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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b ZLA_HERCOND_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_HERCOND_X + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zla_hercond_x.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zla_hercond_x.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zla_hercond_x.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * DOUBLE PRECISION FUNCTION ZLA_HERCOND_X( UPLO, N, A, LDA, AF, 00022 * LDAF, IPIV, X, INFO, 00023 * WORK, RWORK ) 00024 * 00025 * .. Scalar Arguments .. 00026 * CHARACTER UPLO 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_HERCOND_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] 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*16 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*16 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 ZHETRF. 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] X 00095 *> \verbatim 00096 *> X is COMPLEX*16 array, dimension (N) 00097 *> The vector X in the formula op(A) * diag(X). 00098 *> \endverbatim 00099 *> 00100 *> \param[out] INFO 00101 *> \verbatim 00102 *> INFO is INTEGER 00103 *> = 0: Successful exit. 00104 *> i > 0: The ith argument is invalid. 00105 *> \endverbatim 00106 *> 00107 *> \param[in] WORK 00108 *> \verbatim 00109 *> WORK is COMPLEX*16 array, dimension (2*N). 00110 *> Workspace. 00111 *> \endverbatim 00112 *> 00113 *> \param[in] RWORK 00114 *> \verbatim 00115 *> RWORK is DOUBLE PRECISION array, dimension (N). 00116 *> Workspace. 00117 *> \endverbatim 00118 * 00119 * Authors: 00120 * ======== 00121 * 00122 *> \author Univ. of Tennessee 00123 *> \author Univ. of California Berkeley 00124 *> \author Univ. of Colorado Denver 00125 *> \author NAG Ltd. 00126 * 00127 *> \date November 2011 00128 * 00129 *> \ingroup complex16HEcomputational 00130 * 00131 * ===================================================================== 00132 DOUBLE PRECISION FUNCTION ZLA_HERCOND_X( UPLO, N, A, LDA, AF, 00133 $ LDAF, IPIV, X, INFO, 00134 $ WORK, RWORK ) 00135 * 00136 * -- LAPACK computational routine (version 3.4.0) -- 00137 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00138 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00139 * November 2011 00140 * 00141 * .. Scalar Arguments .. 00142 CHARACTER UPLO 00143 INTEGER N, LDA, LDAF, INFO 00144 * .. 00145 * .. Array Arguments .. 00146 INTEGER IPIV( * ) 00147 COMPLEX*16 A( LDA, * ), AF( LDAF, * ), WORK( * ), X( * ) 00148 DOUBLE PRECISION RWORK( * ) 00149 * .. 00150 * 00151 * ===================================================================== 00152 * 00153 * .. Local Scalars .. 00154 INTEGER KASE, I, J 00155 DOUBLE PRECISION AINVNM, ANORM, TMP 00156 LOGICAL UP, UPPER 00157 COMPLEX*16 ZDUM 00158 * .. 00159 * .. Local Arrays .. 00160 INTEGER ISAVE( 3 ) 00161 * .. 00162 * .. External Functions .. 00163 LOGICAL LSAME 00164 EXTERNAL LSAME 00165 * .. 00166 * .. External Subroutines .. 00167 EXTERNAL ZLACN2, ZHETRS, XERBLA 00168 * .. 00169 * .. Intrinsic Functions .. 00170 INTRINSIC ABS, MAX 00171 * .. 00172 * .. Statement Functions .. 00173 DOUBLE PRECISION CABS1 00174 * .. 00175 * .. Statement Function Definitions .. 00176 CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) ) 00177 * .. 00178 * .. Executable Statements .. 00179 * 00180 ZLA_HERCOND_X = 0.0D+0 00181 * 00182 INFO = 0 00183 UPPER = LSAME( UPLO, 'U' ) 00184 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 00185 INFO = -1 00186 ELSE IF ( N.LT.0 ) THEN 00187 INFO = -2 00188 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 00189 INFO = -4 00190 ELSE IF( LDAF.LT.MAX( 1, N ) ) THEN 00191 INFO = -6 00192 END IF 00193 IF( INFO.NE.0 ) THEN 00194 CALL XERBLA( 'ZLA_HERCOND_X', -INFO ) 00195 RETURN 00196 END IF 00197 UP = .FALSE. 00198 IF ( LSAME( UPLO, 'U' ) ) UP = .TRUE. 00199 * 00200 * Compute norm of op(A)*op2(C). 00201 * 00202 ANORM = 0.0D+0 00203 IF ( UP ) THEN 00204 DO I = 1, N 00205 TMP = 0.0D+0 00206 DO J = 1, I 00207 TMP = TMP + CABS1( A( J, I ) * X( J ) ) 00208 END DO 00209 DO J = I+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, I 00219 TMP = TMP + CABS1( A( I, J ) * X( J ) ) 00220 END DO 00221 DO J = I+1, N 00222 TMP = TMP + CABS1( A( J, I ) * X( J ) ) 00223 END DO 00224 RWORK( I ) = TMP 00225 ANORM = MAX( ANORM, TMP ) 00226 END DO 00227 END IF 00228 * 00229 * Quick return if possible. 00230 * 00231 IF( N.EQ.0 ) THEN 00232 ZLA_HERCOND_X = 1.0D+0 00233 RETURN 00234 ELSE IF( ANORM .EQ. 0.0D+0 ) THEN 00235 RETURN 00236 END IF 00237 * 00238 * Estimate the norm of inv(op(A)). 00239 * 00240 AINVNM = 0.0D+0 00241 * 00242 KASE = 0 00243 10 CONTINUE 00244 CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE ) 00245 IF( KASE.NE.0 ) THEN 00246 IF( KASE.EQ.2 ) THEN 00247 * 00248 * Multiply by R. 00249 * 00250 DO I = 1, N 00251 WORK( I ) = WORK( I ) * RWORK( I ) 00252 END DO 00253 * 00254 IF ( UP ) THEN 00255 CALL ZHETRS( 'U', N, 1, AF, LDAF, IPIV, 00256 $ WORK, N, INFO ) 00257 ELSE 00258 CALL ZHETRS( 'L', N, 1, AF, LDAF, IPIV, 00259 $ WORK, N, INFO ) 00260 ENDIF 00261 * 00262 * Multiply by inv(X). 00263 * 00264 DO I = 1, N 00265 WORK( I ) = WORK( I ) / X( I ) 00266 END DO 00267 ELSE 00268 * 00269 * Multiply by inv(X**H). 00270 * 00271 DO I = 1, N 00272 WORK( I ) = WORK( I ) / X( I ) 00273 END DO 00274 * 00275 IF ( UP ) THEN 00276 CALL ZHETRS( 'U', N, 1, AF, LDAF, IPIV, 00277 $ WORK, N, INFO ) 00278 ELSE 00279 CALL ZHETRS( 'L', N, 1, AF, LDAF, IPIV, 00280 $ WORK, N, INFO ) 00281 END IF 00282 * 00283 * Multiply by R. 00284 * 00285 DO I = 1, N 00286 WORK( I ) = WORK( I ) * RWORK( I ) 00287 END DO 00288 END IF 00289 GO TO 10 00290 END IF 00291 * 00292 * Compute the estimate of the reciprocal condition number. 00293 * 00294 IF( AINVNM .NE. 0.0D+0 ) 00295 $ ZLA_HERCOND_X = 1.0D+0 / AINVNM 00296 * 00297 RETURN 00298 * 00299 END