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