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*> \brief \b DPBCON
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> Download DPBCON + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dpbcon.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dpbcon.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dpbcon.f">
*> [TXT]</a>
*
* Definition
* ==========
*
* SUBROUTINE DPBCON( UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK,
* IWORK, INFO )
*
* .. Scalar Arguments ..
* CHARACTER UPLO
* INTEGER INFO, KD, LDAB, N
* DOUBLE PRECISION ANORM, RCOND
* ..
* .. Array Arguments ..
* INTEGER IWORK( * )
* DOUBLE PRECISION AB( LDAB, * ), WORK( * )
* ..
*
* Purpose
* =======
*
*>\details \b Purpose:
*>\verbatim
*>
*> DPBCON estimates the reciprocal of the condition number (in the
*> 1-norm) of a real symmetric positive definite band matrix using the
*> Cholesky factorization A = U**T*U or A = L*L**T computed by DPBTRF.
*>
*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
*> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
*>
*>\endverbatim
*
* Arguments
* =========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> = 'U': Upper triangular factor stored in AB;
*> = 'L': Lower triangular factor stored in AB.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrix A. N >= 0.
*> \endverbatim
*>
*> \param[in] KD
*> \verbatim
*> KD is INTEGER
*> The number of superdiagonals of the matrix A if UPLO = 'U',
*> or the number of subdiagonals if UPLO = 'L'. KD >= 0.
*> \endverbatim
*>
*> \param[in] AB
*> \verbatim
*> AB is DOUBLE PRECISION array, dimension (LDAB,N)
*> The triangular factor U or L from the Cholesky factorization
*> A = U**T*U or A = L*L**T of the band matrix A, stored in the
*> first KD+1 rows of the array. The j-th column of U or L is
*> stored in the j-th column of the array AB as follows:
*> if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
*> if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd).
*> \endverbatim
*>
*> \param[in] LDAB
*> \verbatim
*> LDAB is INTEGER
*> The leading dimension of the array AB. LDAB >= KD+1.
*> \endverbatim
*>
*> \param[in] ANORM
*> \verbatim
*> ANORM is DOUBLE PRECISION
*> The 1-norm (or infinity-norm) of the symmetric band matrix A.
*> \endverbatim
*>
*> \param[out] RCOND
*> \verbatim
*> RCOND is DOUBLE PRECISION
*> The reciprocal of the condition number of the matrix A,
*> computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
*> estimate of the 1-norm of inv(A) computed in this routine.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is DOUBLE PRECISION array, dimension (3*N)
*> \endverbatim
*>
*> \param[out] IWORK
*> \verbatim
*> IWORK is INTEGER array, dimension (N)
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
*>
*
* Authors
* =======
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup doubleOTHERcomputational
*
* =====================================================================
SUBROUTINE DPBCON( UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK,
$ IWORK, INFO )
*
* -- LAPACK computational routine (version 3.3.1) --
* -- 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 INFO, KD, LDAB, N
DOUBLE PRECISION ANORM, RCOND
* ..
* .. Array Arguments ..
INTEGER IWORK( * )
DOUBLE PRECISION AB( LDAB, * ), WORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE, ZERO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
* ..
* .. Local Scalars ..
LOGICAL UPPER
CHARACTER NORMIN
INTEGER IX, KASE
DOUBLE PRECISION AINVNM, SCALE, SCALEL, SCALEU, SMLNUM
* ..
* .. Local Arrays ..
INTEGER ISAVE( 3 )
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER IDAMAX
DOUBLE PRECISION DLAMCH
EXTERNAL LSAME, IDAMAX, DLAMCH
* ..
* .. External Subroutines ..
EXTERNAL DLACN2, DLATBS, DRSCL, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
UPPER = LSAME( UPLO, 'U' )
IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
INFO = -2
ELSE IF( KD.LT.0 ) THEN
INFO = -3
ELSE IF( LDAB.LT.KD+1 ) THEN
INFO = -5
ELSE IF( ANORM.LT.ZERO ) THEN
INFO = -6
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DPBCON', -INFO )
RETURN
END IF
*
* Quick return if possible
*
RCOND = ZERO
IF( N.EQ.0 ) THEN
RCOND = ONE
RETURN
ELSE IF( ANORM.EQ.ZERO ) THEN
RETURN
END IF
*
SMLNUM = DLAMCH( 'Safe minimum' )
*
* Estimate the 1-norm of the inverse.
*
KASE = 0
NORMIN = 'N'
10 CONTINUE
CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
IF( KASE.NE.0 ) THEN
IF( UPPER ) THEN
*
* Multiply by inv(U**T).
*
CALL DLATBS( 'Upper', 'Transpose', 'Non-unit', NORMIN, N,
$ KD, AB, LDAB, WORK, SCALEL, WORK( 2*N+1 ),
$ INFO )
NORMIN = 'Y'
*
* Multiply by inv(U).
*
CALL DLATBS( 'Upper', 'No transpose', 'Non-unit', NORMIN, N,
$ KD, AB, LDAB, WORK, SCALEU, WORK( 2*N+1 ),
$ INFO )
ELSE
*
* Multiply by inv(L).
*
CALL DLATBS( 'Lower', 'No transpose', 'Non-unit', NORMIN, N,
$ KD, AB, LDAB, WORK, SCALEL, WORK( 2*N+1 ),
$ INFO )
NORMIN = 'Y'
*
* Multiply by inv(L**T).
*
CALL DLATBS( 'Lower', 'Transpose', 'Non-unit', NORMIN, N,
$ KD, AB, LDAB, WORK, SCALEU, WORK( 2*N+1 ),
$ INFO )
END IF
*
* Multiply by 1/SCALE if doing so will not cause overflow.
*
SCALE = SCALEL*SCALEU
IF( SCALE.NE.ONE ) THEN
IX = IDAMAX( N, WORK, 1 )
IF( SCALE.LT.ABS( WORK( IX ) )*SMLNUM .OR. SCALE.EQ.ZERO )
$ GO TO 20
CALL DRSCL( N, SCALE, WORK, 1 )
END IF
GO TO 10
END IF
*
* Compute the estimate of the reciprocal condition number.
*
IF( AINVNM.NE.ZERO )
$ RCOND = ( ONE / AINVNM ) / ANORM
*
20 CONTINUE
*
RETURN
*
* End of DPBCON
*
END
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