.TH DSYGST 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) "
.SH NAME
DSYGST - a real symmetric-definite generalized eigenproblem to standard form
.SH SYNOPSIS
.TP 19
SUBROUTINE DSYGST(
ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
.TP 19
.ti +4
CHARACTER
UPLO
.TP 19
.ti +4
INTEGER
INFO, ITYPE, LDA, LDB, N
.TP 19
.ti +4
DOUBLE
PRECISION A( LDA, * ), B( LDB, * )
.SH PURPOSE
DSYGST reduces a real symmetric-definite generalized eigenproblem
to standard form.
If ITYPE = 1, the problem is A*x = lambda*B*x,
.br
and A is overwritten by inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T)
If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or
.br
B*A*x = lambda*x, and A is overwritten by U*A*U**T or L**T*A*L.
B must have been previously factorized as U**T*U or L*L**T by DPOTRF.
.SH ARGUMENTS
.TP 8
ITYPE (input) INTEGER
= 1: compute inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T);
.br
= 2 or 3: compute U*A*U**T or L**T*A*L.
.TP 8
UPLO (input) CHARACTER*1
.br
= \(aqU\(aq: Upper triangle of A is stored and B is factored as
U**T*U;
= \(aqL\(aq: Lower triangle of A is stored and B is factored as
L*L**T.
.TP 8
N (input) INTEGER
The order of the matrices A and B. N >= 0.
.TP 8
A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
On entry, the symmetric matrix A. If UPLO = \(aqU\(aq, the leading
N-by-N upper triangular part of A contains the upper
triangular part of the matrix A, and the strictly lower
triangular part of A is not referenced. If UPLO = \(aqL\(aq, the
leading N-by-N lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.
On exit, if INFO = 0, the transformed matrix, stored in the
same format as A.
.TP 8
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
.TP 8
B (input) DOUBLE PRECISION array, dimension (LDB,N)
The triangular factor from the Cholesky factorization of B,
as returned by DPOTRF.
.TP 8
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
.TP 8
INFO (output) INTEGER
= 0: successful exit
.br
< 0: if INFO = -i, the i-th argument had an illegal value