*> \brief \b DLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix.
*
*  =========== 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.zip?format=zip&filename=/lapack/lapack_routine/dlansy.f"> 
*> [ZIP]</a> 
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlansy.f"> 
*> [TXT]</a>
*> \endhtmlonly 
*
*  Definition:
*  ===========
*
*       DOUBLE PRECISION FUNCTION DLANSY( NORM, UPLO, N, A, LDA, WORK )
* 
*       .. Scalar Arguments ..
*       CHARACTER          NORM, UPLO
*       INTEGER            LDA, N
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION   A( LDA, * ), WORK( * )
*       ..
*  
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DLANSY  returns the value of the one norm,  or the Frobenius norm, or
*> the  infinity norm,  or the  element of  largest absolute value  of a
*> real symmetric matrix A.
*> \endverbatim
*>
*> \return DLANSY
*> \verbatim
*>
*>    DLANSY = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*>             (
*>             ( norm1(A),         NORM = '1', 'O' or 'o'
*>             (
*>             ( normI(A),         NORM = 'I' or 'i'
*>             (
*>             ( normF(A),         NORM = 'F', 'f', 'E' or 'e'
*>
*> where  norm1  denotes the  one norm of a matrix (maximum column sum),
*> normI  denotes the  infinity norm  of a matrix  (maximum row sum) and
*> normF  denotes the  Frobenius norm of a matrix (square root of sum of
*> squares).  Note that  max(abs(A(i,j)))  is not a consistent matrix norm.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] NORM
*> \verbatim
*>          NORM is CHARACTER*1
*>          Specifies the value to be returned in DLANSY as described
*>          above.
*> \endverbatim
*>
*> \param[in] UPLO
*> \verbatim
*>          UPLO is CHARACTER*1
*>          Specifies whether the upper or lower triangular part of the
*>          symmetric matrix A is to be referenced.
*>          = 'U':  Upper triangular part of A is referenced
*>          = 'L':  Lower triangular part of A is referenced
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the matrix A.  N >= 0.  When N = 0, DLANSY is
*>          set to zero.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*>          A is DOUBLE PRECISION array, dimension (LDA,N)
*>          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.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A.  LDA >= max(N,1).
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
*>          where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
*>          WORK is not referenced.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleSYauxiliary
*
*  =====================================================================
      DOUBLE PRECISION FUNCTION GAL_DLANSY(NORM,UPLO,N,A,LDA,WORK)
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTERNORM,UPLO
      INTEGER LDA,N
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION A(LDA,*),WORK(*)
*     ..
*
* =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION ONE,ZERO
      PARAMETER (ONE=1.0D+0,ZERO=0.0D+0)
*     ..
*     .. Local Scalars ..
      INTEGER I,J
      DOUBLE PRECISION ABSA,SCALE,SUM,VALUE
*     ..
*     .. External Subroutines ..
      EXTERNAL GAL_DLASSQ
*     ..
*     .. External Functions ..
      LOGICAL GAL_LSAME,GAL_DISNAN
      EXTERNAL GAL_LSAME,GAL_DISNAN
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC ABS,SQRT
*     ..
*     .. Executable Statements ..
*
      IF(N.EQ.0)THEN
      VALUE=ZERO
      ELSE IF(GAL_LSAME(NORM,'M'))THEN
*
*        Find max(abs(A(i,j))).
*
      VALUE=ZERO
      IF(GAL_LSAME(UPLO,'U'))THEN
      DO 20J=1,N
      DO 10I=1,J
      SUM=ABS(A(I,J))
      IF(VALUE.LT.SUM.OR.GAL_DISNAN(SUM))VALUE=SUM
   10 CONTINUE
   20 CONTINUE
      ELSE 
      DO 40J=1,N
      DO 30I=J,N
      SUM=ABS(A(I,J))
      IF(VALUE.LT.SUM.OR.GAL_DISNAN(SUM))VALUE=SUM
   30 CONTINUE
   40 CONTINUE
      END IF
      ELSE IF((GAL_LSAME(NORM,'I')).OR.(GAL_LSAME(NORM,'O')).OR.
     $(NORM.EQ.'1'))THEN
*
*        Find normI(A) ( = norm1(A), since A is symmetric).
*
      VALUE=ZERO
      IF(GAL_LSAME(UPLO,'U'))THEN
      DO 60J=1,N
      SUM=ZERO
      DO 50I=1,J-1
      ABSA=ABS(A(I,J))
      SUM=SUM+ABSA
      WORK(I)=WORK(I)+ABSA
   50 CONTINUE
      WORK(J)=SUM+ABS(A(J,J))
   60 CONTINUE
      DO 70I=1,N
      SUM=WORK(I)
      IF(VALUE.LT.SUM.OR.GAL_DISNAN(SUM))VALUE=SUM
   70 CONTINUE
      ELSE 
      DO 80I=1,N
      WORK(I)=ZERO
   80 CONTINUE
      DO 100J=1,N
      SUM=WORK(J)+ABS(A(J,J))
      DO 90I=J+1,N
      ABSA=ABS(A(I,J))
      SUM=SUM+ABSA
      WORK(I)=WORK(I)+ABSA
   90 CONTINUE
      IF(VALUE.LT.SUM.OR.GAL_DISNAN(SUM))VALUE=SUM
  100 CONTINUE
      END IF
      ELSE IF((GAL_LSAME(NORM,'F')).OR.(GAL_LSAME(NORM,'E')))THEN
*
*        Find normF(A).
*
      SCALE=ZERO
      SUM=ONE
      IF(GAL_LSAME(UPLO,'U'))THEN
      DO 110J=2,N
      CALL GAL_DLASSQ(J-1,A(1,J),1,SCALE,SUM)
  110 CONTINUE
      ELSE 
      DO 120J=1,N-1
      CALL GAL_DLASSQ(N-J,A(J+1,J),1,SCALE,SUM)
  120 CONTINUE
      END IF
      SUM=2*SUM
      CALL GAL_DLASSQ(N,A,LDA+1,SCALE,SUM)
      VALUE=SCALE*SQRT(SUM)
      END IF
*
      GAL_DLANSY=VALUE
      RETURN
*
*     End of DLANSY
*
      END 
