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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b CLA_HERCOND_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_HERCOND_C + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cla_hercond_c.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cla_hercond_c.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cla_hercond_c.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * REAL FUNCTION CLA_HERCOND_C( UPLO, N, A, LDA, AF, LDAF, IPIV, C, 00022 * CAPPLY, INFO, WORK, RWORK ) 00023 * 00024 * .. Scalar Arguments .. 00025 * CHARACTER UPLO 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 *> CLA_HERCOND_C computes the infinity norm condition number of 00042 *> op(A) * inv(diag(C)) where C is a REAL vector. 00043 *> \endverbatim 00044 * 00045 * Arguments: 00046 * ========== 00047 * 00048 *> \param[in] UPLO 00049 *> \verbatim 00050 *> UPLO is CHARACTER*1 00051 *> = 'U': Upper triangle of A is stored; 00052 *> = 'L': Lower triangle of A is stored. 00053 *> \endverbatim 00054 *> 00055 *> \param[in] N 00056 *> \verbatim 00057 *> N is INTEGER 00058 *> The number of linear equations, i.e., the order of the 00059 *> matrix A. N >= 0. 00060 *> \endverbatim 00061 *> 00062 *> \param[in] A 00063 *> \verbatim 00064 *> A is COMPLEX array, dimension (LDA,N) 00065 *> On entry, the N-by-N matrix A 00066 *> \endverbatim 00067 *> 00068 *> \param[in] LDA 00069 *> \verbatim 00070 *> LDA is INTEGER 00071 *> The leading dimension of the array A. LDA >= max(1,N). 00072 *> \endverbatim 00073 *> 00074 *> \param[in] AF 00075 *> \verbatim 00076 *> AF is COMPLEX array, dimension (LDAF,N) 00077 *> The block diagonal matrix D and the multipliers used to 00078 *> obtain the factor U or L as computed by CHETRF. 00079 *> \endverbatim 00080 *> 00081 *> \param[in] LDAF 00082 *> \verbatim 00083 *> LDAF is INTEGER 00084 *> The leading dimension of the array AF. LDAF >= max(1,N). 00085 *> \endverbatim 00086 *> 00087 *> \param[in] IPIV 00088 *> \verbatim 00089 *> IPIV is INTEGER array, dimension (N) 00090 *> Details of the interchanges and the block structure of D 00091 *> as determined by CHETRF. 00092 *> \endverbatim 00093 *> 00094 *> \param[in] C 00095 *> \verbatim 00096 *> C is REAL array, dimension (N) 00097 *> The vector C in the formula op(A) * inv(diag(C)). 00098 *> \endverbatim 00099 *> 00100 *> \param[in] CAPPLY 00101 *> \verbatim 00102 *> CAPPLY is LOGICAL 00103 *> If .TRUE. then access the vector C in the formula above. 00104 *> \endverbatim 00105 *> 00106 *> \param[out] INFO 00107 *> \verbatim 00108 *> INFO is INTEGER 00109 *> = 0: Successful exit. 00110 *> i > 0: The ith argument is invalid. 00111 *> \endverbatim 00112 *> 00113 *> \param[in] WORK 00114 *> \verbatim 00115 *> WORK is COMPLEX array, dimension (2*N). 00116 *> Workspace. 00117 *> \endverbatim 00118 *> 00119 *> \param[in] RWORK 00120 *> \verbatim 00121 *> RWORK is REAL array, dimension (N). 00122 *> Workspace. 00123 *> \endverbatim 00124 * 00125 * Authors: 00126 * ======== 00127 * 00128 *> \author Univ. of Tennessee 00129 *> \author Univ. of California Berkeley 00130 *> \author Univ. of Colorado Denver 00131 *> \author NAG Ltd. 00132 * 00133 *> \date November 2011 00134 * 00135 *> \ingroup complexHEcomputational 00136 * 00137 * ===================================================================== 00138 REAL FUNCTION CLA_HERCOND_C( UPLO, N, A, LDA, AF, LDAF, IPIV, C, 00139 $ CAPPLY, INFO, WORK, RWORK ) 00140 * 00141 * -- LAPACK computational routine (version 3.4.0) -- 00142 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00143 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00144 * November 2011 00145 * 00146 * .. Scalar Arguments .. 00147 CHARACTER UPLO 00148 LOGICAL CAPPLY 00149 INTEGER N, LDA, LDAF, INFO 00150 * .. 00151 * .. Array Arguments .. 00152 INTEGER IPIV( * ) 00153 COMPLEX A( LDA, * ), AF( LDAF, * ), WORK( * ) 00154 REAL C ( * ), RWORK( * ) 00155 * .. 00156 * 00157 * ===================================================================== 00158 * 00159 * .. Local Scalars .. 00160 INTEGER KASE, I, J 00161 REAL AINVNM, ANORM, TMP 00162 LOGICAL UP, UPPER 00163 COMPLEX ZDUM 00164 * .. 00165 * .. Local Arrays .. 00166 INTEGER ISAVE( 3 ) 00167 * .. 00168 * .. External Functions .. 00169 LOGICAL LSAME 00170 EXTERNAL LSAME 00171 * .. 00172 * .. External Subroutines .. 00173 EXTERNAL CLACN2, CHETRS, XERBLA 00174 * .. 00175 * .. Intrinsic Functions .. 00176 INTRINSIC ABS, MAX 00177 * .. 00178 * .. Statement Functions .. 00179 REAL CABS1 00180 * .. 00181 * .. Statement Function Definitions .. 00182 CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) ) 00183 * .. 00184 * .. Executable Statements .. 00185 * 00186 CLA_HERCOND_C = 0.0E+0 00187 * 00188 INFO = 0 00189 UPPER = LSAME( UPLO, 'U' ) 00190 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 00191 INFO = -1 00192 ELSE IF( N.LT.0 ) THEN 00193 INFO = -2 00194 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 00195 INFO = -4 00196 ELSE IF( LDAF.LT.MAX( 1, N ) ) THEN 00197 INFO = -6 00198 END IF 00199 IF( INFO.NE.0 ) THEN 00200 CALL XERBLA( 'CLA_HERCOND_C', -INFO ) 00201 RETURN 00202 END IF 00203 UP = .FALSE. 00204 IF ( LSAME( UPLO, 'U' ) ) UP = .TRUE. 00205 * 00206 * Compute norm of op(A)*op2(C). 00207 * 00208 ANORM = 0.0E+0 00209 IF ( UP ) THEN 00210 DO I = 1, N 00211 TMP = 0.0E+0 00212 IF ( CAPPLY ) THEN 00213 DO J = 1, I 00214 TMP = TMP + CABS1( A( J, I ) ) / C( J ) 00215 END DO 00216 DO J = I+1, N 00217 TMP = TMP + CABS1( A( I, J ) ) / C( J ) 00218 END DO 00219 ELSE 00220 DO J = 1, I 00221 TMP = TMP + CABS1( A( J, I ) ) 00222 END DO 00223 DO J = I+1, N 00224 TMP = TMP + CABS1( A( I, J ) ) 00225 END DO 00226 END IF 00227 RWORK( I ) = TMP 00228 ANORM = MAX( ANORM, TMP ) 00229 END DO 00230 ELSE 00231 DO I = 1, N 00232 TMP = 0.0E+0 00233 IF ( CAPPLY ) THEN 00234 DO J = 1, I 00235 TMP = TMP + CABS1( A( I, J ) ) / C( J ) 00236 END DO 00237 DO J = I+1, N 00238 TMP = TMP + CABS1( A( J, I ) ) / C( J ) 00239 END DO 00240 ELSE 00241 DO J = 1, I 00242 TMP = TMP + CABS1( A( I, J ) ) 00243 END DO 00244 DO J = I+1, N 00245 TMP = TMP + CABS1( A( J, I ) ) 00246 END DO 00247 END IF 00248 RWORK( I ) = TMP 00249 ANORM = MAX( ANORM, TMP ) 00250 END DO 00251 END IF 00252 * 00253 * Quick return if possible. 00254 * 00255 IF( N.EQ.0 ) THEN 00256 CLA_HERCOND_C = 1.0E+0 00257 RETURN 00258 ELSE IF( ANORM .EQ. 0.0E+0 ) THEN 00259 RETURN 00260 END IF 00261 * 00262 * Estimate the norm of inv(op(A)). 00263 * 00264 AINVNM = 0.0E+0 00265 * 00266 KASE = 0 00267 10 CONTINUE 00268 CALL CLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE ) 00269 IF( KASE.NE.0 ) THEN 00270 IF( KASE.EQ.2 ) THEN 00271 * 00272 * Multiply by R. 00273 * 00274 DO I = 1, N 00275 WORK( I ) = WORK( I ) * RWORK( I ) 00276 END DO 00277 * 00278 IF ( UP ) THEN 00279 CALL CHETRS( 'U', N, 1, AF, LDAF, IPIV, 00280 $ WORK, N, INFO ) 00281 ELSE 00282 CALL CHETRS( 'L', N, 1, AF, LDAF, IPIV, 00283 $ WORK, N, INFO ) 00284 ENDIF 00285 * 00286 * Multiply by inv(C). 00287 * 00288 IF ( CAPPLY ) THEN 00289 DO I = 1, N 00290 WORK( I ) = WORK( I ) * C( I ) 00291 END DO 00292 END IF 00293 ELSE 00294 * 00295 * Multiply by inv(C**H). 00296 * 00297 IF ( CAPPLY ) THEN 00298 DO I = 1, N 00299 WORK( I ) = WORK( I ) * C( I ) 00300 END DO 00301 END IF 00302 * 00303 IF ( UP ) THEN 00304 CALL CHETRS( 'U', N, 1, AF, LDAF, IPIV, 00305 $ WORK, N, INFO ) 00306 ELSE 00307 CALL CHETRS( 'L', N, 1, AF, LDAF, IPIV, 00308 $ WORK, N, INFO ) 00309 END IF 00310 * 00311 * Multiply by R. 00312 * 00313 DO I = 1, N 00314 WORK( I ) = WORK( I ) * RWORK( I ) 00315 END DO 00316 END IF 00317 GO TO 10 00318 END IF 00319 * 00320 * Compute the estimate of the reciprocal condition number. 00321 * 00322 IF( AINVNM .NE. 0.0E+0 ) 00323 $ CLA_HERCOND_C = 1.0E+0 / AINVNM 00324 * 00325 RETURN 00326 * 00327 END