1*> \brief \b CLAVSY_ROOK 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 CLAVSY_ROOK( 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 A( LDA, * ), B( LDB, * ) 21* .. 22* 23* 24*> \par Purpose: 25* ============= 26*> 27*> \verbatim 28*> 29*> CLAVSY_ROOK 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 CSYTRF_ROOK. 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 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 CSYTRF_ROOK. 86*> Stored as a 2-D triangular matrix. 87*> \endverbatim 88*> 89*> \param[in] LDA 90*> \verbatim 91*> LDA is INTEGER 92*> The leading dimension of the array A. LDA >= max(1,N). 93*> \endverbatim 94*> 95*> \param[in] IPIV 96*> \verbatim 97*> IPIV is INTEGER array, dimension (N) 98*> Details of the interchanges and the block structure of D, 99*> as determined by CSYTRF_ROOK. 100*> 101*> If UPLO = 'U': 102*> If IPIV(k) > 0, then rows and columns k and IPIV(k) 103*> were interchanged and D(k,k) is a 1-by-1 diagonal block. 104*> (If IPIV( k ) = k, no interchange was done). 105*> 106*> If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and 107*> columns k and -IPIV(k) were interchanged and rows and 108*> columns k-1 and -IPIV(k-1) were inerchaged, 109*> D(k-1:k,k-1:k) is a 2-by-2 diagonal block. 110*> 111*> If UPLO = 'L': 112*> If IPIV(k) > 0, then rows and columns k and IPIV(k) 113*> were interchanged and D(k,k) is a 1-by-1 diagonal block. 114*> (If IPIV( k ) = k, no interchange was done). 115*> 116*> If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and 117*> columns k and -IPIV(k) were interchanged and rows and 118*> columns k+1 and -IPIV(k+1) were inerchaged, 119*> D(k:k+1,k:k+1) is a 2-by-2 diagonal block. 120*> \endverbatim 121*> 122*> \param[in,out] B 123*> \verbatim 124*> B is COMPLEX array, dimension (LDB,NRHS) 125*> On entry, B contains NRHS vectors of length N. 126*> On exit, B is overwritten with the product A * B. 127*> \endverbatim 128*> 129*> \param[in] LDB 130*> \verbatim 131*> LDB is INTEGER 132*> The leading dimension of the array B. LDB >= max(1,N). 133*> \endverbatim 134*> 135*> \param[out] INFO 136*> \verbatim 137*> INFO is INTEGER 138*> = 0: successful exit 139*> < 0: if INFO = -k, the k-th argument had an illegal value 140*> \endverbatim 141* 142* Authors: 143* ======== 144* 145*> \author Univ. of Tennessee 146*> \author Univ. of California Berkeley 147*> \author Univ. of Colorado Denver 148*> \author NAG Ltd. 149* 150*> \ingroup complex_lin 151* 152* ===================================================================== 153 SUBROUTINE CLAVSY_ROOK( UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, 154 $ B, LDB, INFO ) 155* 156* -- LAPACK test routine -- 157* -- LAPACK is a software package provided by Univ. of Tennessee, -- 158* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 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 A( LDA, * ), B( LDB, * ) 167* .. 168* 169* ===================================================================== 170* 171* .. Parameters .. 172 COMPLEX CONE 173 PARAMETER ( CONE = ( 1.0E+0, 0.0E+0 ) ) 174* .. 175* .. Local Scalars .. 176 LOGICAL NOUNIT 177 INTEGER J, K, KP 178 COMPLEX D11, D12, D21, D22, T1, T2 179* .. 180* .. External Functions .. 181 LOGICAL LSAME 182 EXTERNAL LSAME 183* .. 184* .. External Subroutines .. 185 EXTERNAL CGEMV, CGERU, CSCAL, CSWAP, XERBLA 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( 'CLAVSY_ROOK ', -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 CSCAL( 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 CGERU( 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 CSWAP( 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 CGERU( K-1, NRHS, CONE, A( 1, K ), 1, B( K, 1 ), 290 $ LDB, B( 1, 1 ), LDB ) 291 CALL CGERU( K-1, NRHS, CONE, A( 1, K+1 ), 1, 292 $ B( K+1, 1 ), LDB, B( 1, 1 ), LDB ) 293* 294* Interchange if a permutation was applied at the 295* K-th step of the factorization. 296* 297* Swap the first of pair with IMAXth 298* 299 KP = ABS( IPIV( K ) ) 300 IF( KP.NE.K ) 301 $ CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 302* 303* NOW swap the first of pair with Pth 304* 305 KP = ABS( IPIV( K+1 ) ) 306 IF( KP.NE.K+1 ) 307 $ CALL CSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ), 308 $ LDB ) 309 END IF 310 K = K + 2 311 END IF 312 GO TO 10 313 30 CONTINUE 314* 315* Compute B := L*B 316* where L = P(1)*inv(L(1))* ... *P(m)*inv(L(m)) . 317* 318 ELSE 319* 320* Loop backward applying the transformations to B. 321* 322 K = N 323 40 CONTINUE 324 IF( K.LT.1 ) 325 $ GO TO 60 326* 327* Test the pivot index. If greater than zero, a 1 x 1 328* pivot was used, otherwise a 2 x 2 pivot was used. 329* 330 IF( IPIV( K ).GT.0 ) THEN 331* 332* 1 x 1 pivot block: 333* 334* Multiply by the diagonal element if forming L * D. 335* 336 IF( NOUNIT ) 337 $ CALL CSCAL( NRHS, A( K, K ), B( K, 1 ), LDB ) 338* 339* Multiply by P(K) * inv(L(K)) if K < N. 340* 341 IF( K.NE.N ) THEN 342 KP = IPIV( K ) 343* 344* Apply the transformation. 345* 346 CALL CGERU( N-K, NRHS, CONE, A( K+1, K ), 1, 347 $ B( K, 1 ), LDB, B( K+1, 1 ), LDB ) 348* 349* Interchange if a permutation was applied at the 350* K-th step of the factorization. 351* 352 IF( KP.NE.K ) 353 $ CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 354 END IF 355 K = K - 1 356* 357 ELSE 358* 359* 2 x 2 pivot block: 360* 361* Multiply by the diagonal block if forming L * D. 362* 363 IF( NOUNIT ) THEN 364 D11 = A( K-1, K-1 ) 365 D22 = A( K, K ) 366 D21 = A( K, K-1 ) 367 D12 = D21 368 DO 50 J = 1, NRHS 369 T1 = B( K-1, J ) 370 T2 = B( K, J ) 371 B( K-1, J ) = D11*T1 + D12*T2 372 B( K, J ) = D21*T1 + D22*T2 373 50 CONTINUE 374 END IF 375* 376* Multiply by P(K) * inv(L(K)) if K < N. 377* 378 IF( K.NE.N ) THEN 379* 380* Apply the transformation. 381* 382 CALL CGERU( N-K, NRHS, CONE, A( K+1, K ), 1, 383 $ B( K, 1 ), LDB, B( K+1, 1 ), LDB ) 384 CALL CGERU( N-K, NRHS, CONE, A( K+1, K-1 ), 1, 385 $ B( K-1, 1 ), LDB, B( K+1, 1 ), LDB ) 386* 387* Interchange if a permutation was applied at the 388* K-th step of the factorization. 389* 390* Swap the second of pair with IMAXth 391* 392 KP = ABS( IPIV( K ) ) 393 IF( KP.NE.K ) 394 $ CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 395* 396* NOW swap the first of pair with Pth 397* 398 KP = ABS( IPIV( K-1 ) ) 399 IF( KP.NE.K-1 ) 400 $ CALL CSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ), 401 $ LDB ) 402 END IF 403 K = K - 2 404 END IF 405 GO TO 40 406 60 CONTINUE 407 END IF 408*---------------------------------------- 409* 410* Compute B := A' * B (transpose) 411* 412*---------------------------------------- 413 ELSE IF( LSAME( TRANS, 'T' ) ) THEN 414* 415* Form B := U'*B 416* where U = P(m)*inv(U(m))* ... *P(1)*inv(U(1)) 417* and U' = inv(U'(1))*P(1)* ... *inv(U'(m))*P(m) 418* 419 IF( LSAME( UPLO, 'U' ) ) THEN 420* 421* Loop backward applying the transformations. 422* 423 K = N 424 70 IF( K.LT.1 ) 425 $ GO TO 90 426* 427* 1 x 1 pivot block. 428* 429 IF( IPIV( K ).GT.0 ) THEN 430 IF( K.GT.1 ) THEN 431* 432* Interchange if P(K) != I. 433* 434 KP = IPIV( K ) 435 IF( KP.NE.K ) 436 $ CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 437* 438* Apply the transformation 439* 440 CALL CGEMV( 'Transpose', K-1, NRHS, CONE, B, LDB, 441 $ A( 1, K ), 1, CONE, B( K, 1 ), LDB ) 442 END IF 443 IF( NOUNIT ) 444 $ CALL CSCAL( NRHS, A( K, K ), B( K, 1 ), LDB ) 445 K = K - 1 446* 447* 2 x 2 pivot block. 448* 449 ELSE 450 IF( K.GT.2 ) THEN 451* 452* Swap the second of pair with Pth 453* 454 KP = ABS( IPIV( K ) ) 455 IF( KP.NE.K ) 456 $ CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 457* 458* Now swap the first of pair with IMAX(r)th 459* 460 KP = ABS( IPIV( K-1 ) ) 461 IF( KP.NE.K-1 ) 462 $ CALL CSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ), 463 $ LDB ) 464* 465* Apply the transformations 466* 467 CALL CGEMV( 'Transpose', K-2, NRHS, CONE, B, LDB, 468 $ A( 1, K ), 1, CONE, B( K, 1 ), LDB ) 469 CALL CGEMV( 'Transpose', K-2, NRHS, CONE, B, LDB, 470 $ A( 1, K-1 ), 1, CONE, B( K-1, 1 ), LDB ) 471 END IF 472* 473* Multiply by the diagonal block if non-unit. 474* 475 IF( NOUNIT ) THEN 476 D11 = A( K-1, K-1 ) 477 D22 = A( K, K ) 478 D12 = A( K-1, K ) 479 D21 = D12 480 DO 80 J = 1, NRHS 481 T1 = B( K-1, J ) 482 T2 = B( K, J ) 483 B( K-1, J ) = D11*T1 + D12*T2 484 B( K, J ) = D21*T1 + D22*T2 485 80 CONTINUE 486 END IF 487 K = K - 2 488 END IF 489 GO TO 70 490 90 CONTINUE 491* 492* Form B := L'*B 493* where L = P(1)*inv(L(1))* ... *P(m)*inv(L(m)) 494* and L' = inv(L'(m))*P(m)* ... *inv(L'(1))*P(1) 495* 496 ELSE 497* 498* Loop forward applying the L-transformations. 499* 500 K = 1 501 100 CONTINUE 502 IF( K.GT.N ) 503 $ GO TO 120 504* 505* 1 x 1 pivot block 506* 507 IF( IPIV( K ).GT.0 ) THEN 508 IF( K.LT.N ) THEN 509* 510* Interchange if P(K) != I. 511* 512 KP = IPIV( K ) 513 IF( KP.NE.K ) 514 $ CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 515* 516* Apply the transformation 517* 518 CALL CGEMV( 'Transpose', N-K, NRHS, CONE, B( K+1, 1 ), 519 $ LDB, A( K+1, K ), 1, CONE, B( K, 1 ), LDB ) 520 END IF 521 IF( NOUNIT ) 522 $ CALL CSCAL( NRHS, A( K, K ), B( K, 1 ), LDB ) 523 K = K + 1 524* 525* 2 x 2 pivot block. 526* 527 ELSE 528 IF( K.LT.N-1 ) THEN 529* 530* Swap the first of pair with Pth 531* 532 KP = ABS( IPIV( K ) ) 533 IF( KP.NE.K ) 534 $ CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 535* 536* Now swap the second of pair with IMAX(r)th 537* 538 KP = ABS( IPIV( K+1 ) ) 539 IF( KP.NE.K+1 ) 540 $ CALL CSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ), 541 $ LDB ) 542* 543* Apply the transformation 544* 545 CALL CGEMV( 'Transpose', N-K-1, NRHS, CONE, 546 $ B( K+2, 1 ), LDB, A( K+2, K+1 ), 1, CONE, 547 $ B( K+1, 1 ), LDB ) 548 CALL CGEMV( 'Transpose', N-K-1, NRHS, CONE, 549 $ B( K+2, 1 ), LDB, A( K+2, K ), 1, CONE, 550 $ B( K, 1 ), LDB ) 551 END IF 552* 553* Multiply by the diagonal block if non-unit. 554* 555 IF( NOUNIT ) THEN 556 D11 = A( K, K ) 557 D22 = A( K+1, K+1 ) 558 D21 = A( K+1, K ) 559 D12 = D21 560 DO 110 J = 1, NRHS 561 T1 = B( K, J ) 562 T2 = B( K+1, J ) 563 B( K, J ) = D11*T1 + D12*T2 564 B( K+1, J ) = D21*T1 + D22*T2 565 110 CONTINUE 566 END IF 567 K = K + 2 568 END IF 569 GO TO 100 570 120 CONTINUE 571 END IF 572 END IF 573 RETURN 574* 575* End of CLAVSY_ROOK 576* 577 END 578