ctrcon.f

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*> \brief \b CTRCON
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
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*> \endhtmlonly
*
*  Definition:
*  ===========
*
*       SUBROUTINE CTRCON( NORM, UPLO, DIAG, N, A, LDA, RCOND, WORK,
*                          RWORK, INFO )
*
*       .. Scalar Arguments ..
*       CHARACTER          DIAG, NORM, UPLO
*       INTEGER            INFO, LDA, N
*       REAL               RCOND
*       ..
*       .. Array Arguments ..
*       REAL               RWORK( * )
*       COMPLEX            A( LDA, * ), WORK( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> CTRCON estimates the reciprocal of the condition number of a
*> triangular matrix A, in either the 1-norm or the infinity-norm.
*>
*> The norm of A is computed and an estimate is obtained for
*> norm(inv(A)), then 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] UPLO
*> \verbatim
*>          UPLO is CHARACTER*1
*>          = 'U':  A is upper triangular;
*>          = 'L':  A is lower triangular.
*> \endverbatim
*>
*> \param[in] DIAG
*> \verbatim
*>          DIAG is CHARACTER*1
*>          = 'N':  A is non-unit triangular;
*>          = 'U':  A is unit triangular.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the matrix A.  N >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*>          A is COMPLEX array, dimension (LDA,N)
*>          The triangular matrix A.  If UPLO = 'U', the leading N-by-N
*>          upper triangular part of the array A contains the upper
*>          triangular matrix, and the strictly lower triangular part of
*>          A is not referenced.  If UPLO = 'L', the leading N-by-N lower
*>          triangular part of the array A contains the lower triangular
*>          matrix, and the strictly upper triangular part of A is not
*>          referenced.  If DIAG = 'U', the diagonal elements of A are
*>          also not referenced and are assumed to be 1.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A.  LDA >= max(1,N).
*> \endverbatim
*>
*> \param[out] RCOND
*> \verbatim
*>          RCOND is REAL
*>          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 array, dimension (2*N)
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*>          RWORK is REAL array, dimension (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.
*
*> \ingroup trcon
*
*  =====================================================================
      SUBROUTINE ctrcon( NORM, UPLO, DIAG, N, A, LDA, 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          DIAG, NORM, UPLO
      INTEGER            INFO, LDA, N
      REAL               RCOND
*     ..
*     .. Array Arguments ..
      REAL               RWORK( * )
      COMPLEX            A( LDA, * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ONE, ZERO
      parameter( one = 1.0e+0, zero = 0.0e+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            NOUNIT, ONENRM, UPPER
      CHARACTER          NORMIN
      INTEGER            IX, KASE, KASE1
      REAL               AINVNM, ANORM, SCALE, SMLNUM, XNORM
      COMPLEX            ZDUM
*     ..
*     .. Local Arrays ..
      INTEGER            ISAVE( 3 )
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      INTEGER            ICAMAX
      REAL               CLANTR, SLAMCH
      EXTERNAL           lsame, icamax, clantr, slamch
*     ..
*     .. External Subroutines ..
      EXTERNAL           clacn2, clatrs, csrscl, xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs, aimag, max, real
*     ..
*     .. Statement Functions ..
      REAL               CABS1
*     ..
*     .. Statement Function definitions ..
      cabs1( zdum ) = abs( real( zdum ) ) + abs( aimag( zdum ) )
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      info = 0
      upper = lsame( uplo, 'U' )
      onenrm = norm.EQ.'1' .OR. lsame( norm, 'O' )
      nounit = lsame( diag, 'N' )
*
      IF( .NOT.onenrm .AND. .NOT.lsame( norm, 'I' ) ) THEN
         info = -1
      ELSE IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
         info = -2
      ELSE IF( .NOT.nounit .AND. .NOT.lsame( diag, 'U' ) ) THEN
         info = -3
      ELSE IF( n.LT.0 ) THEN
         info = -4
      ELSE IF( lda.LT.max( 1, n ) ) THEN
         info = -6
      END IF
      IF( info.NE.0 ) THEN
         CALL xerbla( 'CTRCON', -info )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( n.EQ.0 ) THEN
         rcond = one
         RETURN
      END IF
*
      rcond = zero
      smlnum = slamch( 'Safe minimum' )*real( max( 1, n ) )
*
*     Compute the norm of the triangular matrix A.
*
      anorm = clantr( norm, uplo, diag, n, n, a, lda, rwork )
*
*     Continue only if ANORM > 0.
*
      IF( anorm.GT.zero ) THEN
*
*        Estimate the norm of the inverse of A.
*
         ainvnm = zero
         normin = 'N'
         IF( onenrm ) THEN
            kase1 = 1
         ELSE
            kase1 = 2
         END IF
         kase = 0
   10    CONTINUE
         CALL clacn2( n, work( n+1 ), work, ainvnm, kase, isave )
         IF( kase.NE.0 ) THEN
            IF( kase.EQ.kase1 ) THEN
*
*              Multiply by inv(A).
*
               CALL clatrs( uplo, 'No transpose', diag, normin, n, a,
     $                      lda, work, scale, rwork, info )
            ELSE
*
*              Multiply by inv(A**H).
*
               CALL clatrs( uplo, 'Conjugate transpose', diag, normin,
     $                      n, a, lda, work, scale, rwork, info )
            END IF
            normin = 'Y'
*
*           Multiply by 1/SCALE if doing so will not cause overflow.
*
            IF( scale.NE.one ) THEN
               ix = icamax( n, work, 1 )
               xnorm = cabs1( work( ix ) )
               IF( scale.LT.xnorm*smlnum .OR. scale.EQ.zero )
     $            GO TO 20
               CALL csrscl( n, scale, work, 1 )
            END IF
            GO TO 10
         END IF
*
*        Compute the estimate of the reciprocal condition number.
*
         IF( ainvnm.NE.zero )
     $      rcond = ( one / anorm ) / ainvnm
      END IF
*
   20 CONTINUE
      RETURN
*
*     End of CTRCON
*
      END