zla__porcond__c_8f_source.html

*> \brief \b ZLA_PORCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian positive-definite matrices.

*

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

*

* Online html documentation available at

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

*

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*

*  Definition:

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

*

*       DOUBLE PRECISION FUNCTION ZLA_PORCOND_C( UPLO, N, A, LDA, AF,

*                                                LDAF, C, CAPPLY, INFO,

*                                                WORK, RWORK )

*

*       .. Scalar Arguments ..

*       CHARACTER          UPLO

*       LOGICAL            CAPPLY

*       INTEGER            N, LDA, LDAF, INFO

*       ..

*       .. Array Arguments ..

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

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

*       ..

*

*

*> \par Purpose:

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

*>

*> \verbatim

*>

*>    ZLA_PORCOND_C Computes the infinity norm condition number of

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

*> \endverbatim

*

*  Arguments:

*  ==========

*

*> \param[in] UPLO

*> \verbatim

*>          UPLO is CHARACTER*1

*>       = 'U':  Upper triangle of A is stored;

*>       = 'L':  Lower triangle of A is stored.

*> \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 triangular factor U or L from the Cholesky factorization

*>     A = U**H*U or A = L*L**H, as computed by ZPOTRF.

*> \endverbatim

*>

*> \param[in] LDAF

*> \verbatim

*>          LDAF is INTEGER

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

*> \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 complex16POcomputational

*

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


      DOUBLE PRECISION FUNCTION zla_porcond_c( UPLO, N, A, LDA, AF,

     $                                         LDAF, 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          uplo

      LOGICAL            capply

      INTEGER            n, lda, ldaf, info

*     ..

*     .. Array Arguments ..

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

      DOUBLE PRECISION   c( * ), rwork( * )

*     ..

*

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

*

*     .. Local Scalars ..

      INTEGER            kase

      DOUBLE PRECISION   ainvnm, anorm, tmp

      INTEGER            i, j

      LOGICAL            up, upper

      COMPLEX*16         zdum

*     ..

*     .. Local Arrays ..

      INTEGER            isave( 3 )

*     ..

*     .. External Functions ..

      LOGICAL            lsame

      EXTERNAL           lsame

*     ..

*     .. External Subroutines ..

      EXTERNAL           zlacn2, zpotrs, 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_porcond_c = 0.0d+0

*

      info = 0

      upper = lsame( uplo, 'u' )

.NOT..AND..NOT.      IF( UPPER  LSAME( UPLO, 'l' ) ) THEN

         INFO = -1

.LT.      ELSE IF( N0 ) THEN

         INFO = -2

.LT.      ELSE IF( LDAMAX( 1, N ) ) THEN

         INFO = -4

.LT.      ELSE IF( LDAFMAX( 1, N ) ) THEN

         INFO = -6

      END IF

.NE.      IF( INFO0 ) THEN

         CALL XERBLA( 'zla_porcond_c', -INFO )

         RETURN

      END IF

      UP = .FALSE.

      IF ( LSAME( UPLO, 'u' ) ) UP = .TRUE.

*

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

*

      ANORM = 0.0D+0

      IF ( UP ) THEN

         DO I = 1, N

            TMP = 0.0D+0

            IF ( CAPPLY ) THEN

               DO J = 1, I

                  TMP = TMP + CABS1( A( J, I ) ) / C( J )

               END DO

               DO J = I+1, N

                  TMP = TMP + CABS1( A( I, J ) ) / C( J )

               END DO

            ELSE

               DO J = 1, I

                  TMP = TMP + CABS1( A( J, I ) )

               END DO

               DO J = I+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, I

                  TMP = TMP + CABS1( A( I, J ) ) / C( J )

               END DO

               DO J = I+1, N

                  TMP = TMP + CABS1( A( J, I ) ) / C( J )

               END DO

            ELSE

               DO J = 1, I

                  TMP = TMP + CABS1( A( I, J ) )

               END DO

               DO J = I+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.

*

.EQ.      IF( N0 ) THEN

         ZLA_PORCOND_C = 1.0D+0

         RETURN

.EQ.      ELSE IF( ANORM  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 )

.NE.      IF( KASE0 ) THEN

.EQ.         IF( KASE2 ) THEN

*

*           Multiply by R.

*

            DO I = 1, N

               WORK( I ) = WORK( I ) * RWORK( I )

            END DO

*

            IF ( UP ) THEN

               CALL ZPOTRS( 'u', N, 1, AF, LDAF,

     $            WORK, N, INFO )

            ELSE

               CALL ZPOTRS( 'l', N, 1, AF, LDAF,

     $            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 ( UP ) THEN

               CALL ZPOTRS( 'u', N, 1, AF, LDAF,

     $            WORK, N, INFO )

            ELSE

               CALL ZPOTRS( 'l', N, 1, AF, LDAF,

     $            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.

*

.NE.      IF( AINVNM  0.0D+0 )

     $   ZLA_PORCOND_C = 1.0D+0 / AINVNM

*

      RETURN

*

*     End of ZLA_PORCOND_C

*


      END

xerbla
subroutine xerbla(srname, info)
XERBLA
Definition xerbla.f:60

lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:53

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

zla_porcond_c
double precision function zla_porcond_c(uplo, n, a, lda, af, ldaf, c, capply, info, work, rwork)
ZLA_PORCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian positiv...
Definition zla_porcond_c.f:132

zpotrs
subroutine zpotrs(uplo, n, nrhs, a, lda, b, ldb, info)
ZPOTRS
Definition zpotrs.f:110

max
#define max(a, b)
Definition macros.h:21