DOUBLE PRECISION FUNCTION DLA_PORPVGRW( UPLO, NCOLS, A, LDA, AF, \$ LDAF, WORK ) * * -- LAPACK routine (version 3.2.2) -- * -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- * -- Jason Riedy of Univ. of California Berkeley. -- * -- June 2010 -- * * -- 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 .. DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), WORK( * ) * .. * * Purpose * ======= * * DLA_PORPVGRW 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 * ========= * * UPLO (input) CHARACTER*1 * = 'U': Upper triangle of A is stored; * = 'L': Lower triangle of A is stored. * * NCOLS (input) INTEGER * The number of columns of the matrix A. NCOLS >= 0. * * A (input) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (LDAF,N) * The triangular factor U or L from the Cholesky factorization * A = U**T*U or A = L*L**T, as computed by DPOTRF. * * LDAF (input) INTEGER * The leading dimension of the array AF. LDAF >= max(1,N). * * WORK (input) DOUBLE PRECISION array, dimension (2*N) * * ===================================================================== * * .. Local Scalars .. INTEGER I, J DOUBLE PRECISION AMAX, UMAX, RPVGRW LOGICAL UPPER * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, MIN * .. * .. External Functions .. EXTERNAL LSAME, DLASET LOGICAL LSAME * .. * .. Executable Statements .. * UPPER = LSAME( 'Upper', UPLO ) * * DPOTRF 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 = 1.0D+0 DO I = 1, 2*NCOLS WORK( I ) = 0.0D+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 /= 0.0D+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 /= 0.0D+0 ) THEN RPVGRW = MIN( AMAX / UMAX, RPVGRW ) END IF END DO END IF DLA_PORPVGRW = RPVGRW END