SSYGST(3)                  MathKeisan LAPACK routine                 SSYGST(3)



NAME
       SSYGST - a real symmetric-definite generalized eigenproblem to standard
       form

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

           CHARACTER      UPLO

           INTEGER        INFO, ITYPE, LDA, LDB, N

           REAL           A( LDA, * ), B( LDB, * )

PURPOSE
       SSYGST 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 SPOTRF.


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*1
               =  '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) REAL 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) REAL array, dimension (LDB,N)
               The triangular factor from the Cholesky factorization of B,  as
               returned by SPOTRF.

       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 routine (version 3.1)    November 2006                       SSYGST(3)