168 lines
4.9 KiB
Fortran
168 lines
4.9 KiB
Fortran
*> \brief \b ZLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix.
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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*> \htmlonly
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*> Download ZLA_GBRPVGRW + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zla_gbrpvgrw.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zla_gbrpvgrw.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zla_gbrpvgrw.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* DOUBLE PRECISION FUNCTION ZLA_GBRPVGRW( N, KL, KU, NCOLS, AB,
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* LDAB, AFB, LDAFB )
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*
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* .. Scalar Arguments ..
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* INTEGER N, KL, KU, NCOLS, LDAB, LDAFB
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* ..
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* .. Array Arguments ..
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* COMPLEX*16 AB( LDAB, * ), AFB( LDAFB, * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> ZLA_GBRPVGRW computes the reciprocal pivot growth factor
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*> norm(A)/norm(U). The "max absolute element" norm is used. If this is
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*> much less than 1, the stability of the LU factorization of the
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*> (equilibrated) matrix A could be poor. This also means that the
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*> solution X, estimated condition numbers, and error bounds could be
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*> unreliable.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The number of linear equations, i.e., the order of the
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*> matrix A. N >= 0.
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*> \endverbatim
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*>
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*> \param[in] KL
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*> \verbatim
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*> KL is INTEGER
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*> The number of subdiagonals within the band of A. KL >= 0.
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*> \endverbatim
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*>
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*> \param[in] KU
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*> \verbatim
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*> KU is INTEGER
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*> The number of superdiagonals within the band of A. KU >= 0.
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*> \endverbatim
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*>
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*> \param[in] NCOLS
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*> \verbatim
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*> NCOLS is INTEGER
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*> The number of columns of the matrix A. NCOLS >= 0.
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*> \endverbatim
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*>
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*> \param[in] AB
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*> \verbatim
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*> AB is COMPLEX*16 array, dimension (LDAB,N)
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*> On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
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*> The j-th column of A is stored in the j-th column of the
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*> array AB as follows:
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*> AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)
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*> \endverbatim
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*>
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*> \param[in] LDAB
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*> \verbatim
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*> LDAB is INTEGER
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*> The leading dimension of the array AB. LDAB >= KL+KU+1.
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*> \endverbatim
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*>
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*> \param[in] AFB
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*> \verbatim
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*> AFB is COMPLEX*16 array, dimension (LDAFB,N)
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*> Details of the LU factorization of the band matrix A, as
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*> computed by ZGBTRF. U is stored as an upper triangular
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*> band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1,
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*> and the multipliers used during the factorization are stored
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*> in rows KL+KU+2 to 2*KL+KU+1.
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*> \endverbatim
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*>
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*> \param[in] LDAFB
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*> \verbatim
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*> LDAFB is INTEGER
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*> The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1.
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \date September 2012
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*
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*> \ingroup complex16GBcomputational
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*
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* =====================================================================
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DOUBLE PRECISION FUNCTION ZLA_GBRPVGRW( N, KL, KU, NCOLS, AB,
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$ LDAB, AFB, LDAFB )
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*
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* -- LAPACK computational routine (version 3.4.2) --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* September 2012
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*
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* .. Scalar Arguments ..
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INTEGER N, KL, KU, NCOLS, LDAB, LDAFB
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* ..
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* .. Array Arguments ..
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COMPLEX*16 AB( LDAB, * ), AFB( LDAFB, * )
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* ..
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*
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* =====================================================================
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*
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* .. Local Scalars ..
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INTEGER I, J, KD
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DOUBLE PRECISION AMAX, UMAX, RPVGRW
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COMPLEX*16 ZDUM
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, MAX, MIN, REAL, DIMAG
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* ..
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* .. Statement Functions ..
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DOUBLE PRECISION CABS1
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* ..
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* .. Statement Function Definitions ..
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CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
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* ..
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* .. Executable Statements ..
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*
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RPVGRW = 1.0D+0
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KD = KU + 1
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DO J = 1, NCOLS
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AMAX = 0.0D+0
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UMAX = 0.0D+0
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DO I = MAX( J-KU, 1 ), MIN( J+KL, N )
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AMAX = MAX( CABS1( AB( KD+I-J, J ) ), AMAX )
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END DO
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DO I = MAX( J-KU, 1 ), J
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UMAX = MAX( CABS1( AFB( KD+I-J, J ) ), UMAX )
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END DO
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IF ( UMAX /= 0.0D+0 ) THEN
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RPVGRW = MIN( AMAX / UMAX, RPVGRW )
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END IF
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END DO
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ZLA_GBRPVGRW = RPVGRW
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END
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