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REAL FUNCTION SLA_PORPVGRW( UPLO, NCOLS, A, LDA, AF, LDAF, WORK )
*
* -- LAPACK routine (version 3.2) --
* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --
* -- Jason Riedy of Univ. of California Berkeley. --
* -- November 2008 --
*
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley and NAG Ltd. --
*
IMPLICIT NONE
* ..
* .. Scalar Arguments ..
CHARACTER*1 UPLO
INTEGER NCOLS, LDA, LDAF
* ..
* .. Array Arguments ..
REAL A( LDA, * ), AF( LDAF, * ), WORK( * )
* ..
*
* Purpose
* =======
*
* SLA_PORPVGRW computes ... .
*
* Arguments
* =========
*
* =====================================================================
*
* .. Local Scalars ..
INTEGER I, J
REAL AMAX, UMAX, RPVGRW
LOGICAL UPPER
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX, MIN
* ..
* .. External Functions ..
EXTERNAL LSAME, SLASET
LOGICAL LSAME
* ..
* .. Executable Statements ..
*
UPPER = LSAME( 'Upper', UPLO )
*
* SPOTRF will have factored only the NCOLSxNCOLS leading minor, so
* we restrict the growth search to that minor and use only the first
* 2*NCOLS workspace entries.
*
RPVGRW = 1.0
DO I = 1, 2*NCOLS
WORK( I ) = 0.0
END DO
*
* Find the max magnitude entry of each column.
*
IF ( UPPER ) THEN
DO J = 1, NCOLS
DO I = 1, J
WORK( NCOLS+J ) =
$ MAX( ABS( A( I, J ) ), WORK( NCOLS+J ) )
END DO
END DO
ELSE
DO J = 1, NCOLS
DO I = J, NCOLS
WORK( NCOLS+J ) =
$ MAX( ABS( A( I, J ) ), WORK( NCOLS+J ) )
END DO
END DO
END IF
*
* Now find the max magnitude entry of each column of the factor in
* AF. No pivoting, so no permutations.
*
IF ( LSAME( 'Upper', UPLO ) ) THEN
DO J = 1, NCOLS
DO I = 1, J
WORK( J ) = MAX( ABS( AF( I, J ) ), WORK( J ) )
END DO
END DO
ELSE
DO J = 1, NCOLS
DO I = J, NCOLS
WORK( J ) = MAX( ABS( AF( I, J ) ), WORK( J ) )
END DO
END DO
END IF
*
* Compute the *inverse* of the max element growth factor. Dividing
* by zero would imply the largest entry of the factor's column is
* zero. Than can happen when either the column of A is zero or
* massive pivots made the factor underflow to zero. Neither counts
* as growth in itself, so simply ignore terms with zero
* denominators.
*
IF ( LSAME( 'Upper', UPLO ) ) THEN
DO I = 1, NCOLS
UMAX = WORK( I )
AMAX = WORK( NCOLS+I )
IF ( UMAX /= 0.0 ) THEN
RPVGRW = MIN( AMAX / UMAX, RPVGRW )
END IF
END DO
ELSE
DO I = 1, NCOLS
UMAX = WORK( I )
AMAX = WORK( NCOLS+I )
IF ( UMAX /= 0.0 ) THEN
RPVGRW = MIN( AMAX / UMAX, RPVGRW )
END IF
END DO
END IF
SLA_PORPVGRW = RPVGRW
END FUNCTION
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