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*> \brief \b ZLA_GERPVGRW multiplies a square real matrix by a complex matrix.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download ZLA_GERPVGRW + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zla_gerpvgrw.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zla_gerpvgrw.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zla_gerpvgrw.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* DOUBLE PRECISION FUNCTION ZLA_GERPVGRW( N, NCOLS, A, LDA, AF,
* LDAF )
*
* .. Scalar Arguments ..
* INTEGER N, NCOLS, LDA, LDAF
* ..
* .. Array Arguments ..
* COMPLEX*16 A( LDA, * ), AF( LDAF, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*>
*> ZLA_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*16 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*16 array, dimension (LDAF,N)
*> The factors L and U from the factorization
*> A = P*L*U as computed by ZGETRF.
*> \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 June 2016
*
*> \ingroup complex16GEcomputational
*
* =====================================================================
DOUBLE PRECISION FUNCTION ZLA_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..--
* June 2016
*
* .. Scalar Arguments ..
INTEGER N, NCOLS, LDA, LDAF
* ..
* .. Array Arguments ..
COMPLEX*16 A( LDA, * ), AF( LDAF, * )
* ..
*
* =====================================================================
*
* .. Local Scalars ..
INTEGER I, J
DOUBLE PRECISION AMAX, UMAX, RPVGRW
COMPLEX*16 ZDUM
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN, ABS, REAL, DIMAG
* ..
* .. Statement Functions ..
DOUBLE PRECISION CABS1
* ..
* .. Statement Function Definitions ..
CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
* ..
* .. Executable Statements ..
*
RPVGRW = 1.0D+0
DO J = 1, NCOLS
AMAX = 0.0D+0
UMAX = 0.0D+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 /= 0.0D+0 ) THEN
RPVGRW = MIN( AMAX / UMAX, RPVGRW )
END IF
END DO
ZLA_GERPVGRW = RPVGRW
END
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