          SUBROUTINE DSYGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
    *
    *  -- LAPACK routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          UPLO
          INTEGER            INFO, ITYPE, LDA, LDB, N
    *     ..
    *     .. Array Arguments ..
          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*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) 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
    *
    *  =====================================================================
    *
    *     .. Parameters ..
          DOUBLE PRECISION   ONE, HALF
          PARAMETER          ( ONE = 1.0D0, HALF = 0.5D0 )
    *     ..
    *     .. Local Scalars ..
          LOGICAL            UPPER
          INTEGER            K, KB, NB
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           DSYGS2, DSYMM, DSYR2K, DTRMM, DTRSM, XERBLA
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          MAX, MIN
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          INTEGER            ILAENV
          EXTERNAL           LSAME, ILAENV
    *     ..
    *     .. Executable Statements ..
    *
    *     Test the input parameters.
    *
          INFO = 0
          UPPER = LSAME( UPLO, 'U' )
          IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
             INFO = -1
          ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
             INFO = -2
          ELSE IF( N.LT.0 ) THEN
             INFO = -3
          ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
             INFO = -5
          ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
             INFO = -7
          END IF
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'DSYGST', -INFO )
             RETURN
          END IF
    *
    *     Quick return if possible
    *
          IF( N.EQ.0 )
         $   RETURN
    *
    *     Determine the block size for this environment.
    *
          NB = ILAENV( 1, 'DSYGST', UPLO, N, -1, -1, -1 )
    *
          IF( NB.LE.1 .OR. NB.GE.N ) THEN
    *
    *        Use unblocked code
    *
             CALL DSYGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
          ELSE
    *
    *        Use blocked code
    *
             IF( ITYPE.EQ.1 ) THEN
                IF( UPPER ) THEN
    *
    *              Compute inv(U')*A*inv(U)
    *
                   DO 10 K = 1, N, NB
                      KB = MIN( N-K+1, NB )
    *
    *                 Update the upper triangle of A(k:n,k:n)
    *
                      CALL DSYGS2( ITYPE, UPLO, KB, A( K, K ), LDA,
         $                         B( K, K ), LDB, INFO )
                      IF( K+KB.LE.N ) THEN
                         CALL DTRSM( 'Left', UPLO, 'Transpose', 'Non-unit',
         $                           KB, N-K-KB+1, ONE, B( K, K ), LDB,
         $                           A( K, K+KB ), LDA )
                         CALL DSYMM( 'Left', UPLO, KB, N-K-KB+1, -HALF,
         $                           A( K, K ), LDA, B( K, K+KB ), LDB, ONE,
         $                           A( K, K+KB ), LDA )
                         CALL DSYR2K( UPLO, 'Transpose', N-K-KB+1, KB, -ONE,
         $                            A( K, K+KB ), LDA, B( K, K+KB ), LDB,
         $                            ONE, A( K+KB, K+KB ), LDA )
                         CALL DSYMM( 'Left', UPLO, KB, N-K-KB+1, -HALF,
         $                           A( K, K ), LDA, B( K, K+KB ), LDB, ONE,
         $                           A( K, K+KB ), LDA )
                         CALL DTRSM( 'Right', UPLO, 'No transpose',
         $                           'Non-unit', KB, N-K-KB+1, ONE,
         $                           B( K+KB, K+KB ), LDB, A( K, K+KB ),
         $                           LDA )
                      END IF
       10          CONTINUE
                ELSE
    *
    *              Compute inv(L)*A*inv(L')
    *
                   DO 20 K = 1, N, NB
                      KB = MIN( N-K+1, NB )
    *
    *                 Update the lower triangle of A(k:n,k:n)
    *
                      CALL DSYGS2( ITYPE, UPLO, KB, A( K, K ), LDA,
         $                         B( K, K ), LDB, INFO )
                      IF( K+KB.LE.N ) THEN
                         CALL DTRSM( 'Right', UPLO, 'Transpose', 'Non-unit',
         $                           N-K-KB+1, KB, ONE, B( K, K ), LDB,
         $                           A( K+KB, K ), LDA )
                         CALL DSYMM( 'Right', UPLO, N-K-KB+1, KB, -HALF,
         $                           A( K, K ), LDA, B( K+KB, K ), LDB, ONE,
         $                           A( K+KB, K ), LDA )
                         CALL DSYR2K( UPLO, 'No transpose', N-K-KB+1, KB,
         $                            -ONE, A( K+KB, K ), LDA, B( K+KB, K ),
         $                            LDB, ONE, A( K+KB, K+KB ), LDA )
                         CALL DSYMM( 'Right', UPLO, N-K-KB+1, KB, -HALF,
         $                           A( K, K ), LDA, B( K+KB, K ), LDB, ONE,
         $                           A( K+KB, K ), LDA )
                         CALL DTRSM( 'Left', UPLO, 'No transpose',
         $                           'Non-unit', N-K-KB+1, KB, ONE,
         $                           B( K+KB, K+KB ), LDB, A( K+KB, K ),
         $                           LDA )
                      END IF
       20          CONTINUE
                END IF
             ELSE
                IF( UPPER ) THEN
    *
    *              Compute U*A*U'
    *
                   DO 30 K = 1, N, NB
                      KB = MIN( N-K+1, NB )
    *
    *                 Update the upper triangle of A(1:k+kb-1,1:k+kb-1)
    *
                      CALL DTRMM( 'Left', UPLO, 'No transpose', 'Non-unit',
         $                        K-1, KB, ONE, B, LDB, A( 1, K ), LDA )
                      CALL DSYMM( 'Right', UPLO, K-1, KB, HALF, A( K, K ),
         $                        LDA, B( 1, K ), LDB, ONE, A( 1, K ), LDA )
                      CALL DSYR2K( UPLO, 'No transpose', K-1, KB, ONE,
         $                         A( 1, K ), LDA, B( 1, K ), LDB, ONE, A,
         $                         LDA )
                      CALL DSYMM( 'Right', UPLO, K-1, KB, HALF, A( K, K ),
         $                        LDA, B( 1, K ), LDB, ONE, A( 1, K ), LDA )
                      CALL DTRMM( 'Right', UPLO, 'Transpose', 'Non-unit',
         $                        K-1, KB, ONE, B( K, K ), LDB, A( 1, K ),
         $                        LDA )
                      CALL DSYGS2( ITYPE, UPLO, KB, A( K, K ), LDA,
         $                         B( K, K ), LDB, INFO )
       30          CONTINUE
                ELSE
    *
    *              Compute L'*A*L
    *
                   DO 40 K = 1, N, NB
                      KB = MIN( N-K+1, NB )
    *
    *                 Update the lower triangle of A(1:k+kb-1,1:k+kb-1)
    *
                      CALL DTRMM( 'Right', UPLO, 'No transpose', 'Non-unit',
         $                        KB, K-1, ONE, B, LDB, A( K, 1 ), LDA )
                      CALL DSYMM( 'Left', UPLO, KB, K-1, HALF, A( K, K ),
         $                        LDA, B( K, 1 ), LDB, ONE, A( K, 1 ), LDA )
                      CALL DSYR2K( UPLO, 'Transpose', K-1, KB, ONE,
         $                         A( K, 1 ), LDA, B( K, 1 ), LDB, ONE, A,
         $                         LDA )
                      CALL DSYMM( 'Left', UPLO, KB, K-1, HALF, A( K, K ),
         $                        LDA, B( K, 1 ), LDB, ONE, A( K, 1 ), LDA )
                      CALL DTRMM( 'Left', UPLO, 'Transpose', 'Non-unit', KB,
         $                        K-1, ONE, B( K, K ), LDB, A( K, 1 ), LDA )
                      CALL DSYGS2( ITYPE, UPLO, KB, A( K, K ), LDA,
         $                         B( K, K ), LDB, INFO )
       40          CONTINUE
                END IF
             END IF
          END IF
          RETURN
    *
    *     End of DSYGST
    *
          END