You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
244 lines
6.6 KiB
244 lines
6.6 KiB
2 years ago
|
*> \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.
|
||
|
|
*
|
||
|
|
*> \ingroup double_lin
|
||
|
|
*
|
||
|
|
* =====================================================================
|
||
|
|
SUBROUTINE DPBT01( UPLO, N, KD, A, LDA, AFAC, LDAFAC, RWORK,
|
||
|
|
$ 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 ..
|
||
|
|
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
|