*> \brief \b DSYGST
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 
*
*> \htmlonly
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsygst.f"> 
*> [TXT]</a>
*> \endhtmlonly 
*
*  Definition:
*  ===========
*
*       SUBROUTINE DSYGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
* 
*       .. Scalar Arguments ..
*       CHARACTER          UPLO
*       INTEGER            INFO, ITYPE, LDA, LDB, N
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION   A( LDA, * ), B( LDB, * )
*       ..
*  
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> 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.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] ITYPE
*> \verbatim
*>          ITYPE is 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.
*> \endverbatim
*>
*> \param[in] UPLO
*> \verbatim
*>          UPLO is 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.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the matrices A and B.  N >= 0.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*>          A is 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.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A.  LDA >= max(1,N).
*> \endverbatim
*>
*> \param[in] B
*> \verbatim
*>          B is DOUBLE PRECISION array, dimension (LDB,N)
*>          The triangular factor from the Cholesky factorization of B,
*>          as returned by DPOTRF.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*>          LDB is INTEGER
*>          The leading dimension of the array B.  LDB >= max(1,N).
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*>          INFO is INTEGER
*>          = 0:  successful exit
*>          < 0:  if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date November 2011
*
*> \ingroup doubleSYcomputational
*
*  =====================================================================
      SUBROUTINE GAL_DSYGST(ITYPE,UPLO,N,A,LDA,B,LDB,INFO)
*
*  -- LAPACK computational routine (version 3.4.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2011
*
*     .. Scalar Arguments ..
      CHARACTERUPLO
      INTEGER INFO,ITYPE,LDA,LDB,N
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION A(LDA,*),B(LDB,*)
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION ONE,HALF
      PARAMETER (ONE=1.0D0,HALF=0.5D0)
*     ..
*     .. Local Scalars ..
      LOGICAL UPPER
      INTEGER K,KB,NB
*     ..
*     .. External Subroutines ..
      EXTERNAL GAL_DSYGS2,GAL_DSYMM,
     $GAL_DSYR2K,GAL_DTRMM,GAL_DTRSM,GAL_XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC MAX,MIN
*     ..
*     .. External Functions ..
      LOGICAL GAL_LSAME
      INTEGER GAL_ILAENV
      EXTERNAL GAL_LSAME,GAL_ILAENV
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      INFO=0
      UPPER=GAL_LSAME(UPLO,'U')
      IF(ITYPE.LT.1.OR.ITYPE.GT.3)THEN
      INFO=-1
      ELSE IF(.NOT.UPPER.AND..NOT.GAL_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 GAL_XERBLA('GAL_DSYGST',-INFO)
      RETURN
      END IF
*
*     Quick return if possible
*
      IF(N.EQ.0)
     $RETURN
*
*     Determine the block size for this environment.
*
      NB=GAL_ILAENV(1,'GAL_DSYGST',UPLO,N,-1,-1,-1)
*
      IF(NB.LE.1.OR.NB.GE.N)THEN
*
*        Use unblocked code
*
      CALL GAL_DSYGS2(ITYPE,UPLO,N,A,LDA,B,LDB,INFO)
      ELSE 
*
*        Use blocked code
*
      IF(ITYPE.EQ.1)THEN
      IF(UPPER)THEN
*
*              Compute inv(U**T)*A*inv(U)
*
      DO 10K=1,N,NB
      KB=MIN(N-K+1,NB)
*
*                 Update the upper triangle of A(k:n,k:n)
*
      CALL GAL_DSYGS2(ITYPE,UPLO,KB,A(K,K),LDA,
     $B(K,K),LDB,INFO)
      IF(K+KB.LE.N)THEN
      CALL GAL_DTRSM('LEFT',UPLO,'TRANSPOSE','NON-UNIT',
     $KB,N-K-KB+1,ONE,B(K,K),LDB,
     $A(K,K+KB),LDA)
      CALL GAL_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 GAL_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 GAL_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 GAL_DTRSM('RIGHT',UPLO,'NOTRANSPOSE',
     $'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**T)
*
      DO 20K=1,N,NB
      KB=MIN(N-K+1,NB)
*
*                 Update the lower triangle of A(k:n,k:n)
*
      CALL GAL_DSYGS2(ITYPE,UPLO,KB,A(K,K),LDA,
     $B(K,K),LDB,INFO)
      IF(K+KB.LE.N)THEN
      CALL GAL_DTRSM('RIGHT',UPLO,'TRANSPOSE','NON-UNIT',
     $N-K-KB+1,KB,ONE,B(K,K),LDB,
     $A(K+KB,K),LDA)
      CALL GAL_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 GAL_DSYR2K(UPLO,'NOTRANSPOSE',N-K-KB+1,KB,
     $-ONE,A(K+KB,K),LDA,B(K+KB,K),
     $LDB,ONE,A(K+KB,K+KB),LDA)
      CALL GAL_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 GAL_DTRSM('LEFT',UPLO,'NOTRANSPOSE',
     $'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**T
*
      DO 30K=1,N,NB
      KB=MIN(N-K+1,NB)
*
*                 Update the upper triangle of A(1:k+kb-1,1:k+kb-1)
*
      CALL GAL_DTRMM('LEFT',UPLO,'NOTRANSPOSE','NON-UNIT',
     $K-1,KB,ONE,B,LDB,A(1,K),LDA)
      CALL GAL_DSYMM('RIGHT',UPLO,K-1,KB,HALF,A(K,K),
     $LDA,B(1,K),LDB,ONE,A(1,K),LDA)
      CALL GAL_DSYR2K(UPLO,'NOTRANSPOSE',K-1,KB,ONE,
     $A(1,K),LDA,B(1,K),LDB,ONE,A,
     $LDA)
      CALL GAL_DSYMM('RIGHT',UPLO,K-1,KB,HALF,A(K,K),
     $LDA,B(1,K),LDB,ONE,A(1,K),LDA)
      CALL GAL_DTRMM('RIGHT',UPLO,'TRANSPOSE','NON-UNIT',
     $K-1,KB,ONE,B(K,K),LDB,A(1,K),
     $LDA)
      CALL GAL_DSYGS2(ITYPE,UPLO,KB,A(K,K),LDA,
     $B(K,K),LDB,INFO)
   30 CONTINUE
      ELSE 
*
*              Compute L**T*A*L
*
      DO 40K=1,N,NB
      KB=MIN(N-K+1,NB)
*
*                 Update the lower triangle of A(1:k+kb-1,1:k+kb-1)
*
      CALL GAL_DTRMM('RIGHT',UPLO,'NOTRANSPOSE','NON-UNIT',
     $KB,K-1,ONE,B,LDB,A(K,1),LDA)
      CALL GAL_DSYMM('LEFT',UPLO,KB,K-1,HALF,A(K,K),
     $LDA,B(K,1),LDB,ONE,A(K,1),LDA)
      CALL GAL_DSYR2K(UPLO,'TRANSPOSE',K-1,KB,ONE,
     $A(K,1),LDA,B(K,1),LDB,ONE,A,
     $LDA)
      CALL GAL_DSYMM('LEFT',UPLO,KB,K-1,HALF,A(K,K),
     $LDA,B(K,1),LDB,ONE,A(K,1),LDA)
      CALL GAL_DTRMM('LEFT',UPLO,'TRANSPOSE','NON-UNIT',KB,
     $K-1,ONE,B(K,K),LDB,A(K,1),LDA)
      CALL GAL_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 
