sla_gerpvgrw.f

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*> \brief \b SLA_GERPVGRW
*
*  =========== DOCUMENTATION ===========
*
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*            http://www.netlib.org/lapack/explore-html/ 
*
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*
*  Definition:
*  ===========
*
*       REAL FUNCTION SLA_GERPVGRW( N, NCOLS, A, LDA, AF, LDAF )
* 
*       .. Scalar Arguments ..
*       INTEGER            N, NCOLS, LDA, LDAF
*       ..
*       .. Array Arguments ..
*       REAL               A( LDA, * ), AF( LDAF, * )
*       ..
*  
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> SLA_GERPVGRW computes the reciprocal pivot growth factor
*> norm(A)/norm(U). The "max absolute element" norm is used. If this is
*> much less than 1, the stability of the LU factorization of the
*> (equilibrated) matrix A could be poor. This also means that the
*> solution X, estimated condition numbers, and error bounds could be
*> unreliable.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>     The number of linear equations, i.e., the order of the
*>     matrix A.  N >= 0.
*> \endverbatim
*>
*> \param[in] NCOLS
*> \verbatim
*>          NCOLS is INTEGER
*>     The number of columns of the matrix A. NCOLS >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*>          A is REAL array, dimension (LDA,N)
*>     On entry, the N-by-N matrix A.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>     The leading dimension of the array A.  LDA >= max(1,N).
*> \endverbatim
*>
*> \param[in] AF
*> \verbatim
*>          AF is REAL array, dimension (LDAF,N)
*>     The factors L and U from the factorization
*>     A = P*L*U as computed by SGETRF.
*> \endverbatim
*>
*> \param[in] LDAF
*> \verbatim
*>          LDAF is INTEGER
*>     The leading dimension of the array AF.  LDAF >= max(1,N).
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date November 2011
*
*> \ingroup realGEcomputational
*
*  =====================================================================
      REAL FUNCTION sla_gerpvgrw( N, NCOLS, A, LDA, AF, LDAF )
*
*  -- 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 ..
      INTEGER            N, NCOLS, LDA, LDAF
*     ..
*     .. Array Arguments ..
      REAL               A( lda, * ), AF( ldaf, * )
*     ..
*
*  =====================================================================
*
*     .. Local Scalars ..
      INTEGER            I, J
      REAL               AMAX, UMAX, RPVGRW
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs, max, min
*     ..
*     .. Executable Statements ..
*
      rpvgrw = 1.0

      DO j = 1, ncols
         amax = 0.0
         umax = 0.0
         DO i = 1, n
            amax = max( abs( a( i, j ) ), amax )
         END DO
         DO i = 1, j
            umax = max( abs( af( i, j ) ), umax )
         END DO
         IF ( umax /= 0.0 ) THEN
            rpvgrw = min( amax / umax, rpvgrw )
         END IF
      END DO
      sla_gerpvgrw = rpvgrw
      END