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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b CHETRS 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download CHETRS + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/chetrs.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/chetrs.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/chetrs.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE CHETRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO ) 00022 * 00023 * .. Scalar Arguments .. 00024 * CHARACTER UPLO 00025 * INTEGER INFO, LDA, LDB, N, NRHS 00026 * .. 00027 * .. Array Arguments .. 00028 * INTEGER IPIV( * ) 00029 * COMPLEX A( LDA, * ), B( LDB, * ) 00030 * .. 00031 * 00032 * 00033 *> \par Purpose: 00034 * ============= 00035 *> 00036 *> \verbatim 00037 *> 00038 *> CHETRS solves a system of linear equations A*X = B with a complex 00039 *> Hermitian matrix A using the factorization A = U*D*U**H or 00040 *> A = L*D*L**H computed by CHETRF. 00041 *> \endverbatim 00042 * 00043 * Arguments: 00044 * ========== 00045 * 00046 *> \param[in] UPLO 00047 *> \verbatim 00048 *> UPLO is CHARACTER*1 00049 *> Specifies whether the details of the factorization are stored 00050 *> as an upper or lower triangular matrix. 00051 *> = 'U': Upper triangular, form is A = U*D*U**H; 00052 *> = 'L': Lower triangular, form is A = L*D*L**H. 00053 *> \endverbatim 00054 *> 00055 *> \param[in] N 00056 *> \verbatim 00057 *> N is INTEGER 00058 *> The order of the matrix A. N >= 0. 00059 *> \endverbatim 00060 *> 00061 *> \param[in] NRHS 00062 *> \verbatim 00063 *> NRHS is INTEGER 00064 *> The number of right hand sides, i.e., the number of columns 00065 *> of the matrix B. NRHS >= 0. 00066 *> \endverbatim 00067 *> 00068 *> \param[in] A 00069 *> \verbatim 00070 *> A is COMPLEX array, dimension (LDA,N) 00071 *> The block diagonal matrix D and the multipliers used to 00072 *> obtain the factor U or L as computed by CHETRF. 00073 *> \endverbatim 00074 *> 00075 *> \param[in] LDA 00076 *> \verbatim 00077 *> LDA is INTEGER 00078 *> The leading dimension of the array A. LDA >= max(1,N). 00079 *> \endverbatim 00080 *> 00081 *> \param[in] IPIV 00082 *> \verbatim 00083 *> IPIV is INTEGER array, dimension (N) 00084 *> Details of the interchanges and the block structure of D 00085 *> as determined by CHETRF. 00086 *> \endverbatim 00087 *> 00088 *> \param[in,out] B 00089 *> \verbatim 00090 *> B is COMPLEX array, dimension (LDB,NRHS) 00091 *> On entry, the right hand side matrix B. 00092 *> On exit, the solution matrix X. 00093 *> \endverbatim 00094 *> 00095 *> \param[in] LDB 00096 *> \verbatim 00097 *> LDB is INTEGER 00098 *> The leading dimension of the array B. LDB >= max(1,N). 00099 *> \endverbatim 00100 *> 00101 *> \param[out] INFO 00102 *> \verbatim 00103 *> INFO is INTEGER 00104 *> = 0: successful exit 00105 *> < 0: if INFO = -i, the i-th argument had an illegal value 00106 *> \endverbatim 00107 * 00108 * Authors: 00109 * ======== 00110 * 00111 *> \author Univ. of Tennessee 00112 *> \author Univ. of California Berkeley 00113 *> \author Univ. of Colorado Denver 00114 *> \author NAG Ltd. 00115 * 00116 *> \date November 2011 00117 * 00118 *> \ingroup complexHEcomputational 00119 * 00120 * ===================================================================== 00121 SUBROUTINE CHETRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO ) 00122 * 00123 * -- LAPACK computational routine (version 3.4.0) -- 00124 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00125 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00126 * November 2011 00127 * 00128 * .. Scalar Arguments .. 00129 CHARACTER UPLO 00130 INTEGER INFO, LDA, LDB, N, NRHS 00131 * .. 00132 * .. Array Arguments .. 00133 INTEGER IPIV( * ) 00134 COMPLEX A( LDA, * ), B( LDB, * ) 00135 * .. 00136 * 00137 * ===================================================================== 00138 * 00139 * .. Parameters .. 00140 COMPLEX ONE 00141 PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ) ) 00142 * .. 00143 * .. Local Scalars .. 00144 LOGICAL UPPER 00145 INTEGER J, K, KP 00146 REAL S 00147 COMPLEX AK, AKM1, AKM1K, BK, BKM1, DENOM 00148 * .. 00149 * .. External Functions .. 00150 LOGICAL LSAME 00151 EXTERNAL LSAME 00152 * .. 00153 * .. External Subroutines .. 00154 EXTERNAL CGEMV, CGERU, CLACGV, CSSCAL, CSWAP, XERBLA 00155 * .. 00156 * .. Intrinsic Functions .. 00157 INTRINSIC CONJG, MAX, REAL 00158 * .. 00159 * .. Executable Statements .. 00160 * 00161 INFO = 0 00162 UPPER = LSAME( UPLO, 'U' ) 00163 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 00164 INFO = -1 00165 ELSE IF( N.LT.0 ) THEN 00166 INFO = -2 00167 ELSE IF( NRHS.LT.0 ) THEN 00168 INFO = -3 00169 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 00170 INFO = -5 00171 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN 00172 INFO = -8 00173 END IF 00174 IF( INFO.NE.0 ) THEN 00175 CALL XERBLA( 'CHETRS', -INFO ) 00176 RETURN 00177 END IF 00178 * 00179 * Quick return if possible 00180 * 00181 IF( N.EQ.0 .OR. NRHS.EQ.0 ) 00182 $ RETURN 00183 * 00184 IF( UPPER ) THEN 00185 * 00186 * Solve A*X = B, where A = U*D*U**H. 00187 * 00188 * First solve U*D*X = B, overwriting B with X. 00189 * 00190 * K is the main loop index, decreasing from N to 1 in steps of 00191 * 1 or 2, depending on the size of the diagonal blocks. 00192 * 00193 K = N 00194 10 CONTINUE 00195 * 00196 * If K < 1, exit from loop. 00197 * 00198 IF( K.LT.1 ) 00199 $ GO TO 30 00200 * 00201 IF( IPIV( K ).GT.0 ) THEN 00202 * 00203 * 1 x 1 diagonal block 00204 * 00205 * Interchange rows K and IPIV(K). 00206 * 00207 KP = IPIV( K ) 00208 IF( KP.NE.K ) 00209 $ CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 00210 * 00211 * Multiply by inv(U(K)), where U(K) is the transformation 00212 * stored in column K of A. 00213 * 00214 CALL CGERU( K-1, NRHS, -ONE, A( 1, K ), 1, B( K, 1 ), LDB, 00215 $ B( 1, 1 ), LDB ) 00216 * 00217 * Multiply by the inverse of the diagonal block. 00218 * 00219 S = REAL( ONE ) / REAL( A( K, K ) ) 00220 CALL CSSCAL( NRHS, S, B( K, 1 ), LDB ) 00221 K = K - 1 00222 ELSE 00223 * 00224 * 2 x 2 diagonal block 00225 * 00226 * Interchange rows K-1 and -IPIV(K). 00227 * 00228 KP = -IPIV( K ) 00229 IF( KP.NE.K-1 ) 00230 $ CALL CSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ), LDB ) 00231 * 00232 * Multiply by inv(U(K)), where U(K) is the transformation 00233 * stored in columns K-1 and K of A. 00234 * 00235 CALL CGERU( K-2, NRHS, -ONE, A( 1, K ), 1, B( K, 1 ), LDB, 00236 $ B( 1, 1 ), LDB ) 00237 CALL CGERU( K-2, NRHS, -ONE, A( 1, K-1 ), 1, B( K-1, 1 ), 00238 $ LDB, B( 1, 1 ), LDB ) 00239 * 00240 * Multiply by the inverse of the diagonal block. 00241 * 00242 AKM1K = A( K-1, K ) 00243 AKM1 = A( K-1, K-1 ) / AKM1K 00244 AK = A( K, K ) / CONJG( AKM1K ) 00245 DENOM = AKM1*AK - ONE 00246 DO 20 J = 1, NRHS 00247 BKM1 = B( K-1, J ) / AKM1K 00248 BK = B( K, J ) / CONJG( AKM1K ) 00249 B( K-1, J ) = ( AK*BKM1-BK ) / DENOM 00250 B( K, J ) = ( AKM1*BK-BKM1 ) / DENOM 00251 20 CONTINUE 00252 K = K - 2 00253 END IF 00254 * 00255 GO TO 10 00256 30 CONTINUE 00257 * 00258 * Next solve U**H *X = B, overwriting B with X. 00259 * 00260 * K is the main loop index, increasing from 1 to N in steps of 00261 * 1 or 2, depending on the size of the diagonal blocks. 00262 * 00263 K = 1 00264 40 CONTINUE 00265 * 00266 * If K > N, exit from loop. 00267 * 00268 IF( K.GT.N ) 00269 $ GO TO 50 00270 * 00271 IF( IPIV( K ).GT.0 ) THEN 00272 * 00273 * 1 x 1 diagonal block 00274 * 00275 * Multiply by inv(U**H(K)), where U(K) is the transformation 00276 * stored in column K of A. 00277 * 00278 IF( K.GT.1 ) THEN 00279 CALL CLACGV( NRHS, B( K, 1 ), LDB ) 00280 CALL CGEMV( 'Conjugate transpose', K-1, NRHS, -ONE, B, 00281 $ LDB, A( 1, K ), 1, ONE, B( K, 1 ), LDB ) 00282 CALL CLACGV( NRHS, B( K, 1 ), LDB ) 00283 END IF 00284 * 00285 * Interchange rows K and IPIV(K). 00286 * 00287 KP = IPIV( K ) 00288 IF( KP.NE.K ) 00289 $ CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 00290 K = K + 1 00291 ELSE 00292 * 00293 * 2 x 2 diagonal block 00294 * 00295 * Multiply by inv(U**H(K+1)), where U(K+1) is the transformation 00296 * stored in columns K and K+1 of A. 00297 * 00298 IF( K.GT.1 ) THEN 00299 CALL CLACGV( NRHS, B( K, 1 ), LDB ) 00300 CALL CGEMV( 'Conjugate transpose', K-1, NRHS, -ONE, B, 00301 $ LDB, A( 1, K ), 1, ONE, B( K, 1 ), LDB ) 00302 CALL CLACGV( NRHS, B( K, 1 ), LDB ) 00303 * 00304 CALL CLACGV( NRHS, B( K+1, 1 ), LDB ) 00305 CALL CGEMV( 'Conjugate transpose', K-1, NRHS, -ONE, B, 00306 $ LDB, A( 1, K+1 ), 1, ONE, B( K+1, 1 ), LDB ) 00307 CALL CLACGV( NRHS, B( K+1, 1 ), LDB ) 00308 END IF 00309 * 00310 * Interchange rows K and -IPIV(K). 00311 * 00312 KP = -IPIV( K ) 00313 IF( KP.NE.K ) 00314 $ CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 00315 K = K + 2 00316 END IF 00317 * 00318 GO TO 40 00319 50 CONTINUE 00320 * 00321 ELSE 00322 * 00323 * Solve A*X = B, where A = L*D*L**H. 00324 * 00325 * First solve L*D*X = B, overwriting B with X. 00326 * 00327 * K is the main loop index, increasing from 1 to N in steps of 00328 * 1 or 2, depending on the size of the diagonal blocks. 00329 * 00330 K = 1 00331 60 CONTINUE 00332 * 00333 * If K > N, exit from loop. 00334 * 00335 IF( K.GT.N ) 00336 $ GO TO 80 00337 * 00338 IF( IPIV( K ).GT.0 ) THEN 00339 * 00340 * 1 x 1 diagonal block 00341 * 00342 * Interchange rows K and IPIV(K). 00343 * 00344 KP = IPIV( K ) 00345 IF( KP.NE.K ) 00346 $ CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 00347 * 00348 * Multiply by inv(L(K)), where L(K) is the transformation 00349 * stored in column K of A. 00350 * 00351 IF( K.LT.N ) 00352 $ CALL CGERU( N-K, NRHS, -ONE, A( K+1, K ), 1, B( K, 1 ), 00353 $ LDB, B( K+1, 1 ), LDB ) 00354 * 00355 * Multiply by the inverse of the diagonal block. 00356 * 00357 S = REAL( ONE ) / REAL( A( K, K ) ) 00358 CALL CSSCAL( NRHS, S, B( K, 1 ), LDB ) 00359 K = K + 1 00360 ELSE 00361 * 00362 * 2 x 2 diagonal block 00363 * 00364 * Interchange rows K+1 and -IPIV(K). 00365 * 00366 KP = -IPIV( K ) 00367 IF( KP.NE.K+1 ) 00368 $ CALL CSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ), LDB ) 00369 * 00370 * Multiply by inv(L(K)), where L(K) is the transformation 00371 * stored in columns K and K+1 of A. 00372 * 00373 IF( K.LT.N-1 ) THEN 00374 CALL CGERU( N-K-1, NRHS, -ONE, A( K+2, K ), 1, B( K, 1 ), 00375 $ LDB, B( K+2, 1 ), LDB ) 00376 CALL CGERU( N-K-1, NRHS, -ONE, A( K+2, K+1 ), 1, 00377 $ B( K+1, 1 ), LDB, B( K+2, 1 ), LDB ) 00378 END IF 00379 * 00380 * Multiply by the inverse of the diagonal block. 00381 * 00382 AKM1K = A( K+1, K ) 00383 AKM1 = A( K, K ) / CONJG( AKM1K ) 00384 AK = A( K+1, K+1 ) / AKM1K 00385 DENOM = AKM1*AK - ONE 00386 DO 70 J = 1, NRHS 00387 BKM1 = B( K, J ) / CONJG( AKM1K ) 00388 BK = B( K+1, J ) / AKM1K 00389 B( K, J ) = ( AK*BKM1-BK ) / DENOM 00390 B( K+1, J ) = ( AKM1*BK-BKM1 ) / DENOM 00391 70 CONTINUE 00392 K = K + 2 00393 END IF 00394 * 00395 GO TO 60 00396 80 CONTINUE 00397 * 00398 * Next solve L**H *X = B, overwriting B with X. 00399 * 00400 * K is the main loop index, decreasing from N to 1 in steps of 00401 * 1 or 2, depending on the size of the diagonal blocks. 00402 * 00403 K = N 00404 90 CONTINUE 00405 * 00406 * If K < 1, exit from loop. 00407 * 00408 IF( K.LT.1 ) 00409 $ GO TO 100 00410 * 00411 IF( IPIV( K ).GT.0 ) THEN 00412 * 00413 * 1 x 1 diagonal block 00414 * 00415 * Multiply by inv(L**H(K)), where L(K) is the transformation 00416 * stored in column K of A. 00417 * 00418 IF( K.LT.N ) THEN 00419 CALL CLACGV( NRHS, B( K, 1 ), LDB ) 00420 CALL CGEMV( 'Conjugate transpose', N-K, NRHS, -ONE, 00421 $ B( K+1, 1 ), LDB, A( K+1, K ), 1, ONE, 00422 $ B( K, 1 ), LDB ) 00423 CALL CLACGV( NRHS, B( K, 1 ), LDB ) 00424 END IF 00425 * 00426 * Interchange rows K and IPIV(K). 00427 * 00428 KP = IPIV( K ) 00429 IF( KP.NE.K ) 00430 $ CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 00431 K = K - 1 00432 ELSE 00433 * 00434 * 2 x 2 diagonal block 00435 * 00436 * Multiply by inv(L**H(K-1)), where L(K-1) is the transformation 00437 * stored in columns K-1 and K of A. 00438 * 00439 IF( K.LT.N ) THEN 00440 CALL CLACGV( NRHS, B( K, 1 ), LDB ) 00441 CALL CGEMV( 'Conjugate transpose', N-K, NRHS, -ONE, 00442 $ B( K+1, 1 ), LDB, A( K+1, K ), 1, ONE, 00443 $ B( K, 1 ), LDB ) 00444 CALL CLACGV( NRHS, B( K, 1 ), LDB ) 00445 * 00446 CALL CLACGV( NRHS, B( K-1, 1 ), LDB ) 00447 CALL CGEMV( 'Conjugate transpose', N-K, NRHS, -ONE, 00448 $ B( K+1, 1 ), LDB, A( K+1, K-1 ), 1, ONE, 00449 $ B( K-1, 1 ), LDB ) 00450 CALL CLACGV( NRHS, B( K-1, 1 ), LDB ) 00451 END IF 00452 * 00453 * Interchange rows K and -IPIV(K). 00454 * 00455 KP = -IPIV( K ) 00456 IF( KP.NE.K ) 00457 $ CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 00458 K = K - 2 00459 END IF 00460 * 00461 GO TO 90 00462 100 CONTINUE 00463 END IF 00464 * 00465 RETURN 00466 * 00467 * End of CHETRS 00468 * 00469 END