*> \brief \b CQRT12
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       REAL             FUNCTION CQRT12( M, N, A, LDA, S, WORK, LWORK,
*                        RWORK )
*
*       .. Scalar Arguments ..
*       INTEGER            LDA, LWORK, M, N
*       ..
*       .. Array Arguments ..
*       REAL               RWORK( * ), S( * )
*       COMPLEX            A( LDA, * ), WORK( LWORK )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> CQRT12 computes the singular values `svlues' of the upper trapezoid
*> of A(1:M,1:N) and returns the ratio
*>
*>      || svlues -s ||/( ||s||*eps*max(M,N) )
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] M
*> \verbatim
*>          M is INTEGER
*>          The number of rows of the matrix A.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The number of columns of the matrix A.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*>          A is COMPLEX array, dimension (LDA,N)
*>          The M-by-N matrix A. Only the upper trapezoid is referenced.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A.
*> \endverbatim
*>
*> \param[in] S
*> \verbatim
*>          S is REAL array, dimension (min(M,N))
*>          The singular values of the matrix A.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is COMPLEX array, dimension (LWORK)
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*>          LWORK is INTEGER
*>          The length of the array WORK. LWORK >= M*N + 2*min(M,N) +
*>          max(M,N).
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*>          RWORK is REAL array, dimension (4*min(M,N))
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup complex_lin
*
*  =====================================================================
      REAL             FUNCTION CQRT12( M, N, A, LDA, S, WORK, LWORK,
     $                 RWORK )
*
*  -- LAPACK test routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      INTEGER            LDA, LWORK, M, N
*     ..
*     .. Array Arguments ..
      REAL               RWORK( * ), S( * )
      COMPLEX            A( LDA, * ), WORK( LWORK )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ZERO, ONE
      PARAMETER          ( ZERO = 0.0E0, ONE = 1.0E0 )
*     ..
*     .. Local Scalars ..
      INTEGER            I, INFO, ISCL, J, MN
      REAL               ANRM, BIGNUM, NRMSVL, SMLNUM
*     ..
*     .. Local Arrays ..
      REAL               DUMMY( 1 )
*     ..
*     .. External Functions ..
      REAL               CLANGE, SASUM, SLAMCH, SNRM2
      EXTERNAL           CLANGE, SASUM, SLAMCH, SNRM2
*     ..
*     .. External Subroutines ..
      EXTERNAL           CGEBD2, CLASCL, CLASET, SAXPY, SBDSQR, SLASCL,
     $                   XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          CMPLX, MAX, MIN, REAL
*     ..
*     .. Executable Statements ..
*
      CQRT12 = ZERO
*
*     Test that enough workspace is supplied
*
      IF( LWORK.LT.M*N+2*MIN( M, N )+MAX( M, N ) ) THEN
         CALL XERBLA( 'CQRT12', 7 )
         RETURN
      END IF
*
*     Quick return if possible
*
      MN = MIN( M, N )
      IF( MN.LE.ZERO )
     $   RETURN
*
      NRMSVL = SNRM2( MN, S, 1 )
*
*     Copy upper triangle of A into work
*
      CALL CLASET( 'Full', M, N, CMPLX( ZERO ), CMPLX( ZERO ), WORK, M )
      DO J = 1, N
         DO I = 1, MIN( J, M )
            WORK( ( J-1 )*M+I ) = A( I, J )
         END DO
      END DO
*
*     Get machine parameters
*
      SMLNUM = SLAMCH( 'S' ) / SLAMCH( 'P' )
      BIGNUM = ONE / SMLNUM
*
*     Scale work if max entry outside range [SMLNUM,BIGNUM]
*
      ANRM = CLANGE( 'M', M, N, WORK, M, DUMMY )
      ISCL = 0
      IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN
*
*        Scale matrix norm up to SMLNUM
*
         CALL CLASCL( 'G', 0, 0, ANRM, SMLNUM, M, N, WORK, M, INFO )
         ISCL = 1
      ELSE IF( ANRM.GT.BIGNUM ) THEN
*
*        Scale matrix norm down to BIGNUM
*
         CALL CLASCL( 'G', 0, 0, ANRM, BIGNUM, M, N, WORK, M, INFO )
         ISCL = 1
      END IF
*
      IF( ANRM.NE.ZERO ) THEN
*
*        Compute SVD of work
*
         CALL CGEBD2( M, N, WORK, M, RWORK( 1 ), RWORK( MN+1 ),
     $                WORK( M*N+1 ), WORK( M*N+MN+1 ),
     $                WORK( M*N+2*MN+1 ), INFO )
         CALL SBDSQR( 'Upper', MN, 0, 0, 0, RWORK( 1 ), RWORK( MN+1 ),
     $                DUMMY, MN, DUMMY, 1, DUMMY, MN, RWORK( 2*MN+1 ),
     $                INFO )
*
         IF( ISCL.EQ.1 ) THEN
            IF( ANRM.GT.BIGNUM ) THEN
               CALL SLASCL( 'G', 0, 0, BIGNUM, ANRM, MN, 1, RWORK( 1 ),
     $                      MN, INFO )
            END IF
            IF( ANRM.LT.SMLNUM ) THEN
               CALL SLASCL( 'G', 0, 0, SMLNUM, ANRM, MN, 1, RWORK( 1 ),
     $                      MN, INFO )
            END IF
         END IF
*
      ELSE
*
         DO I = 1, MN
            RWORK( I ) = ZERO
         END DO
      END IF
*
*     Compare s and singular values of work
*
      CALL SAXPY( MN, -ONE, S, 1, RWORK( 1 ), 1 )
      CQRT12 = SASUM( MN, RWORK( 1 ), 1 ) /
     $         ( SLAMCH( 'Epsilon' )*REAL( MAX( M, N ) ) )
      IF( NRMSVL.NE.ZERO )
     $   CQRT12 = CQRT12 / NRMSVL
*
      RETURN
*
*     End of CQRT12
*
      END
