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*> \brief \b DPBT01
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE DPBT01( UPLO, N, KD, A, LDA, AFAC, LDAFAC, RWORK,
* RESID )
*
* .. Scalar Arguments ..
* CHARACTER UPLO
* INTEGER KD, LDA, LDAFAC, N
* DOUBLE PRECISION RESID
* ..
* .. Array Arguments ..
* DOUBLE PRECISION A( LDA, * ), AFAC( LDAFAC, * ), RWORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DPBT01 reconstructs a symmetric positive definite band matrix A from
*> its L*L' or U'*U factorization and computes the residual
*> norm( L*L' - A ) / ( N * norm(A) * EPS ) or
*> norm( U'*U - A ) / ( N * norm(A) * EPS ),
*> where EPS is the machine epsilon, L' is the conjugate transpose of
*> L, and U' is the conjugate transpose of U.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> Specifies whether the upper or lower triangular part of the
*> symmetric matrix A is stored:
*> = 'U': Upper triangular
*> = 'L': Lower triangular
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of rows and columns of the matrix A. N >= 0.
*> \endverbatim
*>
*> \param[in] KD
*> \verbatim
*> KD is INTEGER
*> The number of super-diagonals of the matrix A if UPLO = 'U',
*> or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is DOUBLE PRECISION array, dimension (LDA,N)
*> The original symmetric band matrix A. If UPLO = 'U', the
*> upper triangular part of A is stored as a band matrix; if
*> UPLO = 'L', the lower triangular part of A is stored. The
*> columns of the appropriate triangle are stored in the columns
*> of A and the diagonals of the triangle are stored in the rows
*> of A. See DPBTRF for further details.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER.
*> The leading dimension of the array A. LDA >= max(1,KD+1).
*> \endverbatim
*>
*> \param[in] AFAC
*> \verbatim
*> AFAC is DOUBLE PRECISION array, dimension (LDAFAC,N)
*> The factored form of the matrix A. AFAC contains the factor
*> L or U from the L*L' or U'*U factorization in band storage
*> format, as computed by DPBTRF.
*> \endverbatim
*>
*> \param[in] LDAFAC
*> \verbatim
*> LDAFAC is INTEGER
*> The leading dimension of the array AFAC.
*> LDAFAC >= max(1,KD+1).
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*> RWORK is DOUBLE PRECISION array, dimension (N)
*> \endverbatim
*>
*> \param[out] RESID
*> \verbatim
*> RESID is DOUBLE PRECISION
*> If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
*> If UPLO = 'U', norm(U'*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.
*
*> \date November 2011
*
*> \ingroup double_lin
*
* =====================================================================
SUBROUTINE DPBT01( UPLO, N, KD, A, LDA, AFAC, LDAFAC, RWORK,
$ RESID )
*
* -- LAPACK test routine (version 3.1) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
CHARACTER UPLO
INTEGER KD, LDA, LDAFAC, N
DOUBLE PRECISION RESID
* ..
* .. Array Arguments ..
DOUBLE PRECISION A( LDA, * ), AFAC( LDAFAC, * ), RWORK( * )
* ..
*
* =====================================================================
*
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
* ..
* .. Local Scalars ..
INTEGER I, J, K, KC, KLEN, ML, MU
DOUBLE PRECISION ANORM, EPS, T
* ..
* .. External Functions ..
LOGICAL LSAME
DOUBLE PRECISION DDOT, DLAMCH, DLANSB
EXTERNAL LSAME, DDOT, DLAMCH, DLANSB
* ..
* .. External Subroutines ..
EXTERNAL DSCAL, DSYR, DTRMV
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE, MAX, MIN
* ..
* .. Executable Statements ..
*
* Quick exit if N = 0.
*
IF( N.LE.0 ) THEN
RESID = ZERO
RETURN
END IF
*
* Exit with RESID = 1/EPS if ANORM = 0.
*
EPS = DLAMCH( 'Epsilon' )
ANORM = DLANSB( '1', UPLO, N, KD, A, LDA, RWORK )
IF( ANORM.LE.ZERO ) THEN
RESID = ONE / EPS
RETURN
END IF
*
* Compute the product U'*U, overwriting U.
*
IF( LSAME( UPLO, 'U' ) ) THEN
DO 10 K = N, 1, -1
KC = MAX( 1, KD+2-K )
KLEN = KD + 1 - KC
*
* Compute the (K,K) element of the result.
*
T = DDOT( KLEN+1, AFAC( KC, K ), 1, AFAC( KC, K ), 1 )
AFAC( KD+1, K ) = T
*
* Compute the rest of column K.
*
IF( KLEN.GT.0 )
$ CALL DTRMV( 'Upper', 'Transpose', 'Non-unit', KLEN,
$ AFAC( KD+1, K-KLEN ), LDAFAC-1,
$ AFAC( KC, K ), 1 )
*
10 CONTINUE
*
* UPLO = 'L': Compute the product L*L', overwriting L.
*
ELSE
DO 20 K = N, 1, -1
KLEN = MIN( KD, N-K )
*
* Add a multiple of column K of the factor L to each of
* columns K+1 through N.
*
IF( KLEN.GT.0 )
$ CALL DSYR( 'Lower', KLEN, ONE, AFAC( 2, K ), 1,
$ AFAC( 1, K+1 ), LDAFAC-1 )
*
* Scale column K by the diagonal element.
*
T = AFAC( 1, K )
CALL DSCAL( KLEN+1, T, AFAC( 1, K ), 1 )
*
20 CONTINUE
END IF
*
* Compute the difference L*L' - A or U'*U - A.
*
IF( LSAME( UPLO, 'U' ) ) THEN
DO 40 J = 1, N
MU = MAX( 1, KD+2-J )
DO 30 I = MU, KD + 1
AFAC( I, J ) = AFAC( I, J ) - A( I, J )
30 CONTINUE
40 CONTINUE
ELSE
DO 60 J = 1, N
ML = MIN( KD+1, N-J+1 )
DO 50 I = 1, ML
AFAC( I, J ) = AFAC( I, J ) - A( I, J )
50 CONTINUE
60 CONTINUE
END IF
*
* Compute norm( L*L' - A ) / ( N * norm(A) * EPS )
*
RESID = DLANSB( 'I', UPLO, N, KD, AFAC, LDAFAC, RWORK )
*
RESID = ( ( RESID / DBLE( N ) ) / ANORM ) / EPS
*
RETURN
*
* End of DPBT01
*
END
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