zgecon.f

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*> \brief \b ZGECON
*
*  =========== DOCUMENTATION ===========
*
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*            http://www.netlib.org/lapack/explore-html/
*
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*
*  Definition:
*  ===========
*
*       SUBROUTINE ZGECON( NORM, N, A, LDA, ANORM, RCOND, WORK, RWORK,
*                          INFO )
*
*       .. Scalar Arguments ..
*       CHARACTER          NORM
*       INTEGER            INFO, LDA, N
*       DOUBLE PRECISION   ANORM, RCOND
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION   RWORK( * )
*       COMPLEX*16         A( LDA, * ), WORK( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> ZGECON estimates the reciprocal of the condition number of a general
*> complex matrix A, in either the 1-norm or the infinity-norm, using
*> the LU factorization computed by ZGETRF.
*>
*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
*> condition number is computed as
*>    RCOND = 1 / ( norm(A) * norm(inv(A)) ).
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] NORM
*> \verbatim
*>          NORM is CHARACTER*1
*>          Specifies whether the 1-norm condition number or the
*>          infinity-norm condition number is required:
*>          = '1' or 'O':  1-norm;
*>          = 'I':         Infinity-norm.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the matrix A.  N >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*>          A is COMPLEX*16 array, dimension (LDA,N)
*>          The factors L and U from the factorization A = P*L*U
*>          as computed by ZGETRF.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A.  LDA >= max(1,N).
*> \endverbatim
*>
*> \param[in] ANORM
*> \verbatim
*>          ANORM is DOUBLE PRECISION
*>          If NORM = '1' or 'O', the 1-norm of the original matrix A.
*>          If NORM = 'I', the infinity-norm of the original matrix A.
*> \endverbatim
*>
*> \param[out] RCOND
*> \verbatim
*>          RCOND is DOUBLE PRECISION
*>          The reciprocal of the condition number of the matrix A,
*>          computed as RCOND = 1/(norm(A) * norm(inv(A))).
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is COMPLEX*16 array, dimension (2*N)
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*>          RWORK is DOUBLE PRECISION array, dimension (2*N)
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*>          INFO is INTEGER
*>          = 0:  successful exit
*>          < 0:  if INFO = -i, the i-th argument had an illegal value.
*>                NaNs are illegal values for ANORM, and they propagate to
*>                the output parameter RCOND.
*>                Infinity is illegal for ANORM, and it propagates to the output
*>                parameter RCOND as 0.
*>          = 1:  if RCOND = NaN, or
*>                   RCOND = Inf, or
*>                   the computed norm of the inverse of A is 0.
*>                In the latter, RCOND = 0 is returned.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup gecon
*
*  =====================================================================
      SUBROUTINE zgecon( NORM, N, A, LDA, ANORM, RCOND, WORK, RWORK,
     $                   INFO )
*
*  -- 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          NORM
      INTEGER            INFO, LDA, N
      DOUBLE PRECISION   ANORM, RCOND
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   RWORK( * )
      COMPLEX*16         A( LDA, * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE, ZERO
      parameter( one = 1.0d+0, zero = 0.0d+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            ONENRM
      CHARACTER          NORMIN
      INTEGER            IX, KASE, KASE1
      DOUBLE PRECISION   AINVNM, SCALE, SL, SMLNUM, SU, HUGEVAL
      COMPLEX*16         ZDUM
*     ..
*     .. Local Arrays ..
      INTEGER            ISAVE( 3 )
*     ..
*     .. External Functions ..
      LOGICAL            LSAME, DISNAN
      INTEGER            IZAMAX
      DOUBLE PRECISION   DLAMCH
      EXTERNAL           lsame, izamax, dlamch, disnan
*     ..
*     .. External Subroutines ..
      EXTERNAL           xerbla, zdrscl, zlacn2, zlatrs
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs, dble, dimag, max
*     ..
*     .. Statement Functions ..
      DOUBLE PRECISION   CABS1
*     ..
*     .. Statement Function definitions ..
      cabs1( zdum ) = abs( dble( zdum ) ) + abs( dimag( zdum ) )
*     ..
*     .. Executable Statements ..
*
      hugeval = dlamch( 'Overflow' )
*
*     Test the input parameters.
*
      info = 0
      onenrm = norm.EQ.'1' .OR. lsame( norm, 'O' )
      IF( .NOT.onenrm .AND. .NOT.lsame( norm, 'I' ) ) THEN
         info = -1
      ELSE IF( n.LT.0 ) THEN
         info = -2
      ELSE IF( lda.LT.max( 1, n ) ) THEN
         info = -4
      ELSE IF( anorm.LT.zero ) THEN
         info = -5
      END IF
      IF( info.NE.0 ) THEN
         CALL xerbla( 'ZGECON', -info )
         RETURN
      END IF
*
*     Quick return if possible
*
      rcond = zero
      IF( n.EQ.0 ) THEN
         rcond = one
         RETURN
      ELSE IF( anorm.EQ.zero ) THEN
         RETURN
      ELSE IF( disnan( anorm ) ) THEN
         rcond = anorm
         info = -5
         RETURN
      ELSE IF( anorm.GT.hugeval ) THEN
         info = -5
         RETURN
      END IF
*
      smlnum = dlamch( 'Safe minimum' )
*
*     Estimate the norm of inv(A).
*
      ainvnm = zero
      normin = 'N'
      IF( onenrm ) THEN
         kase1 = 1
      ELSE
         kase1 = 2
      END IF
      kase = 0
   10 CONTINUE
      CALL zlacn2( n, work( n+1 ), work, ainvnm, kase, isave )
      IF( kase.NE.0 ) THEN
         IF( kase.EQ.kase1 ) THEN
*
*           Multiply by inv(L).
*
            CALL zlatrs( 'Lower', 'No transpose', 'Unit', normin, n,
     $                   a,
     $                   lda, work, sl, rwork, info )
*
*           Multiply by inv(U).
*
            CALL zlatrs( 'Upper', 'No transpose', 'Non-unit', normin,
     $                   n,
     $                   a, lda, work, su, rwork( n+1 ), info )
         ELSE
*
*           Multiply by inv(U**H).
*
            CALL zlatrs( 'Upper', 'Conjugate transpose', 'Non-unit',
     $                   normin, n, a, lda, work, su, rwork( n+1 ),
     $                   info )
*
*           Multiply by inv(L**H).
*
            CALL zlatrs( 'Lower', 'Conjugate transpose', 'Unit',
     $                   normin,
     $                   n, a, lda, work, sl, rwork, info )
         END IF
*
*        Divide X by 1/(SL*SU) if doing so will not cause overflow.
*
         scale = sl*su
         normin = 'Y'
         IF( scale.NE.one ) THEN
            ix = izamax( n, work, 1 )
            IF( scale.LT.cabs1( work( ix ) )*smlnum .OR. scale.EQ.zero )
     $         GO TO 20
            CALL zdrscl( n, scale, work, 1 )
         END IF
         GO TO 10
      END IF
*
*     Compute the estimate of the reciprocal condition number.
*
      IF( ainvnm.NE.zero ) THEN
         rcond = ( one / ainvnm ) / anorm
      ELSE
         info = 1
         RETURN
      END IF
*
*     Check for NaNs and Infs
*
      IF( disnan( rcond ) .OR. rcond.GT.hugeval )
     $   info = 1
*
   20 CONTINUE
      RETURN
*
*     End of ZGECON
*
      SUBROUTINE zgecon( NORM, N, A, LDA, ANORM, RCOND, WORK, RWORK, …
      END