cla_gerpvgrw.f

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*> \brief \b CLA_GERPVGRW multiplies a square real matrix by a complex matrix.
*
*  =========== DOCUMENTATION ===========
*
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*
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*
*  Definition:
*  ===========
*
*       REAL FUNCTION CLA_GERPVGRW( N, NCOLS, A, LDA, AF, LDAF )
*
*       .. Scalar Arguments ..
*       INTEGER            N, NCOLS, LDA, LDAF
*       ..
*       .. Array Arguments ..
*       COMPLEX            A( LDA, * ), AF( LDAF, * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*>
*> CLA_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 COMPLEX 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 COMPLEX array, dimension (LDAF,N)
*>     The factors L and U from the factorization
*>     A = P*L*U as computed by CGETRF.
*> \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 December 2016
*
*> \ingroup complexGEcomputational
*
*  =====================================================================
      REAL FUNCTION CLA_GERPVGRW( N, NCOLS, A, LDA, AF, LDAF )
*
*  -- LAPACK computational routine (version 3.7.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     December 2016
*
*     .. Scalar Arguments ..
      INTEGER            n, ncols, lda, ldaf
*     ..
*     .. Array Arguments ..
      COMPLEX            a( lda, * ), af( ldaf, * )
*     ..
*
*  =====================================================================
*
*     .. Local Scalars ..
      INTEGER            i, j
      REAL               amax, umax, rpvgrw
      COMPLEX            zdum
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max, min, abs, real, aimag
*     ..
*     .. Statement Functions ..
      REAL               cabs1
*     ..
*     .. Statement Function Definitions ..
      cabs1( zdum ) = abs( real( zdum ) ) + abs( aimag( zdum ) )
*     ..
*     .. Executable Statements ..
*
      rpvgrw = 1.0
 
      DO j = 1, ncols
         amax = 0.0
         umax = 0.0
         DO i = 1, n
            amax = max( cabs1( a( i, j ) ), amax )
         END DO
         DO i = 1, j
            umax = max( cabs1( af( i, j ) ), umax )
         END DO
         IF ( umax /= 0.0 ) THEN
            rpvgrw = min( amax / umax, rpvgrw )
         END IF
      END DO
      cla_gerpvgrw = rpvgrw
      END