d7/d93/zla__gercond__c_8f_source.html

*> \brief \b ZLA_GERCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for general matrices.

*

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

*

* Online html documentation available at

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

*

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*

*  Definition:

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

*

*       DOUBLE PRECISION FUNCTION ZLA_GERCOND_C( TRANS, N, A, LDA, AF,

*                                                LDAF, IPIV, C, CAPPLY,

*                                                INFO, WORK, RWORK )

*

*       .. Scalar Arguments ..

*       CHARACTER          TRANS

*       LOGICAL            CAPPLY

*       INTEGER            N, LDA, LDAF, INFO

*       ..

*       .. Array Arguments ..

*       INTEGER            IPIV( * )

*       COMPLEX*16         A( LDA, * ), AF( LDAF, * ), WORK( * )

*       DOUBLE PRECISION   C( * ), RWORK( * )

*       ..

*

*

*> \par Purpose:

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

*>

*> \verbatim

*>

*>    ZLA_GERCOND_C computes the infinity norm condition number of

*>    op(A) * inv(diag(C)) where C is a DOUBLE PRECISION 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] A

*> \verbatim

*>          A is COMPLEX*16 array, dimension (LDA,N)

*>     On entry, the N-by-N matrix A

*> \endverbatim

*>

*> \param[in] LDA

*> \verbatim

*>          LDA is INTEGER

*>     The leading dimension of the array A.  LDA >= max(1,N).

*> \endverbatim

*>

*> \param[in] AF

*> \verbatim

*>          AF is COMPLEX*16 array, dimension (LDAF,N)

*>     The factors L and U from the factorization

*>     A = P*L*U as computed by ZGETRF.

*> \endverbatim

*>

*> \param[in] LDAF

*> \verbatim

*>          LDAF is INTEGER

*>     The leading dimension of the array AF.  LDAF >= max(1,N).

*> \endverbatim

*>

*> \param[in] IPIV

*> \verbatim

*>          IPIV is INTEGER array, dimension (N)

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

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

*>     with row IPIV(i).

*> \endverbatim

*>

*> \param[in] C

*> \verbatim

*>          C is DOUBLE PRECISION array, dimension (N)

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

*> \endverbatim

*>

*> \param[in] CAPPLY

*> \verbatim

*>          CAPPLY is LOGICAL

*>     If .TRUE. then access the vector C in the formula above.

*> \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*16 array, dimension (2*N).

*>     Workspace.

*> \endverbatim

*>

*> \param[out] RWORK

*> \verbatim

*>          RWORK is DOUBLE PRECISION array, dimension (N).

*>     Workspace.

*> \endverbatim

*

*  Authors:

*  ========

*

*> \author Univ. of Tennessee

*> \author Univ. of California Berkeley

*> \author Univ. of Colorado Denver

*> \author NAG Ltd.

*

*> \ingroup complex16GEcomputational

*

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

      DOUBLE PRECISION FUNCTION zla_gercond_c( TRANS, N, A, LDA, AF,

     $                                         LDAF, IPIV, C, CAPPLY,

     $                                         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

      LOGICAL            capply

      INTEGER            n, lda, ldaf, info

*     ..

*     .. Array Arguments ..

      INTEGER            ipiv( * )

      COMPLEX*16         a( lda, * ), af( ldaf, * ), work( * )

      DOUBLE PRECISION   c( * ), rwork( * )

*     ..

*

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

*

*     .. Local Scalars ..

      LOGICAL            notrans

      INTEGER            kase, i, j

      DOUBLE PRECISION   ainvnm, anorm, tmp

      COMPLEX*16         zdum

*     ..

*     .. Local Arrays ..

      INTEGER            isave( 3 )

*     ..

*     .. External Functions ..

      LOGICAL            lsame

      EXTERNAL           lsame

*     ..

*     .. External Subroutines ..

      EXTERNAL           zlacn2, zgetrs, xerbla

*     ..

*     .. Intrinsic Functions ..

      INTRINSIC          abs, max, real, dimag

*     ..

*     .. Statement Functions ..

      DOUBLE PRECISION   cabs1

*     ..

*     .. Statement Function Definitions ..

      cabs1( zdum ) = abs( dble( zdum ) ) + abs( dimag( zdum ) )

*     ..

*     .. Executable Statements ..

      zla_gercond_c = 0.0d+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( lda.LT.max( 1, n ) ) THEN

         info = -4

      ELSE IF( ldaf.LT.max( 1, n ) ) THEN

         info = -6

      END IF

      IF( info.NE.0 ) THEN

         CALL xerbla( 'ZLA_GERCOND_C', -info )

         RETURN

      END IF

*

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

*

      anorm = 0.0d+0

      IF ( notrans ) THEN

         DO i = 1, n

            tmp = 0.0d+0

            IF ( capply ) THEN

               DO j = 1, n

                  tmp = tmp + cabs1( a( i, j ) ) / c( j )

               END DO

            ELSE

               DO j = 1, n

                  tmp = tmp + cabs1( a( i, j ) )

               END DO

            END IF

            rwork( i ) = tmp

            anorm = max( anorm, tmp )

         END DO

      ELSE

         DO i = 1, n

            tmp = 0.0d+0

            IF ( capply ) THEN

               DO j = 1, n

                  tmp = tmp + cabs1( a( j, i ) ) / c( j )

               END DO

            ELSE

               DO j = 1, n

                  tmp = tmp + cabs1( a( j, i ) )

               END DO

            END IF

            rwork( i ) = tmp

            anorm = max( anorm, tmp )

         END DO

      END IF

*

*     Quick return if possible.

*

      IF( n.EQ.0 ) THEN

         zla_gercond_c = 1.0d+0

         RETURN

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

         RETURN

      END IF

*

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

*

      ainvnm = 0.0d+0

*

      kase = 0

   10 CONTINUE

      CALL zlacn2( 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 zgetrs( 'No transpose', n, 1, af, ldaf, ipiv,

     $            work, n, info )

            ELSE

               CALL zgetrs( 'Conjugate transpose', n, 1, af, ldaf, ipiv,

     $            work, n, info )

            ENDIF

*

*           Multiply by inv(C).

*

            IF ( capply ) THEN

               DO i = 1, n

                  work( i ) = work( i ) * c( i )

               END DO

            END IF

         ELSE

*

*           Multiply by inv(C**H).

*

            IF ( capply ) THEN

               DO i = 1, n

                  work( i ) = work( i ) * c( i )

               END DO

            END IF

*

            IF ( notrans ) THEN

               CALL zgetrs( 'Conjugate transpose', n, 1, af, ldaf, ipiv,

     $            work, n, info )

            ELSE

               CALL zgetrs( 'No transpose', n, 1, af, ldaf, 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. 0.0d+0 )

     $   zla_gercond_c = 1.0d+0 / ainvnm

*

      RETURN

*

*     End of ZLA_GERCOND_C

*

      END

xerbla
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60

lsame
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53

zgetrs
subroutine zgetrs(TRANS, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
ZGETRS
Definition: zgetrs.f:121

zla_gercond_c
double precision function zla_gercond_c(TRANS, N, A, LDA, AF, LDAF, IPIV, C, CAPPLY, INFO, WORK, RWORK)
ZLA_GERCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for general matrices.
Definition: zla_gercond_c.f:143

zlacn2
subroutine zlacn2(N, V, X, EST, KASE, ISAVE)
ZLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
Definition: zlacn2.f:133