cpocon()

subroutine cpocon	(	character	uplo,
		integer	n,
		complex, dimension( lda, * )	a,
		integer	lda,
		real	anorm,
		real	rcond,
		complex, dimension( * )	work,
		real, dimension( * )	rwork,
		integer	info )

CPOCON

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Purpose:

!>
!> CPOCON estimates the reciprocal of the condition number (in the
!> 1-norm) of a complex Hermitian positive definite matrix using the
!> Cholesky factorization A = U**H*U or A = L*L**H computed by CPOTRF.
!>
!> An estimate is obtained for norm(inv(A)), and the reciprocal of the
!> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
!> 

Parameters

[in]	UPLO	!> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !>
[in]	N	!> N is INTEGER !> The order of the matrix A. N >= 0. !>
[in]	A	!> A is COMPLEX array, dimension (LDA,N) !> The triangular factor U or L from the Cholesky factorization !> A = U**H*U or A = L*L**H, as computed by CPOTRF. !>
[in]	LDA	!> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !>
[in]	ANORM	!> ANORM is REAL !> The 1-norm (or infinity-norm) of the Hermitian matrix A. !>
[out]	RCOND	!> 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. !>
[out]	WORK	!> WORK is COMPLEX array, dimension (2*N) !>
[out]	RWORK	!> RWORK is REAL array, dimension (N) !>
[out]	INFO	!> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 117 of file cpocon.f.

*
*  -- 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 ..
      REAL               RWORK( * )
      COMPLEX            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
      COMPLEX            ZDUM
*     ..
*     .. Local Arrays ..
      INTEGER            ISAVE( 3 )
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      INTEGER            ICAMAX
      REAL               SLAMCH
      EXTERNAL           lsame, icamax, 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' )
      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( 'CPOCON', -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 clacn2( n, work( n+1 ), work, ainvnm, kase, isave )
      IF( kase.NE.0 ) THEN
         IF( upper ) THEN
*
*           Multiply by inv(U**H).
*
            CALL clatrs( 'Upper', 'Conjugate transpose', 'Non-unit',
     $                   normin, n, a, lda, work, scalel, rwork, info )
            normin = 'Y'
*
*           Multiply by inv(U).
*
            CALL clatrs( 'Upper', 'No transpose', 'Non-unit', normin,
     $                   n,
     $                   a, lda, work, scaleu, rwork, info )
         ELSE
*
*           Multiply by inv(L).
*
            CALL clatrs( 'Lower', 'No transpose', 'Non-unit', normin,
     $                   n,
     $                   a, lda, work, scalel, rwork, info )
            normin = 'Y'
*
*           Multiply by inv(L**H).
*
            CALL clatrs( 'Lower', 'Conjugate transpose', 'Non-unit',
     $                   normin, n, a, lda, work, scaleu, rwork, info )
         END IF
*
*        Multiply by 1/SCALE if doing so will not cause overflow.
*
         scale = scalel*scaleu
         IF( scale.NE.one ) THEN
            ix = icamax( n, work, 1 )
            IF( scale.LT.cabs1( work( ix ) )*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 / ainvnm ) / anorm
*
   20 CONTINUE
      RETURN
*
*     End of CPOCON
*

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