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*> \brief \b ZLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download ZLA_GBRPVGRW + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zla_gbrpvgrw.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zla_gbrpvgrw.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zla_gbrpvgrw.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* DOUBLE PRECISION FUNCTION ZLA_GBRPVGRW( N, KL, KU, NCOLS, AB,
* LDAB, AFB, LDAFB )
*
* .. Scalar Arguments ..
* INTEGER N, KL, KU, NCOLS, LDAB, LDAFB
* ..
* .. Array Arguments ..
* COMPLEX*16 AB( LDAB, * ), AFB( LDAFB, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZLA_GBRPVGRW 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] KL
*> \verbatim
*> KL is INTEGER
*> The number of subdiagonals within the band of A. KL >= 0.
*> \endverbatim
*>
*> \param[in] KU
*> \verbatim
*> KU is INTEGER
*> The number of superdiagonals within the band of A. KU >= 0.
*> \endverbatim
*>
*> \param[in] NCOLS
*> \verbatim
*> NCOLS is INTEGER
*> The number of columns of the matrix A. NCOLS >= 0.
*> \endverbatim
*>
*> \param[in] AB
*> \verbatim
*> AB is COMPLEX*16 array, dimension (LDAB,N)
*> On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
*> The j-th column of A is stored in the j-th column of the
*> array AB as follows:
*> AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)
*> \endverbatim
*>
*> \param[in] LDAB
*> \verbatim
*> LDAB is INTEGER
*> The leading dimension of the array AB. LDAB >= KL+KU+1.
*> \endverbatim
*>
*> \param[in] AFB
*> \verbatim
*> AFB is COMPLEX*16 array, dimension (LDAFB,N)
*> Details of the LU factorization of the band matrix A, as
*> computed by ZGBTRF. U is stored as an upper triangular
*> band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1,
*> and the multipliers used during the factorization are stored
*> in rows KL+KU+2 to 2*KL+KU+1.
*> \endverbatim
*>
*> \param[in] LDAFB
*> \verbatim
*> LDAFB is INTEGER
*> The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup complex16GBcomputational
*
* =====================================================================
DOUBLE PRECISION FUNCTION ZLA_GBRPVGRW( N, KL, KU, NCOLS, AB,
$ LDAB, AFB, LDAFB )
*
* -- 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, KL, KU, NCOLS, LDAB, LDAFB
* ..
* .. Array Arguments ..
COMPLEX*16 AB( LDAB, * ), AFB( LDAFB, * )
* ..
*
* =====================================================================
*
* .. Local Scalars ..
INTEGER I, J, KD
DOUBLE PRECISION AMAX, UMAX, RPVGRW
COMPLEX*16 ZDUM
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX, MIN, REAL, DIMAG
* ..
* .. Statement Functions ..
DOUBLE PRECISION CABS1
* ..
* .. Statement Function Definitions ..
CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
* ..
* .. Executable Statements ..
*
RPVGRW = 1.0D+0
KD = KU + 1
DO J = 1, NCOLS
AMAX = 0.0D+0
UMAX = 0.0D+0
DO I = MAX( J-KU, 1 ), MIN( J+KL, N )
AMAX = MAX( CABS1( AB( KD+I-J, J ) ), AMAX )
END DO
DO I = MAX( J-KU, 1 ), J
UMAX = MAX( CABS1( AFB( KD+I-J, J ) ), UMAX )
END DO
IF ( UMAX /= 0.0D+0 ) THEN
RPVGRW = MIN( AMAX / UMAX, RPVGRW )
END IF
END DO
ZLA_GBRPVGRW = RPVGRW
END
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