dd/dda/cla__gbrcond__x_8f_source.html

*> \brief \b CLA_GBRCOND_X computes the infinity norm condition number of op(A)*diag(x) for general banded matrices.

*

*  =========== DOCUMENTATION ===========

*

* Online html documentation available at

*            http://www.netlib.org/lapack/explore-html/

*

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*

*  Definition:

*  ===========

*

*       REAL FUNCTION CLA_GBRCOND_X( TRANS, N, KL, KU, AB, LDAB, AFB,

*                                    LDAFB, IPIV, X, INFO, WORK, RWORK )

*

*       .. Scalar Arguments ..

*       CHARACTER          TRANS

*       INTEGER            N, KL, KU, KD, KE, LDAB, LDAFB, INFO

*       ..

*       .. Array Arguments ..

*       INTEGER            IPIV( * )

*       COMPLEX            AB( LDAB, * ), AFB( LDAFB, * ), WORK( * ),

*      $                   X( * )

*       REAL               RWORK( * )

*       ..

*

*

*> \par Purpose:

*  =============

*>

*> \verbatim

*>

*>    CLA_GBRCOND_X Computes the infinity norm condition number of

*>    op(A) * diag(X) where X is a COMPLEX vector.

*> \endverbatim

*

*  Arguments:

*  ==========

*

*> \param[in] TRANS

*> \verbatim

*>          TRANS is CHARACTER*1

*>     Specifies the form of the system of equations:

*>       = 'N':  A * X = B     (No transpose)

*>       = 'T':  A**T * X = B  (Transpose)

*>       = 'C':  A**H * X = B  (Conjugate Transpose = Transpose)

*> \endverbatim

*>

*> \param[in] N

*> \verbatim

*>          N is INTEGER

*>     The number of linear equations, i.e., the order of the

*>     matrix A.  N >= 0.

*> \endverbatim

*>

*> \param[in] KL

*> \verbatim

*>          KL is INTEGER

*>     The number of subdiagonals within the band of A.  KL >= 0.

*> \endverbatim

*>

*> \param[in] KU

*> \verbatim

*>          KU is INTEGER

*>     The number of superdiagonals within the band of A.  KU >= 0.

*> \endverbatim

*>

*> \param[in] AB

*> \verbatim

*>          AB is COMPLEX array, dimension (LDAB,N)

*>     On entry, the matrix A in band storage, in rows 1 to KL+KU+1.

*>     The j-th column of A is stored in the j-th column of the

*>     array AB as follows:

*>     AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)

*> \endverbatim

*>

*> \param[in] LDAB

*> \verbatim

*>          LDAB is INTEGER

*>     The leading dimension of the array AB.  LDAB >= KL+KU+1.

*> \endverbatim

*>

*> \param[in] AFB

*> \verbatim

*>          AFB is COMPLEX array, dimension (LDAFB,N)

*>     Details of the LU factorization of the band matrix A, as

*>     computed by CGBTRF.  U is stored as an upper triangular

*>     band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1,

*>     and the multipliers used during the factorization are stored

*>     in rows KL+KU+2 to 2*KL+KU+1.

*> \endverbatim

*>

*> \param[in] LDAFB

*> \verbatim

*>          LDAFB is INTEGER

*>     The leading dimension of the array AFB.  LDAFB >= 2*KL+KU+1.

*> \endverbatim

*>

*> \param[in] IPIV

*> \verbatim

*>          IPIV is INTEGER array, dimension (N)

*>     The pivot indices from the factorization A = P*L*U

*>     as computed by CGBTRF; row i of the matrix was interchanged

*>     with row IPIV(i).

*> \endverbatim

*>

*> \param[in] X

*> \verbatim

*>          X is COMPLEX array, dimension (N)

*>     The vector X in the formula op(A) * diag(X).

*> \endverbatim

*>

*> \param[out] INFO

*> \verbatim

*>          INFO is INTEGER

*>       = 0:  Successful exit.

*>     i > 0:  The ith argument is invalid.

*> \endverbatim

*>

*> \param[out] WORK

*> \verbatim

*>          WORK is COMPLEX array, dimension (2*N).

*>     Workspace.

*> \endverbatim

*>

*> \param[out] RWORK

*> \verbatim

*>          RWORK is REAL array, dimension (N).

*>     Workspace.

*> \endverbatim

*

*  Authors:

*  ========

*

*> \author Univ. of Tennessee

*> \author Univ. of California Berkeley

*> \author Univ. of Colorado Denver

*> \author NAG Ltd.

*

*> \ingroup la_gbrcond

*

*  =====================================================================


      REAL function cla_gbrcond_x( trans, n, kl, ku, ab, ldab, afb,

     $                             ldafb, ipiv, x, info, work, rwork )

*

*  -- 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          trans

      INTEGER            n, kl, ku, kd, ke, ldab, ldafb, info

*     ..

*     .. Array Arguments ..

      INTEGER            ipiv( * )

      COMPLEX            ab( ldab, * ), afb( ldafb, * ), work( * ),

     $                   x( * )

      REAL               rwork( * )

*     ..

*

*  =====================================================================

*

*     .. Local Scalars ..

      LOGICAL            notrans

      INTEGER            kase, i, j

      REAL               ainvnm, anorm, tmp

      COMPLEX            zdum

*     ..

*     .. Local Arrays ..

      INTEGER            isave( 3 )

*     ..

*     .. External Functions ..

      LOGICAL            lsame

      EXTERNAL           lsame

*     ..

*     .. External Subroutines ..

      EXTERNAL           clacn2, cgbtrs, xerbla

*     ..

*     .. Intrinsic Functions ..

      INTRINSIC          abs, max

*     ..

*     .. Statement Functions ..

      REAL               cabs1

*     ..

*     .. Statement Function Definitions ..

      cabs1( zdum ) = abs( real( zdum ) ) + abs( aimag( zdum ) )

*     ..

*     .. Executable Statements ..

*

      cla_gbrcond_x = 0.0e+0

*

      info = 0

      notrans = lsame( trans, 'N' )

      IF ( .NOT. notrans .AND. .NOT. lsame(trans, 'T') .AND. .NOT.

     $     lsame( trans, 'C' ) ) THEN

         info = -1

      ELSE IF( n.LT.0 ) THEN

         info = -2

      ELSE IF( kl.LT.0 .OR. kl.GT.n-1 ) THEN

         info = -3

      ELSE IF( ku.LT.0 .OR. ku.GT.n-1 ) THEN

         info = -4

      ELSE IF( ldab.LT.kl+ku+1 ) THEN

         info = -6

      ELSE IF( ldafb.LT.2*kl+ku+1 ) THEN

         info = -8

      END IF

      IF( info.NE.0 ) THEN

         CALL xerbla( 'CLA_GBRCOND_X', -info )

         RETURN

      END IF

*

*     Compute norm of op(A)*op2(C).

*

      kd = ku + 1

      ke = kl + 1

      anorm = 0.0

      IF ( notrans ) THEN

         DO i = 1, n

            tmp = 0.0e+0

            DO j = max( i-kl, 1 ), min( i+ku, n )

               tmp = tmp + cabs1( ab( kd+i-j, j) * x( j ) )

            END DO

            rwork( i ) = tmp

            anorm = max( anorm, tmp )

         END DO

      ELSE

         DO i = 1, n

            tmp = 0.0e+0

            DO j = max( i-kl, 1 ), min( i+ku, n )

               tmp = tmp + cabs1( ab( ke-i+j, i ) * x( j ) )

            END DO

            rwork( i ) = tmp

            anorm = max( anorm, tmp )

         END DO

      END IF

*

*     Quick return if possible.

*

      IF( n.EQ.0 ) THEN

         cla_gbrcond_x = 1.0e+0

         RETURN

      ELSE IF( anorm .EQ. 0.0e+0 ) THEN

         RETURN

      END IF

*

*     Estimate the norm of inv(op(A)).

*

      ainvnm = 0.0e+0

*

      kase = 0

   10 CONTINUE

      CALL clacn2( n, work( n+1 ), work, ainvnm, kase, isave )

      IF( kase.NE.0 ) THEN

         IF( kase.EQ.2 ) THEN

*

*           Multiply by R.

*

            DO i = 1, n

               work( i ) = work( i ) * rwork( i )

            END DO

*

            IF ( notrans ) THEN

               CALL cgbtrs( 'No transpose', n, kl, ku, 1, afb, ldafb,

     $              ipiv, work, n, info )

            ELSE

               CALL cgbtrs( 'Conjugate transpose', n, kl, ku, 1, afb,

     $              ldafb, ipiv, work, n, info )

            ENDIF

*

*           Multiply by inv(X).

*

            DO i = 1, n

               work( i ) = work( i ) / x( i )

            END DO

         ELSE

*

*           Multiply by inv(X**H).

*

            DO i = 1, n

               work( i ) = work( i ) / x( i )

            END DO

*

            IF ( notrans ) THEN

               CALL cgbtrs( 'Conjugate transpose', n, kl, ku, 1, afb,

     $              ldafb, ipiv, work, n, info )

            ELSE

               CALL cgbtrs( 'No transpose', n, kl, ku, 1, afb, ldafb,

     $              ipiv, work, n, info )

            END IF

*

*           Multiply by R.

*

            DO i = 1, n

               work( i ) = work( i ) * rwork( i )

            END DO

         END IF

         GO TO 10

      END IF

*

*     Compute the estimate of the reciprocal condition number.

*

      IF( ainvnm .NE. 0.0e+0 )

     $   cla_gbrcond_x = 1.0e+0 / ainvnm

*

      RETURN

*

*     End of CLA_GBRCOND_X

*


      END

xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285

cgbtrs
subroutine cgbtrs(trans, n, kl, ku, nrhs, ab, ldab, ipiv, b, ldb, info)
CGBTRS
Definition cgbtrs.f:137

cla_gbrcond_x
real function cla_gbrcond_x(trans, n, kl, ku, ab, ldab, afb, ldafb, ipiv, x, info, work, rwork)
CLA_GBRCOND_X computes the infinity norm condition number of op(A)*diag(x) for general banded matrice...
Definition cla_gbrcond_x.f:151

clacn2
subroutine clacn2(n, v, x, est, kase, isave)
CLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
Definition clacn2.f:131

lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48