1*> \brief \b DLAVSY_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 DLAVSY_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* DOUBLE PRECISION A( LDA, * ), B( LDB, * ) 21* .. 22* 23* 24*> \par Purpose: 25* ============= 26*> 27*> \verbatim 28*> 29*> DLAVSY_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 DSYTRF_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*> If TRANS = 'C', multiplies by U' or D * U' (or L' or D * L') 37*> \endverbatim 38* 39* Arguments: 40* ========== 41* 42*> \param[in] UPLO 43*> \verbatim 44*> UPLO is CHARACTER*1 45*> Specifies whether the factor stored in A is upper or lower 46*> triangular. 47*> = 'U': Upper triangular 48*> = 'L': Lower triangular 49*> \endverbatim 50*> 51*> \param[in] TRANS 52*> \verbatim 53*> TRANS is CHARACTER*1 54*> Specifies the operation to be performed: 55*> = 'N': x := A*x 56*> = 'T': x := A'*x 57*> = 'C': x := A'*x 58*> \endverbatim 59*> 60*> \param[in] DIAG 61*> \verbatim 62*> DIAG is CHARACTER*1 63*> Specifies whether or not the diagonal blocks are unit 64*> matrices. If the diagonal blocks are assumed to be unit, 65*> then A = U or A = L, otherwise A = U*D or A = L*D. 66*> = 'U': Diagonal blocks are assumed to be unit matrices. 67*> = 'N': Diagonal blocks are assumed to be non-unit matrices. 68*> \endverbatim 69*> 70*> \param[in] N 71*> \verbatim 72*> N is INTEGER 73*> The number of rows and columns of the matrix A. N >= 0. 74*> \endverbatim 75*> 76*> \param[in] NRHS 77*> \verbatim 78*> NRHS is INTEGER 79*> The number of right hand sides, i.e., the number of vectors 80*> x to be multiplied by A. NRHS >= 0. 81*> \endverbatim 82*> 83*> \param[in] A 84*> \verbatim 85*> A is DOUBLE PRECISION array, dimension (LDA,N) 86*> The block diagonal matrix D and the multipliers used to 87*> obtain the factor U or L as computed by DSYTRF_ROOK. 88*> Stored as a 2-D triangular matrix. 89*> \endverbatim 90*> 91*> \param[in] LDA 92*> \verbatim 93*> LDA is INTEGER 94*> The leading dimension of the array A. LDA >= max(1,N). 95*> \endverbatim 96*> 97*> \param[in] IPIV 98*> \verbatim 99*> IPIV is INTEGER array, dimension (N) 100*> Details of the interchanges and the block structure of D, 101*> as determined by DSYTRF_ROOK. 102*> 103*> If UPLO = 'U': 104*> If IPIV(k) > 0, then rows and columns k and IPIV(k) 105*> were interchanged and D(k,k) is a 1-by-1 diagonal block. 106*> (If IPIV( k ) = k, no interchange was done). 107*> 108*> If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and 109*> columns k and -IPIV(k) were interchanged and rows and 110*> columns k-1 and -IPIV(k-1) were inerchaged, 111*> D(k-1:k,k-1:k) is a 2-by-2 diagonal block. 112*> 113*> If UPLO = 'L': 114*> If IPIV(k) > 0, then rows and columns k and IPIV(k) 115*> were interchanged and D(k,k) is a 1-by-1 diagonal block. 116*> (If IPIV( k ) = k, no interchange was done). 117*> 118*> If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and 119*> columns k and -IPIV(k) were interchanged and rows and 120*> columns k+1 and -IPIV(k+1) were inerchaged, 121*> D(k:k+1,k:k+1) is a 2-by-2 diagonal block. 122*> \endverbatim 123*> 124*> \param[in,out] B 125*> \verbatim 126*> B is DOUBLE PRECISION array, dimension (LDB,NRHS) 127*> On entry, B contains NRHS vectors of length N. 128*> On exit, B is overwritten with the product A * B. 129*> \endverbatim 130*> 131*> \param[in] LDB 132*> \verbatim 133*> LDB is INTEGER 134*> The leading dimension of the array B. LDB >= max(1,N). 135*> \endverbatim 136*> 137*> \param[out] INFO 138*> \verbatim 139*> INFO is INTEGER 140*> = 0: successful exit 141*> < 0: if INFO = -k, the k-th argument had an illegal value 142*> \endverbatim 143* 144* Authors: 145* ======== 146* 147*> \author Univ. of Tennessee 148*> \author Univ. of California Berkeley 149*> \author Univ. of Colorado Denver 150*> \author NAG Ltd. 151* 152*> \date November 2013 153* 154*> \ingroup double_lin 155* 156* ===================================================================== 157 SUBROUTINE DLAVSY_ROOK( UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, 158 $ B, LDB, INFO ) 159* 160* -- LAPACK test routine (version 3.5.0) -- 161* -- LAPACK is a software package provided by Univ. of Tennessee, -- 162* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 163* November 2013 164* 165* .. Scalar Arguments .. 166 CHARACTER DIAG, TRANS, UPLO 167 INTEGER INFO, LDA, LDB, N, NRHS 168* .. 169* .. Array Arguments .. 170 INTEGER IPIV( * ) 171 DOUBLE PRECISION A( LDA, * ), B( LDB, * ) 172* .. 173* 174* ===================================================================== 175* 176* .. Parameters .. 177 DOUBLE PRECISION ONE 178 PARAMETER ( ONE = 1.0D+0 ) 179* .. 180* .. Local Scalars .. 181 LOGICAL NOUNIT 182 INTEGER J, K, KP 183 DOUBLE PRECISION D11, D12, D21, D22, T1, T2 184* .. 185* .. External Functions .. 186 LOGICAL LSAME 187 EXTERNAL LSAME 188* .. 189* .. External Subroutines .. 190 EXTERNAL DGEMV, DGER, DSCAL, DSWAP, XERBLA 191* .. 192* .. Intrinsic Functions .. 193 INTRINSIC ABS, MAX 194* .. 195* .. Executable Statements .. 196* 197* Test the input parameters. 198* 199 INFO = 0 200 IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 201 INFO = -1 202 ELSE IF( .NOT.LSAME( TRANS, 'N' ) .AND. .NOT. 203 $ LSAME( TRANS, 'T' ) .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN 204 INFO = -2 205 ELSE IF( .NOT.LSAME( DIAG, 'U' ) .AND. .NOT.LSAME( DIAG, 'N' ) ) 206 $ THEN 207 INFO = -3 208 ELSE IF( N.LT.0 ) THEN 209 INFO = -4 210 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 211 INFO = -6 212 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN 213 INFO = -9 214 END IF 215 IF( INFO.NE.0 ) THEN 216 CALL XERBLA( 'DLAVSY_ROOK ', -INFO ) 217 RETURN 218 END IF 219* 220* Quick return if possible. 221* 222 IF( N.EQ.0 ) 223 $ RETURN 224* 225 NOUNIT = LSAME( DIAG, 'N' ) 226*------------------------------------------ 227* 228* Compute B := A * B (No transpose) 229* 230*------------------------------------------ 231 IF( LSAME( TRANS, 'N' ) ) THEN 232* 233* Compute B := U*B 234* where U = P(m)*inv(U(m))* ... *P(1)*inv(U(1)) 235* 236 IF( LSAME( UPLO, 'U' ) ) THEN 237* 238* Loop forward applying the transformations. 239* 240 K = 1 241 10 CONTINUE 242 IF( K.GT.N ) 243 $ GO TO 30 244 IF( IPIV( K ).GT.0 ) THEN 245* 246* 1 x 1 pivot block 247* 248* Multiply by the diagonal element if forming U * D. 249* 250 IF( NOUNIT ) 251 $ CALL DSCAL( NRHS, A( K, K ), B( K, 1 ), LDB ) 252* 253* Multiply by P(K) * inv(U(K)) if K > 1. 254* 255 IF( K.GT.1 ) THEN 256* 257* Apply the transformation. 258* 259 CALL DGER( K-1, NRHS, ONE, A( 1, K ), 1, B( K, 1 ), 260 $ LDB, B( 1, 1 ), LDB ) 261* 262* Interchange if P(K) .ne. I. 263* 264 KP = IPIV( K ) 265 IF( KP.NE.K ) 266 $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 267 END IF 268 K = K + 1 269 ELSE 270* 271* 2 x 2 pivot block 272* 273* Multiply by the diagonal block if forming U * D. 274* 275 IF( NOUNIT ) THEN 276 D11 = A( K, K ) 277 D22 = A( K+1, K+1 ) 278 D12 = A( K, K+1 ) 279 D21 = D12 280 DO 20 J = 1, NRHS 281 T1 = B( K, J ) 282 T2 = B( K+1, J ) 283 B( K, J ) = D11*T1 + D12*T2 284 B( K+1, J ) = D21*T1 + D22*T2 285 20 CONTINUE 286 END IF 287* 288* Multiply by P(K) * inv(U(K)) if K > 1. 289* 290 IF( K.GT.1 ) THEN 291* 292* Apply the transformations. 293* 294 CALL DGER( K-1, NRHS, ONE, A( 1, K ), 1, B( K, 1 ), 295 $ LDB, B( 1, 1 ), LDB ) 296 CALL DGER( K-1, NRHS, ONE, A( 1, K+1 ), 1, 297 $ B( K+1, 1 ), LDB, B( 1, 1 ), LDB ) 298* 299* Interchange if a permutation was applied at the 300* K-th step of the factorization. 301* 302* Swap the first of pair with IMAXth 303* 304 KP = ABS( IPIV( K ) ) 305 IF( KP.NE.K ) 306 $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 307* 308* NOW swap the first of pair with Pth 309* 310 KP = ABS( IPIV( K+1 ) ) 311 IF( KP.NE.K+1 ) 312 $ CALL DSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ), 313 $ LDB ) 314 END IF 315 K = K + 2 316 END IF 317 GO TO 10 318 30 CONTINUE 319* 320* Compute B := L*B 321* where L = P(1)*inv(L(1))* ... *P(m)*inv(L(m)) . 322* 323 ELSE 324* 325* Loop backward applying the transformations to B. 326* 327 K = N 328 40 CONTINUE 329 IF( K.LT.1 ) 330 $ GO TO 60 331* 332* Test the pivot index. If greater than zero, a 1 x 1 333* pivot was used, otherwise a 2 x 2 pivot was used. 334* 335 IF( IPIV( K ).GT.0 ) THEN 336* 337* 1 x 1 pivot block: 338* 339* Multiply by the diagonal element if forming L * D. 340* 341 IF( NOUNIT ) 342 $ CALL DSCAL( NRHS, A( K, K ), B( K, 1 ), LDB ) 343* 344* Multiply by P(K) * inv(L(K)) if K < N. 345* 346 IF( K.NE.N ) THEN 347 KP = IPIV( K ) 348* 349* Apply the transformation. 350* 351 CALL DGER( N-K, NRHS, ONE, A( K+1, K ), 1, B( K, 1 ), 352 $ LDB, B( K+1, 1 ), LDB ) 353* 354* Interchange if a permutation was applied at the 355* K-th step of the factorization. 356* 357 IF( KP.NE.K ) 358 $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 359 END IF 360 K = K - 1 361* 362 ELSE 363* 364* 2 x 2 pivot block: 365* 366* Multiply by the diagonal block if forming L * D. 367* 368 IF( NOUNIT ) THEN 369 D11 = A( K-1, K-1 ) 370 D22 = A( K, K ) 371 D21 = A( K, K-1 ) 372 D12 = D21 373 DO 50 J = 1, NRHS 374 T1 = B( K-1, J ) 375 T2 = B( K, J ) 376 B( K-1, J ) = D11*T1 + D12*T2 377 B( K, J ) = D21*T1 + D22*T2 378 50 CONTINUE 379 END IF 380* 381* Multiply by P(K) * inv(L(K)) if K < N. 382* 383 IF( K.NE.N ) THEN 384* 385* Apply the transformation. 386* 387 CALL DGER( N-K, NRHS, ONE, A( K+1, K ), 1, B( K, 1 ), 388 $ LDB, B( K+1, 1 ), LDB ) 389 CALL DGER( N-K, NRHS, ONE, A( K+1, K-1 ), 1, 390 $ B( K-1, 1 ), LDB, B( K+1, 1 ), LDB ) 391* 392* Interchange if a permutation was applied at the 393* K-th step of the factorization. 394* 395* Swap the second of pair with IMAXth 396* 397 KP = ABS( IPIV( K ) ) 398 IF( KP.NE.K ) 399 $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 400* 401* NOW swap the first of pair with Pth 402* 403 KP = ABS( IPIV( K-1 ) ) 404 IF( KP.NE.K-1 ) 405 $ CALL DSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ), 406 $ LDB ) 407 END IF 408 K = K - 2 409 END IF 410 GO TO 40 411 60 CONTINUE 412 END IF 413*---------------------------------------- 414* 415* Compute B := A' * B (transpose) 416* 417*---------------------------------------- 418 ELSE 419* 420* Form B := U'*B 421* where U = P(m)*inv(U(m))* ... *P(1)*inv(U(1)) 422* and U' = inv(U'(1))*P(1)* ... *inv(U'(m))*P(m) 423* 424 IF( LSAME( UPLO, 'U' ) ) THEN 425* 426* Loop backward applying the transformations. 427* 428 K = N 429 70 CONTINUE 430 IF( K.LT.1 ) 431 $ GO TO 90 432* 433* 1 x 1 pivot block. 434* 435 IF( IPIV( K ).GT.0 ) THEN 436 IF( K.GT.1 ) THEN 437* 438* Interchange if P(K) .ne. I. 439* 440 KP = IPIV( K ) 441 IF( KP.NE.K ) 442 $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 443* 444* Apply the transformation 445* 446 CALL DGEMV( 'Transpose', K-1, NRHS, ONE, B, LDB, 447 $ A( 1, K ), 1, ONE, B( K, 1 ), LDB ) 448 END IF 449 IF( NOUNIT ) 450 $ CALL DSCAL( NRHS, A( K, K ), B( K, 1 ), LDB ) 451 K = K - 1 452* 453* 2 x 2 pivot block. 454* 455 ELSE 456 IF( K.GT.2 ) THEN 457* 458* Swap the second of pair with Pth 459* 460 KP = ABS( IPIV( K ) ) 461 IF( KP.NE.K ) 462 $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 463* 464* Now swap the first of pair with IMAX(r)th 465* 466 KP = ABS( IPIV( K-1 ) ) 467 IF( KP.NE.K-1 ) 468 $ CALL DSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ), 469 $ LDB ) 470* 471* Apply the transformations 472* 473 CALL DGEMV( 'Transpose', K-2, NRHS, ONE, B, LDB, 474 $ A( 1, K ), 1, ONE, B( K, 1 ), LDB ) 475 CALL DGEMV( 'Transpose', K-2, NRHS, ONE, B, LDB, 476 $ A( 1, K-1 ), 1, ONE, B( K-1, 1 ), LDB ) 477 END IF 478* 479* Multiply by the diagonal block if non-unit. 480* 481 IF( NOUNIT ) THEN 482 D11 = A( K-1, K-1 ) 483 D22 = A( K, K ) 484 D12 = A( K-1, K ) 485 D21 = D12 486 DO 80 J = 1, NRHS 487 T1 = B( K-1, J ) 488 T2 = B( K, J ) 489 B( K-1, J ) = D11*T1 + D12*T2 490 B( K, J ) = D21*T1 + D22*T2 491 80 CONTINUE 492 END IF 493 K = K - 2 494 END IF 495 GO TO 70 496 90 CONTINUE 497* 498* Form B := L'*B 499* where L = P(1)*inv(L(1))* ... *P(m)*inv(L(m)) 500* and L' = inv(L'(m))*P(m)* ... *inv(L'(1))*P(1) 501* 502 ELSE 503* 504* Loop forward applying the L-transformations. 505* 506 K = 1 507 100 CONTINUE 508 IF( K.GT.N ) 509 $ GO TO 120 510* 511* 1 x 1 pivot block 512* 513 IF( IPIV( K ).GT.0 ) THEN 514 IF( K.LT.N ) THEN 515* 516* Interchange if P(K) .ne. I. 517* 518 KP = IPIV( K ) 519 IF( KP.NE.K ) 520 $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 521* 522* Apply the transformation 523* 524 CALL DGEMV( 'Transpose', N-K, NRHS, ONE, B( K+1, 1 ), 525 $ LDB, A( K+1, K ), 1, ONE, B( K, 1 ), LDB ) 526 END IF 527 IF( NOUNIT ) 528 $ CALL DSCAL( NRHS, A( K, K ), B( K, 1 ), LDB ) 529 K = K + 1 530* 531* 2 x 2 pivot block. 532* 533 ELSE 534 IF( K.LT.N-1 ) THEN 535* 536* Swap the first of pair with Pth 537* 538 KP = ABS( IPIV( K ) ) 539 IF( KP.NE.K ) 540 $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 541* 542* Now swap the second of pair with IMAX(r)th 543* 544 KP = ABS( IPIV( K+1 ) ) 545 IF( KP.NE.K+1 ) 546 $ CALL DSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ), 547 $ LDB ) 548* 549* Apply the transformation 550* 551 CALL DGEMV( 'Transpose', N-K-1, NRHS, ONE, 552 $ B( K+2, 1 ), LDB, A( K+2, K+1 ), 1, ONE, 553 $ B( K+1, 1 ), LDB ) 554 CALL DGEMV( 'Transpose', N-K-1, NRHS, ONE, 555 $ B( K+2, 1 ), LDB, A( K+2, K ), 1, ONE, 556 $ B( K, 1 ), LDB ) 557 END IF 558* 559* Multiply by the diagonal block if non-unit. 560* 561 IF( NOUNIT ) THEN 562 D11 = A( K, K ) 563 D22 = A( K+1, K+1 ) 564 D21 = A( K+1, K ) 565 D12 = D21 566 DO 110 J = 1, NRHS 567 T1 = B( K, J ) 568 T2 = B( K+1, J ) 569 B( K, J ) = D11*T1 + D12*T2 570 B( K+1, J ) = D21*T1 + D22*T2 571 110 CONTINUE 572 END IF 573 K = K + 2 574 END IF 575 GO TO 100 576 120 CONTINUE 577 END IF 578* 579 END IF 580 RETURN 581* 582* End of DLAVSY_ROOK 583* 584 END 585