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309 lines
8.5 KiB
309 lines
8.5 KiB
2 years ago
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*> \brief \b DGBCON
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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 DGBCON + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgbcon.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/dgbcon.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/dgbcon.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 DGBCON( NORM, N, KL, KU, AB, LDAB, IPIV, ANORM, RCOND,
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* WORK, IWORK, INFO )
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*
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* .. Scalar Arguments ..
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* CHARACTER NORM
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* INTEGER INFO, KL, KU, 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 IPIV( * ), 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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*> DGBCON estimates the reciprocal of the condition number of a real
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*> general band matrix A, in either the 1-norm or the infinity-norm,
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*> using the LU factorization computed by DGBTRF.
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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
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*> RCOND = 1 / ( norm(A) * 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] NORM
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*> \verbatim
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*> NORM is CHARACTER*1
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*> Specifies whether the 1-norm condition number or the
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*> infinity-norm condition number is required:
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*> = '1' or 'O': 1-norm;
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*> = 'I': Infinity-norm.
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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] 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] AB
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*> \verbatim
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*> AB is DOUBLE PRECISION array, dimension (LDAB,N)
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*> Details of the LU factorization of the band matrix A, as
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*> computed by DGBTRF. U is stored as an upper triangular band
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*> matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
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*> the multipliers used during the factorization are stored in
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*> rows KL+KU+2 to 2*KL+KU+1.
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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 >= 2*KL+KU+1.
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*> \endverbatim
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*>
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*> \param[in] IPIV
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*> \verbatim
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*> IPIV is INTEGER array, dimension (N)
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*> The pivot indices; for 1 <= i <= N, row i of the matrix was
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*> interchanged with row IPIV(i).
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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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*> If NORM = '1' or 'O', the 1-norm of the original matrix A.
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*> If NORM = 'I', the infinity-norm of the original 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/(norm(A) * norm(inv(A))).
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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 doubleGBcomputational
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*
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* =====================================================================
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SUBROUTINE DGBCON( NORM, N, KL, KU, AB, LDAB, IPIV, ANORM, RCOND,
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$ WORK, 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 NORM
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INTEGER INFO, KL, KU, 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 IPIV( * ), 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 LNOTI, ONENRM
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CHARACTER NORMIN
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INTEGER IX, J, JP, KASE, KASE1, KD, LM
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DOUBLE PRECISION AINVNM, SCALE, SMLNUM, T
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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 DDOT, DLAMCH
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EXTERNAL LSAME, IDAMAX, DDOT, DLAMCH
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* ..
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* .. External Subroutines ..
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EXTERNAL DAXPY, DLACN2, DLATBS, DRSCL, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, MIN
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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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ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' )
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IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) 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( KL.LT.0 ) THEN
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INFO = -3
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ELSE IF( KU.LT.0 ) THEN
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INFO = -4
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ELSE IF( LDAB.LT.2*KL+KU+1 ) THEN
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INFO = -6
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ELSE IF( ANORM.LT.ZERO ) THEN
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INFO = -8
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'DGBCON', -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 norm of inv(A).
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*
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AINVNM = ZERO
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NORMIN = 'N'
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IF( ONENRM ) THEN
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KASE1 = 1
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ELSE
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KASE1 = 2
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END IF
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KD = KL + KU + 1
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LNOTI = KL.GT.0
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KASE = 0
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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( KASE.EQ.KASE1 ) THEN
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*
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* Multiply by inv(L).
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*
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IF( LNOTI ) THEN
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DO 20 J = 1, N - 1
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LM = MIN( KL, N-J )
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JP = IPIV( J )
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T = WORK( JP )
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IF( JP.NE.J ) THEN
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WORK( JP ) = WORK( J )
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WORK( J ) = T
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END IF
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CALL DAXPY( LM, -T, AB( KD+1, J ), 1, WORK( J+1 ), 1 )
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20 CONTINUE
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END IF
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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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$ KL+KU, AB, LDAB, WORK, SCALE, 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(U**T).
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*
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CALL DLATBS( 'Upper', 'Transpose', 'Non-unit', NORMIN, N,
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$ KL+KU, AB, LDAB, WORK, SCALE, WORK( 2*N+1 ),
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$ INFO )
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*
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* Multiply by inv(L**T).
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*
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IF( LNOTI ) THEN
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DO 30 J = N - 1, 1, -1
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LM = MIN( KL, N-J )
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WORK( J ) = WORK( J ) - DDOT( LM, AB( KD+1, J ), 1,
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$ WORK( J+1 ), 1 )
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JP = IPIV( J )
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IF( JP.NE.J ) THEN
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T = WORK( JP )
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WORK( JP ) = WORK( J )
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WORK( J ) = T
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END IF
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30 CONTINUE
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END IF
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END IF
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*
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* Divide X by 1/SCALE if doing so will not cause overflow.
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*
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NORMIN = 'Y'
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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 40
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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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40 CONTINUE
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RETURN
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*
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* End of DGBCON
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*
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END
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