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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b SLA_PORCOND 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download SLA_PORCOND + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sla_porcond.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sla_porcond.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sla_porcond.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * REAL FUNCTION SLA_PORCOND( UPLO, N, A, LDA, AF, LDAF, CMODE, C, 00022 * INFO, WORK, IWORK ) 00023 * 00024 * .. Scalar Arguments .. 00025 * CHARACTER UPLO 00026 * INTEGER N, LDA, LDAF, INFO, CMODE 00027 * REAL A( LDA, * ), AF( LDAF, * ), WORK( * ), 00028 * $ C( * ) 00029 * .. 00030 * .. Array Arguments .. 00031 * INTEGER IWORK( * ) 00032 * .. 00033 * 00034 * 00035 *> \par Purpose: 00036 * ============= 00037 *> 00038 *> \verbatim 00039 *> 00040 *> SLA_PORCOND Estimates the Skeel condition number of op(A) * op2(C) 00041 *> where op2 is determined by CMODE as follows 00042 *> CMODE = 1 op2(C) = C 00043 *> CMODE = 0 op2(C) = I 00044 *> CMODE = -1 op2(C) = inv(C) 00045 *> The Skeel condition number cond(A) = norminf( |inv(A)||A| ) 00046 *> is computed by computing scaling factors R such that 00047 *> diag(R)*A*op2(C) is row equilibrated and computing the standard 00048 *> infinity-norm condition number. 00049 *> \endverbatim 00050 * 00051 * Arguments: 00052 * ========== 00053 * 00054 *> \param[in] UPLO 00055 *> \verbatim 00056 *> UPLO is CHARACTER*1 00057 *> = 'U': Upper triangle of A is stored; 00058 *> = 'L': Lower triangle of A is stored. 00059 *> \endverbatim 00060 *> 00061 *> \param[in] N 00062 *> \verbatim 00063 *> N is INTEGER 00064 *> The number of linear equations, i.e., the order of the 00065 *> matrix A. N >= 0. 00066 *> \endverbatim 00067 *> 00068 *> \param[in] A 00069 *> \verbatim 00070 *> A is REAL array, dimension (LDA,N) 00071 *> On entry, the N-by-N matrix A. 00072 *> \endverbatim 00073 *> 00074 *> \param[in] LDA 00075 *> \verbatim 00076 *> LDA is INTEGER 00077 *> The leading dimension of the array A. LDA >= max(1,N). 00078 *> \endverbatim 00079 *> 00080 *> \param[in] AF 00081 *> \verbatim 00082 *> AF is REAL array, dimension (LDAF,N) 00083 *> The triangular factor U or L from the Cholesky factorization 00084 *> A = U**T*U or A = L*L**T, as computed by SPOTRF. 00085 *> \endverbatim 00086 *> 00087 *> \param[in] LDAF 00088 *> \verbatim 00089 *> LDAF is INTEGER 00090 *> The leading dimension of the array AF. LDAF >= max(1,N). 00091 *> \endverbatim 00092 *> 00093 *> \param[in] CMODE 00094 *> \verbatim 00095 *> CMODE is INTEGER 00096 *> Determines op2(C) in the formula op(A) * op2(C) as follows: 00097 *> CMODE = 1 op2(C) = C 00098 *> CMODE = 0 op2(C) = I 00099 *> CMODE = -1 op2(C) = inv(C) 00100 *> \endverbatim 00101 *> 00102 *> \param[in] C 00103 *> \verbatim 00104 *> C is REAL array, dimension (N) 00105 *> The vector C in the formula op(A) * op2(C). 00106 *> \endverbatim 00107 *> 00108 *> \param[out] INFO 00109 *> \verbatim 00110 *> INFO is INTEGER 00111 *> = 0: Successful exit. 00112 *> i > 0: The ith argument is invalid. 00113 *> \endverbatim 00114 *> 00115 *> \param[in] WORK 00116 *> \verbatim 00117 *> WORK is REAL array, dimension (3*N). 00118 *> Workspace. 00119 *> \endverbatim 00120 *> 00121 *> \param[in] IWORK 00122 *> \verbatim 00123 *> IWORK is INTEGER array, dimension (N). 00124 *> Workspace. 00125 *> \endverbatim 00126 * 00127 * Authors: 00128 * ======== 00129 * 00130 *> \author Univ. of Tennessee 00131 *> \author Univ. of California Berkeley 00132 *> \author Univ. of Colorado Denver 00133 *> \author NAG Ltd. 00134 * 00135 *> \date November 2011 00136 * 00137 *> \ingroup realPOcomputational 00138 * 00139 * ===================================================================== 00140 REAL FUNCTION SLA_PORCOND( UPLO, N, A, LDA, AF, LDAF, CMODE, C, 00141 $ INFO, WORK, IWORK ) 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 INTEGER N, LDA, LDAF, INFO, CMODE 00151 REAL A( LDA, * ), AF( LDAF, * ), WORK( * ), 00152 $ C( * ) 00153 * .. 00154 * .. Array Arguments .. 00155 INTEGER IWORK( * ) 00156 * .. 00157 * 00158 * ===================================================================== 00159 * 00160 * .. Local Scalars .. 00161 INTEGER KASE, I, J 00162 REAL AINVNM, TMP 00163 LOGICAL UP 00164 * .. 00165 * .. Array Arguments .. 00166 INTEGER ISAVE( 3 ) 00167 * .. 00168 * .. External Functions .. 00169 LOGICAL LSAME 00170 INTEGER ISAMAX 00171 EXTERNAL LSAME, ISAMAX 00172 * .. 00173 * .. External Subroutines .. 00174 EXTERNAL SLACN2, SPOTRS, XERBLA 00175 * .. 00176 * .. Intrinsic Functions .. 00177 INTRINSIC ABS, MAX 00178 * .. 00179 * .. Executable Statements .. 00180 * 00181 SLA_PORCOND = 0.0 00182 * 00183 INFO = 0 00184 IF( N.LT.0 ) THEN 00185 INFO = -2 00186 END IF 00187 IF( INFO.NE.0 ) THEN 00188 CALL XERBLA( 'SLA_PORCOND', -INFO ) 00189 RETURN 00190 END IF 00191 00192 IF( N.EQ.0 ) THEN 00193 SLA_PORCOND = 1.0 00194 RETURN 00195 END IF 00196 UP = .FALSE. 00197 IF ( LSAME( UPLO, 'U' ) ) UP = .TRUE. 00198 * 00199 * Compute the equilibration matrix R such that 00200 * inv(R)*A*C has unit 1-norm. 00201 * 00202 IF ( UP ) THEN 00203 DO I = 1, N 00204 TMP = 0.0 00205 IF ( CMODE .EQ. 1 ) THEN 00206 DO J = 1, I 00207 TMP = TMP + ABS( A( J, I ) * C( J ) ) 00208 END DO 00209 DO J = I+1, N 00210 TMP = TMP + ABS( A( I, J ) * C( J ) ) 00211 END DO 00212 ELSE IF ( CMODE .EQ. 0 ) THEN 00213 DO J = 1, I 00214 TMP = TMP + ABS( A( J, I ) ) 00215 END DO 00216 DO J = I+1, N 00217 TMP = TMP + ABS( A( I, J ) ) 00218 END DO 00219 ELSE 00220 DO J = 1, I 00221 TMP = TMP + ABS( A( J ,I ) / C( J ) ) 00222 END DO 00223 DO J = I+1, N 00224 TMP = TMP + ABS( A( I, J ) / C( J ) ) 00225 END DO 00226 END IF 00227 WORK( 2*N+I ) = TMP 00228 END DO 00229 ELSE 00230 DO I = 1, N 00231 TMP = 0.0 00232 IF ( CMODE .EQ. 1 ) THEN 00233 DO J = 1, I 00234 TMP = TMP + ABS( A( I, J ) * C( J ) ) 00235 END DO 00236 DO J = I+1, N 00237 TMP = TMP + ABS( A( J, I ) * C( J ) ) 00238 END DO 00239 ELSE IF ( CMODE .EQ. 0 ) THEN 00240 DO J = 1, I 00241 TMP = TMP + ABS( A( I, J ) ) 00242 END DO 00243 DO J = I+1, N 00244 TMP = TMP + ABS( A( J, I ) ) 00245 END DO 00246 ELSE 00247 DO J = 1, I 00248 TMP = TMP + ABS( A( I, J ) / C( J ) ) 00249 END DO 00250 DO J = I+1, N 00251 TMP = TMP + ABS( A( J, I ) / C( J ) ) 00252 END DO 00253 END IF 00254 WORK( 2*N+I ) = TMP 00255 END DO 00256 ENDIF 00257 * 00258 * Estimate the norm of inv(op(A)). 00259 * 00260 AINVNM = 0.0 00261 00262 KASE = 0 00263 10 CONTINUE 00264 CALL SLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE ) 00265 IF( KASE.NE.0 ) THEN 00266 IF( KASE.EQ.2 ) THEN 00267 * 00268 * Multiply by R. 00269 * 00270 DO I = 1, N 00271 WORK( I ) = WORK( I ) * WORK( 2*N+I ) 00272 END DO 00273 00274 IF (UP) THEN 00275 CALL SPOTRS( 'Upper', N, 1, AF, LDAF, WORK, N, INFO ) 00276 ELSE 00277 CALL SPOTRS( 'Lower', N, 1, AF, LDAF, WORK, N, INFO ) 00278 ENDIF 00279 * 00280 * Multiply by inv(C). 00281 * 00282 IF ( CMODE .EQ. 1 ) THEN 00283 DO I = 1, N 00284 WORK( I ) = WORK( I ) / C( I ) 00285 END DO 00286 ELSE IF ( CMODE .EQ. -1 ) THEN 00287 DO I = 1, N 00288 WORK( I ) = WORK( I ) * C( I ) 00289 END DO 00290 END IF 00291 ELSE 00292 * 00293 * Multiply by inv(C**T). 00294 * 00295 IF ( CMODE .EQ. 1 ) THEN 00296 DO I = 1, N 00297 WORK( I ) = WORK( I ) / C( I ) 00298 END DO 00299 ELSE IF ( CMODE .EQ. -1 ) 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 SPOTRS( 'Upper', N, 1, AF, LDAF, WORK, N, INFO ) 00307 ELSE 00308 CALL SPOTRS( 'Lower', N, 1, AF, LDAF, WORK, N, INFO ) 00309 ENDIF 00310 * 00311 * Multiply by R. 00312 * 00313 DO I = 1, N 00314 WORK( I ) = WORK( I ) * WORK( 2*N+I ) 00315 END DO 00316 END IF 00317 GO TO 10 00318 END IF 00319 * 00320 * Compute the estimate of the reciprocal condition number. 00321 * 00322 IF( AINVNM .NE. 0.0 ) 00323 $ SLA_PORCOND = ( 1.0 / AINVNM ) 00324 * 00325 RETURN 00326 * 00327 END