1*> \brief \b ZLAVSY 2* 3* =========== DOCUMENTATION =========== 4* 5* Online html documentation available at 6* http://www.netlib.org/lapack/explore-html/ 7* 8* Definition: 9* =========== 10* 11* SUBROUTINE ZLAVSY( UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B, 12* LDB, INFO ) 13* 14* .. Scalar Arguments .. 15* CHARACTER DIAG, TRANS, UPLO 16* INTEGER INFO, LDA, LDB, N, NRHS 17* .. 18* .. Array Arguments .. 19* INTEGER IPIV( * ) 20* COMPLEX*16 A( LDA, * ), B( LDB, * ) 21* .. 22* 23* 24*> \par Purpose: 25* ============= 26*> 27*> \verbatim 28*> 29*> ZLAVSY performs one of the matrix-vector operations 30*> x := A*x or x := A'*x, 31*> where x is an N element vector and A is one of the factors 32*> from the block U*D*U' or L*D*L' factorization computed by ZSYTRF. 33*> 34*> If TRANS = 'N', multiplies by U or U * D (or L or L * D) 35*> If TRANS = 'T', multiplies by U' or D * U' (or L' or D * L') 36*> \endverbatim 37* 38* Arguments: 39* ========== 40* 41*> \param[in] UPLO 42*> \verbatim 43*> UPLO is CHARACTER*1 44*> Specifies whether the factor stored in A is upper or lower 45*> triangular. 46*> = 'U': Upper triangular 47*> = 'L': Lower triangular 48*> \endverbatim 49*> 50*> \param[in] TRANS 51*> \verbatim 52*> TRANS is CHARACTER*1 53*> Specifies the operation to be performed: 54*> = 'N': x := A*x 55*> = 'T': x := A'*x 56*> \endverbatim 57*> 58*> \param[in] DIAG 59*> \verbatim 60*> DIAG is CHARACTER*1 61*> Specifies whether or not the diagonal blocks are unit 62*> matrices. If the diagonal blocks are assumed to be unit, 63*> then A = U or A = L, otherwise A = U*D or A = L*D. 64*> = 'U': Diagonal blocks are assumed to be unit matrices. 65*> = 'N': Diagonal blocks are assumed to be non-unit matrices. 66*> \endverbatim 67*> 68*> \param[in] N 69*> \verbatim 70*> N is INTEGER 71*> The number of rows and columns of the matrix A. N >= 0. 72*> \endverbatim 73*> 74*> \param[in] NRHS 75*> \verbatim 76*> NRHS is INTEGER 77*> The number of right hand sides, i.e., the number of vectors 78*> x to be multiplied by A. NRHS >= 0. 79*> \endverbatim 80*> 81*> \param[in] A 82*> \verbatim 83*> A is COMPLEX*16 array, dimension (LDA,N) 84*> The block diagonal matrix D and the multipliers used to 85*> obtain the factor U or L as computed by ZSYTRF. 86*> \endverbatim 87*> 88*> \param[in] LDA 89*> \verbatim 90*> LDA is INTEGER 91*> The leading dimension of the array A. LDA >= max(1,N). 92*> \endverbatim 93*> 94*> \param[in] IPIV 95*> \verbatim 96*> IPIV is INTEGER array, dimension (N) 97*> Details of the interchanges and the block structure of D, 98*> as determined by ZSYTRF or ZHETRF. 99*> 100*> If UPLO = 'U': 101*> If IPIV(k) > 0, then rows and columns k and IPIV(k) 102*> were interchanged and D(k,k) is a 1-by-1 diagonal block. 103*> (If IPIV( k ) = k, no interchange was done). 104*> 105*> If IPIV(k) = IPIV(k-1) < 0, then rows and 106*> columns k-1 and -IPIV(k) were interchanged, 107*> D(k-1:k,k-1:k) is a 2-by-2 diagonal block. 108*> 109*> If UPLO = 'L': 110*> If IPIV(k) > 0, then rows and columns k and IPIV(k) 111*> were interchanged and D(k,k) is a 1-by-1 diagonal block. 112*> (If IPIV( k ) = k, no interchange was done). 113*> 114*> If IPIV(k) = IPIV(k+1) < 0, then rows and 115*> columns k+1 and -IPIV(k) were interchanged, 116*> D(k:k+1,k:k+1) is a 2-by-2 diagonal block. 117*> \endverbatim 118*> 119*> \param[in,out] B 120*> \verbatim 121*> B is COMPLEX*16 array, dimension (LDB,NRHS) 122*> On entry, B contains NRHS vectors of length N. 123*> On exit, B is overwritten with the product A * B. 124*> \endverbatim 125*> 126*> \param[in] LDB 127*> \verbatim 128*> LDB is INTEGER 129*> The leading dimension of the array B. LDB >= max(1,N). 130*> \endverbatim 131*> 132*> \param[out] INFO 133*> \verbatim 134*> INFO is INTEGER 135*> = 0: successful exit 136*> < 0: if INFO = -k, the k-th argument had an illegal value 137*> \endverbatim 138* 139* Authors: 140* ======== 141* 142*> \author Univ. of Tennessee 143*> \author Univ. of California Berkeley 144*> \author Univ. of Colorado Denver 145*> \author NAG Ltd. 146* 147*> \date April 2012 148* 149*> \ingroup complex16_lin 150* 151* ===================================================================== 152 SUBROUTINE ZLAVSY( UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B, 153 $ LDB, INFO ) 154* 155* -- LAPACK test routine (version 3.4.1) -- 156* -- LAPACK is a software package provided by Univ. of Tennessee, -- 157* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 158* April 2012 159* 160* .. Scalar Arguments .. 161 CHARACTER DIAG, TRANS, UPLO 162 INTEGER INFO, LDA, LDB, N, NRHS 163* .. 164* .. Array Arguments .. 165 INTEGER IPIV( * ) 166 COMPLEX*16 A( LDA, * ), B( LDB, * ) 167* .. 168* 169* ===================================================================== 170* 171* .. Parameters .. 172 COMPLEX*16 CONE 173 PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) ) 174* .. 175* .. Local Scalars .. 176 LOGICAL NOUNIT 177 INTEGER J, K, KP 178 COMPLEX*16 D11, D12, D21, D22, T1, T2 179* .. 180* .. External Functions .. 181 LOGICAL LSAME 182 EXTERNAL LSAME 183* .. 184* .. External Subroutines .. 185 EXTERNAL XERBLA, ZGEMV, ZGERU, ZSCAL, ZSWAP 186* .. 187* .. Intrinsic Functions .. 188 INTRINSIC ABS, MAX 189* .. 190* .. Executable Statements .. 191* 192* Test the input parameters. 193* 194 INFO = 0 195 IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 196 INFO = -1 197 ELSE IF( .NOT.LSAME( TRANS, 'N' ) .AND. .NOT.LSAME( TRANS, 'T' ) ) 198 $ THEN 199 INFO = -2 200 ELSE IF( .NOT.LSAME( DIAG, 'U' ) .AND. .NOT.LSAME( DIAG, 'N' ) ) 201 $ THEN 202 INFO = -3 203 ELSE IF( N.LT.0 ) THEN 204 INFO = -4 205 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 206 INFO = -6 207 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN 208 INFO = -9 209 END IF 210 IF( INFO.NE.0 ) THEN 211 CALL XERBLA( 'ZLAVSY ', -INFO ) 212 RETURN 213 END IF 214* 215* Quick return if possible. 216* 217 IF( N.EQ.0 ) 218 $ RETURN 219* 220 NOUNIT = LSAME( DIAG, 'N' ) 221*------------------------------------------ 222* 223* Compute B := A * B (No transpose) 224* 225*------------------------------------------ 226 IF( LSAME( TRANS, 'N' ) ) THEN 227* 228* Compute B := U*B 229* where U = P(m)*inv(U(m))* ... *P(1)*inv(U(1)) 230* 231 IF( LSAME( UPLO, 'U' ) ) THEN 232* 233* Loop forward applying the transformations. 234* 235 K = 1 236 10 CONTINUE 237 IF( K.GT.N ) 238 $ GO TO 30 239 IF( IPIV( K ).GT.0 ) THEN 240* 241* 1 x 1 pivot block 242* 243* Multiply by the diagonal element if forming U * D. 244* 245 IF( NOUNIT ) 246 $ CALL ZSCAL( NRHS, A( K, K ), B( K, 1 ), LDB ) 247* 248* Multiply by P(K) * inv(U(K)) if K > 1. 249* 250 IF( K.GT.1 ) THEN 251* 252* Apply the transformation. 253* 254 CALL ZGERU( K-1, NRHS, CONE, A( 1, K ), 1, B( K, 1 ), 255 $ LDB, B( 1, 1 ), LDB ) 256* 257* Interchange if P(K) != I. 258* 259 KP = IPIV( K ) 260 IF( KP.NE.K ) 261 $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 262 END IF 263 K = K + 1 264 ELSE 265* 266* 2 x 2 pivot block 267* 268* Multiply by the diagonal block if forming U * D. 269* 270 IF( NOUNIT ) THEN 271 D11 = A( K, K ) 272 D22 = A( K+1, K+1 ) 273 D12 = A( K, K+1 ) 274 D21 = D12 275 DO 20 J = 1, NRHS 276 T1 = B( K, J ) 277 T2 = B( K+1, J ) 278 B( K, J ) = D11*T1 + D12*T2 279 B( K+1, J ) = D21*T1 + D22*T2 280 20 CONTINUE 281 END IF 282* 283* Multiply by P(K) * inv(U(K)) if K > 1. 284* 285 IF( K.GT.1 ) THEN 286* 287* Apply the transformations. 288* 289 CALL ZGERU( K-1, NRHS, CONE, A( 1, K ), 1, B( K, 1 ), 290 $ LDB, B( 1, 1 ), LDB ) 291 CALL ZGERU( K-1, NRHS, CONE, A( 1, K+1 ), 1, 292 $ B( K+1, 1 ), LDB, B( 1, 1 ), LDB ) 293* 294* Interchange if P(K) != I. 295* 296 KP = ABS( IPIV( K ) ) 297 IF( KP.NE.K ) 298 $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 299 END IF 300 K = K + 2 301 END IF 302 GO TO 10 303 30 CONTINUE 304* 305* Compute B := L*B 306* where L = P(1)*inv(L(1))* ... *P(m)*inv(L(m)) . 307* 308 ELSE 309* 310* Loop backward applying the transformations to B. 311* 312 K = N 313 40 CONTINUE 314 IF( K.LT.1 ) 315 $ GO TO 60 316* 317* Test the pivot index. If greater than zero, a 1 x 1 318* pivot was used, otherwise a 2 x 2 pivot was used. 319* 320 IF( IPIV( K ).GT.0 ) THEN 321* 322* 1 x 1 pivot block: 323* 324* Multiply by the diagonal element if forming L * D. 325* 326 IF( NOUNIT ) 327 $ CALL ZSCAL( NRHS, A( K, K ), B( K, 1 ), LDB ) 328* 329* Multiply by P(K) * inv(L(K)) if K < N. 330* 331 IF( K.NE.N ) THEN 332 KP = IPIV( K ) 333* 334* Apply the transformation. 335* 336 CALL ZGERU( N-K, NRHS, CONE, A( K+1, K ), 1, 337 $ B( K, 1 ), LDB, B( K+1, 1 ), LDB ) 338* 339* Interchange if a permutation was applied at the 340* K-th step of the factorization. 341* 342 IF( KP.NE.K ) 343 $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 344 END IF 345 K = K - 1 346* 347 ELSE 348* 349* 2 x 2 pivot block: 350* 351* Multiply by the diagonal block if forming L * D. 352* 353 IF( NOUNIT ) THEN 354 D11 = A( K-1, K-1 ) 355 D22 = A( K, K ) 356 D21 = A( K, K-1 ) 357 D12 = D21 358 DO 50 J = 1, NRHS 359 T1 = B( K-1, J ) 360 T2 = B( K, J ) 361 B( K-1, J ) = D11*T1 + D12*T2 362 B( K, J ) = D21*T1 + D22*T2 363 50 CONTINUE 364 END IF 365* 366* Multiply by P(K) * inv(L(K)) if K < N. 367* 368 IF( K.NE.N ) THEN 369* 370* Apply the transformation. 371* 372 CALL ZGERU( N-K, NRHS, CONE, A( K+1, K ), 1, 373 $ B( K, 1 ), LDB, B( K+1, 1 ), LDB ) 374 CALL ZGERU( N-K, NRHS, CONE, A( K+1, K-1 ), 1, 375 $ B( K-1, 1 ), LDB, B( K+1, 1 ), LDB ) 376* 377* Interchange if a permutation was applied at the 378* K-th step of the factorization. 379* 380 KP = ABS( IPIV( K ) ) 381 IF( KP.NE.K ) 382 $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 383 END IF 384 K = K - 2 385 END IF 386 GO TO 40 387 60 CONTINUE 388 END IF 389*---------------------------------------- 390* 391* Compute B := A' * B (transpose) 392* 393*---------------------------------------- 394 ELSE IF( LSAME( TRANS, 'T' ) ) THEN 395* 396* Form B := U'*B 397* where U = P(m)*inv(U(m))* ... *P(1)*inv(U(1)) 398* and U' = inv(U'(1))*P(1)* ... *inv(U'(m))*P(m) 399* 400 IF( LSAME( UPLO, 'U' ) ) THEN 401* 402* Loop backward applying the transformations. 403* 404 K = N 405 70 CONTINUE 406 IF( K.LT.1 ) 407 $ GO TO 90 408* 409* 1 x 1 pivot block. 410* 411 IF( IPIV( K ).GT.0 ) THEN 412 IF( K.GT.1 ) THEN 413* 414* Interchange if P(K) != I. 415* 416 KP = IPIV( K ) 417 IF( KP.NE.K ) 418 $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 419* 420* Apply the transformation 421* 422 CALL ZGEMV( 'Transpose', K-1, NRHS, CONE, B, LDB, 423 $ A( 1, K ), 1, CONE, B( K, 1 ), LDB ) 424 END IF 425 IF( NOUNIT ) 426 $ CALL ZSCAL( NRHS, A( K, K ), B( K, 1 ), LDB ) 427 K = K - 1 428* 429* 2 x 2 pivot block. 430* 431 ELSE 432 IF( K.GT.2 ) THEN 433* 434* Interchange if P(K) != I. 435* 436 KP = ABS( IPIV( K ) ) 437 IF( KP.NE.K-1 ) 438 $ CALL ZSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ), 439 $ LDB ) 440* 441* Apply the transformations 442* 443 CALL ZGEMV( 'Transpose', K-2, NRHS, CONE, B, LDB, 444 $ A( 1, K ), 1, CONE, B( K, 1 ), LDB ) 445 CALL ZGEMV( 'Transpose', K-2, NRHS, CONE, B, LDB, 446 $ A( 1, K-1 ), 1, CONE, B( K-1, 1 ), LDB ) 447 END IF 448* 449* Multiply by the diagonal block if non-unit. 450* 451 IF( NOUNIT ) THEN 452 D11 = A( K-1, K-1 ) 453 D22 = A( K, K ) 454 D12 = A( K-1, K ) 455 D21 = D12 456 DO 80 J = 1, NRHS 457 T1 = B( K-1, J ) 458 T2 = B( K, J ) 459 B( K-1, J ) = D11*T1 + D12*T2 460 B( K, J ) = D21*T1 + D22*T2 461 80 CONTINUE 462 END IF 463 K = K - 2 464 END IF 465 GO TO 70 466 90 CONTINUE 467* 468* Form B := L'*B 469* where L = P(1)*inv(L(1))* ... *P(m)*inv(L(m)) 470* and L' = inv(L'(m))*P(m)* ... *inv(L'(1))*P(1) 471* 472 ELSE 473* 474* Loop forward applying the L-transformations. 475* 476 K = 1 477 100 CONTINUE 478 IF( K.GT.N ) 479 $ GO TO 120 480* 481* 1 x 1 pivot block 482* 483 IF( IPIV( K ).GT.0 ) THEN 484 IF( K.LT.N ) THEN 485* 486* Interchange if P(K) != I. 487* 488 KP = IPIV( K ) 489 IF( KP.NE.K ) 490 $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 491* 492* Apply the transformation 493* 494 CALL ZGEMV( 'Transpose', N-K, NRHS, CONE, B( K+1, 1 ), 495 $ LDB, A( K+1, K ), 1, CONE, B( K, 1 ), LDB ) 496 END IF 497 IF( NOUNIT ) 498 $ CALL ZSCAL( NRHS, A( K, K ), B( K, 1 ), LDB ) 499 K = K + 1 500* 501* 2 x 2 pivot block. 502* 503 ELSE 504 IF( K.LT.N-1 ) THEN 505* 506* Interchange if P(K) != I. 507* 508 KP = ABS( IPIV( K ) ) 509 IF( KP.NE.K+1 ) 510 $ CALL ZSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ), 511 $ LDB ) 512* 513* Apply the transformation 514* 515 CALL ZGEMV( 'Transpose', N-K-1, NRHS, CONE, 516 $ B( K+2, 1 ), LDB, A( K+2, K+1 ), 1, CONE, 517 $ B( K+1, 1 ), LDB ) 518 CALL ZGEMV( 'Transpose', N-K-1, NRHS, CONE, 519 $ B( K+2, 1 ), LDB, A( K+2, K ), 1, CONE, 520 $ B( K, 1 ), LDB ) 521 END IF 522* 523* Multiply by the diagonal block if non-unit. 524* 525 IF( NOUNIT ) THEN 526 D11 = A( K, K ) 527 D22 = A( K+1, K+1 ) 528 D21 = A( K+1, K ) 529 D12 = D21 530 DO 110 J = 1, NRHS 531 T1 = B( K, J ) 532 T2 = B( K+1, J ) 533 B( K, J ) = D11*T1 + D12*T2 534 B( K+1, J ) = D21*T1 + D22*T2 535 110 CONTINUE 536 END IF 537 K = K + 2 538 END IF 539 GO TO 100 540 120 CONTINUE 541 END IF 542 END IF 543 RETURN 544* 545* End of ZLAVSY 546* 547 END 548