00001 REAL FUNCTION SLA_RPVGRW( N, NCOLS, A, LDA, AF, LDAF ) 00002 * 00003 * -- LAPACK routine (version 3.2.2) -- 00004 * -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- 00005 * -- Jason Riedy of Univ. of California Berkeley. -- 00006 * -- June 2010 -- 00007 * 00008 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00009 * -- Univ. of California Berkeley and NAG Ltd. -- 00010 * 00011 IMPLICIT NONE 00012 * .. 00013 * .. Scalar Arguments .. 00014 INTEGER N, NCOLS, LDA, LDAF 00015 * .. 00016 * .. Array Arguments .. 00017 REAL A( LDA, * ), AF( LDAF, * ) 00018 * .. 00019 * 00020 * Purpose 00021 * ======= 00022 * 00023 * SLA_RPVGRW computes the reciprocal pivot growth factor 00024 * norm(A)/norm(U). The "max absolute element" norm is used. If this is 00025 * much less than 1, the stability of the LU factorization of the 00026 * (equilibrated) matrix A could be poor. This also means that the 00027 * solution X, estimated condition numbers, and error bounds could be 00028 * unreliable. 00029 * 00030 * Arguments 00031 * ========= 00032 * 00033 * N (input) INTEGER 00034 * The number of linear equations, i.e., the order of the 00035 * matrix A. N >= 0. 00036 * 00037 * NCOLS (input) INTEGER 00038 * The number of columns of the matrix A. NCOLS >= 0. 00039 * 00040 * A (input) REAL array, dimension (LDA,N) 00041 * On entry, the N-by-N matrix A. 00042 * 00043 * LDA (input) INTEGER 00044 * The leading dimension of the array A. LDA >= max(1,N). 00045 * 00046 * AF (input) REAL array, dimension (LDAF,N) 00047 * The factors L and U from the factorization 00048 * A = P*L*U as computed by SGETRF. 00049 * 00050 * LDAF (input) INTEGER 00051 * The leading dimension of the array AF. LDAF >= max(1,N). 00052 * 00053 * ===================================================================== 00054 * 00055 * .. Local Scalars .. 00056 INTEGER I, J 00057 REAL AMAX, UMAX, RPVGRW 00058 * .. 00059 * .. Intrinsic Functions .. 00060 INTRINSIC ABS, MAX, MIN 00061 * .. 00062 * .. Executable Statements .. 00063 * 00064 RPVGRW = 1.0 00065 00066 DO J = 1, NCOLS 00067 AMAX = 0.0 00068 UMAX = 0.0 00069 DO I = 1, N 00070 AMAX = MAX( ABS( A( I, J ) ), AMAX ) 00071 END DO 00072 DO I = 1, J 00073 UMAX = MAX( ABS( AF( I, J ) ), UMAX ) 00074 END DO 00075 IF ( UMAX /= 0.0 ) THEN 00076 RPVGRW = MIN( AMAX / UMAX, RPVGRW ) 00077 END IF 00078 END DO 00079 SLA_RPVGRW = RPVGRW 00080 END
1.7.2