|
1
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 |
REAL FUNCTION SLA_PORCOND( UPLO, N, A, LDA, AF, LDAF, CMODE, C,
$ INFO, WORK, IWORK ) * * -- LAPACK routine (version 3.2.1) -- * -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- * -- Jason Riedy of Univ. of California Berkeley. -- * -- April 2009 -- * * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley and NAG Ltd. -- * IMPLICIT NONE * .. * .. Scalar Arguments .. CHARACTER UPLO INTEGER N, LDA, LDAF, INFO, CMODE REAL A( LDA, * ), AF( LDAF, * ), WORK( * ), $ C( * ) * .. * .. Array Arguments .. INTEGER IWORK( * ) * .. * * Purpose * ======= * * SLA_PORCOND Estimates the Skeel condition number of op(A) * op2(C) * where op2 is determined by CMODE as follows * CMODE = 1 op2(C) = C * CMODE = 0 op2(C) = I * CMODE = -1 op2(C) = inv(C) * The Skeel condition number cond(A) = norminf( |inv(A)||A| ) * is computed by computing scaling factors R such that * diag(R)*A*op2(C) is row equilibrated and computing the standard * infinity-norm condition number. * * Arguments * ========== * * UPLO (input) CHARACTER*1 * = 'U': Upper triangle of A is stored; * = 'L': Lower triangle of A is stored. * * N (input) INTEGER * The number of linear equations, i.e., the order of the * matrix A. N >= 0. * * A (input) REAL array, dimension (LDA,N) * On entry, the N-by-N matrix A. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N). * * AF (input) REAL array, dimension (LDAF,N) * The triangular factor U or L from the Cholesky factorization * A = U**T*U or A = L*L**T, as computed by SPOTRF. * * LDAF (input) INTEGER * The leading dimension of the array AF. LDAF >= max(1,N). * * CMODE (input) INTEGER * Determines op2(C) in the formula op(A) * op2(C) as follows: * CMODE = 1 op2(C) = C * CMODE = 0 op2(C) = I * CMODE = -1 op2(C) = inv(C) * * C (input) REAL array, dimension (N) * The vector C in the formula op(A) * op2(C). * * INFO (output) INTEGER * = 0: Successful exit. * i > 0: The ith argument is invalid. * * WORK (input) REAL array, dimension (3*N). * Workspace. * * IWORK (input) INTEGER array, dimension (N). * Workspace. * * ===================================================================== * * .. Local Scalars .. INTEGER KASE, I, J REAL AINVNM, TMP LOGICAL UP * .. * .. Array Arguments .. INTEGER ISAVE( 3 ) * .. * .. External Functions .. LOGICAL LSAME INTEGER ISAMAX EXTERNAL LSAME, ISAMAX * .. * .. External Subroutines .. EXTERNAL SLACN2, SPOTRS, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX * .. * .. Executable Statements .. * SLA_PORCOND = 0.0 * INFO = 0 IF( N.LT.0 ) THEN INFO = -2 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'SLA_PORCOND', -INFO ) RETURN END IF IF( N.EQ.0 ) THEN SLA_PORCOND = 1.0 RETURN END IF UP = .FALSE. IF ( LSAME( UPLO, 'U' ) ) UP = .TRUE. * * Compute the equilibration matrix R such that * inv(R)*A*C has unit 1-norm. * IF ( UP ) THEN DO I = 1, N TMP = 0.0 IF ( CMODE .EQ. 1 ) THEN DO J = 1, I TMP = TMP + ABS( A( J, I ) * C( J ) ) END DO DO J = I+1, N TMP = TMP + ABS( A( I, J ) * C( J ) ) END DO ELSE IF ( CMODE .EQ. 0 ) THEN DO J = 1, I TMP = TMP + ABS( A( J, I ) ) END DO DO J = I+1, N TMP = TMP + ABS( A( I, J ) ) END DO ELSE DO J = 1, I TMP = TMP + ABS( A( J ,I ) / C( J ) ) END DO DO J = I+1, N TMP = TMP + ABS( A( I, J ) / C( J ) ) END DO END IF WORK( 2*N+I ) = TMP END DO ELSE DO I = 1, N TMP = 0.0 IF ( CMODE .EQ. 1 ) THEN DO J = 1, I TMP = TMP + ABS( A( I, J ) * C( J ) ) END DO DO J = I+1, N TMP = TMP + ABS( A( J, I ) * C( J ) ) END DO ELSE IF ( CMODE .EQ. 0 ) THEN DO J = 1, I TMP = TMP + ABS( A( I, J ) ) END DO DO J = I+1, N TMP = TMP + ABS( A( J, I ) ) END DO ELSE DO J = 1, I TMP = TMP + ABS( A( I, J ) / C( J ) ) END DO DO J = I+1, N TMP = TMP + ABS( A( J, I ) / C( J ) ) END DO END IF WORK( 2*N+I ) = TMP END DO ENDIF * * Estimate the norm of inv(op(A)). * AINVNM = 0.0 KASE = 0 10 CONTINUE CALL SLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE ) IF( KASE.NE.0 ) THEN IF( KASE.EQ.2 ) THEN * * Multiply by R. * DO I = 1, N WORK( I ) = WORK( I ) * WORK( 2*N+I ) END DO IF (UP) THEN CALL SPOTRS( 'Upper', N, 1, AF, LDAF, WORK, N, INFO ) ELSE CALL SPOTRS( 'Lower', N, 1, AF, LDAF, WORK, N, INFO ) ENDIF * * Multiply by inv(C). * IF ( CMODE .EQ. 1 ) THEN DO I = 1, N WORK( I ) = WORK( I ) / C( I ) END DO ELSE IF ( CMODE .EQ. -1 ) THEN DO I = 1, N WORK( I ) = WORK( I ) * C( I ) END DO END IF ELSE * * Multiply by inv(C**T). * IF ( CMODE .EQ. 1 ) THEN DO I = 1, N WORK( I ) = WORK( I ) / C( I ) END DO ELSE IF ( CMODE .EQ. -1 ) THEN DO I = 1, N WORK( I ) = WORK( I ) * C( I ) END DO END IF IF ( UP ) THEN CALL SPOTRS( 'Upper', N, 1, AF, LDAF, WORK, N, INFO ) ELSE CALL SPOTRS( 'Lower', N, 1, AF, LDAF, WORK, N, INFO ) ENDIF * * Multiply by R. * DO I = 1, N WORK( I ) = WORK( I ) * WORK( 2*N+I ) END DO END IF GO TO 10 END IF * * Compute the estimate of the reciprocal condition number. * IF( AINVNM .NE. 0.0 ) $ SLA_PORCOND = ( 1.0 / AINVNM ) * RETURN * END |