cla_gercond_x.f

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*> \brief \b CLA_GERCOND_X computes the infinity norm condition number of op(A)*diag(x) for general matrices.
*
*  =========== DOCUMENTATION ===========
*
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*
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*
*  Definition:
*  ===========
*
*       REAL FUNCTION CLA_GERCOND_X( TRANS, N, A, LDA, AF, LDAF, IPIV, X,
*                                    INFO, WORK, RWORK )
*
*       .. Scalar Arguments ..
*       CHARACTER          TRANS
*       INTEGER            N, LDA, LDAF, INFO
*       ..
*       .. Array Arguments ..
*       INTEGER            IPIV( * )
*       COMPLEX            A( LDA, * ), AF( LDAF, * ), WORK( * ), X( * )
*       REAL               RWORK( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*>
*>    CLA_GERCOND_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] A
*> \verbatim
*>          A is COMPLEX 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 array, dimension (LDAF,N)
*>     The factors L and U from the factorization
*>     A = P*L*U as computed by CGETRF.
*> \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 CGETRF; 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 complexGEcomputational
*
*  =====================================================================
      REAL function cla_gercond_x( trans, n, a, lda, af, ldaf, 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, lda, ldaf, info
*     ..
*     .. Array Arguments ..
      INTEGER            ipiv( * )
      COMPLEX            a( lda, * ), af( ldaf, * ), work( * ), x( * )
      REAL               rwork( * )
*     ..
*
*  =====================================================================
*
*     .. Local Scalars ..
      LOGICAL            notrans
      INTEGER            kase
      REAL               ainvnm, anorm, tmp
      INTEGER            i, j
      COMPLEX            zdum
*     ..
*     .. Local Arrays ..
      INTEGER            isave( 3 )
*     ..
*     .. External Functions ..
      LOGICAL            lsame
      EXTERNAL           lsame
*     ..
*     .. External Subroutines ..
      EXTERNAL           clacn2, cgetrs, xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs, max, real, aimag
*     ..
*     .. Statement Functions ..
      REAL               cabs1
*     ..
*     .. Statement Function Definitions ..
      cabs1( zdum ) = abs( real( zdum ) ) + abs( aimag( zdum ) )
*     ..
*     .. Executable Statements ..
*
      cla_gercond_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( 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( 'CLA_GERCOND_X', -info )
         RETURN
      END IF
*
*     Compute norm of op(A)*op2(C).
*
      anorm = 0.0
      IF ( notrans ) THEN
         DO i = 1, n
            tmp = 0.0e+0
            DO j = 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 = 0.0e+0
            DO j = 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.
*
      IF( n.EQ.0 ) THEN
         cla_gercond_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 cgetrs( 'No transpose', n, 1, af, ldaf, ipiv,
     $            work, n, info )
            ELSE
               CALL cgetrs( 'Conjugate transpose', n, 1, af, ldaf, 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 cgetrs( 'Conjugate transpose', n, 1, af, ldaf, ipiv,
     $            work, n, info )
            ELSE
               CALL cgetrs( '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. 0.0e+0 )
     $   cla_gercond_x = 1.0e+0 / ainvnm
*
      RETURN
*
*     End of CLA_GERCOND_X
*
      END