spocon.f

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      SUBROUTINE spocon( UPLO, N, A, LDA, ANORM, RCOND, WORK, IWORK,
     $                   info )
*
*  -- LAPACK routine (version 3.2) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     November 2006
*
*     Modified to call SLACN2 in place of SLACON, 7 Feb 03, SJH.
*
*     .. Scalar Arguments ..
      CHARACTER          uplo
      INTEGER            info, lda, n
      REAL               anorm, rcond
*     ..
*     .. Array Arguments ..
      INTEGER            iwork( * )
      REAL               a( lda, * ), work( * )
*     ..
*
*  Purpose
*  =======
*
*  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))).
*
*  Arguments
*  =========
*
*  UPLO    (input) CHARACTER*1
*          = 'U':  Upper triangle of A is stored;
*          = 'L':  Lower triangle of A is stored.
*
*  N       (input) INTEGER
*          The order of the matrix A.  N >= 0.
*
*  A       (input) 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.
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A.  LDA >= max(1,N).
*
*  ANORM   (input) REAL
*          The 1-norm (or infinity-norm) of the symmetric matrix A.
*
*  RCOND   (output) 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.
*
*  WORK    (workspace) REAL array, dimension (3*N)
*
*  IWORK   (workspace) INTEGER array, dimension (N)
*
*  INFO    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument had an illegal value
*
*  =====================================================================
*
*     .. 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').
*
            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').
*
            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