zla_porcond_x.f

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*> \brief \b ZLA_PORCOND_X computes the infinity norm condition number of op(A)*diag(x) 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_X( UPLO, N, A, LDA, AF,
*                                                LDAF, X, INFO, WORK,
*                                                RWORK )
*
*       .. Scalar Arguments ..
*       CHARACTER          UPLO
*       INTEGER            N, LDA, LDAF, INFO
*       ..
*       .. Array Arguments ..
*       COMPLEX*16         A( LDA, * ), AF( LDAF, * ), WORK( * ), X( * )
*       DOUBLE PRECISION   RWORK( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*>    ZLA_PORCOND_X Computes the infinity norm condition number of
*>    op(A) * diag(X) where X is a COMPLEX*16 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] X
*> \verbatim
*>          X is COMPLEX*16 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*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_x( UPLO, N, A, LDA, AF,
     $                                         LDAF, 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          uplo
      INTEGER            n, lda, ldaf, info
*     ..
*     .. Array Arguments ..
      COMPLEX*16         a( lda, * ), af( ldaf, * ), work( * ), x( * )
      DOUBLE PRECISION   rwork( * )
*     ..
*
*  =====================================================================
*
*     .. Local Scalars ..
      INTEGER            kase, i, j
      DOUBLE PRECISION   ainvnm, anorm, tmp
      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_x = 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_x', -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
            DO J = 1, I
               TMP = TMP + CABS1( A( J, I ) * X( J ) )
            END DO
            DO J = I+1, N
               TMP = TMP + CABS1( A( I, J ) * X( J ) )
            END DO
            RWORK( I ) = TMP
            ANORM = MAX( ANORM, TMP )
         END DO
      ELSE
         DO I = 1, N
            TMP = 0.0D+0
            DO J = 1, I
               TMP = TMP + CABS1( A( I, J ) * X( J ) )
            END DO
            DO J = I+1, N
               TMP = TMP + CABS1( A( J, I ) * X( J ) )
            END DO
            RWORK( I ) = TMP
            ANORM = MAX( ANORM, TMP )
         END DO
      END IF
*
*     Quick return if possible.
*
.EQ.      IF( N0 ) THEN
         ZLA_PORCOND_X = 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(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 ( 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_X = 1.0D+0 / AINVNM
*
      RETURN
*
*     End of ZLA_PORCOND_X
*
      END