*> \brief \b DPBCON * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DPBCON + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * 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( * ) * .. * * *> \par 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. * *> \ingroup doubleOTHERcomputational * * ===================================================================== SUBROUTINE DPBCON( UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK, \$ IWORK, INFO ) * * -- LAPACK computational 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 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