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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b ZHPTRS 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download ZHPTRS + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhptrs.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhptrs.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhptrs.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE ZHPTRS( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO ) 00022 * 00023 * .. Scalar Arguments .. 00024 * CHARACTER UPLO 00025 * INTEGER INFO, LDB, N, NRHS 00026 * .. 00027 * .. Array Arguments .. 00028 * INTEGER IPIV( * ) 00029 * COMPLEX*16 AP( * ), B( LDB, * ) 00030 * .. 00031 * 00032 * 00033 *> \par Purpose: 00034 * ============= 00035 *> 00036 *> \verbatim 00037 *> 00038 *> ZHPTRS solves a system of linear equations A*X = B with a complex 00039 *> Hermitian matrix A stored in packed format using the factorization 00040 *> A = U*D*U**H or A = L*D*L**H computed by ZHPTRF. 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] AP 00069 *> \verbatim 00070 *> AP is COMPLEX*16 array, dimension (N*(N+1)/2) 00071 *> The block diagonal matrix D and the multipliers used to 00072 *> obtain the factor U or L as computed by ZHPTRF, stored as a 00073 *> packed triangular matrix. 00074 *> \endverbatim 00075 *> 00076 *> \param[in] IPIV 00077 *> \verbatim 00078 *> IPIV is INTEGER array, dimension (N) 00079 *> Details of the interchanges and the block structure of D 00080 *> as determined by ZHPTRF. 00081 *> \endverbatim 00082 *> 00083 *> \param[in,out] B 00084 *> \verbatim 00085 *> B is COMPLEX*16 array, dimension (LDB,NRHS) 00086 *> On entry, the right hand side matrix B. 00087 *> On exit, the solution matrix X. 00088 *> \endverbatim 00089 *> 00090 *> \param[in] LDB 00091 *> \verbatim 00092 *> LDB is INTEGER 00093 *> The leading dimension of the array B. LDB >= max(1,N). 00094 *> \endverbatim 00095 *> 00096 *> \param[out] INFO 00097 *> \verbatim 00098 *> INFO is INTEGER 00099 *> = 0: successful exit 00100 *> < 0: if INFO = -i, the i-th argument had an illegal value 00101 *> \endverbatim 00102 * 00103 * Authors: 00104 * ======== 00105 * 00106 *> \author Univ. of Tennessee 00107 *> \author Univ. of California Berkeley 00108 *> \author Univ. of Colorado Denver 00109 *> \author NAG Ltd. 00110 * 00111 *> \date November 2011 00112 * 00113 *> \ingroup complex16OTHERcomputational 00114 * 00115 * ===================================================================== 00116 SUBROUTINE ZHPTRS( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO ) 00117 * 00118 * -- LAPACK computational routine (version 3.4.0) -- 00119 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00120 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00121 * November 2011 00122 * 00123 * .. Scalar Arguments .. 00124 CHARACTER UPLO 00125 INTEGER INFO, LDB, N, NRHS 00126 * .. 00127 * .. Array Arguments .. 00128 INTEGER IPIV( * ) 00129 COMPLEX*16 AP( * ), B( LDB, * ) 00130 * .. 00131 * 00132 * ===================================================================== 00133 * 00134 * .. Parameters .. 00135 COMPLEX*16 ONE 00136 PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) 00137 * .. 00138 * .. Local Scalars .. 00139 LOGICAL UPPER 00140 INTEGER J, K, KC, KP 00141 DOUBLE PRECISION S 00142 COMPLEX*16 AK, AKM1, AKM1K, BK, BKM1, DENOM 00143 * .. 00144 * .. External Functions .. 00145 LOGICAL LSAME 00146 EXTERNAL LSAME 00147 * .. 00148 * .. External Subroutines .. 00149 EXTERNAL XERBLA, ZDSCAL, ZGEMV, ZGERU, ZLACGV, ZSWAP 00150 * .. 00151 * .. Intrinsic Functions .. 00152 INTRINSIC DBLE, DCONJG, MAX 00153 * .. 00154 * .. Executable Statements .. 00155 * 00156 INFO = 0 00157 UPPER = LSAME( UPLO, 'U' ) 00158 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 00159 INFO = -1 00160 ELSE IF( N.LT.0 ) THEN 00161 INFO = -2 00162 ELSE IF( NRHS.LT.0 ) THEN 00163 INFO = -3 00164 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN 00165 INFO = -7 00166 END IF 00167 IF( INFO.NE.0 ) THEN 00168 CALL XERBLA( 'ZHPTRS', -INFO ) 00169 RETURN 00170 END IF 00171 * 00172 * Quick return if possible 00173 * 00174 IF( N.EQ.0 .OR. NRHS.EQ.0 ) 00175 $ RETURN 00176 * 00177 IF( UPPER ) THEN 00178 * 00179 * Solve A*X = B, where A = U*D*U**H. 00180 * 00181 * First solve U*D*X = B, overwriting B with X. 00182 * 00183 * K is the main loop index, decreasing from N to 1 in steps of 00184 * 1 or 2, depending on the size of the diagonal blocks. 00185 * 00186 K = N 00187 KC = N*( N+1 ) / 2 + 1 00188 10 CONTINUE 00189 * 00190 * If K < 1, exit from loop. 00191 * 00192 IF( K.LT.1 ) 00193 $ GO TO 30 00194 * 00195 KC = KC - K 00196 IF( IPIV( K ).GT.0 ) THEN 00197 * 00198 * 1 x 1 diagonal block 00199 * 00200 * Interchange rows K and IPIV(K). 00201 * 00202 KP = IPIV( K ) 00203 IF( KP.NE.K ) 00204 $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 00205 * 00206 * Multiply by inv(U(K)), where U(K) is the transformation 00207 * stored in column K of A. 00208 * 00209 CALL ZGERU( K-1, NRHS, -ONE, AP( KC ), 1, B( K, 1 ), LDB, 00210 $ B( 1, 1 ), LDB ) 00211 * 00212 * Multiply by the inverse of the diagonal block. 00213 * 00214 S = DBLE( ONE ) / DBLE( AP( KC+K-1 ) ) 00215 CALL ZDSCAL( NRHS, S, B( K, 1 ), LDB ) 00216 K = K - 1 00217 ELSE 00218 * 00219 * 2 x 2 diagonal block 00220 * 00221 * Interchange rows K-1 and -IPIV(K). 00222 * 00223 KP = -IPIV( K ) 00224 IF( KP.NE.K-1 ) 00225 $ CALL ZSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ), LDB ) 00226 * 00227 * Multiply by inv(U(K)), where U(K) is the transformation 00228 * stored in columns K-1 and K of A. 00229 * 00230 CALL ZGERU( K-2, NRHS, -ONE, AP( KC ), 1, B( K, 1 ), LDB, 00231 $ B( 1, 1 ), LDB ) 00232 CALL ZGERU( K-2, NRHS, -ONE, AP( KC-( K-1 ) ), 1, 00233 $ B( K-1, 1 ), LDB, B( 1, 1 ), LDB ) 00234 * 00235 * Multiply by the inverse of the diagonal block. 00236 * 00237 AKM1K = AP( KC+K-2 ) 00238 AKM1 = AP( KC-1 ) / AKM1K 00239 AK = AP( KC+K-1 ) / DCONJG( AKM1K ) 00240 DENOM = AKM1*AK - ONE 00241 DO 20 J = 1, NRHS 00242 BKM1 = B( K-1, J ) / AKM1K 00243 BK = B( K, J ) / DCONJG( AKM1K ) 00244 B( K-1, J ) = ( AK*BKM1-BK ) / DENOM 00245 B( K, J ) = ( AKM1*BK-BKM1 ) / DENOM 00246 20 CONTINUE 00247 KC = KC - K + 1 00248 K = K - 2 00249 END IF 00250 * 00251 GO TO 10 00252 30 CONTINUE 00253 * 00254 * Next solve U**H *X = B, overwriting B with X. 00255 * 00256 * K is the main loop index, increasing from 1 to N in steps of 00257 * 1 or 2, depending on the size of the diagonal blocks. 00258 * 00259 K = 1 00260 KC = 1 00261 40 CONTINUE 00262 * 00263 * If K > N, exit from loop. 00264 * 00265 IF( K.GT.N ) 00266 $ GO TO 50 00267 * 00268 IF( IPIV( K ).GT.0 ) THEN 00269 * 00270 * 1 x 1 diagonal block 00271 * 00272 * Multiply by inv(U**H(K)), where U(K) is the transformation 00273 * stored in column K of A. 00274 * 00275 IF( K.GT.1 ) THEN 00276 CALL ZLACGV( NRHS, B( K, 1 ), LDB ) 00277 CALL ZGEMV( 'Conjugate transpose', K-1, NRHS, -ONE, B, 00278 $ LDB, AP( KC ), 1, ONE, B( K, 1 ), LDB ) 00279 CALL ZLACGV( NRHS, B( K, 1 ), LDB ) 00280 END IF 00281 * 00282 * Interchange rows K and IPIV(K). 00283 * 00284 KP = IPIV( K ) 00285 IF( KP.NE.K ) 00286 $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 00287 KC = KC + K 00288 K = K + 1 00289 ELSE 00290 * 00291 * 2 x 2 diagonal block 00292 * 00293 * Multiply by inv(U**H(K+1)), where U(K+1) is the transformation 00294 * stored in columns K and K+1 of A. 00295 * 00296 IF( K.GT.1 ) THEN 00297 CALL ZLACGV( NRHS, B( K, 1 ), LDB ) 00298 CALL ZGEMV( 'Conjugate transpose', K-1, NRHS, -ONE, B, 00299 $ LDB, AP( KC ), 1, ONE, B( K, 1 ), LDB ) 00300 CALL ZLACGV( NRHS, B( K, 1 ), LDB ) 00301 * 00302 CALL ZLACGV( NRHS, B( K+1, 1 ), LDB ) 00303 CALL ZGEMV( 'Conjugate transpose', K-1, NRHS, -ONE, B, 00304 $ LDB, AP( KC+K ), 1, ONE, B( K+1, 1 ), LDB ) 00305 CALL ZLACGV( NRHS, B( K+1, 1 ), LDB ) 00306 END IF 00307 * 00308 * Interchange rows K and -IPIV(K). 00309 * 00310 KP = -IPIV( K ) 00311 IF( KP.NE.K ) 00312 $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 00313 KC = KC + 2*K + 1 00314 K = K + 2 00315 END IF 00316 * 00317 GO TO 40 00318 50 CONTINUE 00319 * 00320 ELSE 00321 * 00322 * Solve A*X = B, where A = L*D*L**H. 00323 * 00324 * First solve L*D*X = B, overwriting B with X. 00325 * 00326 * K is the main loop index, increasing from 1 to N in steps of 00327 * 1 or 2, depending on the size of the diagonal blocks. 00328 * 00329 K = 1 00330 KC = 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 ZSWAP( 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 ZGERU( N-K, NRHS, -ONE, AP( KC+1 ), 1, B( K, 1 ), 00353 $ LDB, B( K+1, 1 ), LDB ) 00354 * 00355 * Multiply by the inverse of the diagonal block. 00356 * 00357 S = DBLE( ONE ) / DBLE( AP( KC ) ) 00358 CALL ZDSCAL( NRHS, S, B( K, 1 ), LDB ) 00359 KC = KC + N - K + 1 00360 K = K + 1 00361 ELSE 00362 * 00363 * 2 x 2 diagonal block 00364 * 00365 * Interchange rows K+1 and -IPIV(K). 00366 * 00367 KP = -IPIV( K ) 00368 IF( KP.NE.K+1 ) 00369 $ CALL ZSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ), LDB ) 00370 * 00371 * Multiply by inv(L(K)), where L(K) is the transformation 00372 * stored in columns K and K+1 of A. 00373 * 00374 IF( K.LT.N-1 ) THEN 00375 CALL ZGERU( N-K-1, NRHS, -ONE, AP( KC+2 ), 1, B( K, 1 ), 00376 $ LDB, B( K+2, 1 ), LDB ) 00377 CALL ZGERU( N-K-1, NRHS, -ONE, AP( KC+N-K+2 ), 1, 00378 $ B( K+1, 1 ), LDB, B( K+2, 1 ), LDB ) 00379 END IF 00380 * 00381 * Multiply by the inverse of the diagonal block. 00382 * 00383 AKM1K = AP( KC+1 ) 00384 AKM1 = AP( KC ) / DCONJG( AKM1K ) 00385 AK = AP( KC+N-K+1 ) / AKM1K 00386 DENOM = AKM1*AK - ONE 00387 DO 70 J = 1, NRHS 00388 BKM1 = B( K, J ) / DCONJG( AKM1K ) 00389 BK = B( K+1, J ) / AKM1K 00390 B( K, J ) = ( AK*BKM1-BK ) / DENOM 00391 B( K+1, J ) = ( AKM1*BK-BKM1 ) / DENOM 00392 70 CONTINUE 00393 KC = KC + 2*( N-K ) + 1 00394 K = K + 2 00395 END IF 00396 * 00397 GO TO 60 00398 80 CONTINUE 00399 * 00400 * Next solve L**H *X = B, overwriting B with X. 00401 * 00402 * K is the main loop index, decreasing from N to 1 in steps of 00403 * 1 or 2, depending on the size of the diagonal blocks. 00404 * 00405 K = N 00406 KC = N*( N+1 ) / 2 + 1 00407 90 CONTINUE 00408 * 00409 * If K < 1, exit from loop. 00410 * 00411 IF( K.LT.1 ) 00412 $ GO TO 100 00413 * 00414 KC = KC - ( N-K+1 ) 00415 IF( IPIV( K ).GT.0 ) THEN 00416 * 00417 * 1 x 1 diagonal block 00418 * 00419 * Multiply by inv(L**H(K)), where L(K) is the transformation 00420 * stored in column K of A. 00421 * 00422 IF( K.LT.N ) THEN 00423 CALL ZLACGV( NRHS, B( K, 1 ), LDB ) 00424 CALL ZGEMV( 'Conjugate transpose', N-K, NRHS, -ONE, 00425 $ B( K+1, 1 ), LDB, AP( KC+1 ), 1, ONE, 00426 $ B( K, 1 ), LDB ) 00427 CALL ZLACGV( NRHS, B( K, 1 ), LDB ) 00428 END IF 00429 * 00430 * Interchange rows K and IPIV(K). 00431 * 00432 KP = IPIV( K ) 00433 IF( KP.NE.K ) 00434 $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 00435 K = K - 1 00436 ELSE 00437 * 00438 * 2 x 2 diagonal block 00439 * 00440 * Multiply by inv(L**H(K-1)), where L(K-1) is the transformation 00441 * stored in columns K-1 and K of A. 00442 * 00443 IF( K.LT.N ) THEN 00444 CALL ZLACGV( NRHS, B( K, 1 ), LDB ) 00445 CALL ZGEMV( 'Conjugate transpose', N-K, NRHS, -ONE, 00446 $ B( K+1, 1 ), LDB, AP( KC+1 ), 1, ONE, 00447 $ B( K, 1 ), LDB ) 00448 CALL ZLACGV( NRHS, B( K, 1 ), LDB ) 00449 * 00450 CALL ZLACGV( NRHS, B( K-1, 1 ), LDB ) 00451 CALL ZGEMV( 'Conjugate transpose', N-K, NRHS, -ONE, 00452 $ B( K+1, 1 ), LDB, AP( KC-( N-K ) ), 1, ONE, 00453 $ B( K-1, 1 ), LDB ) 00454 CALL ZLACGV( NRHS, B( K-1, 1 ), LDB ) 00455 END IF 00456 * 00457 * Interchange rows K and -IPIV(K). 00458 * 00459 KP = -IPIV( K ) 00460 IF( KP.NE.K ) 00461 $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 00462 KC = KC - ( N-K+2 ) 00463 K = K - 2 00464 END IF 00465 * 00466 GO TO 90 00467 100 CONTINUE 00468 END IF 00469 * 00470 RETURN 00471 * 00472 * End of ZHPTRS 00473 * 00474 END