00001 DOUBLE PRECISION FUNCTION DLA_PORPVGRW( UPLO, NCOLS, A, LDA, AF, 00002 $ LDAF, WORK ) 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 CHARACTER*1 UPLO 00016 INTEGER NCOLS, LDA, LDAF 00017 * .. 00018 * .. Array Arguments .. 00019 DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), WORK( * ) 00020 * .. 00021 * 00022 * Purpose 00023 * ======= 00024 * 00025 * DLA_PORPVGRW computes the reciprocal pivot growth factor 00026 * norm(A)/norm(U). The "max absolute element" norm is used. If this is 00027 * much less than 1, the stability of the LU factorization of the 00028 * (equilibrated) matrix A could be poor. This also means that the 00029 * solution X, estimated condition numbers, and error bounds could be 00030 * unreliable. 00031 * 00032 * Arguments 00033 * ========= 00034 * 00035 * UPLO (input) CHARACTER*1 00036 * = 'U': Upper triangle of A is stored; 00037 * = 'L': Lower triangle of A is stored. 00038 * 00039 * NCOLS (input) INTEGER 00040 * The number of columns of the matrix A. NCOLS >= 0. 00041 * 00042 * A (input) DOUBLE PRECISION array, dimension (LDA,N) 00043 * On entry, the N-by-N matrix A. 00044 * 00045 * LDA (input) INTEGER 00046 * The leading dimension of the array A. LDA >= max(1,N). 00047 * 00048 * AF (input) DOUBLE PRECISION array, dimension (LDAF,N) 00049 * The triangular factor U or L from the Cholesky factorization 00050 * A = U**T*U or A = L*L**T, as computed by DPOTRF. 00051 * 00052 * LDAF (input) INTEGER 00053 * The leading dimension of the array AF. LDAF >= max(1,N). 00054 * 00055 * WORK (input) DOUBLE PRECISION array, dimension (2*N) 00056 * 00057 * ===================================================================== 00058 * 00059 * .. Local Scalars .. 00060 INTEGER I, J 00061 DOUBLE PRECISION AMAX, UMAX, RPVGRW 00062 LOGICAL UPPER 00063 * .. 00064 * .. Intrinsic Functions .. 00065 INTRINSIC ABS, MAX, MIN 00066 * .. 00067 * .. External Functions .. 00068 EXTERNAL LSAME, DLASET 00069 LOGICAL LSAME 00070 * .. 00071 * .. Executable Statements .. 00072 * 00073 UPPER = LSAME( 'Upper', UPLO ) 00074 * 00075 * DPOTRF will have factored only the NCOLSxNCOLS leading minor, so 00076 * we restrict the growth search to that minor and use only the first 00077 * 2*NCOLS workspace entries. 00078 * 00079 RPVGRW = 1.0D+0 00080 DO I = 1, 2*NCOLS 00081 WORK( I ) = 0.0D+0 00082 END DO 00083 * 00084 * Find the max magnitude entry of each column. 00085 * 00086 IF ( UPPER ) THEN 00087 DO J = 1, NCOLS 00088 DO I = 1, J 00089 WORK( NCOLS+J ) = 00090 $ MAX( ABS( A( I, J ) ), WORK( NCOLS+J ) ) 00091 END DO 00092 END DO 00093 ELSE 00094 DO J = 1, NCOLS 00095 DO I = J, NCOLS 00096 WORK( NCOLS+J ) = 00097 $ MAX( ABS( A( I, J ) ), WORK( NCOLS+J ) ) 00098 END DO 00099 END DO 00100 END IF 00101 * 00102 * Now find the max magnitude entry of each column of the factor in 00103 * AF. No pivoting, so no permutations. 00104 * 00105 IF ( LSAME( 'Upper', UPLO ) ) THEN 00106 DO J = 1, NCOLS 00107 DO I = 1, J 00108 WORK( J ) = MAX( ABS( AF( I, J ) ), WORK( J ) ) 00109 END DO 00110 END DO 00111 ELSE 00112 DO J = 1, NCOLS 00113 DO I = J, NCOLS 00114 WORK( J ) = MAX( ABS( AF( I, J ) ), WORK( J ) ) 00115 END DO 00116 END DO 00117 END IF 00118 * 00119 * Compute the *inverse* of the max element growth factor. Dividing 00120 * by zero would imply the largest entry of the factor's column is 00121 * zero. Than can happen when either the column of A is zero or 00122 * massive pivots made the factor underflow to zero. Neither counts 00123 * as growth in itself, so simply ignore terms with zero 00124 * denominators. 00125 * 00126 IF ( LSAME( 'Upper', UPLO ) ) THEN 00127 DO I = 1, NCOLS 00128 UMAX = WORK( I ) 00129 AMAX = WORK( NCOLS+I ) 00130 IF ( UMAX /= 0.0D+0 ) THEN 00131 RPVGRW = MIN( AMAX / UMAX, RPVGRW ) 00132 END IF 00133 END DO 00134 ELSE 00135 DO I = 1, NCOLS 00136 UMAX = WORK( I ) 00137 AMAX = WORK( NCOLS+I ) 00138 IF ( UMAX /= 0.0D+0 ) THEN 00139 RPVGRW = MIN( AMAX / UMAX, RPVGRW ) 00140 END IF 00141 END DO 00142 END IF 00143 00144 DLA_PORPVGRW = RPVGRW 00145 END
1.7.2