/* nag_zhpgst (f08tsc) Example Program. * * Copyright 2001 Numerical Algorithms Group. * * Mark 7, 2001. */ #include #include #include #include #include int main(void) { /* Scalars */ Integer i, j, n, ap_len, bp_len, d_len, e_len, tau_len; Integer exit_status=0; NagError fail; Nag_UploType uplo; Nag_OrderType order; /* Arrays */ char uplo_char[2]; Complex *ap=0, *bp=0, *tau=0; double *d=0, *e=0; #ifdef NAG_COLUMN_MAJOR #define A_UPPER(I,J) ap[J*(J-1)/2 + I - 1] #define A_LOWER(I,J) ap[(2*n-J)*(J-1)/2 + I - 1] #define B_UPPER(I,J) bp[J*(J-1)/2 + I - 1] #define B_LOWER(I,J) bp[(2*n-J)*(J-1)/2 + I - 1] order = Nag_ColMajor; #else #define A_LOWER(I,J) ap[I*(I-1)/2 + J - 1] #define A_UPPER(I,J) ap[(2*n-I)*(I-1)/2 + J - 1] #define B_LOWER(I,J) bp[I*(I-1)/2 + J - 1] #define B_UPPER(I,J) bp[(2*n-I)*(I-1)/2 + J - 1] order = Nag_RowMajor; #endif INIT_FAIL(fail); Vprintf("nag_zhpgst (f08tsc) Example Program Results\n\n"); /* Skip heading in data file */ Vscanf("%*[^\n] "); Vscanf("%ld%*[^\n] ", &n); ap_len = n * (n +1 )/2; bp_len = n * (n +1 )/2; d_len = n; e_len = n-1; tau_len = n; /* Allocate memory */ if ( !(ap = NAG_ALLOC(ap_len, Complex)) || !(bp = NAG_ALLOC(bp_len, Complex)) || !(d = NAG_ALLOC(d_len, double)) || !(e = NAG_ALLOC(e_len, double)) || !(tau = NAG_ALLOC(tau_len, Complex)) ) { 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 , %lf )", &A_UPPER(i,j).re, &A_UPPER(i,j).im); } } Vscanf("%*[^\n] "); for (i = 1; i <= n; ++i) { for (j = i; j <= n; ++j) { Vscanf(" ( %lf , %lf )", &B_UPPER(i,j).re, &B_UPPER(i,j).im); } } Vscanf("%*[^\n] "); } else { for (i = 1; i <= n; ++i) { for (j = 1; j <= i; ++j) { Vscanf(" ( %lf , %lf )", &A_LOWER(i,j).re, &A_LOWER(i,j).im); } } Vscanf("%*[^\n] "); for (i = 1; i <= n; ++i) { for (j = 1; j <= i; ++j) { Vscanf(" ( %lf , %lf )", &B_LOWER(i,j).re, &B_LOWER(i,j).im); } } Vscanf("%*[^\n] "); } /* Compute the Cholesky factorization of B */ /* nag_zpptrf (f07grc). * Cholesky factorization of complex Hermitian * positive-definite matrix, packed storage */ nag_zpptrf(order, uplo, n, bp, &fail); if (fail.code != NE_NOERROR) { Vprintf("Error from nag_dpptrf (f07gdc).\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_zhpgst (f08tsc). * Reduction to standard form of complex Hermitian-definite * generalized eigenproblem Ax~=~lambda~Bx, ABx~=~lambda~x * or BAx~=~lambda~x, packed storage, B factorized by * nag_zpptrf (f07grc) */ nag_zhpgst(order, Nag_Compute_1, uplo, n, ap, bp, &fail); if (fail.code != NE_NOERROR) { Vprintf("Error from nag_zhpgst (f08tsc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Reduce C to tridiagonal form T = (Q**T)*C*Q */ /* nag_zhptrd (f08gsc). * Unitary reduction of complex Hermitian matrix to real * symmetric tridiagonal form, packed storage */ nag_zhptrd(order, uplo, n, ap, d, e, tau, &fail); if (fail.code != NE_NOERROR) { Vprintf("Error from nag_zhptrd (f08gsc).\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 || i==n ?"\n":" "); Vprintf("\n"); END: if (ap) NAG_FREE(ap); if (bp) NAG_FREE(bp); if (d) NAG_FREE(d); if (e) NAG_FREE(e); if (tau) NAG_FREE(tau); return exit_status; }