail); if (fail.code != NE_NOERROR) { Vprintf("Error from nag_dpotrf (f07fdc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Reduce the problem to standard form C*y = lambda*y, storing */ /* the result in A */ /* nag_dsygst (f08sec). * Reduction to standard form of real symmetric-definite * generalized eigenproblem Ax~=~lambda~Bx, ABx~=~lambda~x * or BAx~=~lambda~x, B factorized by nag_dpotrf (f07fdc) */ nag_dsygst(order, Nag_Compute_1, uplo, n, a, pda, b, pdb, &fail); if (fail.code != NE_NOERROR) { Vprintf("Error from nag_dsygst (f08sec).\n%s\n", fail.message); exit_status = 1; goto END; } /* Reduce C to tridiagonal form T = (Q**T)*C*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; goto END; } /* Calculate the eigenvalues of T (same as C) */ /* nag_dsterf (f08jfc). * All eigenvalues of real symmetric tridiagonal matrix, * root-free variant of QL or QR */ nag_dsterf(n, d, e, &fail); if (fail.code != NE_NOERROR) { Vprintf("Error from nag_dsterf (f08jfc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Print eigenvalues */ Vprintf("Eigenvalues\n"); for (i = 1; i <= n; ++i) Vprintf("%8.4f%s", d[i-1], i%9==0 ?"\n":" "); Vprintf("\n"); END: if (a) NAG_FREE(a); if (b) NAG_FREE(b); if (d) NAG_FREE(d); if (e) NAG_FREE(e); if (tau) NAG_FREE(tau); return exit_status; }