00001 REAL FUNCTION SLA_PORPVGRW( UPLO, NCOLS, A, LDA, AF, LDAF, WORK ) 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 CHARACTER*1 UPLO 00015 INTEGER NCOLS, LDA, LDAF 00016 * .. 00017 * .. Array Arguments .. 00018 REAL A( LDA, * ), AF( LDAF, * ), WORK( * ) 00019 * .. 00020 * 00021 * Purpose 00022 * ======= 00023 * 00024 * SLA_PORPVGRW 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 * UPLO (input) CHARACTER*1 00035 * = 'U': Upper triangle of A is stored; 00036 * = 'L': Lower triangle of A is stored. 00037 * 00038 * NCOLS (input) INTEGER 00039 * The number of columns of the matrix A. NCOLS >= 0. 00040 * 00041 * A (input) REAL array, dimension (LDA,N) 00042 * On entry, the N-by-N matrix A. 00043 * 00044 * LDA (input) INTEGER 00045 * The leading dimension of the array A. LDA >= max(1,N). 00046 * 00047 * AF (input) REAL array, dimension (LDAF,N) 00048 * The triangular factor U or L from the Cholesky factorization 00049 * A = U**T*U or A = L*L**T, as computed by SPOTRF. 00050 * 00051 * LDAF (input) INTEGER 00052 * The leading dimension of the array AF. LDAF >= max(1,N). 00053 * 00054 * WORK (input) REAL array, dimension (2*N) 00055 * 00056 * ===================================================================== 00057 * 00058 * .. Local Scalars .. 00059 INTEGER I, J 00060 REAL AMAX, UMAX, RPVGRW 00061 LOGICAL UPPER 00062 * .. 00063 * .. Intrinsic Functions .. 00064 INTRINSIC ABS, MAX, MIN 00065 * .. 00066 * .. External Functions .. 00067 EXTERNAL LSAME, SLASET 00068 LOGICAL LSAME 00069 * .. 00070 * .. Executable Statements .. 00071 * 00072 UPPER = LSAME( 'Upper', UPLO ) 00073 * 00074 * SPOTRF will have factored only the NCOLSxNCOLS leading minor, so 00075 * we restrict the growth search to that minor and use only the first 00076 * 2*NCOLS workspace entries. 00077 * 00078 RPVGRW = 1.0 00079 DO I = 1, 2*NCOLS 00080 WORK( I ) = 0.0 00081 END DO 00082 * 00083 * Find the max magnitude entry of each column. 00084 * 00085 IF ( UPPER ) THEN 00086 DO J = 1, NCOLS 00087 DO I = 1, J 00088 WORK( NCOLS+J ) = 00089 $ MAX( ABS( A( I, J ) ), WORK( NCOLS+J ) ) 00090 END DO 00091 END DO 00092 ELSE 00093 DO J = 1, NCOLS 00094 DO I = J, NCOLS 00095 WORK( NCOLS+J ) = 00096 $ MAX( ABS( A( I, J ) ), WORK( NCOLS+J ) ) 00097 END DO 00098 END DO 00099 END IF 00100 * 00101 * Now find the max magnitude entry of each column of the factor in 00102 * AF. No pivoting, so no permutations. 00103 * 00104 IF ( LSAME( 'Upper', UPLO ) ) THEN 00105 DO J = 1, NCOLS 00106 DO I = 1, J 00107 WORK( J ) = MAX( ABS( AF( I, J ) ), WORK( J ) ) 00108 END DO 00109 END DO 00110 ELSE 00111 DO J = 1, NCOLS 00112 DO I = J, NCOLS 00113 WORK( J ) = MAX( ABS( AF( I, J ) ), WORK( J ) ) 00114 END DO 00115 END DO 00116 END IF 00117 * 00118 * Compute the *inverse* of the max element growth factor. Dividing 00119 * by zero would imply the largest entry of the factor's column is 00120 * zero. Than can happen when either the column of A is zero or 00121 * massive pivots made the factor underflow to zero. Neither counts 00122 * as growth in itself, so simply ignore terms with zero 00123 * denominators. 00124 * 00125 IF ( LSAME( 'Upper', UPLO ) ) THEN 00126 DO I = 1, NCOLS 00127 UMAX = WORK( I ) 00128 AMAX = WORK( NCOLS+I ) 00129 IF ( UMAX /= 0.0 ) THEN 00130 RPVGRW = MIN( AMAX / UMAX, RPVGRW ) 00131 END IF 00132 END DO 00133 ELSE 00134 DO I = 1, NCOLS 00135 UMAX = WORK( I ) 00136 AMAX = WORK( NCOLS+I ) 00137 IF ( UMAX /= 0.0 ) THEN 00138 RPVGRW = MIN( AMAX / UMAX, RPVGRW ) 00139 END IF 00140 END DO 00141 END IF 00142 00143 SLA_PORPVGRW = RPVGRW 00144 END
1.7.2