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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b ZLA_GERCOND_X 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download ZLA_GERCOND_X + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zla_gercond_x.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zla_gercond_x.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zla_gercond_x.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * DOUBLE PRECISION FUNCTION ZLA_GERCOND_X( TRANS, N, A, LDA, AF, 00022 * LDAF, IPIV, X, INFO, 00023 * WORK, RWORK ) 00024 * 00025 * .. Scalar Arguments .. 00026 * CHARACTER TRANS 00027 * INTEGER N, LDA, LDAF, INFO 00028 * .. 00029 * .. Array Arguments .. 00030 * INTEGER IPIV( * ) 00031 * COMPLEX*16 A( LDA, * ), AF( LDAF, * ), WORK( * ), X( * ) 00032 * DOUBLE PRECISION RWORK( * ) 00033 * .. 00034 * 00035 * 00036 *> \par Purpose: 00037 * ============= 00038 *> 00039 *> \verbatim 00040 *> 00041 *> ZLA_GERCOND_X computes the infinity norm condition number of 00042 *> op(A) * diag(X) where X is a COMPLEX*16 vector. 00043 *> \endverbatim 00044 * 00045 * Arguments: 00046 * ========== 00047 * 00048 *> \param[in] TRANS 00049 *> \verbatim 00050 *> TRANS is CHARACTER*1 00051 *> Specifies the form of the system of equations: 00052 *> = 'N': A * X = B (No transpose) 00053 *> = 'T': A**T * X = B (Transpose) 00054 *> = 'C': A**H * X = B (Conjugate Transpose = Transpose) 00055 *> \endverbatim 00056 *> 00057 *> \param[in] N 00058 *> \verbatim 00059 *> N is INTEGER 00060 *> The number of linear equations, i.e., the order of the 00061 *> matrix A. N >= 0. 00062 *> \endverbatim 00063 *> 00064 *> \param[in] A 00065 *> \verbatim 00066 *> A is COMPLEX*16 array, dimension (LDA,N) 00067 *> On entry, the N-by-N matrix A. 00068 *> \endverbatim 00069 *> 00070 *> \param[in] LDA 00071 *> \verbatim 00072 *> LDA is INTEGER 00073 *> The leading dimension of the array A. LDA >= max(1,N). 00074 *> \endverbatim 00075 *> 00076 *> \param[in] AF 00077 *> \verbatim 00078 *> AF is COMPLEX*16 array, dimension (LDAF,N) 00079 *> The factors L and U from the factorization 00080 *> A = P*L*U as computed by ZGETRF. 00081 *> \endverbatim 00082 *> 00083 *> \param[in] LDAF 00084 *> \verbatim 00085 *> LDAF is INTEGER 00086 *> The leading dimension of the array AF. LDAF >= max(1,N). 00087 *> \endverbatim 00088 *> 00089 *> \param[in] IPIV 00090 *> \verbatim 00091 *> IPIV is INTEGER array, dimension (N) 00092 *> The pivot indices from the factorization A = P*L*U 00093 *> as computed by ZGETRF; row i of the matrix was interchanged 00094 *> with row IPIV(i). 00095 *> \endverbatim 00096 *> 00097 *> \param[in] X 00098 *> \verbatim 00099 *> X is COMPLEX*16 array, dimension (N) 00100 *> The vector X in the formula op(A) * diag(X). 00101 *> \endverbatim 00102 *> 00103 *> \param[out] INFO 00104 *> \verbatim 00105 *> INFO is INTEGER 00106 *> = 0: Successful exit. 00107 *> i > 0: The ith argument is invalid. 00108 *> \endverbatim 00109 *> 00110 *> \param[in] WORK 00111 *> \verbatim 00112 *> WORK is COMPLEX*16 array, dimension (2*N). 00113 *> Workspace. 00114 *> \endverbatim 00115 *> 00116 *> \param[in] RWORK 00117 *> \verbatim 00118 *> RWORK is DOUBLE PRECISION array, dimension (N). 00119 *> Workspace. 00120 *> \endverbatim 00121 * 00122 * Authors: 00123 * ======== 00124 * 00125 *> \author Univ. of Tennessee 00126 *> \author Univ. of California Berkeley 00127 *> \author Univ. of Colorado Denver 00128 *> \author NAG Ltd. 00129 * 00130 *> \date November 2011 00131 * 00132 *> \ingroup complex16GEcomputational 00133 * 00134 * ===================================================================== 00135 DOUBLE PRECISION FUNCTION ZLA_GERCOND_X( TRANS, N, A, LDA, AF, 00136 $ LDAF, IPIV, X, INFO, 00137 $ WORK, RWORK ) 00138 * 00139 * -- LAPACK computational routine (version 3.4.0) -- 00140 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00141 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00142 * November 2011 00143 * 00144 * .. Scalar Arguments .. 00145 CHARACTER TRANS 00146 INTEGER N, LDA, LDAF, INFO 00147 * .. 00148 * .. Array Arguments .. 00149 INTEGER IPIV( * ) 00150 COMPLEX*16 A( LDA, * ), AF( LDAF, * ), WORK( * ), X( * ) 00151 DOUBLE PRECISION RWORK( * ) 00152 * .. 00153 * 00154 * ===================================================================== 00155 * 00156 * .. Local Scalars .. 00157 LOGICAL NOTRANS 00158 INTEGER KASE 00159 DOUBLE PRECISION AINVNM, ANORM, TMP 00160 INTEGER I, J 00161 COMPLEX*16 ZDUM 00162 * .. 00163 * .. Local Arrays .. 00164 INTEGER ISAVE( 3 ) 00165 * .. 00166 * .. External Functions .. 00167 LOGICAL LSAME 00168 EXTERNAL LSAME 00169 * .. 00170 * .. External Subroutines .. 00171 EXTERNAL ZLACN2, ZGETRS, XERBLA 00172 * .. 00173 * .. Intrinsic Functions .. 00174 INTRINSIC ABS, MAX, REAL, DIMAG 00175 * .. 00176 * .. Statement Functions .. 00177 DOUBLE PRECISION CABS1 00178 * .. 00179 * .. Statement Function Definitions .. 00180 CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) ) 00181 * .. 00182 * .. Executable Statements .. 00183 * 00184 ZLA_GERCOND_X = 0.0D+0 00185 * 00186 INFO = 0 00187 NOTRANS = LSAME( TRANS, 'N' ) 00188 IF ( .NOT. NOTRANS .AND. .NOT. LSAME( TRANS, 'T' ) .AND. .NOT. 00189 $ LSAME( TRANS, 'C' ) ) THEN 00190 INFO = -1 00191 ELSE IF( N.LT.0 ) THEN 00192 INFO = -2 00193 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 00194 INFO = -4 00195 ELSE IF( LDAF.LT.MAX( 1, N ) ) THEN 00196 INFO = -6 00197 END IF 00198 IF( INFO.NE.0 ) THEN 00199 CALL XERBLA( 'ZLA_GERCOND_X', -INFO ) 00200 RETURN 00201 END IF 00202 * 00203 * Compute norm of op(A)*op2(C). 00204 * 00205 ANORM = 0.0D+0 00206 IF ( NOTRANS ) THEN 00207 DO I = 1, N 00208 TMP = 0.0D+0 00209 DO J = 1, N 00210 TMP = TMP + CABS1( A( I, J ) * X( J ) ) 00211 END DO 00212 RWORK( I ) = TMP 00213 ANORM = MAX( ANORM, TMP ) 00214 END DO 00215 ELSE 00216 DO I = 1, N 00217 TMP = 0.0D+0 00218 DO J = 1, N 00219 TMP = TMP + CABS1( A( J, I ) * X( J ) ) 00220 END DO 00221 RWORK( I ) = TMP 00222 ANORM = MAX( ANORM, TMP ) 00223 END DO 00224 END IF 00225 * 00226 * Quick return if possible. 00227 * 00228 IF( N.EQ.0 ) THEN 00229 ZLA_GERCOND_X = 1.0D+0 00230 RETURN 00231 ELSE IF( ANORM .EQ. 0.0D+0 ) THEN 00232 RETURN 00233 END IF 00234 * 00235 * Estimate the norm of inv(op(A)). 00236 * 00237 AINVNM = 0.0D+0 00238 * 00239 KASE = 0 00240 10 CONTINUE 00241 CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE ) 00242 IF( KASE.NE.0 ) THEN 00243 IF( KASE.EQ.2 ) THEN 00244 * Multiply by R. 00245 DO I = 1, N 00246 WORK( I ) = WORK( I ) * RWORK( I ) 00247 END DO 00248 * 00249 IF ( NOTRANS ) THEN 00250 CALL ZGETRS( 'No transpose', N, 1, AF, LDAF, IPIV, 00251 $ WORK, N, INFO ) 00252 ELSE 00253 CALL ZGETRS( 'Conjugate transpose', N, 1, AF, LDAF, IPIV, 00254 $ WORK, N, INFO ) 00255 ENDIF 00256 * 00257 * Multiply by inv(X). 00258 * 00259 DO I = 1, N 00260 WORK( I ) = WORK( I ) / X( I ) 00261 END DO 00262 ELSE 00263 * 00264 * Multiply by inv(X**H). 00265 * 00266 DO I = 1, N 00267 WORK( I ) = WORK( I ) / X( I ) 00268 END DO 00269 * 00270 IF ( NOTRANS ) THEN 00271 CALL ZGETRS( 'Conjugate transpose', N, 1, AF, LDAF, IPIV, 00272 $ WORK, N, INFO ) 00273 ELSE 00274 CALL ZGETRS( 'No transpose', N, 1, AF, LDAF, IPIV, 00275 $ WORK, N, INFO ) 00276 END IF 00277 * 00278 * Multiply by R. 00279 * 00280 DO I = 1, N 00281 WORK( I ) = WORK( I ) * RWORK( I ) 00282 END DO 00283 END IF 00284 GO TO 10 00285 END IF 00286 * 00287 * Compute the estimate of the reciprocal condition number. 00288 * 00289 IF( AINVNM .NE. 0.0D+0 ) 00290 $ ZLA_GERCOND_X = 1.0D+0 / AINVNM 00291 * 00292 RETURN 00293 * 00294 END