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LAPACK
3.4.0
LAPACK: Linear Algebra PACKage
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LAPACK
3.4.0
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b ZLAVSY 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 * Definition: 00009 * =========== 00010 * 00011 * SUBROUTINE ZLAVSY( UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B, 00012 * LDB, INFO ) 00013 * 00014 * .. Scalar Arguments .. 00015 * CHARACTER DIAG, TRANS, UPLO 00016 * INTEGER INFO, LDA, LDB, N, NRHS 00017 * .. 00018 * .. Array Arguments .. 00019 * INTEGER IPIV( * ) 00020 * COMPLEX*16 A( LDA, * ), B( LDB, * ) 00021 * .. 00022 * 00023 * 00024 *> \par Purpose: 00025 * ============= 00026 *> 00027 *> \verbatim 00028 *> 00029 *> ZLAVSY performs one of the matrix-vector operations 00030 *> x := A*x or x := A'*x, 00031 *> where x is an N element vector and A is one of the factors 00032 *> from the symmetric factorization computed by ZSYTRF. 00033 *> ZSYTRF produces a factorization of the form 00034 *> U * D * U' or L * D * L' , 00035 *> where U (or L) is a product of permutation and unit upper (lower) 00036 *> triangular matrices, U' (or L') is the transpose of 00037 *> U (or L), and D is symmetric and block diagonal with 1 x 1 and 00038 *> 2 x 2 diagonal blocks. The multipliers for the transformations 00039 *> and the upper or lower triangular parts of the diagonal blocks 00040 *> are stored in the leading upper or lower triangle of the 2-D 00041 *> array A. 00042 *> 00043 *> If TRANS = 'N' or 'n', ZLAVSY multiplies either by U or U * D 00044 *> (or L or L * D). 00045 *> If TRANS = 'T' or 't', ZLAVSY multiplies either by U' or D * U' 00046 *> (or L' or D * L' ). 00047 *> \endverbatim 00048 * 00049 * Arguments: 00050 * ========== 00051 * 00052 *> \verbatim 00053 *> UPLO - CHARACTER*1 00054 *> On entry, UPLO specifies whether the triangular matrix 00055 *> stored in A is upper or lower triangular. 00056 *> UPLO = 'U' or 'u' The matrix is upper triangular. 00057 *> UPLO = 'L' or 'l' The matrix is lower triangular. 00058 *> Unchanged on exit. 00059 *> 00060 *> TRANS - CHARACTER*1 00061 *> On entry, TRANS specifies the operation to be performed as 00062 *> follows: 00063 *> TRANS = 'N' or 'n' x := A*x. 00064 *> TRANS = 'T' or 't' x := A'*x. 00065 *> Unchanged on exit. 00066 *> 00067 *> DIAG - CHARACTER*1 00068 *> On entry, DIAG specifies whether the diagonal blocks are 00069 *> assumed to be unit matrices: 00070 *> DIAG = 'U' or 'u' Diagonal blocks are unit matrices. 00071 *> DIAG = 'N' or 'n' Diagonal blocks are non-unit. 00072 *> Unchanged on exit. 00073 *> 00074 *> N - INTEGER 00075 *> On entry, N specifies the order of the matrix A. 00076 *> N must be at least zero. 00077 *> Unchanged on exit. 00078 *> 00079 *> NRHS - INTEGER 00080 *> On entry, NRHS specifies the number of right hand sides, 00081 *> i.e., the number of vectors x to be multiplied by A. 00082 *> NRHS must be at least zero. 00083 *> Unchanged on exit. 00084 *> 00085 *> A - COMPLEX*16 array, dimension( LDA, N ) 00086 *> On entry, A contains a block diagonal matrix and the 00087 *> multipliers of the transformations used to obtain it, 00088 *> stored as a 2-D triangular matrix. 00089 *> Unchanged on exit. 00090 *> 00091 *> LDA - INTEGER 00092 *> On entry, LDA specifies the first dimension of A as declared 00093 *> in the calling ( sub ) program. LDA must be at least 00094 *> max( 1, N ). 00095 *> Unchanged on exit. 00096 *> 00097 *> IPIV - INTEGER array, dimension( N ) 00098 *> On entry, IPIV contains the vector of pivot indices as 00099 *> determined by ZSYTRF or ZHETRF. 00100 *> If IPIV( K ) = K, no interchange was done. 00101 *> If IPIV( K ) <> K but IPIV( K ) > 0, then row K was inter- 00102 *> changed with row IPIV( K ) and a 1 x 1 pivot block was used. 00103 *> If IPIV( K ) < 0 and UPLO = 'U', then row K-1 was exchanged 00104 *> with row | IPIV( K ) | and a 2 x 2 pivot block was used. 00105 *> If IPIV( K ) < 0 and UPLO = 'L', then row K+1 was exchanged 00106 *> with row | IPIV( K ) | and a 2 x 2 pivot block was used. 00107 *> 00108 *> B - COMPLEX*16 array, dimension( LDB, NRHS ) 00109 *> On entry, B contains NRHS vectors of length N. 00110 *> On exit, B is overwritten with the product A * B. 00111 *> 00112 *> LDB - INTEGER 00113 *> On entry, LDB contains the leading dimension of B as 00114 *> declared in the calling program. LDB must be at least 00115 *> max( 1, N ). 00116 *> Unchanged on exit. 00117 *> 00118 *> INFO - INTEGER 00119 *> INFO is the error flag. 00120 *> On exit, a value of 0 indicates a successful exit. 00121 *> A negative value, say -K, indicates that the K-th argument 00122 *> has an illegal value. 00123 *> \endverbatim 00124 * 00125 * Authors: 00126 * ======== 00127 * 00128 *> \author Univ. of Tennessee 00129 *> \author Univ. of California Berkeley 00130 *> \author Univ. of Colorado Denver 00131 *> \author NAG Ltd. 00132 * 00133 *> \date November 2011 00134 * 00135 *> \ingroup complex16_lin 00136 * 00137 * ===================================================================== 00138 SUBROUTINE ZLAVSY( UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B, 00139 $ LDB, INFO ) 00140 * 00141 * -- LAPACK test routine (version 3.4.0) -- 00142 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00143 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00144 * November 2011 00145 * 00146 * .. Scalar Arguments .. 00147 CHARACTER DIAG, TRANS, UPLO 00148 INTEGER INFO, LDA, LDB, N, NRHS 00149 * .. 00150 * .. Array Arguments .. 00151 INTEGER IPIV( * ) 00152 COMPLEX*16 A( LDA, * ), B( LDB, * ) 00153 * .. 00154 * 00155 * ===================================================================== 00156 * 00157 * .. Parameters .. 00158 COMPLEX*16 ONE 00159 PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) 00160 * .. 00161 * .. Local Scalars .. 00162 LOGICAL NOUNIT 00163 INTEGER J, K, KP 00164 COMPLEX*16 D11, D12, D21, D22, T1, T2 00165 * .. 00166 * .. External Functions .. 00167 LOGICAL LSAME 00168 EXTERNAL LSAME 00169 * .. 00170 * .. External Subroutines .. 00171 EXTERNAL XERBLA, ZGEMV, ZGERU, ZSCAL, ZSWAP 00172 * .. 00173 * .. Intrinsic Functions .. 00174 INTRINSIC ABS, MAX 00175 * .. 00176 * .. Executable Statements .. 00177 * 00178 * Test the input parameters. 00179 * 00180 INFO = 0 00181 IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 00182 INFO = -1 00183 ELSE IF( .NOT.LSAME( TRANS, 'N' ) .AND. .NOT.LSAME( TRANS, 'T' ) ) 00184 $ THEN 00185 INFO = -2 00186 ELSE IF( .NOT.LSAME( DIAG, 'U' ) .AND. .NOT.LSAME( DIAG, 'N' ) ) 00187 $ THEN 00188 INFO = -3 00189 ELSE IF( N.LT.0 ) THEN 00190 INFO = -4 00191 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 00192 INFO = -6 00193 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN 00194 INFO = -9 00195 END IF 00196 IF( INFO.NE.0 ) THEN 00197 CALL XERBLA( 'ZLAVSY ', -INFO ) 00198 RETURN 00199 END IF 00200 * 00201 * Quick return if possible. 00202 * 00203 IF( N.EQ.0 ) 00204 $ RETURN 00205 * 00206 NOUNIT = LSAME( DIAG, 'N' ) 00207 *------------------------------------------ 00208 * 00209 * Compute B := A * B (No transpose) 00210 * 00211 *------------------------------------------ 00212 IF( LSAME( TRANS, 'N' ) ) THEN 00213 * 00214 * Compute B := U*B 00215 * where U = P(m)*inv(U(m))* ... *P(1)*inv(U(1)) 00216 * 00217 IF( LSAME( UPLO, 'U' ) ) THEN 00218 * 00219 * Loop forward applying the transformations. 00220 * 00221 K = 1 00222 10 CONTINUE 00223 IF( K.GT.N ) 00224 $ GO TO 30 00225 IF( IPIV( K ).GT.0 ) THEN 00226 * 00227 * 1 x 1 pivot block 00228 * 00229 * Multiply by the diagonal element if forming U * D. 00230 * 00231 IF( NOUNIT ) 00232 $ CALL ZSCAL( NRHS, A( K, K ), B( K, 1 ), LDB ) 00233 * 00234 * Multiply by P(K) * inv(U(K)) if K > 1. 00235 * 00236 IF( K.GT.1 ) THEN 00237 * 00238 * Apply the transformation. 00239 * 00240 CALL ZGERU( K-1, NRHS, ONE, A( 1, K ), 1, B( K, 1 ), 00241 $ LDB, B( 1, 1 ), LDB ) 00242 * 00243 * Interchange if P(K) != I. 00244 * 00245 KP = IPIV( K ) 00246 IF( KP.NE.K ) 00247 $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 00248 END IF 00249 K = K + 1 00250 ELSE 00251 * 00252 * 2 x 2 pivot block 00253 * 00254 * Multiply by the diagonal block if forming U * D. 00255 * 00256 IF( NOUNIT ) THEN 00257 D11 = A( K, K ) 00258 D22 = A( K+1, K+1 ) 00259 D12 = A( K, K+1 ) 00260 D21 = D12 00261 DO 20 J = 1, NRHS 00262 T1 = B( K, J ) 00263 T2 = B( K+1, J ) 00264 B( K, J ) = D11*T1 + D12*T2 00265 B( K+1, J ) = D21*T1 + D22*T2 00266 20 CONTINUE 00267 END IF 00268 * 00269 * Multiply by P(K) * inv(U(K)) if K > 1. 00270 * 00271 IF( K.GT.1 ) THEN 00272 * 00273 * Apply the transformations. 00274 * 00275 CALL ZGERU( K-1, NRHS, ONE, A( 1, K ), 1, B( K, 1 ), 00276 $ LDB, B( 1, 1 ), LDB ) 00277 CALL ZGERU( K-1, NRHS, ONE, A( 1, K+1 ), 1, 00278 $ B( K+1, 1 ), LDB, B( 1, 1 ), LDB ) 00279 * 00280 * Interchange if P(K) != I. 00281 * 00282 KP = ABS( IPIV( K ) ) 00283 IF( KP.NE.K ) 00284 $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 00285 END IF 00286 K = K + 2 00287 END IF 00288 GO TO 10 00289 30 CONTINUE 00290 * 00291 * Compute B := L*B 00292 * where L = P(1)*inv(L(1))* ... *P(m)*inv(L(m)) . 00293 * 00294 ELSE 00295 * 00296 * Loop backward applying the transformations to B. 00297 * 00298 K = N 00299 40 CONTINUE 00300 IF( K.LT.1 ) 00301 $ GO TO 60 00302 * 00303 * Test the pivot index. If greater than zero, a 1 x 1 00304 * pivot was used, otherwise a 2 x 2 pivot was used. 00305 * 00306 IF( IPIV( K ).GT.0 ) THEN 00307 * 00308 * 1 x 1 pivot block: 00309 * 00310 * Multiply by the diagonal element if forming L * D. 00311 * 00312 IF( NOUNIT ) 00313 $ CALL ZSCAL( NRHS, A( K, K ), B( K, 1 ), LDB ) 00314 * 00315 * Multiply by P(K) * inv(L(K)) if K < N. 00316 * 00317 IF( K.NE.N ) THEN 00318 KP = IPIV( K ) 00319 * 00320 * Apply the transformation. 00321 * 00322 CALL ZGERU( N-K, NRHS, ONE, A( K+1, K ), 1, B( K, 1 ), 00323 $ LDB, B( K+1, 1 ), LDB ) 00324 * 00325 * Interchange if a permutation was applied at the 00326 * K-th step of the factorization. 00327 * 00328 IF( KP.NE.K ) 00329 $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 00330 END IF 00331 K = K - 1 00332 * 00333 ELSE 00334 * 00335 * 2 x 2 pivot block: 00336 * 00337 * Multiply by the diagonal block if forming L * D. 00338 * 00339 IF( NOUNIT ) THEN 00340 D11 = A( K-1, K-1 ) 00341 D22 = A( K, K ) 00342 D21 = A( K, K-1 ) 00343 D12 = D21 00344 DO 50 J = 1, NRHS 00345 T1 = B( K-1, J ) 00346 T2 = B( K, J ) 00347 B( K-1, J ) = D11*T1 + D12*T2 00348 B( K, J ) = D21*T1 + D22*T2 00349 50 CONTINUE 00350 END IF 00351 * 00352 * Multiply by P(K) * inv(L(K)) if K < N. 00353 * 00354 IF( K.NE.N ) THEN 00355 * 00356 * Apply the transformation. 00357 * 00358 CALL ZGERU( N-K, NRHS, ONE, A( K+1, K ), 1, B( K, 1 ), 00359 $ LDB, B( K+1, 1 ), LDB ) 00360 CALL ZGERU( N-K, NRHS, ONE, A( K+1, K-1 ), 1, 00361 $ B( K-1, 1 ), LDB, B( K+1, 1 ), LDB ) 00362 * 00363 * Interchange if a permutation was applied at the 00364 * K-th step of the factorization. 00365 * 00366 KP = ABS( IPIV( K ) ) 00367 IF( KP.NE.K ) 00368 $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 00369 END IF 00370 K = K - 2 00371 END IF 00372 GO TO 40 00373 60 CONTINUE 00374 END IF 00375 *---------------------------------------- 00376 * 00377 * Compute B := A' * B (transpose) 00378 * 00379 *---------------------------------------- 00380 ELSE IF( LSAME( TRANS, 'T' ) ) THEN 00381 * 00382 * Form B := U'*B 00383 * where U = P(m)*inv(U(m))* ... *P(1)*inv(U(1)) 00384 * and U' = inv(U'(1))*P(1)* ... *inv(U'(m))*P(m) 00385 * 00386 IF( LSAME( UPLO, 'U' ) ) THEN 00387 * 00388 * Loop backward applying the transformations. 00389 * 00390 K = N 00391 70 CONTINUE 00392 IF( K.LT.1 ) 00393 $ GO TO 90 00394 * 00395 * 1 x 1 pivot block. 00396 * 00397 IF( IPIV( K ).GT.0 ) THEN 00398 IF( K.GT.1 ) THEN 00399 * 00400 * Interchange if P(K) != I. 00401 * 00402 KP = IPIV( K ) 00403 IF( KP.NE.K ) 00404 $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 00405 * 00406 * Apply the transformation 00407 * 00408 CALL ZGEMV( 'Transpose', K-1, NRHS, ONE, B, LDB, 00409 $ A( 1, K ), 1, ONE, B( K, 1 ), LDB ) 00410 END IF 00411 IF( NOUNIT ) 00412 $ CALL ZSCAL( NRHS, A( K, K ), B( K, 1 ), LDB ) 00413 K = K - 1 00414 * 00415 * 2 x 2 pivot block. 00416 * 00417 ELSE 00418 IF( K.GT.2 ) THEN 00419 * 00420 * Interchange if P(K) != I. 00421 * 00422 KP = ABS( IPIV( K ) ) 00423 IF( KP.NE.K-1 ) 00424 $ CALL ZSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ), 00425 $ LDB ) 00426 * 00427 * Apply the transformations 00428 * 00429 CALL ZGEMV( 'Transpose', K-2, NRHS, ONE, B, LDB, 00430 $ A( 1, K ), 1, ONE, B( K, 1 ), LDB ) 00431 CALL ZGEMV( 'Transpose', K-2, NRHS, ONE, B, LDB, 00432 $ A( 1, K-1 ), 1, ONE, B( K-1, 1 ), LDB ) 00433 END IF 00434 * 00435 * Multiply by the diagonal block if non-unit. 00436 * 00437 IF( NOUNIT ) THEN 00438 D11 = A( K-1, K-1 ) 00439 D22 = A( K, K ) 00440 D12 = A( K-1, K ) 00441 D21 = D12 00442 DO 80 J = 1, NRHS 00443 T1 = B( K-1, J ) 00444 T2 = B( K, J ) 00445 B( K-1, J ) = D11*T1 + D12*T2 00446 B( K, J ) = D21*T1 + D22*T2 00447 80 CONTINUE 00448 END IF 00449 K = K - 2 00450 END IF 00451 GO TO 70 00452 90 CONTINUE 00453 * 00454 * Form B := L'*B 00455 * where L = P(1)*inv(L(1))* ... *P(m)*inv(L(m)) 00456 * and L' = inv(L'(m))*P(m)* ... *inv(L'(1))*P(1) 00457 * 00458 ELSE 00459 * 00460 * Loop forward applying the L-transformations. 00461 * 00462 K = 1 00463 100 CONTINUE 00464 IF( K.GT.N ) 00465 $ GO TO 120 00466 * 00467 * 1 x 1 pivot block 00468 * 00469 IF( IPIV( K ).GT.0 ) THEN 00470 IF( K.LT.N ) THEN 00471 * 00472 * Interchange if P(K) != I. 00473 * 00474 KP = IPIV( K ) 00475 IF( KP.NE.K ) 00476 $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 00477 * 00478 * Apply the transformation 00479 * 00480 CALL ZGEMV( 'Transpose', N-K, NRHS, ONE, B( K+1, 1 ), 00481 $ LDB, A( K+1, K ), 1, ONE, B( K, 1 ), LDB ) 00482 END IF 00483 IF( NOUNIT ) 00484 $ CALL ZSCAL( NRHS, A( K, K ), B( K, 1 ), LDB ) 00485 K = K + 1 00486 * 00487 * 2 x 2 pivot block. 00488 * 00489 ELSE 00490 IF( K.LT.N-1 ) THEN 00491 * 00492 * Interchange if P(K) != I. 00493 * 00494 KP = ABS( IPIV( K ) ) 00495 IF( KP.NE.K+1 ) 00496 $ CALL ZSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ), 00497 $ LDB ) 00498 * 00499 * Apply the transformation 00500 * 00501 CALL ZGEMV( 'Transpose', N-K-1, NRHS, ONE, 00502 $ B( K+2, 1 ), LDB, A( K+2, K+1 ), 1, ONE, 00503 $ B( K+1, 1 ), LDB ) 00504 CALL ZGEMV( 'Transpose', N-K-1, NRHS, ONE, 00505 $ B( K+2, 1 ), LDB, A( K+2, K ), 1, ONE, 00506 $ B( K, 1 ), LDB ) 00507 END IF 00508 * 00509 * Multiply by the diagonal block if non-unit. 00510 * 00511 IF( NOUNIT ) THEN 00512 D11 = A( K, K ) 00513 D22 = A( K+1, K+1 ) 00514 D21 = A( K+1, K ) 00515 D12 = D21 00516 DO 110 J = 1, NRHS 00517 T1 = B( K, J ) 00518 T2 = B( K+1, J ) 00519 B( K, J ) = D11*T1 + D12*T2 00520 B( K+1, J ) = D21*T1 + D22*T2 00521 110 CONTINUE 00522 END IF 00523 K = K + 2 00524 END IF 00525 GO TO 100 00526 120 CONTINUE 00527 END IF 00528 END IF 00529 RETURN 00530 * 00531 * End of ZLAVSY 00532 * 00533 END
1.7.6.1 
