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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b CLA_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 CLA_HERCOND_X + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cla_hercond_x.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cla_hercond_x.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cla_hercond_x.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * REAL FUNCTION CLA_HERCOND_X( UPLO, N, A, LDA, AF, LDAF, IPIV, X, 00022 * INFO, WORK, RWORK ) 00023 * 00024 * .. Scalar Arguments .. 00025 * CHARACTER UPLO 00026 * INTEGER N, LDA, LDAF, INFO 00027 * .. 00028 * .. Array Arguments .. 00029 * INTEGER IPIV( * ) 00030 * COMPLEX A( LDA, * ), AF( LDAF, * ), WORK( * ), X( * ) 00031 * REAL RWORK( * ) 00032 * .. 00033 * 00034 * 00035 *> \par Purpose: 00036 * ============= 00037 *> 00038 *> \verbatim 00039 *> 00040 *> CLA_HERCOND_X computes the infinity norm condition number of 00041 *> op(A) * diag(X) where X is a COMPLEX vector. 00042 *> \endverbatim 00043 * 00044 * Arguments: 00045 * ========== 00046 * 00047 *> \param[in] UPLO 00048 *> \verbatim 00049 *> UPLO is CHARACTER*1 00050 *> = 'U': Upper triangle of A is stored; 00051 *> = 'L': Lower triangle of A is stored. 00052 *> \endverbatim 00053 *> 00054 *> \param[in] N 00055 *> \verbatim 00056 *> N is INTEGER 00057 *> The number of linear equations, i.e., the order of the 00058 *> matrix A. N >= 0. 00059 *> \endverbatim 00060 *> 00061 *> \param[in] A 00062 *> \verbatim 00063 *> A is COMPLEX array, dimension (LDA,N) 00064 *> On entry, the N-by-N matrix A. 00065 *> \endverbatim 00066 *> 00067 *> \param[in] LDA 00068 *> \verbatim 00069 *> LDA is INTEGER 00070 *> The leading dimension of the array A. LDA >= max(1,N). 00071 *> \endverbatim 00072 *> 00073 *> \param[in] AF 00074 *> \verbatim 00075 *> AF is COMPLEX array, dimension (LDAF,N) 00076 *> The block diagonal matrix D and the multipliers used to 00077 *> obtain the factor U or L as computed by CHETRF. 00078 *> \endverbatim 00079 *> 00080 *> \param[in] LDAF 00081 *> \verbatim 00082 *> LDAF is INTEGER 00083 *> The leading dimension of the array AF. LDAF >= max(1,N). 00084 *> \endverbatim 00085 *> 00086 *> \param[in] IPIV 00087 *> \verbatim 00088 *> IPIV is INTEGER array, dimension (N) 00089 *> Details of the interchanges and the block structure of D 00090 *> as determined by CHETRF. 00091 *> \endverbatim 00092 *> 00093 *> \param[in] X 00094 *> \verbatim 00095 *> X is COMPLEX array, dimension (N) 00096 *> The vector X in the formula op(A) * diag(X). 00097 *> \endverbatim 00098 *> 00099 *> \param[out] INFO 00100 *> \verbatim 00101 *> INFO is INTEGER 00102 *> = 0: Successful exit. 00103 *> i > 0: The ith argument is invalid. 00104 *> \endverbatim 00105 *> 00106 *> \param[in] WORK 00107 *> \verbatim 00108 *> WORK is COMPLEX array, dimension (2*N). 00109 *> Workspace. 00110 *> \endverbatim 00111 *> 00112 *> \param[in] RWORK 00113 *> \verbatim 00114 *> RWORK is REAL array, dimension (N). 00115 *> Workspace. 00116 *> \endverbatim 00117 * 00118 * Authors: 00119 * ======== 00120 * 00121 *> \author Univ. of Tennessee 00122 *> \author Univ. of California Berkeley 00123 *> \author Univ. of Colorado Denver 00124 *> \author NAG Ltd. 00125 * 00126 *> \date November 2011 00127 * 00128 *> \ingroup complexHEcomputational 00129 * 00130 * ===================================================================== 00131 REAL FUNCTION CLA_HERCOND_X( UPLO, N, A, LDA, AF, LDAF, IPIV, X, 00132 $ INFO, WORK, RWORK ) 00133 * 00134 * -- LAPACK computational routine (version 3.4.0) -- 00135 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00136 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00137 * November 2011 00138 * 00139 * .. Scalar Arguments .. 00140 CHARACTER UPLO 00141 INTEGER N, LDA, LDAF, INFO 00142 * .. 00143 * .. Array Arguments .. 00144 INTEGER IPIV( * ) 00145 COMPLEX A( LDA, * ), AF( LDAF, * ), WORK( * ), X( * ) 00146 REAL RWORK( * ) 00147 * .. 00148 * 00149 * ===================================================================== 00150 * 00151 * .. Local Scalars .. 00152 INTEGER KASE, I, J 00153 REAL AINVNM, ANORM, TMP 00154 LOGICAL UP, UPPER 00155 COMPLEX ZDUM 00156 * .. 00157 * .. Local Arrays .. 00158 INTEGER ISAVE( 3 ) 00159 * .. 00160 * .. External Functions .. 00161 LOGICAL LSAME 00162 EXTERNAL LSAME 00163 * .. 00164 * .. External Subroutines .. 00165 EXTERNAL CLACN2, CHETRS, XERBLA 00166 * .. 00167 * .. Intrinsic Functions .. 00168 INTRINSIC ABS, MAX 00169 * .. 00170 * .. Statement Functions .. 00171 REAL CABS1 00172 * .. 00173 * .. Statement Function Definitions .. 00174 CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) ) 00175 * .. 00176 * .. Executable Statements .. 00177 * 00178 CLA_HERCOND_X = 0.0E+0 00179 * 00180 INFO = 0 00181 UPPER = LSAME( UPLO, 'U' ) 00182 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 00183 INFO = -1 00184 ELSE IF ( N.LT.0 ) THEN 00185 INFO = -2 00186 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 00187 INFO = -4 00188 ELSE IF( LDAF.LT.MAX( 1, N ) ) THEN 00189 INFO = -6 00190 END IF 00191 IF( INFO.NE.0 ) THEN 00192 CALL XERBLA( 'CLA_HERCOND_X', -INFO ) 00193 RETURN 00194 END IF 00195 UP = .FALSE. 00196 IF ( LSAME( UPLO, 'U' ) ) UP = .TRUE. 00197 * 00198 * Compute norm of op(A)*op2(C). 00199 * 00200 ANORM = 0.0 00201 IF ( UP ) THEN 00202 DO I = 1, N 00203 TMP = 0.0E+0 00204 DO J = 1, I 00205 TMP = TMP + CABS1( A( J, I ) * X( J ) ) 00206 END DO 00207 DO J = I+1, N 00208 TMP = TMP + CABS1( A( I, J ) * X( J ) ) 00209 END DO 00210 RWORK( I ) = TMP 00211 ANORM = MAX( ANORM, TMP ) 00212 END DO 00213 ELSE 00214 DO I = 1, N 00215 TMP = 0.0E+0 00216 DO J = 1, I 00217 TMP = TMP + CABS1( A( I, J ) * X( J ) ) 00218 END DO 00219 DO J = I+1, N 00220 TMP = TMP + CABS1( A( J, I ) * X( J ) ) 00221 END DO 00222 RWORK( I ) = TMP 00223 ANORM = MAX( ANORM, TMP ) 00224 END DO 00225 END IF 00226 * 00227 * Quick return if possible. 00228 * 00229 IF( N.EQ.0 ) THEN 00230 CLA_HERCOND_X = 1.0E+0 00231 RETURN 00232 ELSE IF( ANORM .EQ. 0.0E+0 ) THEN 00233 RETURN 00234 END IF 00235 * 00236 * Estimate the norm of inv(op(A)). 00237 * 00238 AINVNM = 0.0E+0 00239 * 00240 KASE = 0 00241 10 CONTINUE 00242 CALL CLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE ) 00243 IF( KASE.NE.0 ) THEN 00244 IF( KASE.EQ.2 ) THEN 00245 * 00246 * Multiply by R. 00247 * 00248 DO I = 1, N 00249 WORK( I ) = WORK( I ) * RWORK( I ) 00250 END DO 00251 * 00252 IF ( UP ) THEN 00253 CALL CHETRS( 'U', N, 1, AF, LDAF, IPIV, 00254 $ WORK, N, INFO ) 00255 ELSE 00256 CALL CHETRS( 'L', N, 1, AF, LDAF, IPIV, 00257 $ WORK, N, INFO ) 00258 ENDIF 00259 * 00260 * Multiply by inv(X). 00261 * 00262 DO I = 1, N 00263 WORK( I ) = WORK( I ) / X( I ) 00264 END DO 00265 ELSE 00266 * 00267 * Multiply by inv(X**H). 00268 * 00269 DO I = 1, N 00270 WORK( I ) = WORK( I ) / X( I ) 00271 END DO 00272 * 00273 IF ( UP ) THEN 00274 CALL CHETRS( 'U', N, 1, AF, LDAF, IPIV, 00275 $ WORK, N, INFO ) 00276 ELSE 00277 CALL CHETRS( 'L', N, 1, AF, LDAF, IPIV, 00278 $ WORK, N, INFO ) 00279 END IF 00280 * 00281 * Multiply by R. 00282 * 00283 DO I = 1, N 00284 WORK( I ) = WORK( I ) * RWORK( I ) 00285 END DO 00286 END IF 00287 GO TO 10 00288 END IF 00289 * 00290 * Compute the estimate of the reciprocal condition number. 00291 * 00292 IF( AINVNM .NE. 0.0E+0 ) 00293 $ CLA_HERCOND_X = 1.0E+0 / AINVNM 00294 * 00295 RETURN 00296 * 00297 END