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*> \brief \b ZGBT01
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZGBT01( M, N, KL, KU, A, LDA, AFAC, LDAFAC, IPIV, WORK,
* RESID )
*
* .. Scalar Arguments ..
* INTEGER KL, KU, LDA, LDAFAC, M, N
* DOUBLE PRECISION RESID
* ..
* .. Array Arguments ..
* INTEGER IPIV( * )
* COMPLEX*16 A( LDA, * ), AFAC( LDAFAC, * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZGBT01 reconstructs a band matrix A from its L*U factorization and
*> computes the residual:
*> norm(L*U - A) / ( N * norm(A) * EPS ),
*> where EPS is the machine epsilon.
*>
*> The expression L*U - A is computed one column at a time, so A and
*> AFAC are not modified.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The number of rows of the matrix A. M >= 0.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of columns 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,out] A
*> \verbatim
*> A is COMPLEX*16 array, dimension (LDA,N)
*> The original matrix A in band storage, stored in rows 1 to
*> KL+KU+1.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER.
*> The leading dimension of the array A. LDA >= max(1,KL+KU+1).
*> \endverbatim
*>
*> \param[in] AFAC
*> \verbatim
*> AFAC is COMPLEX*16 array, dimension (LDAFAC,N)
*> The factored form of the matrix A. AFAC contains the banded
*> factors L and U from the L*U factorization, 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. See ZGBTRF for further details.
*> \endverbatim
*>
*> \param[in] LDAFAC
*> \verbatim
*> LDAFAC is INTEGER
*> The leading dimension of the array AFAC.
*> LDAFAC >= max(1,2*KL*KU+1).
*> \endverbatim
*>
*> \param[in] IPIV
*> \verbatim
*> IPIV is INTEGER array, dimension (min(M,N))
*> The pivot indices from ZGBTRF.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is COMPLEX*16 array, dimension (2*KL+KU+1)
*> \endverbatim
*>
*> \param[out] RESID
*> \verbatim
*> RESID is DOUBLE PRECISION
*> norm(L*U - A) / ( N * norm(A) * EPS )
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup complex16_lin
*
* =====================================================================
SUBROUTINE ZGBT01( M, N, KL, KU, A, LDA, AFAC, LDAFAC, IPIV, WORK,
$ RESID )
*
* -- LAPACK test routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
INTEGER KL, KU, LDA, LDAFAC, M, N
DOUBLE PRECISION RESID
* ..
* .. Array Arguments ..
INTEGER IPIV( * )
COMPLEX*16 A( LDA, * ), AFAC( LDAFAC, * ), WORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
* ..
* .. Local Scalars ..
INTEGER I, I1, I2, IL, IP, IW, J, JL, JU, JUA, KD, LENJ
DOUBLE PRECISION ANORM, EPS
COMPLEX*16 T
* ..
* .. External Functions ..
DOUBLE PRECISION DLAMCH, DZASUM
EXTERNAL DLAMCH, DZASUM
* ..
* .. External Subroutines ..
EXTERNAL ZAXPY, ZCOPY
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE, DCMPLX, MAX, MIN
* ..
* .. Executable Statements ..
*
* Quick exit if M = 0 or N = 0.
*
RESID = ZERO
IF( M.LE.0 .OR. N.LE.0 )
$ RETURN
*
* Determine EPS and the norm of A.
*
EPS = DLAMCH( 'Epsilon' )
KD = KU + 1
ANORM = ZERO
DO 10 J = 1, N
I1 = MAX( KD+1-J, 1 )
I2 = MIN( KD+M-J, KL+KD )
IF( I2.GE.I1 )
$ ANORM = MAX( ANORM, DZASUM( I2-I1+1, A( I1, J ), 1 ) )
10 CONTINUE
*
* Compute one column at a time of L*U - A.
*
KD = KL + KU + 1
DO 40 J = 1, N
*
* Copy the J-th column of U to WORK.
*
JU = MIN( KL+KU, J-1 )
JL = MIN( KL, M-J )
LENJ = MIN( M, J ) - J + JU + 1
IF( LENJ.GT.0 ) THEN
CALL ZCOPY( LENJ, AFAC( KD-JU, J ), 1, WORK, 1 )
DO 20 I = LENJ + 1, JU + JL + 1
WORK( I ) = ZERO
20 CONTINUE
*
* Multiply by the unit lower triangular matrix L. Note that L
* is stored as a product of transformations and permutations.
*
DO 30 I = MIN( M-1, J ), J - JU, -1
IL = MIN( KL, M-I )
IF( IL.GT.0 ) THEN
IW = I - J + JU + 1
T = WORK( IW )
CALL ZAXPY( IL, T, AFAC( KD+1, I ), 1, WORK( IW+1 ),
$ 1 )
IP = IPIV( I )
IF( I.NE.IP ) THEN
IP = IP - J + JU + 1
WORK( IW ) = WORK( IP )
WORK( IP ) = T
END IF
END IF
30 CONTINUE
*
* Subtract the corresponding column of A.
*
JUA = MIN( JU, KU )
IF( JUA+JL+1.GT.0 )
$ CALL ZAXPY( JUA+JL+1, -DCMPLX( ONE ), A( KU+1-JUA, J ),
$ 1, WORK( JU+1-JUA ), 1 )
*
* Compute the 1-norm of the column.
*
RESID = MAX( RESID, DZASUM( JU+JL+1, WORK, 1 ) )
END IF
40 CONTINUE
*
* Compute norm(L*U - A) / ( N * norm(A) * EPS )
*
IF( ANORM.LE.ZERO ) THEN
IF( RESID.NE.ZERO )
$ RESID = ONE / EPS
ELSE
RESID = ( ( RESID / DBLE( N ) ) / ANORM ) / EPS
END IF
*
RETURN
*
* End of ZGBT01
*
END
|
