sla_gerpvgrw()

real function sla_gerpvgrw	(	integer	n,
		integer	ncols,
		real, dimension( lda, * )	a,
		integer	lda,
		real, dimension( ldaf, * )	af,
		integer	ldaf
	)

SLA_GERPVGRW

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Purpose:

 SLA_GERPVGRW computes the reciprocal pivot growth factor
 norm(A)/norm(U). The "max absolute element" norm is used. If this is
 much less than 1, the stability of the LU factorization of the
 (equilibrated) matrix A could be poor. This also means that the
 solution X, estimated condition numbers, and error bounds could be
 unreliable.

Parameters

[in]	N	N is INTEGER The number of linear equations, i.e., the order of the matrix A. N >= 0.
[in]	NCOLS	NCOLS is INTEGER The number of columns of the matrix A. NCOLS >= 0.
[in]	A	A is REAL array, dimension (LDA,N) On entry, the N-by-N matrix A.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
[in]	AF	AF is REAL array, dimension (LDAF,N) The factors L and U from the factorization A = P*L*U as computed by SGETRF.
[in]	LDAF	LDAF is INTEGER The leading dimension of the array AF. LDAF >= max(1,N).

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 96 of file sla_gerpvgrw.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 ..
      INTEGER            N, NCOLS, LDA, LDAF
*     ..
*     .. Array Arguments ..
      REAL               A( LDA, * ), AF( LDAF, * )
*     ..
*
*  =====================================================================
*
*     .. Local Scalars ..
      INTEGER            I, J
      REAL               AMAX, UMAX, RPVGRW
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs, max, min
*     ..
*     .. Executable Statements ..
*
      rpvgrw = 1.0
 
      DO j = 1, ncols
         amax = 0.0
         umax = 0.0
         DO i = 1, n
            amax = max( abs( a( i, j ) ), amax )
         END DO
         DO i = 1, j
            umax = max( abs( af( i, j ) ), umax )
         END DO
         IF ( umax /= 0.0 ) THEN
            rpvgrw = min( amax / umax, rpvgrw )
         END IF
      END DO
      sla_gerpvgrw = rpvgrw
*
*     End of SLA_GERPVGRW
*

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