dsygs2(3S)

NAME
     DSYGS2 - reduce a real symmetric-definite generalized eigenproblem 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, * )

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

PURPOSE
     DSYGS2 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')*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 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.

SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

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