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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b CLA_SYRCOND_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_SYRCOND_C + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cla_syrcond_c.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cla_syrcond_c.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cla_syrcond_c.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * REAL FUNCTION CLA_SYRCOND_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_SYRCOND_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 CSYTRF. 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 CSYTRF. 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 complexSYcomputational 00136 * 00137 * ===================================================================== 00138 REAL FUNCTION CLA_SYRCOND_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 00161 REAL AINVNM, ANORM, TMP 00162 INTEGER I, J 00163 LOGICAL UP, UPPER 00164 COMPLEX ZDUM 00165 * .. 00166 * .. Local Arrays .. 00167 INTEGER ISAVE( 3 ) 00168 * .. 00169 * .. External Functions .. 00170 LOGICAL LSAME 00171 EXTERNAL LSAME 00172 * .. 00173 * .. External Subroutines .. 00174 EXTERNAL CLACN2, CSYTRS, XERBLA 00175 * .. 00176 * .. Intrinsic Functions .. 00177 INTRINSIC ABS, MAX 00178 * .. 00179 * .. Statement Functions .. 00180 REAL CABS1 00181 * .. 00182 * .. Statement Function Definitions .. 00183 CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) ) 00184 * .. 00185 * .. Executable Statements .. 00186 * 00187 CLA_SYRCOND_C = 0.0E+0 00188 * 00189 INFO = 0 00190 UPPER = LSAME( UPLO, 'U' ) 00191 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 00192 INFO = -1 00193 ELSE IF( N.LT.0 ) THEN 00194 INFO = -2 00195 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 00196 INFO = -4 00197 ELSE IF( LDAF.LT.MAX( 1, N ) ) THEN 00198 INFO = -6 00199 END IF 00200 IF( INFO.NE.0 ) THEN 00201 CALL XERBLA( 'CLA_SYRCOND_C', -INFO ) 00202 RETURN 00203 END IF 00204 UP = .FALSE. 00205 IF ( LSAME( UPLO, 'U' ) ) UP = .TRUE. 00206 * 00207 * Compute norm of op(A)*op2(C). 00208 * 00209 ANORM = 0.0E+0 00210 IF ( UP ) THEN 00211 DO I = 1, N 00212 TMP = 0.0E+0 00213 IF ( CAPPLY ) THEN 00214 DO J = 1, I 00215 TMP = TMP + CABS1( A( J, I ) ) / C( J ) 00216 END DO 00217 DO J = I+1, N 00218 TMP = TMP + CABS1( A( I, J ) ) / C( J ) 00219 END DO 00220 ELSE 00221 DO J = 1, I 00222 TMP = TMP + CABS1( A( J, I ) ) 00223 END DO 00224 DO J = I+1, N 00225 TMP = TMP + CABS1( A( I, J ) ) 00226 END DO 00227 END IF 00228 RWORK( I ) = TMP 00229 ANORM = MAX( ANORM, TMP ) 00230 END DO 00231 ELSE 00232 DO I = 1, N 00233 TMP = 0.0E+0 00234 IF ( CAPPLY ) THEN 00235 DO J = 1, I 00236 TMP = TMP + CABS1( A( I, J ) ) / C( J ) 00237 END DO 00238 DO J = I+1, N 00239 TMP = TMP + CABS1( A( J, I ) ) / C( J ) 00240 END DO 00241 ELSE 00242 DO J = 1, I 00243 TMP = TMP + CABS1( A( I, J ) ) 00244 END DO 00245 DO J = I+1, N 00246 TMP = TMP + CABS1( A( J, I ) ) 00247 END DO 00248 END IF 00249 RWORK( I ) = TMP 00250 ANORM = MAX( ANORM, TMP ) 00251 END DO 00252 END IF 00253 * 00254 * Quick return if possible. 00255 * 00256 IF( N.EQ.0 ) THEN 00257 CLA_SYRCOND_C = 1.0E+0 00258 RETURN 00259 ELSE IF( ANORM .EQ. 0.0E+0 ) THEN 00260 RETURN 00261 END IF 00262 * 00263 * Estimate the norm of inv(op(A)). 00264 * 00265 AINVNM = 0.0E+0 00266 * 00267 KASE = 0 00268 10 CONTINUE 00269 CALL CLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE ) 00270 IF( KASE.NE.0 ) THEN 00271 IF( KASE.EQ.2 ) THEN 00272 * 00273 * Multiply by R. 00274 * 00275 DO I = 1, N 00276 WORK( I ) = WORK( I ) * RWORK( I ) 00277 END DO 00278 * 00279 IF ( UP ) THEN 00280 CALL CSYTRS( 'U', N, 1, AF, LDAF, IPIV, 00281 $ WORK, N, INFO ) 00282 ELSE 00283 CALL CSYTRS( 'L', N, 1, AF, LDAF, IPIV, 00284 $ WORK, N, INFO ) 00285 ENDIF 00286 * 00287 * Multiply by inv(C). 00288 * 00289 IF ( CAPPLY ) THEN 00290 DO I = 1, N 00291 WORK( I ) = WORK( I ) * C( I ) 00292 END DO 00293 END IF 00294 ELSE 00295 * 00296 * Multiply by inv(C**T). 00297 * 00298 IF ( CAPPLY ) THEN 00299 DO I = 1, N 00300 WORK( I ) = WORK( I ) * C( I ) 00301 END DO 00302 END IF 00303 * 00304 IF ( UP ) THEN 00305 CALL CSYTRS( 'U', N, 1, AF, LDAF, IPIV, 00306 $ WORK, N, INFO ) 00307 ELSE 00308 CALL CSYTRS( 'L', N, 1, AF, LDAF, IPIV, 00309 $ WORK, N, INFO ) 00310 END IF 00311 * 00312 * Multiply by R. 00313 * 00314 DO I = 1, N 00315 WORK( I ) = WORK( I ) * RWORK( I ) 00316 END DO 00317 END IF 00318 GO TO 10 00319 END IF 00320 * 00321 * Compute the estimate of the reciprocal condition number. 00322 * 00323 IF( AINVNM .NE. 0.0E+0 ) 00324 $ CLA_SYRCOND_C = 1.0E+0 / AINVNM 00325 * 00326 RETURN 00327 * 00328 END