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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b SLA_SYRCOND 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download SLA_SYRCOND + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sla_syrcond.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sla_syrcond.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sla_syrcond.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * REAL FUNCTION SLA_SYRCOND( UPLO, N, A, LDA, AF, LDAF, IPIV, CMODE, 00022 * C, INFO, WORK, IWORK ) 00023 * 00024 * .. Scalar Arguments .. 00025 * CHARACTER UPLO 00026 * INTEGER N, LDA, LDAF, INFO, CMODE 00027 * .. 00028 * .. Array Arguments 00029 * INTEGER IWORK( * ), IPIV( * ) 00030 * REAL A( LDA, * ), AF( LDAF, * ), WORK( * ), C( * ) 00031 * .. 00032 * 00033 * 00034 *> \par Purpose: 00035 * ============= 00036 *> 00037 *> \verbatim 00038 *> 00039 *> SLA_SYRCOND estimates the Skeel condition number of op(A) * op2(C) 00040 *> where op2 is determined by CMODE as follows 00041 *> CMODE = 1 op2(C) = C 00042 *> CMODE = 0 op2(C) = I 00043 *> CMODE = -1 op2(C) = inv(C) 00044 *> The Skeel condition number cond(A) = norminf( |inv(A)||A| ) 00045 *> is computed by computing scaling factors R such that 00046 *> diag(R)*A*op2(C) is row equilibrated and computing the standard 00047 *> infinity-norm condition number. 00048 *> \endverbatim 00049 * 00050 * Arguments: 00051 * ========== 00052 * 00053 *> \param[in] UPLO 00054 *> \verbatim 00055 *> UPLO is CHARACTER*1 00056 *> = 'U': Upper triangle of A is stored; 00057 *> = 'L': Lower triangle of A is stored. 00058 *> \endverbatim 00059 *> 00060 *> \param[in] N 00061 *> \verbatim 00062 *> N is INTEGER 00063 *> The number of linear equations, i.e., the order of the 00064 *> matrix A. N >= 0. 00065 *> \endverbatim 00066 *> 00067 *> \param[in] A 00068 *> \verbatim 00069 *> A is REAL array, dimension (LDA,N) 00070 *> On entry, the N-by-N matrix A. 00071 *> \endverbatim 00072 *> 00073 *> \param[in] LDA 00074 *> \verbatim 00075 *> LDA is INTEGER 00076 *> The leading dimension of the array A. LDA >= max(1,N). 00077 *> \endverbatim 00078 *> 00079 *> \param[in] AF 00080 *> \verbatim 00081 *> AF is REAL array, dimension (LDAF,N) 00082 *> The block diagonal matrix D and the multipliers used to 00083 *> obtain the factor U or L as computed by SSYTRF. 00084 *> \endverbatim 00085 *> 00086 *> \param[in] LDAF 00087 *> \verbatim 00088 *> LDAF is INTEGER 00089 *> The leading dimension of the array AF. LDAF >= max(1,N). 00090 *> \endverbatim 00091 *> 00092 *> \param[in] IPIV 00093 *> \verbatim 00094 *> IPIV is INTEGER array, dimension (N) 00095 *> Details of the interchanges and the block structure of D 00096 *> as determined by SSYTRF. 00097 *> \endverbatim 00098 *> 00099 *> \param[in] CMODE 00100 *> \verbatim 00101 *> CMODE is INTEGER 00102 *> Determines op2(C) in the formula op(A) * op2(C) as follows: 00103 *> CMODE = 1 op2(C) = C 00104 *> CMODE = 0 op2(C) = I 00105 *> CMODE = -1 op2(C) = inv(C) 00106 *> \endverbatim 00107 *> 00108 *> \param[in] C 00109 *> \verbatim 00110 *> C is REAL array, dimension (N) 00111 *> The vector C in the formula op(A) * op2(C). 00112 *> \endverbatim 00113 *> 00114 *> \param[out] INFO 00115 *> \verbatim 00116 *> INFO is INTEGER 00117 *> = 0: Successful exit. 00118 *> i > 0: The ith argument is invalid. 00119 *> \endverbatim 00120 *> 00121 *> \param[in] WORK 00122 *> \verbatim 00123 *> WORK is REAL array, dimension (3*N). 00124 *> Workspace. 00125 *> \endverbatim 00126 *> 00127 *> \param[in] IWORK 00128 *> \verbatim 00129 *> IWORK is INTEGER array, dimension (N). 00130 *> Workspace. 00131 *> \endverbatim 00132 * 00133 * Authors: 00134 * ======== 00135 * 00136 *> \author Univ. of Tennessee 00137 *> \author Univ. of California Berkeley 00138 *> \author Univ. of Colorado Denver 00139 *> \author NAG Ltd. 00140 * 00141 *> \date November 2011 00142 * 00143 *> \ingroup realSYcomputational 00144 * 00145 * ===================================================================== 00146 REAL FUNCTION SLA_SYRCOND( UPLO, N, A, LDA, AF, LDAF, IPIV, CMODE, 00147 $ C, INFO, WORK, IWORK ) 00148 * 00149 * -- LAPACK computational routine (version 3.4.0) -- 00150 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00151 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00152 * November 2011 00153 * 00154 * .. Scalar Arguments .. 00155 CHARACTER UPLO 00156 INTEGER N, LDA, LDAF, INFO, CMODE 00157 * .. 00158 * .. Array Arguments 00159 INTEGER IWORK( * ), IPIV( * ) 00160 REAL A( LDA, * ), AF( LDAF, * ), WORK( * ), C( * ) 00161 * .. 00162 * 00163 * ===================================================================== 00164 * 00165 * .. Local Scalars .. 00166 CHARACTER NORMIN 00167 INTEGER KASE, I, J 00168 REAL AINVNM, SMLNUM, TMP 00169 LOGICAL UP 00170 * .. 00171 * .. Local Arrays .. 00172 INTEGER ISAVE( 3 ) 00173 * .. 00174 * .. External Functions .. 00175 LOGICAL LSAME 00176 INTEGER ISAMAX 00177 REAL SLAMCH 00178 EXTERNAL LSAME, ISAMAX, SLAMCH 00179 * .. 00180 * .. External Subroutines .. 00181 EXTERNAL SLACN2, SLATRS, SRSCL, XERBLA, SSYTRS 00182 * .. 00183 * .. Intrinsic Functions .. 00184 INTRINSIC ABS, MAX 00185 * .. 00186 * .. Executable Statements .. 00187 * 00188 SLA_SYRCOND = 0.0 00189 * 00190 INFO = 0 00191 IF( N.LT.0 ) THEN 00192 INFO = -2 00193 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 00194 INFO = -4 00195 ELSE IF( LDAF.LT.MAX( 1, N ) ) THEN 00196 INFO = -6 00197 END IF 00198 IF( INFO.NE.0 ) THEN 00199 CALL XERBLA( 'SLA_SYRCOND', -INFO ) 00200 RETURN 00201 END IF 00202 IF( N.EQ.0 ) THEN 00203 SLA_SYRCOND = 1.0 00204 RETURN 00205 END IF 00206 UP = .FALSE. 00207 IF ( LSAME( UPLO, 'U' ) ) UP = .TRUE. 00208 * 00209 * Compute the equilibration matrix R such that 00210 * inv(R)*A*C has unit 1-norm. 00211 * 00212 IF ( UP ) THEN 00213 DO I = 1, N 00214 TMP = 0.0 00215 IF ( CMODE .EQ. 1 ) THEN 00216 DO J = 1, I 00217 TMP = TMP + ABS( A( J, I ) * C( J ) ) 00218 END DO 00219 DO J = I+1, N 00220 TMP = TMP + ABS( A( I, J ) * C( J ) ) 00221 END DO 00222 ELSE IF ( CMODE .EQ. 0 ) THEN 00223 DO J = 1, I 00224 TMP = TMP + ABS( A( J, I ) ) 00225 END DO 00226 DO J = I+1, N 00227 TMP = TMP + ABS( A( I, J ) ) 00228 END DO 00229 ELSE 00230 DO J = 1, I 00231 TMP = TMP + ABS( A( J, I ) / C( J ) ) 00232 END DO 00233 DO J = I+1, N 00234 TMP = TMP + ABS( A( I, J ) / C( J ) ) 00235 END DO 00236 END IF 00237 WORK( 2*N+I ) = TMP 00238 END DO 00239 ELSE 00240 DO I = 1, N 00241 TMP = 0.0 00242 IF ( CMODE .EQ. 1 ) THEN 00243 DO J = 1, I 00244 TMP = TMP + ABS( A( I, J ) * C( J ) ) 00245 END DO 00246 DO J = I+1, N 00247 TMP = TMP + ABS( A( J, I ) * C( J ) ) 00248 END DO 00249 ELSE IF ( CMODE .EQ. 0 ) THEN 00250 DO J = 1, I 00251 TMP = TMP + ABS( A( I, J ) ) 00252 END DO 00253 DO J = I+1, N 00254 TMP = TMP + ABS( A( J, I ) ) 00255 END DO 00256 ELSE 00257 DO J = 1, I 00258 TMP = TMP + ABS( A( I, J) / C( J ) ) 00259 END DO 00260 DO J = I+1, N 00261 TMP = TMP + ABS( A( J, I) / C( J ) ) 00262 END DO 00263 END IF 00264 WORK( 2*N+I ) = TMP 00265 END DO 00266 ENDIF 00267 * 00268 * Estimate the norm of inv(op(A)). 00269 * 00270 SMLNUM = SLAMCH( 'Safe minimum' ) 00271 AINVNM = 0.0 00272 NORMIN = 'N' 00273 00274 KASE = 0 00275 10 CONTINUE 00276 CALL SLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE ) 00277 IF( KASE.NE.0 ) THEN 00278 IF( KASE.EQ.2 ) THEN 00279 * 00280 * Multiply by R. 00281 * 00282 DO I = 1, N 00283 WORK( I ) = WORK( I ) * WORK( 2*N+I ) 00284 END DO 00285 00286 IF ( UP ) THEN 00287 CALL SSYTRS( 'U', N, 1, AF, LDAF, IPIV, WORK, N, INFO ) 00288 ELSE 00289 CALL SSYTRS( 'L', N, 1, AF, LDAF, IPIV, WORK, N, INFO ) 00290 ENDIF 00291 * 00292 * Multiply by inv(C). 00293 * 00294 IF ( CMODE .EQ. 1 ) THEN 00295 DO I = 1, N 00296 WORK( I ) = WORK( I ) / C( I ) 00297 END DO 00298 ELSE IF ( CMODE .EQ. -1 ) THEN 00299 DO I = 1, N 00300 WORK( I ) = WORK( I ) * C( I ) 00301 END DO 00302 END IF 00303 ELSE 00304 * 00305 * Multiply by inv(C**T). 00306 * 00307 IF ( CMODE .EQ. 1 ) THEN 00308 DO I = 1, N 00309 WORK( I ) = WORK( I ) / C( I ) 00310 END DO 00311 ELSE IF ( CMODE .EQ. -1 ) THEN 00312 DO I = 1, N 00313 WORK( I ) = WORK( I ) * C( I ) 00314 END DO 00315 END IF 00316 00317 IF ( UP ) THEN 00318 CALL SSYTRS( 'U', N, 1, AF, LDAF, IPIV, WORK, N, INFO ) 00319 ELSE 00320 CALL SSYTRS( 'L', N, 1, AF, LDAF, IPIV, WORK, N, INFO ) 00321 ENDIF 00322 * 00323 * Multiply by R. 00324 * 00325 DO I = 1, N 00326 WORK( I ) = WORK( I ) * WORK( 2*N+I ) 00327 END DO 00328 END IF 00329 * 00330 GO TO 10 00331 END IF 00332 * 00333 * Compute the estimate of the reciprocal condition number. 00334 * 00335 IF( AINVNM .NE. 0.0 ) 00336 $ SLA_SYRCOND = ( 1.0 / AINVNM ) 00337 * 00338 RETURN 00339 * 00340 END