dgecon()

subroutine dgecon	(	character	norm,
		integer	n,
		double precision, dimension( lda, * )	a,
		integer	lda,
		double precision	anorm,
		double precision	rcond,
		double precision, dimension( * )	work,
		integer, dimension( * )	iwork,
		integer	info
	)

DGECON

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Purpose:

 DGECON 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 DGETRF.

 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)) ).

Parameters

[in]	NORM	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.
[in]	N	N is INTEGER The order of the matrix A. N >= 0.
[in]	A	A is DOUBLE PRECISION array, dimension (LDA,N) The factors L and U from the factorization A = P*L*U as computed by DGETRF.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
[in]	ANORM	ANORM is DOUBLE PRECISION If NORM = '1' or 'O', the 1-norm of the original matrix A. If NORM = 'I', the infinity-norm of the original matrix A.
[out]	RCOND	RCOND is DOUBLE PRECISION The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))).
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (4*N)
[out]	IWORK	IWORK is INTEGER array, dimension (N)
[out]	INFO	INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value. NaNs are illegal values for ANORM, and they propagate to the output parameter RCOND. Infinity is illegal for ANORM, and it propagates to the output parameter RCOND as 0. = 1: if RCOND = NaN, or RCOND = Inf, or the computed norm of the inverse of A is 0. In the latter, RCOND = 0 is returned.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 130 of file dgecon.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          NORM
      INTEGER            INFO, LDA, N
      DOUBLE PRECISION   ANORM, RCOND
*     ..
*     .. Array Arguments ..
      INTEGER            IWORK( * )
      DOUBLE PRECISION   A( LDA, * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE, ZERO
      parameter( one = 1.0d+0, zero = 0.0d+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            ONENRM
      CHARACTER          NORMIN
      INTEGER            IX, KASE, KASE1
      DOUBLE PRECISION   AINVNM, SCALE, SL, SMLNUM, SU, HUGEVAL
*     ..
*     .. Local Arrays ..
      INTEGER            ISAVE( 3 )
*     ..
*     .. External Functions ..
      LOGICAL            LSAME, DISNAN
      INTEGER            IDAMAX
      DOUBLE PRECISION   DLAMCH
      EXTERNAL           lsame, idamax, dlamch, disnan
*     ..
*     .. External Subroutines ..
      EXTERNAL           dlacn2, dlatrs, drscl, xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs, max
*     ..
*     .. Executable Statements ..
*
      hugeval = dlamch( 'Overflow' )
*
*     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( 'DGECON', -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
      ELSE IF( disnan( anorm ) ) THEN
         rcond = anorm
         info = -5
         RETURN
      ELSE IF( anorm.GT.hugeval ) THEN
         info = -5
         RETURN
      END IF
*
      smlnum = dlamch( '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 dlacn2( n, work( n+1 ), work, iwork, ainvnm, kase, isave )
      IF( kase.NE.0 ) THEN
         IF( kase.EQ.kase1 ) THEN
*
*           Multiply by inv(L).
*
            CALL dlatrs( 'Lower', 'No transpose', 'Unit', normin, n, a,
     $                   lda, work, sl, work( 2*n+1 ), info )
*
*           Multiply by inv(U).
*
            CALL dlatrs( 'Upper', 'No transpose', 'Non-unit', normin, n,
     $                   a, lda, work, su, work( 3*n+1 ), info )
         ELSE
*
*           Multiply by inv(U**T).
*
            CALL dlatrs( 'Upper', 'Transpose', 'Non-unit', normin, n, a,
     $                   lda, work, su, work( 3*n+1 ), info )
*
*           Multiply by inv(L**T).
*
            CALL dlatrs( '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'
         IF( scale.NE.one ) THEN
            ix = idamax( n, work, 1 )
            IF( scale.LT.abs( work( ix ) )*smlnum .OR. scale.EQ.zero )
     $         GO TO 20
            CALL drscl( n, scale, work, 1 )
         END IF
         GO TO 10
      END IF
*
*     Compute the estimate of the reciprocal condition number.
*
      IF( ainvnm.NE.zero ) THEN
         rcond = ( one / ainvnm ) / anorm
      ELSE
         info = 1
         RETURN
      END IF
*
*     Check for NaNs and Infs
*
      IF( disnan( rcond ) .OR. rcond.GT.hugeval )
     $   info = 1
*
   20 CONTINUE
      RETURN
*
*     End of DGECON
*

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