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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b CLA_PORCOND_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_PORCOND_C + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cla_porcond_c.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cla_porcond_c.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cla_porcond_c.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * REAL FUNCTION CLA_PORCOND_C( UPLO, N, A, LDA, AF, LDAF, C, CAPPLY, 00022 * INFO, WORK, RWORK ) 00023 * 00024 * .. Scalar Arguments .. 00025 * CHARACTER UPLO 00026 * LOGICAL CAPPLY 00027 * INTEGER N, LDA, LDAF, INFO 00028 * .. 00029 * .. Array Arguments .. 00030 * COMPLEX A( LDA, * ), AF( LDAF, * ), WORK( * ) 00031 * REAL C( * ), RWORK( * ) 00032 * .. 00033 * 00034 * 00035 *> \par Purpose: 00036 * ============= 00037 *> 00038 *> \verbatim 00039 *> 00040 *> CLA_PORCOND_C Computes the infinity norm condition number of 00041 *> op(A) * inv(diag(C)) where C is a DOUBLE PRECISION 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 triangular factor U or L from the Cholesky factorization 00077 *> A = U**H*U or A = L*L**H, as computed by CPOTRF. 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] C 00087 *> \verbatim 00088 *> C is REAL array, dimension (N) 00089 *> The vector C in the formula op(A) * inv(diag(C)). 00090 *> \endverbatim 00091 *> 00092 *> \param[in] CAPPLY 00093 *> \verbatim 00094 *> CAPPLY is LOGICAL 00095 *> If .TRUE. then access the vector C in the formula above. 00096 *> \endverbatim 00097 *> 00098 *> \param[out] INFO 00099 *> \verbatim 00100 *> INFO is INTEGER 00101 *> = 0: Successful exit. 00102 *> i > 0: The ith argument is invalid. 00103 *> \endverbatim 00104 *> 00105 *> \param[in] WORK 00106 *> \verbatim 00107 *> WORK is COMPLEX array, dimension (2*N). 00108 *> Workspace. 00109 *> \endverbatim 00110 *> 00111 *> \param[in] RWORK 00112 *> \verbatim 00113 *> RWORK is REAL array, dimension (N). 00114 *> Workspace. 00115 *> \endverbatim 00116 * 00117 * Authors: 00118 * ======== 00119 * 00120 *> \author Univ. of Tennessee 00121 *> \author Univ. of California Berkeley 00122 *> \author Univ. of Colorado Denver 00123 *> \author NAG Ltd. 00124 * 00125 *> \date November 2011 00126 * 00127 *> \ingroup complexPOcomputational 00128 * 00129 * ===================================================================== 00130 REAL FUNCTION CLA_PORCOND_C( UPLO, N, A, LDA, AF, LDAF, C, CAPPLY, 00131 $ INFO, WORK, RWORK ) 00132 * 00133 * -- LAPACK computational routine (version 3.4.0) -- 00134 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00135 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00136 * November 2011 00137 * 00138 * .. Scalar Arguments .. 00139 CHARACTER UPLO 00140 LOGICAL CAPPLY 00141 INTEGER N, LDA, LDAF, INFO 00142 * .. 00143 * .. Array Arguments .. 00144 COMPLEX A( LDA, * ), AF( LDAF, * ), WORK( * ) 00145 REAL C( * ), RWORK( * ) 00146 * .. 00147 * 00148 * ===================================================================== 00149 * 00150 * .. Local Scalars .. 00151 INTEGER KASE 00152 REAL AINVNM, ANORM, TMP 00153 INTEGER I, J 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, CPOTRS, XERBLA 00166 * .. 00167 * .. Intrinsic Functions .. 00168 INTRINSIC ABS, MAX, REAL, AIMAG 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_PORCOND_C = 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_PORCOND_C', -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 = 0.0E+0 00201 IF ( UP ) THEN 00202 DO I = 1, N 00203 TMP = 0.0E+0 00204 IF ( CAPPLY ) THEN 00205 DO J = 1, I 00206 TMP = TMP + CABS1( A( J, I ) ) / C( J ) 00207 END DO 00208 DO J = I+1, N 00209 TMP = TMP + CABS1( A( I, J ) ) / C( J ) 00210 END DO 00211 ELSE 00212 DO J = 1, I 00213 TMP = TMP + CABS1( A( J, I ) ) 00214 END DO 00215 DO J = I+1, N 00216 TMP = TMP + CABS1( A( I, J ) ) 00217 END DO 00218 END IF 00219 RWORK( I ) = TMP 00220 ANORM = MAX( ANORM, TMP ) 00221 END DO 00222 ELSE 00223 DO I = 1, N 00224 TMP = 0.0E+0 00225 IF ( CAPPLY ) THEN 00226 DO J = 1, I 00227 TMP = TMP + CABS1( A( I, J ) ) / C( J ) 00228 END DO 00229 DO J = I+1, N 00230 TMP = TMP + CABS1( A( J, I ) ) / C( J ) 00231 END DO 00232 ELSE 00233 DO J = 1, I 00234 TMP = TMP + CABS1( A( I, J ) ) 00235 END DO 00236 DO J = I+1, N 00237 TMP = TMP + CABS1( A( J, I ) ) 00238 END DO 00239 END IF 00240 RWORK( I ) = TMP 00241 ANORM = MAX( ANORM, TMP ) 00242 END DO 00243 END IF 00244 * 00245 * Quick return if possible. 00246 * 00247 IF( N.EQ.0 ) THEN 00248 CLA_PORCOND_C = 1.0E+0 00249 RETURN 00250 ELSE IF( ANORM .EQ. 0.0E+0 ) THEN 00251 RETURN 00252 END IF 00253 * 00254 * Estimate the norm of inv(op(A)). 00255 * 00256 AINVNM = 0.0E+0 00257 * 00258 KASE = 0 00259 10 CONTINUE 00260 CALL CLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE ) 00261 IF( KASE.NE.0 ) THEN 00262 IF( KASE.EQ.2 ) THEN 00263 * 00264 * Multiply by R. 00265 * 00266 DO I = 1, N 00267 WORK( I ) = WORK( I ) * RWORK( I ) 00268 END DO 00269 * 00270 IF ( UP ) THEN 00271 CALL CPOTRS( 'U', N, 1, AF, LDAF, 00272 $ WORK, N, INFO ) 00273 ELSE 00274 CALL CPOTRS( 'L', N, 1, AF, LDAF, 00275 $ WORK, N, INFO ) 00276 ENDIF 00277 * 00278 * Multiply by inv(C). 00279 * 00280 IF ( CAPPLY ) THEN 00281 DO I = 1, N 00282 WORK( I ) = WORK( I ) * C( I ) 00283 END DO 00284 END IF 00285 ELSE 00286 * 00287 * Multiply by inv(C**H). 00288 * 00289 IF ( CAPPLY ) THEN 00290 DO I = 1, N 00291 WORK( I ) = WORK( I ) * C( I ) 00292 END DO 00293 END IF 00294 * 00295 IF ( UP ) THEN 00296 CALL CPOTRS( 'U', N, 1, AF, LDAF, 00297 $ WORK, N, INFO ) 00298 ELSE 00299 CALL CPOTRS( 'L', N, 1, AF, LDAF, 00300 $ WORK, N, INFO ) 00301 END IF 00302 * 00303 * Multiply by R. 00304 * 00305 DO I = 1, N 00306 WORK( I ) = WORK( I ) * RWORK( I ) 00307 END DO 00308 END IF 00309 GO TO 10 00310 END IF 00311 * 00312 * Compute the estimate of the reciprocal condition number. 00313 * 00314 IF( AINVNM .NE. 0.0E+0 ) 00315 $ CLA_PORCOND_C = 1.0E+0 / AINVNM 00316 * 00317 RETURN 00318 * 00319 END