00001 REAL FUNCTION CLA_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 COMPLEX A( LDA, * ), AF( LDAF, * ) 00019 REAL WORK( * ) 00020 * .. 00021 * 00022 * Purpose 00023 * ======= 00024 * 00025 * CLA_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) COMPLEX 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) COMPLEX 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 CPOTRF. 00051 * 00052 * LDAF (input) INTEGER 00053 * The leading dimension of the array AF. LDAF >= max(1,N). 00054 * 00055 * WORK (input) COMPLEX array, dimension (2*N) 00056 * 00057 * ===================================================================== 00058 * 00059 * .. Local Scalars .. 00060 INTEGER I, J 00061 REAL AMAX, UMAX, RPVGRW 00062 LOGICAL UPPER 00063 COMPLEX ZDUM 00064 * .. 00065 * .. External Functions .. 00066 EXTERNAL LSAME, CLASET 00067 LOGICAL LSAME 00068 * .. 00069 * .. Intrinsic Functions .. 00070 INTRINSIC ABS, MAX, MIN, REAL, AIMAG 00071 * .. 00072 * .. Statement Functions .. 00073 REAL CABS1 00074 * .. 00075 * .. Statement Function Definitions .. 00076 CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) ) 00077 * .. 00078 * .. Executable Statements .. 00079 UPPER = LSAME( 'Upper', UPLO ) 00080 * 00081 * SPOTRF will have factored only the NCOLSxNCOLS leading minor, so 00082 * we restrict the growth search to that minor and use only the first 00083 * 2*NCOLS workspace entries. 00084 * 00085 RPVGRW = 1.0 00086 DO I = 1, 2*NCOLS 00087 WORK( I ) = 0.0 00088 END DO 00089 * 00090 * Find the max magnitude entry of each column. 00091 * 00092 IF ( UPPER ) THEN 00093 DO J = 1, NCOLS 00094 DO I = 1, J 00095 WORK( NCOLS+J ) = 00096 $ MAX( CABS1( A( I, J ) ), WORK( NCOLS+J ) ) 00097 END DO 00098 END DO 00099 ELSE 00100 DO J = 1, NCOLS 00101 DO I = J, NCOLS 00102 WORK( NCOLS+J ) = 00103 $ MAX( CABS1( A( I, J ) ), WORK( NCOLS+J ) ) 00104 END DO 00105 END DO 00106 END IF 00107 * 00108 * Now find the max magnitude entry of each column of the factor in 00109 * AF. No pivoting, so no permutations. 00110 * 00111 IF ( LSAME( 'Upper', UPLO ) ) THEN 00112 DO J = 1, NCOLS 00113 DO I = 1, J 00114 WORK( J ) = MAX( CABS1( AF( I, J ) ), WORK( J ) ) 00115 END DO 00116 END DO 00117 ELSE 00118 DO J = 1, NCOLS 00119 DO I = J, NCOLS 00120 WORK( J ) = MAX( CABS1( AF( I, J ) ), WORK( J ) ) 00121 END DO 00122 END DO 00123 END IF 00124 * 00125 * Compute the *inverse* of the max element growth factor. Dividing 00126 * by zero would imply the largest entry of the factor's column is 00127 * zero. Than can happen when either the column of A is zero or 00128 * massive pivots made the factor underflow to zero. Neither counts 00129 * as growth in itself, so simply ignore terms with zero 00130 * denominators. 00131 * 00132 IF ( LSAME( 'Upper', UPLO ) ) THEN 00133 DO I = 1, NCOLS 00134 UMAX = WORK( I ) 00135 AMAX = WORK( NCOLS+I ) 00136 IF ( UMAX /= 0.0 ) THEN 00137 RPVGRW = MIN( AMAX / UMAX, RPVGRW ) 00138 END IF 00139 END DO 00140 ELSE 00141 DO I = 1, NCOLS 00142 UMAX = WORK( I ) 00143 AMAX = WORK( NCOLS+I ) 00144 IF ( UMAX /= 0.0 ) THEN 00145 RPVGRW = MIN( AMAX / UMAX, RPVGRW ) 00146 END IF 00147 END DO 00148 END IF 00149 00150 CLA_PORPVGRW = RPVGRW 00151 END
1.7.2