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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b ZLA_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 ZLA_HERCOND_C + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zla_hercond_c.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zla_hercond_c.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zla_hercond_c.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * DOUBLE PRECISION FUNCTION ZLA_HERCOND_C( UPLO, N, A, LDA, AF, 00022 * LDAF, IPIV, C, CAPPLY, 00023 * INFO, WORK, RWORK ) 00024 * 00025 * .. Scalar Arguments .. 00026 * CHARACTER UPLO 00027 * LOGICAL CAPPLY 00028 * INTEGER N, LDA, LDAF, INFO 00029 * .. 00030 * .. Array Arguments .. 00031 * INTEGER IPIV( * ) 00032 * COMPLEX*16 A( LDA, * ), AF( LDAF, * ), WORK( * ) 00033 * DOUBLE PRECISION C ( * ), RWORK( * ) 00034 * .. 00035 * 00036 * 00037 *> \par Purpose: 00038 * ============= 00039 *> 00040 *> \verbatim 00041 *> 00042 *> ZLA_HERCOND_C computes the infinity norm condition number of 00043 *> op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector. 00044 *> \endverbatim 00045 * 00046 * Arguments: 00047 * ========== 00048 * 00049 *> \param[in] UPLO 00050 *> \verbatim 00051 *> UPLO is CHARACTER*1 00052 *> = 'U': Upper triangle of A is stored; 00053 *> = 'L': Lower triangle of A is stored. 00054 *> \endverbatim 00055 *> 00056 *> \param[in] N 00057 *> \verbatim 00058 *> N is INTEGER 00059 *> The number of linear equations, i.e., the order of the 00060 *> matrix A. N >= 0. 00061 *> \endverbatim 00062 *> 00063 *> \param[in] A 00064 *> \verbatim 00065 *> A is COMPLEX*16 array, dimension (LDA,N) 00066 *> On entry, the N-by-N matrix A 00067 *> \endverbatim 00068 *> 00069 *> \param[in] LDA 00070 *> \verbatim 00071 *> LDA is INTEGER 00072 *> The leading dimension of the array A. LDA >= max(1,N). 00073 *> \endverbatim 00074 *> 00075 *> \param[in] AF 00076 *> \verbatim 00077 *> AF is COMPLEX*16 array, dimension (LDAF,N) 00078 *> The block diagonal matrix D and the multipliers used to 00079 *> obtain the factor U or L as computed by ZHETRF. 00080 *> \endverbatim 00081 *> 00082 *> \param[in] LDAF 00083 *> \verbatim 00084 *> LDAF is INTEGER 00085 *> The leading dimension of the array AF. LDAF >= max(1,N). 00086 *> \endverbatim 00087 *> 00088 *> \param[in] IPIV 00089 *> \verbatim 00090 *> IPIV is INTEGER array, dimension (N) 00091 *> Details of the interchanges and the block structure of D 00092 *> as determined by CHETRF. 00093 *> \endverbatim 00094 *> 00095 *> \param[in] C 00096 *> \verbatim 00097 *> C is DOUBLE PRECISION array, dimension (N) 00098 *> The vector C in the formula op(A) * inv(diag(C)). 00099 *> \endverbatim 00100 *> 00101 *> \param[in] CAPPLY 00102 *> \verbatim 00103 *> CAPPLY is LOGICAL 00104 *> If .TRUE. then access the vector C in the formula above. 00105 *> \endverbatim 00106 *> 00107 *> \param[out] INFO 00108 *> \verbatim 00109 *> INFO is INTEGER 00110 *> = 0: Successful exit. 00111 *> i > 0: The ith argument is invalid. 00112 *> \endverbatim 00113 *> 00114 *> \param[in] WORK 00115 *> \verbatim 00116 *> WORK is COMPLEX*16 array, dimension (2*N). 00117 *> Workspace. 00118 *> \endverbatim 00119 *> 00120 *> \param[in] RWORK 00121 *> \verbatim 00122 *> RWORK is DOUBLE PRECISION array, dimension (N). 00123 *> Workspace. 00124 *> \endverbatim 00125 * 00126 * Authors: 00127 * ======== 00128 * 00129 *> \author Univ. of Tennessee 00130 *> \author Univ. of California Berkeley 00131 *> \author Univ. of Colorado Denver 00132 *> \author NAG Ltd. 00133 * 00134 *> \date November 2011 00135 * 00136 *> \ingroup complex16HEcomputational 00137 * 00138 * ===================================================================== 00139 DOUBLE PRECISION FUNCTION ZLA_HERCOND_C( UPLO, N, A, LDA, AF, 00140 $ LDAF, IPIV, C, CAPPLY, 00141 $ INFO, WORK, RWORK ) 00142 * 00143 * -- LAPACK computational routine (version 3.4.0) -- 00144 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00145 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00146 * November 2011 00147 * 00148 * .. Scalar Arguments .. 00149 CHARACTER UPLO 00150 LOGICAL CAPPLY 00151 INTEGER N, LDA, LDAF, INFO 00152 * .. 00153 * .. Array Arguments .. 00154 INTEGER IPIV( * ) 00155 COMPLEX*16 A( LDA, * ), AF( LDAF, * ), WORK( * ) 00156 DOUBLE PRECISION C ( * ), RWORK( * ) 00157 * .. 00158 * 00159 * ===================================================================== 00160 * 00161 * .. Local Scalars .. 00162 INTEGER KASE, I, J 00163 DOUBLE PRECISION AINVNM, ANORM, TMP 00164 LOGICAL UP, UPPER 00165 COMPLEX*16 ZDUM 00166 * .. 00167 * .. Local Arrays .. 00168 INTEGER ISAVE( 3 ) 00169 * .. 00170 * .. External Functions .. 00171 LOGICAL LSAME 00172 EXTERNAL LSAME 00173 * .. 00174 * .. External Subroutines .. 00175 EXTERNAL ZLACN2, ZHETRS, XERBLA 00176 * .. 00177 * .. Intrinsic Functions .. 00178 INTRINSIC ABS, MAX 00179 * .. 00180 * .. Statement Functions .. 00181 DOUBLE PRECISION CABS1 00182 * .. 00183 * .. Statement Function Definitions .. 00184 CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) ) 00185 * .. 00186 * .. Executable Statements .. 00187 * 00188 ZLA_HERCOND_C = 0.0D+0 00189 * 00190 INFO = 0 00191 UPPER = LSAME( UPLO, 'U' ) 00192 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 00193 INFO = -1 00194 ELSE IF( N.LT.0 ) THEN 00195 INFO = -2 00196 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 00197 INFO = -4 00198 ELSE IF( LDAF.LT.MAX( 1, N ) ) THEN 00199 INFO = -6 00200 END IF 00201 IF( INFO.NE.0 ) THEN 00202 CALL XERBLA( 'ZLA_HERCOND_C', -INFO ) 00203 RETURN 00204 END IF 00205 UP = .FALSE. 00206 IF ( LSAME( UPLO, 'U' ) ) UP = .TRUE. 00207 * 00208 * Compute norm of op(A)*op2(C). 00209 * 00210 ANORM = 0.0D+0 00211 IF ( UP ) THEN 00212 DO I = 1, N 00213 TMP = 0.0D+0 00214 IF ( CAPPLY ) THEN 00215 DO J = 1, I 00216 TMP = TMP + CABS1( A( J, I ) ) / C( J ) 00217 END DO 00218 DO J = I+1, N 00219 TMP = TMP + CABS1( A( I, J ) ) / C( J ) 00220 END DO 00221 ELSE 00222 DO J = 1, I 00223 TMP = TMP + CABS1( A( J, I ) ) 00224 END DO 00225 DO J = I+1, N 00226 TMP = TMP + CABS1( A( I, J ) ) 00227 END DO 00228 END IF 00229 RWORK( I ) = TMP 00230 ANORM = MAX( ANORM, TMP ) 00231 END DO 00232 ELSE 00233 DO I = 1, N 00234 TMP = 0.0D+0 00235 IF ( CAPPLY ) THEN 00236 DO J = 1, I 00237 TMP = TMP + CABS1( A( I, J ) ) / C( J ) 00238 END DO 00239 DO J = I+1, N 00240 TMP = TMP + CABS1( A( J, I ) ) / C( J ) 00241 END DO 00242 ELSE 00243 DO J = 1, I 00244 TMP = TMP + CABS1( A( I, J ) ) 00245 END DO 00246 DO J = I+1, N 00247 TMP = TMP + CABS1( A( J, I ) ) 00248 END DO 00249 END IF 00250 RWORK( I ) = TMP 00251 ANORM = MAX( ANORM, TMP ) 00252 END DO 00253 END IF 00254 * 00255 * Quick return if possible. 00256 * 00257 IF( N.EQ.0 ) THEN 00258 ZLA_HERCOND_C = 1.0D+0 00259 RETURN 00260 ELSE IF( ANORM .EQ. 0.0D+0 ) THEN 00261 RETURN 00262 END IF 00263 * 00264 * Estimate the norm of inv(op(A)). 00265 * 00266 AINVNM = 0.0D+0 00267 * 00268 KASE = 0 00269 10 CONTINUE 00270 CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE ) 00271 IF( KASE.NE.0 ) THEN 00272 IF( KASE.EQ.2 ) THEN 00273 * 00274 * Multiply by R. 00275 * 00276 DO I = 1, N 00277 WORK( I ) = WORK( I ) * RWORK( I ) 00278 END DO 00279 * 00280 IF ( UP ) THEN 00281 CALL ZHETRS( 'U', N, 1, AF, LDAF, IPIV, 00282 $ WORK, N, INFO ) 00283 ELSE 00284 CALL ZHETRS( 'L', N, 1, AF, LDAF, IPIV, 00285 $ WORK, N, INFO ) 00286 ENDIF 00287 * 00288 * Multiply by inv(C). 00289 * 00290 IF ( CAPPLY ) THEN 00291 DO I = 1, N 00292 WORK( I ) = WORK( I ) * C( I ) 00293 END DO 00294 END IF 00295 ELSE 00296 * 00297 * Multiply by inv(C**H). 00298 * 00299 IF ( CAPPLY ) THEN 00300 DO I = 1, N 00301 WORK( I ) = WORK( I ) * C( I ) 00302 END DO 00303 END IF 00304 * 00305 IF ( UP ) THEN 00306 CALL ZHETRS( 'U', N, 1, AF, LDAF, IPIV, 00307 $ WORK, N, INFO ) 00308 ELSE 00309 CALL ZHETRS( 'L', N, 1, AF, LDAF, IPIV, 00310 $ WORK, N, INFO ) 00311 END IF 00312 * 00313 * Multiply by R. 00314 * 00315 DO I = 1, N 00316 WORK( I ) = WORK( I ) * RWORK( I ) 00317 END DO 00318 END IF 00319 GO TO 10 00320 END IF 00321 * 00322 * Compute the estimate of the reciprocal condition number. 00323 * 00324 IF( AINVNM .NE. 0.0D+0 ) 00325 $ ZLA_HERCOND_C = 1.0D+0 / AINVNM 00326 * 00327 RETURN 00328 * 00329 END