chpcon.f

Go to the documentation of this file.

*> \brief \b CHPCON
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 
*
*> \htmlonly
*> Download CHPCON + dependencies 
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/chpcon.f"> 
*> [TGZ]</a> 
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/chpcon.f"> 
*> [ZIP]</a> 
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/chpcon.f"> 
*> [TXT]</a>
*> \endhtmlonly 
*
*  Definition:
*  ===========
*
*       SUBROUTINE CHPCON( UPLO, N, AP, IPIV, ANORM, RCOND, WORK, INFO )
* 
*       .. Scalar Arguments ..
*       CHARACTER          UPLO
*       INTEGER            INFO, N
*       REAL               ANORM, RCOND
*       ..
*       .. Array Arguments ..
*       INTEGER            IPIV( * )
*       COMPLEX            AP( * ), WORK( * )
*       ..
*  
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> CHPCON estimates the reciprocal of the condition number of a complex
*> Hermitian packed matrix A using the factorization A = U*D*U**H or
*> A = L*D*L**H computed by CHPTRF.
*>
*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
*> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] UPLO
*> \verbatim
*>          UPLO is CHARACTER*1
*>          Specifies whether the details of the factorization are stored
*>          as an upper or lower triangular matrix.
*>          = 'U':  Upper triangular, form is A = U*D*U**H;
*>          = 'L':  Lower triangular, form is A = L*D*L**H.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the matrix A.  N >= 0.
*> \endverbatim
*>
*> \param[in] AP
*> \verbatim
*>          AP is COMPLEX array, dimension (N*(N+1)/2)
*>          The block diagonal matrix D and the multipliers used to
*>          obtain the factor U or L as computed by CHPTRF, stored as a
*>          packed triangular matrix.
*> \endverbatim
*>
*> \param[in] IPIV
*> \verbatim
*>          IPIV is INTEGER array, dimension (N)
*>          Details of the interchanges and the block structure of D
*>          as determined by CHPTRF.
*> \endverbatim
*>
*> \param[in] ANORM
*> \verbatim
*>          ANORM is REAL
*>          The 1-norm of the original matrix A.
*> \endverbatim
*>
*> \param[out] RCOND
*> \verbatim
*>          RCOND is REAL
*>          The reciprocal of the condition number of the matrix A,
*>          computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
*>          estimate of the 1-norm of inv(A) computed in this routine.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is COMPLEX 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
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date November 2011
*
*> \ingroup complexOTHERcomputational
*
*  =====================================================================
      SUBROUTINE chpcon( UPLO, N, AP, IPIV, ANORM, RCOND, WORK, INFO )
*
*  -- LAPACK computational routine (version 3.4.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2011
*
*     .. Scalar Arguments ..
      CHARACTER          uplo
      INTEGER            info, n
      REAL               anorm, rcond
*     ..
*     .. Array Arguments ..
      INTEGER            ipiv( * )
      COMPLEX            ap( * ), work( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               one, zero
      parameter( one = 1.0e+0, zero = 0.0e+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            upper
      INTEGER            i, ip, kase
      REAL               ainvnm
*     ..
*     .. Local Arrays ..
      INTEGER            isave( 3 )
*     ..
*     .. External Functions ..
      LOGICAL            lsame
      EXTERNAL           lsame
*     ..
*     .. External Subroutines ..
      EXTERNAL           chptrs, clacn2, xerbla
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      info = 0
      upper = lsame( uplo, 'U' )
      IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
         info = -1
      ELSE IF( n.LT.0 ) THEN
         info = -2
      ELSE IF( anorm.LT.zero ) THEN
         info = -5
      END IF
      IF( info.NE.0 ) THEN
         CALL xerbla( 'CHPCON', -info )
         return
      END IF
*
*     Quick return if possible
*
      rcond = zero
      IF( n.EQ.0 ) THEN
         rcond = one
         return
      ELSE IF( anorm.LE.zero ) THEN
         return
      END IF
*
*     Check that the diagonal matrix D is nonsingular.
*
      IF( upper ) THEN
*
*        Upper triangular storage: examine D from bottom to top
*
         ip = n*( n+1 ) / 2
         DO 10 i = n, 1, -1
            IF( ipiv( i ).GT.0 .AND. ap( ip ).EQ.zero )
     $         return
            ip = ip - i
   10    continue
      ELSE
*
*        Lower triangular storage: examine D from top to bottom.
*
         ip = 1
         DO 20 i = 1, n
            IF( ipiv( i ).GT.0 .AND. ap( ip ).EQ.zero )
     $         return
            ip = ip + n - i + 1
   20    continue
      END IF
*
*     Estimate the 1-norm of the inverse.
*
      kase = 0
   30 continue
      CALL clacn2( n, work( n+1 ), work, ainvnm, kase, isave )
      IF( kase.NE.0 ) THEN
*
*        Multiply by inv(L*D*L**H) or inv(U*D*U**H).
*
         CALL chptrs( uplo, n, 1, ap, ipiv, work, n, info )
         go to 30
      END IF
*
*     Compute the estimate of the reciprocal condition number.
*
      IF( ainvnm.NE.zero )
     $   rcond = ( one / ainvnm ) / anorm
*
      return
*
*     End of CHPCON
*
      END