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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b CLA_GERCOND_C 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download CLA_GERCOND_C + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cla_gercond_c.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cla_gercond_c.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cla_gercond_c.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * REAL FUNCTION CLA_GERCOND_C( TRANS, N, A, LDA, AF, LDAF, IPIV, C, 00022 * CAPPLY, INFO, WORK, RWORK ) 00023 * 00024 * .. Scalar Aguments .. 00025 * CHARACTER TRANS 00026 * LOGICAL CAPPLY 00027 * INTEGER N, LDA, LDAF, INFO 00028 * .. 00029 * .. Array Arguments .. 00030 * INTEGER IPIV( * ) 00031 * COMPLEX A( LDA, * ), AF( LDAF, * ), WORK( * ) 00032 * REAL C( * ), RWORK( * ) 00033 * .. 00034 * 00035 * 00036 *> \par Purpose: 00037 * ============= 00038 *> 00039 *> \verbatim 00040 *> 00041 *> 00042 *> CLA_GERCOND_C computes the infinity norm condition number of 00043 *> op(A) * inv(diag(C)) where C is a REAL vector. 00044 *> \endverbatim 00045 * 00046 * Arguments: 00047 * ========== 00048 * 00049 *> \param[in] TRANS 00050 *> \verbatim 00051 *> TRANS is CHARACTER*1 00052 *> Specifies the form of the system of equations: 00053 *> = 'N': A * X = B (No transpose) 00054 *> = 'T': A**T * X = B (Transpose) 00055 *> = 'C': A**H * X = B (Conjugate Transpose = Transpose) 00056 *> \endverbatim 00057 *> 00058 *> \param[in] N 00059 *> \verbatim 00060 *> N is INTEGER 00061 *> The number of linear equations, i.e., the order of the 00062 *> matrix A. N >= 0. 00063 *> \endverbatim 00064 *> 00065 *> \param[in] A 00066 *> \verbatim 00067 *> A is COMPLEX array, dimension (LDA,N) 00068 *> On entry, the N-by-N matrix A 00069 *> \endverbatim 00070 *> 00071 *> \param[in] LDA 00072 *> \verbatim 00073 *> LDA is INTEGER 00074 *> The leading dimension of the array A. LDA >= max(1,N). 00075 *> \endverbatim 00076 *> 00077 *> \param[in] AF 00078 *> \verbatim 00079 *> AF is COMPLEX array, dimension (LDAF,N) 00080 *> The factors L and U from the factorization 00081 *> A = P*L*U as computed by CGETRF. 00082 *> \endverbatim 00083 *> 00084 *> \param[in] LDAF 00085 *> \verbatim 00086 *> LDAF is INTEGER 00087 *> The leading dimension of the array AF. LDAF >= max(1,N). 00088 *> \endverbatim 00089 *> 00090 *> \param[in] IPIV 00091 *> \verbatim 00092 *> IPIV is INTEGER array, dimension (N) 00093 *> The pivot indices from the factorization A = P*L*U 00094 *> as computed by CGETRF; row i of the matrix was interchanged 00095 *> with row IPIV(i). 00096 *> \endverbatim 00097 *> 00098 *> \param[in] C 00099 *> \verbatim 00100 *> C is REAL array, dimension (N) 00101 *> The vector C in the formula op(A) * inv(diag(C)). 00102 *> \endverbatim 00103 *> 00104 *> \param[in] CAPPLY 00105 *> \verbatim 00106 *> CAPPLY is LOGICAL 00107 *> If .TRUE. then access the vector C in the formula above. 00108 *> \endverbatim 00109 *> 00110 *> \param[out] INFO 00111 *> \verbatim 00112 *> INFO is INTEGER 00113 *> = 0: Successful exit. 00114 *> i > 0: The ith argument is invalid. 00115 *> \endverbatim 00116 *> 00117 *> \param[in] WORK 00118 *> \verbatim 00119 *> WORK is COMPLEX array, dimension (2*N). 00120 *> Workspace. 00121 *> \endverbatim 00122 *> 00123 *> \param[in] RWORK 00124 *> \verbatim 00125 *> RWORK is REAL array, dimension (N). 00126 *> Workspace. 00127 *> \endverbatim 00128 * 00129 * Authors: 00130 * ======== 00131 * 00132 *> \author Univ. of Tennessee 00133 *> \author Univ. of California Berkeley 00134 *> \author Univ. of Colorado Denver 00135 *> \author NAG Ltd. 00136 * 00137 *> \date November 2011 00138 * 00139 *> \ingroup complexGEcomputational 00140 * 00141 * ===================================================================== 00142 REAL FUNCTION CLA_GERCOND_C( TRANS, N, A, LDA, AF, LDAF, IPIV, C, 00143 $ CAPPLY, INFO, WORK, RWORK ) 00144 * 00145 * -- LAPACK computational routine (version 3.4.0) -- 00146 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00147 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00148 * November 2011 00149 * 00150 * .. Scalar Aguments .. 00151 CHARACTER TRANS 00152 LOGICAL CAPPLY 00153 INTEGER N, LDA, LDAF, INFO 00154 * .. 00155 * .. Array Arguments .. 00156 INTEGER IPIV( * ) 00157 COMPLEX A( LDA, * ), AF( LDAF, * ), WORK( * ) 00158 REAL C( * ), RWORK( * ) 00159 * .. 00160 * 00161 * ===================================================================== 00162 * 00163 * .. Local Scalars .. 00164 LOGICAL NOTRANS 00165 INTEGER KASE, I, J 00166 REAL AINVNM, ANORM, TMP 00167 COMPLEX ZDUM 00168 * .. 00169 * .. Local Arrays .. 00170 INTEGER ISAVE( 3 ) 00171 * .. 00172 * .. External Functions .. 00173 LOGICAL LSAME 00174 EXTERNAL LSAME 00175 * .. 00176 * .. External Subroutines .. 00177 EXTERNAL CLACN2, CGETRS, XERBLA 00178 * .. 00179 * .. Intrinsic Functions .. 00180 INTRINSIC ABS, MAX, REAL, AIMAG 00181 * .. 00182 * .. Statement Functions .. 00183 REAL CABS1 00184 * .. 00185 * .. Statement Function Definitions .. 00186 CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) ) 00187 * .. 00188 * .. Executable Statements .. 00189 CLA_GERCOND_C = 0.0E+0 00190 * 00191 INFO = 0 00192 NOTRANS = LSAME( TRANS, 'N' ) 00193 IF ( .NOT. NOTRANS .AND. .NOT. LSAME( TRANS, 'T' ) .AND. .NOT. 00194 $ LSAME( TRANS, 'C' ) ) THEN 00195 INFO = -1 00196 ELSE IF( N.LT.0 ) THEN 00197 INFO = -2 00198 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 00199 INFO = -4 00200 ELSE IF( LDAF.LT.MAX( 1, N ) ) THEN 00201 INFO = -6 00202 END IF 00203 IF( INFO.NE.0 ) THEN 00204 CALL XERBLA( 'CLA_GERCOND_C', -INFO ) 00205 RETURN 00206 END IF 00207 * 00208 * Compute norm of op(A)*op2(C). 00209 * 00210 ANORM = 0.0E+0 00211 IF ( NOTRANS ) THEN 00212 DO I = 1, N 00213 TMP = 0.0E+0 00214 IF ( CAPPLY ) THEN 00215 DO J = 1, N 00216 TMP = TMP + CABS1( A( I, J ) ) / C( J ) 00217 END DO 00218 ELSE 00219 DO J = 1, N 00220 TMP = TMP + CABS1( A( I, J ) ) 00221 END DO 00222 END IF 00223 RWORK( I ) = TMP 00224 ANORM = MAX( ANORM, TMP ) 00225 END DO 00226 ELSE 00227 DO I = 1, N 00228 TMP = 0.0E+0 00229 IF ( CAPPLY ) THEN 00230 DO J = 1, N 00231 TMP = TMP + CABS1( A( J, I ) ) / C( J ) 00232 END DO 00233 ELSE 00234 DO J = 1, N 00235 TMP = TMP + CABS1( A( J, I ) ) 00236 END DO 00237 END IF 00238 RWORK( I ) = TMP 00239 ANORM = MAX( ANORM, TMP ) 00240 END DO 00241 END IF 00242 * 00243 * Quick return if possible. 00244 * 00245 IF( N.EQ.0 ) THEN 00246 CLA_GERCOND_C = 1.0E+0 00247 RETURN 00248 ELSE IF( ANORM .EQ. 0.0E+0 ) THEN 00249 RETURN 00250 END IF 00251 * 00252 * Estimate the norm of inv(op(A)). 00253 * 00254 AINVNM = 0.0E+0 00255 * 00256 KASE = 0 00257 10 CONTINUE 00258 CALL CLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE ) 00259 IF( KASE.NE.0 ) THEN 00260 IF( KASE.EQ.2 ) THEN 00261 * 00262 * Multiply by R. 00263 * 00264 DO I = 1, N 00265 WORK( I ) = WORK( I ) * RWORK( I ) 00266 END DO 00267 * 00268 IF (NOTRANS) THEN 00269 CALL CGETRS( 'No transpose', N, 1, AF, LDAF, IPIV, 00270 $ WORK, N, INFO ) 00271 ELSE 00272 CALL CGETRS( 'Conjugate transpose', N, 1, AF, LDAF, IPIV, 00273 $ WORK, N, INFO ) 00274 ENDIF 00275 * 00276 * Multiply by inv(C). 00277 * 00278 IF ( CAPPLY ) THEN 00279 DO I = 1, N 00280 WORK( I ) = WORK( I ) * C( I ) 00281 END DO 00282 END IF 00283 ELSE 00284 * 00285 * Multiply by inv(C**H). 00286 * 00287 IF ( CAPPLY ) THEN 00288 DO I = 1, N 00289 WORK( I ) = WORK( I ) * C( I ) 00290 END DO 00291 END IF 00292 * 00293 IF ( NOTRANS ) THEN 00294 CALL CGETRS( 'Conjugate transpose', N, 1, AF, LDAF, IPIV, 00295 $ WORK, N, INFO ) 00296 ELSE 00297 CALL CGETRS( 'No transpose', N, 1, AF, LDAF, IPIV, 00298 $ WORK, N, INFO ) 00299 END IF 00300 * 00301 * Multiply by R. 00302 * 00303 DO I = 1, N 00304 WORK( I ) = WORK( I ) * RWORK( I ) 00305 END DO 00306 END IF 00307 GO TO 10 00308 END IF 00309 * 00310 * Compute the estimate of the reciprocal condition number. 00311 * 00312 IF( AINVNM .NE. 0.0E+0 ) 00313 $ CLA_GERCOND_C = 1.0E+0 / AINVNM 00314 * 00315 RETURN 00316 * 00317 END