NAME

DSYGST - reduce a real symmetric-definite generalized eigenproblem to standard form

SYNOPSIS

SUBROUTINE DSYGST(
ITYPE, UPLO, N, A, LDA, B, LDB, INFO )

CHARACTER UPLO

INTEGER INFO, ITYPE, LDA, LDB, N

DOUBLE PRECISION A( LDA, ∗ ), B( LDB, ∗ )

PURPOSE

DSYGST reduces a real symmetric-definite generalized eigenproblem to standard form. 
 
If ITYPE = 1, the problem is A∗x = lambda∗B∗x,
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
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.
 

ARGUMENTS

ITYPE   (input) INTEGER
= 1: compute inv(U∗∗T)∗A∗inv(U) or inv(L)∗A∗inv(L∗∗T);
= 2 or 3: compute U∗A∗U∗∗T or L∗∗T∗A∗L.

UPLO    (input) CHARACTER
= ’U’:  Upper triangle of A is stored and B is factored as U∗∗T∗U; = ’L’:  Lower triangle of A is stored and B is factored as L∗L∗∗T.

N       (input) INTEGER
The order of the matrices A and B.  N >= 0.

A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
On entry, the symmetric matrix A.  If UPLO = ’U’, 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 = ’L’, 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.

LDA     (input) INTEGER
The leading dimension of the array A.  LDA >= max(1,N).

B       (input) DOUBLE PRECISION array, dimension (LDB,N)
The triangular factor from the Cholesky factorization of B, as returned by DPOTRF.

LDB     (input) INTEGER
The leading dimension of the array B.  LDB >= max(1,N).

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value

  —  LAPACK version 2.0  —  08 October 1994