|
LAPACK 3.3.0
|
|
LAPACK 3.3.0
|
00001 SUBROUTINE ZLAVSP( UPLO, TRANS, DIAG, N, NRHS, A, IPIV, B, LDB, 00002 $ INFO ) 00003 * 00004 * -- LAPACK auxiliary routine (version 3.1) -- 00005 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. 00006 * November 2006 00007 * 00008 * .. Scalar Arguments .. 00009 CHARACTER DIAG, TRANS, UPLO 00010 INTEGER INFO, LDB, N, NRHS 00011 * .. 00012 * .. Array Arguments .. 00013 INTEGER IPIV( * ) 00014 COMPLEX*16 A( * ), B( LDB, * ) 00015 * .. 00016 * 00017 * Purpose 00018 * ======= 00019 * 00020 * ZLAVSP performs one of the matrix-vector operations 00021 * x := A*x or x := A^T*x, 00022 * where x is an N element vector and A is one of the factors 00023 * from the symmetric factorization computed by ZSPTRF. 00024 * ZSPTRF produces a factorization of the form 00025 * U * D * U^T or L * D * L^T, 00026 * where U (or L) is a product of permutation and unit upper (lower) 00027 * triangular matrices, U^T (or L^T) is the transpose of 00028 * U (or L), and D is symmetric and block diagonal with 1 x 1 and 00029 * 2 x 2 diagonal blocks. The multipliers for the transformations 00030 * and the upper or lower triangular parts of the diagonal blocks 00031 * are stored columnwise in packed format in the linear array A. 00032 * 00033 * If TRANS = 'N' or 'n', ZLAVSP multiplies either by U or U * D 00034 * (or L or L * D). 00035 * If TRANS = 'C' or 'c', ZLAVSP multiplies either by U^T or D * U^T 00036 * (or L^T or D * L^T ). 00037 * 00038 * Arguments 00039 * ========== 00040 * 00041 * UPLO - CHARACTER*1 00042 * On entry, UPLO specifies whether the triangular matrix 00043 * stored in A is upper or lower triangular. 00044 * UPLO = 'U' or 'u' The matrix is upper triangular. 00045 * UPLO = 'L' or 'l' The matrix is lower triangular. 00046 * Unchanged on exit. 00047 * 00048 * TRANS - CHARACTER*1 00049 * On entry, TRANS specifies the operation to be performed as 00050 * follows: 00051 * TRANS = 'N' or 'n' x := A*x. 00052 * TRANS = 'T' or 't' x := A^T*x. 00053 * Unchanged on exit. 00054 * 00055 * DIAG - CHARACTER*1 00056 * On entry, DIAG specifies whether the diagonal blocks are 00057 * assumed to be unit matrices, as follows: 00058 * DIAG = 'U' or 'u' Diagonal blocks are unit matrices. 00059 * DIAG = 'N' or 'n' Diagonal blocks are non-unit. 00060 * Unchanged on exit. 00061 * 00062 * N - INTEGER 00063 * On entry, N specifies the order of the matrix A. 00064 * N must be at least zero. 00065 * Unchanged on exit. 00066 * 00067 * NRHS - INTEGER 00068 * On entry, NRHS specifies the number of right hand sides, 00069 * i.e., the number of vectors x to be multiplied by A. 00070 * NRHS must be at least zero. 00071 * Unchanged on exit. 00072 * 00073 * A - COMPLEX*16 array, dimension( N*(N+1)/2 ) 00074 * On entry, A contains a block diagonal matrix and the 00075 * multipliers of the transformations used to obtain it, 00076 * stored as a packed triangular matrix. 00077 * Unchanged on exit. 00078 * 00079 * IPIV - INTEGER array, dimension( N ) 00080 * On entry, IPIV contains the vector of pivot indices as 00081 * determined by ZSPTRF. 00082 * If IPIV( K ) = K, no interchange was done. 00083 * If IPIV( K ) <> K but IPIV( K ) > 0, then row K was inter- 00084 * changed with row IPIV( K ) and a 1 x 1 pivot block was used. 00085 * If IPIV( K ) < 0 and UPLO = 'U', then row K-1 was exchanged 00086 * with row | IPIV( K ) | and a 2 x 2 pivot block was used. 00087 * If IPIV( K ) < 0 and UPLO = 'L', then row K+1 was exchanged 00088 * with row | IPIV( K ) | and a 2 x 2 pivot block was used. 00089 * 00090 * B - COMPLEX*16 array, dimension( LDB, NRHS ) 00091 * On entry, B contains NRHS vectors of length N. 00092 * On exit, B is overwritten with the product A * B. 00093 * 00094 * LDB - INTEGER 00095 * On entry, LDB contains the leading dimension of B as 00096 * declared in the calling program. LDB must be at least 00097 * max( 1, N ). 00098 * Unchanged on exit. 00099 * 00100 * INFO - INTEGER 00101 * INFO is the error flag. 00102 * On exit, a value of 0 indicates a successful exit. 00103 * A negative value, say -K, indicates that the K-th argument 00104 * has an illegal value. 00105 * 00106 * ===================================================================== 00107 * 00108 * .. Parameters .. 00109 COMPLEX*16 ONE 00110 PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) 00111 * .. 00112 * .. Local Scalars .. 00113 LOGICAL NOUNIT 00114 INTEGER J, K, KC, KCNEXT, KP 00115 COMPLEX*16 D11, D12, D21, D22, T1, T2 00116 * .. 00117 * .. External Functions .. 00118 LOGICAL LSAME 00119 EXTERNAL LSAME 00120 * .. 00121 * .. External Subroutines .. 00122 EXTERNAL XERBLA, ZGEMV, ZGERU, ZSCAL, ZSWAP 00123 * .. 00124 * .. Intrinsic Functions .. 00125 INTRINSIC ABS, MAX 00126 * .. 00127 * .. Executable Statements .. 00128 * 00129 * Test the input parameters. 00130 * 00131 INFO = 0 00132 IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 00133 INFO = -1 00134 ELSE IF( .NOT.LSAME( TRANS, 'N' ) .AND. .NOT.LSAME( TRANS, 'T' ) ) 00135 $ THEN 00136 INFO = -2 00137 ELSE IF( .NOT.LSAME( DIAG, 'U' ) .AND. .NOT.LSAME( DIAG, 'N' ) ) 00138 $ THEN 00139 INFO = -3 00140 ELSE IF( N.LT.0 ) THEN 00141 INFO = -4 00142 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN 00143 INFO = -8 00144 END IF 00145 IF( INFO.NE.0 ) THEN 00146 CALL XERBLA( 'ZLAVSP ', -INFO ) 00147 RETURN 00148 END IF 00149 * 00150 * Quick return if possible. 00151 * 00152 IF( N.EQ.0 ) 00153 $ RETURN 00154 * 00155 NOUNIT = LSAME( DIAG, 'N' ) 00156 *------------------------------------------ 00157 * 00158 * Compute B := A * B (No transpose) 00159 * 00160 *------------------------------------------ 00161 IF( LSAME( TRANS, 'N' ) ) THEN 00162 * 00163 * Compute B := U*B 00164 * where U = P(m)*inv(U(m))* ... *P(1)*inv(U(1)) 00165 * 00166 IF( LSAME( UPLO, 'U' ) ) THEN 00167 * 00168 * Loop forward applying the transformations. 00169 * 00170 K = 1 00171 KC = 1 00172 10 CONTINUE 00173 IF( K.GT.N ) 00174 $ GO TO 30 00175 * 00176 * 1 x 1 pivot block 00177 * 00178 IF( IPIV( K ).GT.0 ) THEN 00179 * 00180 * Multiply by the diagonal element if forming U * D. 00181 * 00182 IF( NOUNIT ) 00183 $ CALL ZSCAL( NRHS, A( KC+K-1 ), B( K, 1 ), LDB ) 00184 * 00185 * Multiply by P(K) * inv(U(K)) if K > 1. 00186 * 00187 IF( K.GT.1 ) THEN 00188 * 00189 * Apply the transformation. 00190 * 00191 CALL ZGERU( K-1, NRHS, ONE, A( KC ), 1, B( K, 1 ), 00192 $ LDB, B( 1, 1 ), LDB ) 00193 * 00194 * Interchange if P(K) != I. 00195 * 00196 KP = IPIV( K ) 00197 IF( KP.NE.K ) 00198 $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 00199 END IF 00200 KC = KC + K 00201 K = K + 1 00202 ELSE 00203 * 00204 * 2 x 2 pivot block 00205 * 00206 KCNEXT = KC + K 00207 * 00208 * Multiply by the diagonal block if forming U * D. 00209 * 00210 IF( NOUNIT ) THEN 00211 D11 = A( KCNEXT-1 ) 00212 D22 = A( KCNEXT+K ) 00213 D12 = A( KCNEXT+K-1 ) 00214 D21 = D12 00215 DO 20 J = 1, NRHS 00216 T1 = B( K, J ) 00217 T2 = B( K+1, J ) 00218 B( K, J ) = D11*T1 + D12*T2 00219 B( K+1, J ) = D21*T1 + D22*T2 00220 20 CONTINUE 00221 END IF 00222 * 00223 * Multiply by P(K) * inv(U(K)) if K > 1. 00224 * 00225 IF( K.GT.1 ) THEN 00226 * 00227 * Apply the transformations. 00228 * 00229 CALL ZGERU( K-1, NRHS, ONE, A( KC ), 1, B( K, 1 ), 00230 $ LDB, B( 1, 1 ), LDB ) 00231 CALL ZGERU( K-1, NRHS, ONE, A( KCNEXT ), 1, 00232 $ B( K+1, 1 ), LDB, B( 1, 1 ), LDB ) 00233 * 00234 * Interchange if P(K) != I. 00235 * 00236 KP = ABS( IPIV( K ) ) 00237 IF( KP.NE.K ) 00238 $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 00239 END IF 00240 KC = KCNEXT + K + 1 00241 K = K + 2 00242 END IF 00243 GO TO 10 00244 30 CONTINUE 00245 * 00246 * Compute B := L*B 00247 * where L = P(1)*inv(L(1))* ... *P(m)*inv(L(m)) . 00248 * 00249 ELSE 00250 * 00251 * Loop backward applying the transformations to B. 00252 * 00253 K = N 00254 KC = N*( N+1 ) / 2 + 1 00255 40 CONTINUE 00256 IF( K.LT.1 ) 00257 $ GO TO 60 00258 KC = KC - ( N-K+1 ) 00259 * 00260 * Test the pivot index. If greater than zero, a 1 x 1 00261 * pivot was used, otherwise a 2 x 2 pivot was used. 00262 * 00263 IF( IPIV( K ).GT.0 ) THEN 00264 * 00265 * 1 x 1 pivot block: 00266 * 00267 * Multiply by the diagonal element if forming L * D. 00268 * 00269 IF( NOUNIT ) 00270 $ CALL ZSCAL( NRHS, A( KC ), B( K, 1 ), LDB ) 00271 * 00272 * Multiply by P(K) * inv(L(K)) if K < N. 00273 * 00274 IF( K.NE.N ) THEN 00275 KP = IPIV( K ) 00276 * 00277 * Apply the transformation. 00278 * 00279 CALL ZGERU( N-K, NRHS, ONE, A( KC+1 ), 1, B( K, 1 ), 00280 $ LDB, B( K+1, 1 ), LDB ) 00281 * 00282 * Interchange if a permutation was applied at the 00283 * K-th step of the factorization. 00284 * 00285 IF( KP.NE.K ) 00286 $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 00287 END IF 00288 K = K - 1 00289 * 00290 ELSE 00291 * 00292 * 2 x 2 pivot block: 00293 * 00294 KCNEXT = KC - ( N-K+2 ) 00295 * 00296 * Multiply by the diagonal block if forming L * D. 00297 * 00298 IF( NOUNIT ) THEN 00299 D11 = A( KCNEXT ) 00300 D22 = A( KC ) 00301 D21 = A( KCNEXT+1 ) 00302 D12 = D21 00303 DO 50 J = 1, NRHS 00304 T1 = B( K-1, J ) 00305 T2 = B( K, J ) 00306 B( K-1, J ) = D11*T1 + D12*T2 00307 B( K, J ) = D21*T1 + D22*T2 00308 50 CONTINUE 00309 END IF 00310 * 00311 * Multiply by P(K) * inv(L(K)) if K < N. 00312 * 00313 IF( K.NE.N ) THEN 00314 * 00315 * Apply the transformation. 00316 * 00317 CALL ZGERU( N-K, NRHS, ONE, A( KC+1 ), 1, B( K, 1 ), 00318 $ LDB, B( K+1, 1 ), LDB ) 00319 CALL ZGERU( N-K, NRHS, ONE, A( KCNEXT+2 ), 1, 00320 $ B( K-1, 1 ), LDB, B( K+1, 1 ), LDB ) 00321 * 00322 * Interchange if a permutation was applied at the 00323 * K-th step of the factorization. 00324 * 00325 KP = ABS( IPIV( K ) ) 00326 IF( KP.NE.K ) 00327 $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 00328 END IF 00329 KC = KCNEXT 00330 K = K - 2 00331 END IF 00332 GO TO 40 00333 60 CONTINUE 00334 END IF 00335 *------------------------------------------------- 00336 * 00337 * Compute B := A^T * B (transpose) 00338 * 00339 *------------------------------------------------- 00340 ELSE 00341 * 00342 * Form B := U^T*B 00343 * where U = P(m)*inv(U(m))* ... *P(1)*inv(U(1)) 00344 * and U^T = inv(U^T(1))*P(1)* ... *inv(U^T(m))*P(m) 00345 * 00346 IF( LSAME( UPLO, 'U' ) ) THEN 00347 * 00348 * Loop backward applying the transformations. 00349 * 00350 K = N 00351 KC = N*( N+1 ) / 2 + 1 00352 70 CONTINUE 00353 IF( K.LT.1 ) 00354 $ GO TO 90 00355 KC = KC - K 00356 * 00357 * 1 x 1 pivot block. 00358 * 00359 IF( IPIV( K ).GT.0 ) THEN 00360 IF( K.GT.1 ) THEN 00361 * 00362 * Interchange if P(K) != I. 00363 * 00364 KP = IPIV( K ) 00365 IF( KP.NE.K ) 00366 $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 00367 * 00368 * Apply the transformation: 00369 * y := y - B' * conjg(x) 00370 * where x is a column of A and y is a row of B. 00371 * 00372 CALL ZGEMV( 'Transpose', K-1, NRHS, ONE, B, LDB, 00373 $ A( KC ), 1, ONE, B( K, 1 ), LDB ) 00374 END IF 00375 IF( NOUNIT ) 00376 $ CALL ZSCAL( NRHS, A( KC+K-1 ), B( K, 1 ), LDB ) 00377 K = K - 1 00378 * 00379 * 2 x 2 pivot block. 00380 * 00381 ELSE 00382 KCNEXT = KC - ( K-1 ) 00383 IF( K.GT.2 ) THEN 00384 * 00385 * Interchange if P(K) != I. 00386 * 00387 KP = ABS( IPIV( K ) ) 00388 IF( KP.NE.K-1 ) 00389 $ CALL ZSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ), 00390 $ LDB ) 00391 * 00392 * Apply the transformations. 00393 * 00394 CALL ZGEMV( 'Transpose', K-2, NRHS, ONE, B, LDB, 00395 $ A( KC ), 1, ONE, B( K, 1 ), LDB ) 00396 * 00397 CALL ZGEMV( 'Transpose', K-2, NRHS, ONE, B, LDB, 00398 $ A( KCNEXT ), 1, ONE, B( K-1, 1 ), LDB ) 00399 END IF 00400 * 00401 * Multiply by the diagonal block if non-unit. 00402 * 00403 IF( NOUNIT ) THEN 00404 D11 = A( KC-1 ) 00405 D22 = A( KC+K-1 ) 00406 D12 = A( KC+K-2 ) 00407 D21 = D12 00408 DO 80 J = 1, NRHS 00409 T1 = B( K-1, J ) 00410 T2 = B( K, J ) 00411 B( K-1, J ) = D11*T1 + D12*T2 00412 B( K, J ) = D21*T1 + D22*T2 00413 80 CONTINUE 00414 END IF 00415 KC = KCNEXT 00416 K = K - 2 00417 END IF 00418 GO TO 70 00419 90 CONTINUE 00420 * 00421 * Form B := L^T*B 00422 * where L = P(1)*inv(L(1))* ... *P(m)*inv(L(m)) 00423 * and L^T = inv(L(m))*P(m)* ... *inv(L(1))*P(1) 00424 * 00425 ELSE 00426 * 00427 * Loop forward applying the L-transformations. 00428 * 00429 K = 1 00430 KC = 1 00431 100 CONTINUE 00432 IF( K.GT.N ) 00433 $ GO TO 120 00434 * 00435 * 1 x 1 pivot block 00436 * 00437 IF( IPIV( K ).GT.0 ) THEN 00438 IF( K.LT.N ) THEN 00439 * 00440 * Interchange if P(K) != I. 00441 * 00442 KP = IPIV( K ) 00443 IF( KP.NE.K ) 00444 $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 00445 * 00446 * Apply the transformation 00447 * 00448 CALL ZGEMV( 'Transpose', N-K, NRHS, ONE, B( K+1, 1 ), 00449 $ LDB, A( KC+1 ), 1, ONE, B( K, 1 ), LDB ) 00450 END IF 00451 IF( NOUNIT ) 00452 $ CALL ZSCAL( NRHS, A( KC ), B( K, 1 ), LDB ) 00453 KC = KC + N - K + 1 00454 K = K + 1 00455 * 00456 * 2 x 2 pivot block. 00457 * 00458 ELSE 00459 KCNEXT = KC + N - K + 1 00460 IF( K.LT.N-1 ) THEN 00461 * 00462 * Interchange if P(K) != I. 00463 * 00464 KP = ABS( IPIV( K ) ) 00465 IF( KP.NE.K+1 ) 00466 $ CALL ZSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ), 00467 $ LDB ) 00468 * 00469 * Apply the transformation 00470 * 00471 CALL ZGEMV( 'Transpose', N-K-1, NRHS, ONE, 00472 $ B( K+2, 1 ), LDB, A( KCNEXT+1 ), 1, ONE, 00473 $ B( K+1, 1 ), LDB ) 00474 * 00475 CALL ZGEMV( 'Transpose', N-K-1, NRHS, ONE, 00476 $ B( K+2, 1 ), LDB, A( KC+2 ), 1, ONE, 00477 $ B( K, 1 ), LDB ) 00478 END IF 00479 * 00480 * Multiply by the diagonal block if non-unit. 00481 * 00482 IF( NOUNIT ) THEN 00483 D11 = A( KC ) 00484 D22 = A( KCNEXT ) 00485 D21 = A( KC+1 ) 00486 D12 = D21 00487 DO 110 J = 1, NRHS 00488 T1 = B( K, J ) 00489 T2 = B( K+1, J ) 00490 B( K, J ) = D11*T1 + D12*T2 00491 B( K+1, J ) = D21*T1 + D22*T2 00492 110 CONTINUE 00493 END IF 00494 KC = KCNEXT + ( N-K ) 00495 K = K + 2 00496 END IF 00497 GO TO 100 00498 120 CONTINUE 00499 END IF 00500 * 00501 END IF 00502 RETURN 00503 * 00504 * End of ZLAVSP 00505 * 00506 END
1.7.3 
