spocon.f

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*> \brief \b SPOCON
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
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*
*  Definition:
*  ===========
*
*       SUBROUTINE SPOCON( UPLO, N, A, LDA, ANORM, RCOND, WORK, IWORK,
*                          INFO )
*
*       .. Scalar Arguments ..
*       CHARACTER          UPLO
*       INTEGER            INFO, LDA, N
*       REAL               ANORM, RCOND
*       ..
*       .. Array Arguments ..
*       INTEGER            IWORK( * )
*       REAL               A( LDA, * ), WORK( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> SPOCON estimates the reciprocal of the condition number (in the
*> 1-norm) of a real symmetric positive definite matrix using the
*> Cholesky factorization A = U**T*U or A = L*L**T computed by SPOTRF.
*>
*> 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
*>          = 'U':  Upper triangle of A is stored;
*>          = 'L':  Lower triangle of A is stored.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the matrix A.  N >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*>          A is REAL array, dimension (LDA,N)
*>          The triangular factor U or L from the Cholesky factorization
*>          A = U**T*U or A = L*L**T, as computed by SPOTRF.
*> \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 REAL
*>          The 1-norm (or infinity-norm) of the symmetric 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 REAL array, dimension (3*N)
*> \endverbatim
*>
*> \param[out] IWORK
*> \verbatim
*>          IWORK is INTEGER 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 pocon
*
*  =====================================================================
      SUBROUTINE spocon( UPLO, N, A, LDA, ANORM, RCOND, WORK, IWORK,
     $                   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          UPLO
      INTEGER            INFO, LDA, N
      REAL               ANORM, RCOND
*     ..
*     .. Array Arguments ..
      INTEGER            IWORK( * )
      REAL               A( LDA, * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ONE, ZERO
      parameter( one = 1.0e+0, zero = 0.0e+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            UPPER
      CHARACTER          NORMIN
      INTEGER            IX, KASE
      REAL               AINVNM, SCALE, SCALEL, SCALEU, SMLNUM
*     ..
*     .. Local Arrays ..
      INTEGER            ISAVE( 3 )
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      INTEGER            ISAMAX
      REAL               SLAMCH
      EXTERNAL           lsame, isamax, slamch
*     ..
*     .. External Subroutines ..
      EXTERNAL           slacn2, slatrs, srscl, xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs, max
*     ..
*     .. 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( 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( 'SPOCON', -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
      END IF
*
      smlnum = slamch( 'Safe minimum' )
*
*     Estimate the 1-norm of inv(A).
*
      kase = 0
      normin = 'N'
   10 CONTINUE
      CALL slacn2( n, work( n+1 ), work, iwork, ainvnm, kase, isave )
      IF( kase.NE.0 ) THEN
         IF( upper ) THEN
*
*           Multiply by inv(U**T).
*
            CALL slatrs( 'Upper', 'Transpose', 'Non-unit', normin, n,
     $                   a,
     $                   lda, work, scalel, work( 2*n+1 ), info )
            normin = 'Y'
*
*           Multiply by inv(U).
*
            CALL slatrs( 'Upper', 'No transpose', 'Non-unit', normin,
     $                   n,
     $                   a, lda, work, scaleu, work( 2*n+1 ), info )
         ELSE
*
*           Multiply by inv(L).
*
            CALL slatrs( 'Lower', 'No transpose', 'Non-unit', normin,
     $                   n,
     $                   a, lda, work, scalel, work( 2*n+1 ), info )
            normin = 'Y'
*
*           Multiply by inv(L**T).
*
            CALL slatrs( 'Lower', 'Transpose', 'Non-unit', normin, n,
     $                   a,
     $                   lda, work, scaleu, work( 2*n+1 ), info )
         END IF
*
*        Multiply by 1/SCALE if doing so will not cause overflow.
*
         scale = scalel*scaleu
         IF( scale.NE.one ) THEN
            ix = isamax( n, work, 1 )
            IF( scale.LT.abs( work( ix ) )*smlnum .OR. scale.EQ.zero )
     $         GO TO 20
            CALL srscl( 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 / ainvnm ) / anorm
*
   20 CONTINUE
      RETURN
*
*     End of SPOCON
*
      END