sgecon.f

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*> \brief \b SGECON
*
*  =========== DOCUMENTATION ===========
*
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*            http://www.netlib.org/lapack/explore-html/
*
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*
*  Definition:
*  ===========
*
*       SUBROUTINE SGECON( NORM, N, A, LDA, ANORM, RCOND, WORK, IWORK,
*                          INFO )
*
*       .. Scalar Arguments ..
*       CHARACTER          NORM
*       INTEGER            INFO, LDA, N
*       REAL               ANORM, RCOND
*       ..
*       .. Array Arguments ..
*       INTEGER            IWORK( * )
*       REAL               A( LDA, * ), WORK( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> SGECON estimates the reciprocal of the condition number of a general
*> real matrix A, in either the 1-norm or the infinity-norm, using
*> the LU factorization computed by SGETRF.
*>
*> 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 REAL array, dimension (LDA,N)
*>          The factors L and U from the factorization A = P*L*U
*>          as computed by SGETRF.
*> \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
*>          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 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 REAL array, dimension (4*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 realGEcomputational
*
*  =====================================================================
      SUBROUTINE sgecon( NORM, 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          NORM
      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            ONENRM
      CHARACTER          NORMIN
      INTEGER            IX, KASE, KASE1
      REAL               AINVNM, SCALE, SL, SMLNUM, SU
*     ..
*     .. 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
      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( 'sgecon', -INFO )
         RETURN
      END IF
*
*     Quick return if possible
*
      RCOND = ZERO
.EQ.      IF( N0 ) THEN
         RCOND = ONE
         RETURN
.EQ.      ELSE IF( ANORMZERO ) THEN
         RETURN
      END IF
*
      SMLNUM = SLAMCH( '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 SLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
.NE.      IF( KASE0 ) THEN
.EQ.         IF( KASEKASE1 ) THEN
*
*           Multiply by inv(L).
*
            CALL SLATRS( 'lower', 'no transpose', 'unit', NORMIN, N, A,
     $                   LDA, WORK, SL, WORK( 2*N+1 ), INFO )
*
*           Multiply by inv(U).
*
            CALL SLATRS( 'upper', 'no transpose', 'non-unit', NORMIN, N,
     $                   A, LDA, WORK, SU, WORK( 3*N+1 ), INFO )
         ELSE
*
*           Multiply by inv(U**T).
*
            CALL SLATRS( 'upper', 'transpose', 'non-unit', NORMIN, N, A,
     $                   LDA, WORK, SU, WORK( 3*N+1 ), INFO )
*
*           Multiply by inv(L**T).
*
            CALL SLATRS( 'lower', 'transpose', 'unit', NORMIN, N, A,
     $                   LDA, WORK, SL, WORK( 2*N+1 ), INFO )
         END IF
*
*        Divide X by 1/(SL*SU) if doing so will not cause overflow.
*
         SCALE = SL*SU
         NORMIN = 'y'
.NE.         IF( SCALEONE ) THEN
            IX = ISAMAX( N, WORK, 1 )
.LT..OR..EQ.            IF( SCALEABS( WORK( IX ) )*SMLNUM  SCALEZERO )
     $         GO TO 20
            CALL SRSCL( N, SCALE, WORK, 1 )
         END IF
         GO TO 10
      END IF
*
*     Compute the estimate of the reciprocal condition number.
*
.NE.      IF( AINVNMZERO )
     $   RCOND = ( ONE / AINVNM ) / ANORM
*
   20 CONTINUE
      RETURN
*
*     End of SGECON
*
      END