|
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 |
DOUBLE PRECISION FUNCTION ZLA_GERCOND_C( TRANS, N, A, LDA, AF,
$ LDAF, IPIV, C, CAPPLY, $ INFO, WORK, RWORK ) * * -- 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 Aguments .. CHARACTER TRANS LOGICAL CAPPLY INTEGER N, LDA, LDAF, INFO * .. * .. Array Arguments .. INTEGER IPIV( * ) COMPLEX*16 A( LDA, * ), AF( LDAF, * ), WORK( * ) DOUBLE PRECISION C( * ), RWORK( * ) * .. * * Purpose * ======= * * ZLA_GERCOND_C computes the infinity norm condition number of * op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector. * * Arguments * ========= * * TRANS (input) CHARACTER*1 * Specifies the form of the system of equations: * = 'N': A * X = B (No transpose) * = 'T': A**T * X = B (Transpose) * = 'C': A**H * X = B (Conjugate Transpose = Transpose) * * N (input) INTEGER * The number of linear equations, i.e., the order of the * matrix A. N >= 0. * * A (input) COMPLEX*16 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) COMPLEX*16 array, dimension (LDAF,N) * The factors L and U from the factorization * A = P*L*U as computed by ZGETRF. * * LDAF (input) INTEGER * The leading dimension of the array AF. LDAF >= max(1,N). * * IPIV (input) INTEGER array, dimension (N) * The pivot indices from the factorization A = P*L*U * as computed by ZGETRF; row i of the matrix was interchanged * with row IPIV(i). * * C (input) DOUBLE PRECISION array, dimension (N) * The vector C in the formula op(A) * inv(diag(C)). * * CAPPLY (input) LOGICAL * If .TRUE. then access the vector C in the formula above. * * INFO (output) INTEGER * = 0: Successful exit. * i > 0: The ith argument is invalid. * * WORK (input) COMPLEX*16 array, dimension (2*N). * Workspace. * * RWORK (input) DOUBLE PRECISION array, dimension (N). * Workspace. * * ===================================================================== * * .. Local Scalars .. LOGICAL NOTRANS INTEGER KASE, I, J DOUBLE PRECISION AINVNM, ANORM, TMP COMPLEX*16 ZDUM * .. * .. Local Arrays .. INTEGER ISAVE( 3 ) * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL ZLACN2, ZGETRS, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, REAL, DIMAG * .. * .. Statement Functions .. DOUBLE PRECISION CABS1 * .. * .. Statement Function Definitions .. CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) ) * .. * .. Executable Statements .. ZLA_GERCOND_C = 0.0D+0 * INFO = 0 NOTRANS = LSAME( TRANS, 'N' ) IF ( .NOT. NOTRANS .AND. .NOT. LSAME( TRANS, 'T' ) .AND. .NOT. $ LSAME( TRANS, 'C' ) ) THEN ELSE IF( N.LT.0 ) THEN INFO = -2 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZLA_GERCOND_C', -INFO ) RETURN END IF * * Compute norm of op(A)*op2(C). * ANORM = 0.0D+0 IF ( NOTRANS ) THEN DO I = 1, N TMP = 0.0D+0 IF ( CAPPLY ) THEN DO J = 1, N TMP = TMP + CABS1( A( I, J ) ) / C( J ) END DO ELSE DO J = 1, N TMP = TMP + CABS1( A( I, J ) ) END DO END IF RWORK( I ) = TMP ANORM = MAX( ANORM, TMP ) END DO ELSE DO I = 1, N TMP = 0.0D+0 IF ( CAPPLY ) THEN DO J = 1, N TMP = TMP + CABS1( A( J, I ) ) / C( J ) END DO ELSE DO J = 1, N TMP = TMP + CABS1( A( J, I ) ) END DO END IF RWORK( I ) = TMP ANORM = MAX( ANORM, TMP ) END DO END IF * * Quick return if possible. * IF( N.EQ.0 ) THEN ZLA_GERCOND_C = 1.0D+0 RETURN ELSE IF( ANORM .EQ. 0.0D+0 ) THEN RETURN END IF * * Estimate the norm of inv(op(A)). * AINVNM = 0.0D+0 * KASE = 0 10 CONTINUE CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE ) IF( KASE.NE.0 ) THEN IF( KASE.EQ.2 ) THEN * * Multiply by R. * DO I = 1, N WORK( I ) = WORK( I ) * RWORK( I ) END DO * IF (NOTRANS) THEN CALL ZGETRS( 'No transpose', N, 1, AF, LDAF, IPIV, $ WORK, N, INFO ) ELSE CALL ZGETRS( 'Conjugate transpose', N, 1, AF, LDAF, IPIV, $ WORK, N, INFO ) ENDIF * * Multiply by inv(C). * IF ( CAPPLY ) THEN DO I = 1, N WORK( I ) = WORK( I ) * C( I ) END DO END IF ELSE * * Multiply by inv(C**H). * IF ( CAPPLY ) THEN DO I = 1, N WORK( I ) = WORK( I ) * C( I ) END DO END IF * IF ( NOTRANS ) THEN CALL ZGETRS( 'Conjugate transpose', N, 1, AF, LDAF, IPIV, $ WORK, N, INFO ) ELSE CALL ZGETRS( 'No transpose', N, 1, AF, LDAF, IPIV, $ WORK, N, INFO ) END IF * * Multiply by R. * DO I = 1, N WORK( I ) = WORK( I ) * RWORK( I ) END DO END IF GO TO 10 END IF * * Compute the estimate of the reciprocal condition number. * IF( AINVNM .NE. 0.0D+0 ) $ ZLA_GERCOND_C = 1.0D+0 / AINVNM * RETURN * END |