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NAME
     dsygs2 - reduce a real symmetric-definite generalized eigen-
     problem to standard form

SYNOPSIS
     SUBROUTINE DSYGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )

     CHARACTER UPLO

     INTEGER INFO, ITYPE, LDA, LDB, N

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



     #include <sunperf.h>

     void dsygs2(int itype, char uplo, int  n,  double  *da,  int
               lda, double *db, int ldb, int *info) ;

PURPOSE
     DSYGS2 reduces a real symmetric-definite generalized  eigen-
     problem to standard form.

     If ITYPE = 1, the problem is A*x = lambda*B*x,
     and A is overwritten by inv(U')*A*inv(U) or inv(L)*A*inv(L')

     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` or L'*A*L.

     B must have been previously factorized as U'*U  or  L*L'  by
     DPOTRF.


ARGUMENTS
     ITYPE     (input) INTEGER
               = 1: compute inv(U')*A*inv(U) or inv(L)*A*inv(L');
               = 2 or 3: compute U*A*U' or L'*A*L.

     UPLO      (input) CHARACTER
               Specifies whether the upper  or  lower  triangular
               part  of the symmetric matrix A is stored, and how
               B has been factorized.  = 'U':  Upper triangular
               = 'L':  Lower triangular

     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 tri-
               angular 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 factoriza-
               tion 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 ille-
               gal value.

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