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268 lines
7.5 KiB
268 lines
7.5 KiB
*> \brief \b DPBCON
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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 DPBCON + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dpbcon.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/dpbcon.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/dpbcon.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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* SUBROUTINE DPBCON( UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK,
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* IWORK, INFO )
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*
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* .. Scalar Arguments ..
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* CHARACTER UPLO
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* INTEGER INFO, KD, LDAB, N
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* DOUBLE PRECISION ANORM, RCOND
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* ..
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* .. Array Arguments ..
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* INTEGER IWORK( * )
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* DOUBLE PRECISION AB( LDAB, * ), WORK( * )
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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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*> DPBCON estimates the reciprocal of the condition number (in the
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*> 1-norm) of a real symmetric positive definite band matrix using the
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*> Cholesky factorization A = U**T*U or A = L*L**T computed by DPBTRF.
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*>
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*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
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*> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
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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] UPLO
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*> \verbatim
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*> UPLO is CHARACTER*1
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*> = 'U': Upper triangular factor stored in AB;
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*> = 'L': Lower triangular factor stored in AB.
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*> \endverbatim
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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 order of the matrix A. N >= 0.
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*> \endverbatim
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*>
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*> \param[in] KD
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*> \verbatim
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*> KD is INTEGER
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*> The number of superdiagonals of the matrix A if UPLO = 'U',
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*> or the number of subdiagonals if UPLO = 'L'. KD >= 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 DOUBLE PRECISION array, dimension (LDAB,N)
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*> The triangular factor U or L from the Cholesky factorization
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*> A = U**T*U or A = L*L**T of the band matrix A, stored in the
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*> first KD+1 rows of the array. The j-th column of U or L is
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*> stored in the j-th column of the array AB as follows:
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*> if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
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*> if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd).
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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 >= KD+1.
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*> \endverbatim
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*>
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*> \param[in] ANORM
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*> \verbatim
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*> ANORM is DOUBLE PRECISION
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*> The 1-norm (or infinity-norm) of the symmetric band matrix A.
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*> \endverbatim
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*>
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*> \param[out] RCOND
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*> \verbatim
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*> RCOND is DOUBLE PRECISION
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*> The reciprocal of the condition number of the matrix A,
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*> computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
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*> estimate of the 1-norm of inv(A) computed in this routine.
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is DOUBLE PRECISION array, dimension (3*N)
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*> \endverbatim
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*>
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*> \param[out] IWORK
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*> \verbatim
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*> IWORK is INTEGER array, dimension (N)
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*> \endverbatim
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*>
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*> \param[out] INFO
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*> \verbatim
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*> INFO is INTEGER
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*> = 0: successful exit
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*> < 0: if INFO = -i, the i-th argument had an illegal value
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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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*> \ingroup doubleOTHERcomputational
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*
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* =====================================================================
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SUBROUTINE DPBCON( UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK,
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$ IWORK, INFO )
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*
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* -- LAPACK computational routine --
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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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*
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* .. Scalar Arguments ..
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CHARACTER UPLO
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INTEGER INFO, KD, LDAB, N
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DOUBLE PRECISION ANORM, RCOND
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* ..
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* .. Array Arguments ..
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INTEGER IWORK( * )
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DOUBLE PRECISION AB( LDAB, * ), WORK( * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ONE, ZERO
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PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
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* ..
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* .. Local Scalars ..
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LOGICAL UPPER
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CHARACTER NORMIN
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INTEGER IX, KASE
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DOUBLE PRECISION AINVNM, SCALE, SCALEL, SCALEU, SMLNUM
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* ..
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* .. Local Arrays ..
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INTEGER ISAVE( 3 )
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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INTEGER IDAMAX
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DOUBLE PRECISION DLAMCH
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EXTERNAL LSAME, IDAMAX, DLAMCH
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* ..
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* .. External Subroutines ..
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EXTERNAL DLACN2, DLATBS, DRSCL, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS
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* ..
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* .. Executable Statements ..
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*
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* Test the input parameters.
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*
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INFO = 0
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UPPER = LSAME( UPLO, 'U' )
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IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
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INFO = -1
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ELSE IF( N.LT.0 ) THEN
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INFO = -2
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ELSE IF( KD.LT.0 ) THEN
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INFO = -3
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ELSE IF( LDAB.LT.KD+1 ) THEN
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INFO = -5
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ELSE IF( ANORM.LT.ZERO ) THEN
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INFO = -6
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'DPBCON', -INFO )
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RETURN
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END IF
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*
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* Quick return if possible
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*
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RCOND = ZERO
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IF( N.EQ.0 ) THEN
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RCOND = ONE
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RETURN
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ELSE IF( ANORM.EQ.ZERO ) THEN
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RETURN
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END IF
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*
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SMLNUM = DLAMCH( 'Safe minimum' )
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*
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* Estimate the 1-norm of the inverse.
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*
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KASE = 0
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NORMIN = 'N'
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10 CONTINUE
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CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
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IF( KASE.NE.0 ) THEN
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IF( UPPER ) THEN
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*
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* Multiply by inv(U**T).
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*
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CALL DLATBS( 'Upper', 'Transpose', 'Non-unit', NORMIN, N,
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$ KD, AB, LDAB, WORK, SCALEL, WORK( 2*N+1 ),
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$ INFO )
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NORMIN = 'Y'
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*
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* Multiply by inv(U).
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*
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CALL DLATBS( 'Upper', 'No transpose', 'Non-unit', NORMIN, N,
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$ KD, AB, LDAB, WORK, SCALEU, WORK( 2*N+1 ),
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$ INFO )
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ELSE
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*
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* Multiply by inv(L).
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*
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CALL DLATBS( 'Lower', 'No transpose', 'Non-unit', NORMIN, N,
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$ KD, AB, LDAB, WORK, SCALEL, WORK( 2*N+1 ),
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$ INFO )
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NORMIN = 'Y'
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*
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* Multiply by inv(L**T).
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*
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CALL DLATBS( 'Lower', 'Transpose', 'Non-unit', NORMIN, N,
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$ KD, AB, LDAB, WORK, SCALEU, WORK( 2*N+1 ),
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$ INFO )
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END IF
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*
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* Multiply by 1/SCALE if doing so will not cause overflow.
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*
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SCALE = SCALEL*SCALEU
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IF( SCALE.NE.ONE ) THEN
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IX = IDAMAX( N, WORK, 1 )
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IF( SCALE.LT.ABS( WORK( IX ) )*SMLNUM .OR. SCALE.EQ.ZERO )
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$ GO TO 20
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CALL DRSCL( N, SCALE, WORK, 1 )
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END IF
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GO TO 10
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END IF
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*
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* Compute the estimate of the reciprocal condition number.
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*
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IF( AINVNM.NE.ZERO )
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$ RCOND = ( ONE / AINVNM ) / ANORM
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*
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20 CONTINUE
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*
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RETURN
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*
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* End of DPBCON
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*
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END
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