00001 DOUBLE PRECISION FUNCTION DLA_GBRPVGRW( N, KL, KU, NCOLS, AB, 00002 $ LDAB, AFB, LDAFB ) 00003 * 00004 * -- LAPACK routine (version 3.2.2) -- 00005 * -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- 00006 * -- Jason Riedy of Univ. of California Berkeley. -- 00007 * -- June 2010 -- 00008 * 00009 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00010 * -- Univ. of California Berkeley and NAG Ltd. -- 00011 * 00012 IMPLICIT NONE 00013 * .. 00014 * .. Scalar Arguments .. 00015 INTEGER N, KL, KU, NCOLS, LDAB, LDAFB 00016 * .. 00017 * .. Array Arguments .. 00018 DOUBLE PRECISION AB( LDAB, * ), AFB( LDAFB, * ) 00019 * .. 00020 * 00021 * Purpose 00022 * ======= 00023 * 00024 * DLA_GBRPVGRW computes the reciprocal pivot growth factor 00025 * norm(A)/norm(U). The "max absolute element" norm is used. If this is 00026 * much less than 1, the stability of the LU factorization of the 00027 * (equilibrated) matrix A could be poor. This also means that the 00028 * solution X, estimated condition numbers, and error bounds could be 00029 * unreliable. 00030 * 00031 * Arguments 00032 * ========= 00033 * 00034 * N (input) INTEGER 00035 * The number of linear equations, i.e., the order of the 00036 * matrix A. N >= 0. 00037 * 00038 * KL (input) INTEGER 00039 * The number of subdiagonals within the band of A. KL >= 0. 00040 * 00041 * KU (input) INTEGER 00042 * The number of superdiagonals within the band of A. KU >= 0. 00043 * 00044 * NCOLS (input) INTEGER 00045 * The number of columns of the matrix A. NCOLS >= 0. 00046 * 00047 * AB (input) DOUBLE PRECISION array, dimension (LDAB,N) 00048 * On entry, the matrix A in band storage, in rows 1 to KL+KU+1. 00049 * The j-th column of A is stored in the j-th column of the 00050 * array AB as follows: 00051 * AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl) 00052 * 00053 * LDAB (input) INTEGER 00054 * The leading dimension of the array AB. LDAB >= KL+KU+1. 00055 * 00056 * AFB (input) DOUBLE PRECISION array, dimension (LDAFB,N) 00057 * Details of the LU factorization of the band matrix A, as 00058 * computed by DGBTRF. U is stored as an upper triangular 00059 * band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, 00060 * and the multipliers used during the factorization are stored 00061 * in rows KL+KU+2 to 2*KL+KU+1. 00062 * 00063 * LDAFB (input) INTEGER 00064 * The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1. 00065 * 00066 * ===================================================================== 00067 * 00068 * .. Local Scalars .. 00069 INTEGER I, J, KD 00070 DOUBLE PRECISION AMAX, UMAX, RPVGRW 00071 * .. 00072 * .. Intrinsic Functions .. 00073 INTRINSIC ABS, MAX, MIN 00074 * .. 00075 * .. Executable Statements .. 00076 * 00077 RPVGRW = 1.0D+0 00078 00079 KD = KU + 1 00080 DO J = 1, NCOLS 00081 AMAX = 0.0D+0 00082 UMAX = 0.0D+0 00083 DO I = MAX( J-KU, 1 ), MIN( J+KL, N ) 00084 AMAX = MAX( ABS( AB( KD+I-J, J)), AMAX ) 00085 END DO 00086 DO I = MAX( J-KU, 1 ), J 00087 UMAX = MAX( ABS( AFB( KD+I-J, J ) ), UMAX ) 00088 END DO 00089 IF ( UMAX /= 0.0D+0 ) THEN 00090 RPVGRW = MIN( AMAX / UMAX, RPVGRW ) 00091 END IF 00092 END DO 00093 DLA_GBRPVGRW = RPVGRW 00094 END
1.7.2