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REAL FUNCTION SLA_RPVGRW( N, NCOLS, A, LDA, AF, LDAF )
*
* -- LAPACK routine (version 3.2.1) --
* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --
* -- Jason Riedy of Univ. of California Berkeley. --
* -- April 2009 --
*
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley and NAG Ltd. --
*
IMPLICIT NONE
* ..
* .. Scalar Arguments ..
INTEGER N, NCOLS, LDA, LDAF
* ..
* .. Array Arguments ..
REAL A( LDA, * ), AF( LDAF, * )
* ..
*
* Purpose
* =======
*
* SLA_RPVGRW 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.
*
* Arguments
* =========
*
* N (input) INTEGER
* The number of linear equations, i.e., the order of the
* matrix A. N >= 0.
*
* NCOLS (input) INTEGER
* The number of columns of the matrix A. NCOLS >= 0.
*
* A (input) REAL array, dimension (LDA,N)
* On entry, the N-by-N matrix A.
*
* LDA (input) INTEGER
* The leading dimension of the array A. LDA >= max(1,N).
*
* AF (input) REAL array, dimension (LDAF,N)
* The factors L and U from the factorization
* A = P*L*U as computed by SGETRF.
*
* LDAF (input) INTEGER
* The leading dimension of the array AF. LDAF >= max(1,N).
*
* =====================================================================
*
* .. 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_RPVGRW = RPVGRW
END
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