1*> \brief \b DTFTTP copies a triangular matrix from the rectangular full packed format (TF) to the standard packed format (TP). 2* 3* =========== DOCUMENTATION =========== 4* 5* Online html documentation available at 6* http://www.netlib.org/lapack/explore-html/ 7* 8*> \htmlonly 9*> Download DTFTTP + dependencies 10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtfttp.f"> 11*> [TGZ]</a> 12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtfttp.f"> 13*> [ZIP]</a> 14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtfttp.f"> 15*> [TXT]</a> 16*> \endhtmlonly 17* 18* Definition: 19* =========== 20* 21* SUBROUTINE DTFTTP( TRANSR, UPLO, N, ARF, AP, INFO ) 22* 23* .. Scalar Arguments .. 24* CHARACTER TRANSR, UPLO 25* INTEGER INFO, N 26* .. 27* .. Array Arguments .. 28* DOUBLE PRECISION AP( 0: * ), ARF( 0: * ) 29* .. 30* 31* 32*> \par Purpose: 33* ============= 34*> 35*> \verbatim 36*> 37*> DTFTTP copies a triangular matrix A from rectangular full packed 38*> format (TF) to standard packed format (TP). 39*> \endverbatim 40* 41* Arguments: 42* ========== 43* 44*> \param[in] TRANSR 45*> \verbatim 46*> TRANSR is CHARACTER*1 47*> = 'N': ARF is in Normal format; 48*> = 'T': ARF is in Transpose format; 49*> \endverbatim 50*> 51*> \param[in] UPLO 52*> \verbatim 53*> UPLO is CHARACTER*1 54*> = 'U': A is upper triangular; 55*> = 'L': A is lower triangular. 56*> \endverbatim 57*> 58*> \param[in] N 59*> \verbatim 60*> N is INTEGER 61*> The order of the matrix A. N >= 0. 62*> \endverbatim 63*> 64*> \param[in] ARF 65*> \verbatim 66*> ARF is DOUBLE PRECISION array, dimension ( N*(N+1)/2 ), 67*> On entry, the upper or lower triangular matrix A stored in 68*> RFP format. For a further discussion see Notes below. 69*> \endverbatim 70*> 71*> \param[out] AP 72*> \verbatim 73*> AP is DOUBLE PRECISION array, dimension ( N*(N+1)/2 ), 74*> On exit, the upper or lower triangular matrix A, packed 75*> columnwise in a linear array. The j-th column of A is stored 76*> in the array AP as follows: 77*> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; 78*> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. 79*> \endverbatim 80*> 81*> \param[out] INFO 82*> \verbatim 83*> INFO is INTEGER 84*> = 0: successful exit 85*> < 0: if INFO = -i, the i-th argument had an illegal value 86*> \endverbatim 87* 88* Authors: 89* ======== 90* 91*> \author Univ. of Tennessee 92*> \author Univ. of California Berkeley 93*> \author Univ. of Colorado Denver 94*> \author NAG Ltd. 95* 96*> \ingroup doubleOTHERcomputational 97* 98*> \par Further Details: 99* ===================== 100*> 101*> \verbatim 102*> 103*> We first consider Rectangular Full Packed (RFP) Format when N is 104*> even. We give an example where N = 6. 105*> 106*> AP is Upper AP is Lower 107*> 108*> 00 01 02 03 04 05 00 109*> 11 12 13 14 15 10 11 110*> 22 23 24 25 20 21 22 111*> 33 34 35 30 31 32 33 112*> 44 45 40 41 42 43 44 113*> 55 50 51 52 53 54 55 114*> 115*> 116*> Let TRANSR = 'N'. RFP holds AP as follows: 117*> For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last 118*> three columns of AP upper. The lower triangle A(4:6,0:2) consists of 119*> the transpose of the first three columns of AP upper. 120*> For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first 121*> three columns of AP lower. The upper triangle A(0:2,0:2) consists of 122*> the transpose of the last three columns of AP lower. 123*> This covers the case N even and TRANSR = 'N'. 124*> 125*> RFP A RFP A 126*> 127*> 03 04 05 33 43 53 128*> 13 14 15 00 44 54 129*> 23 24 25 10 11 55 130*> 33 34 35 20 21 22 131*> 00 44 45 30 31 32 132*> 01 11 55 40 41 42 133*> 02 12 22 50 51 52 134*> 135*> Now let TRANSR = 'T'. RFP A in both UPLO cases is just the 136*> transpose of RFP A above. One therefore gets: 137*> 138*> 139*> RFP A RFP A 140*> 141*> 03 13 23 33 00 01 02 33 00 10 20 30 40 50 142*> 04 14 24 34 44 11 12 43 44 11 21 31 41 51 143*> 05 15 25 35 45 55 22 53 54 55 22 32 42 52 144*> 145*> 146*> We then consider Rectangular Full Packed (RFP) Format when N is 147*> odd. We give an example where N = 5. 148*> 149*> AP is Upper AP is Lower 150*> 151*> 00 01 02 03 04 00 152*> 11 12 13 14 10 11 153*> 22 23 24 20 21 22 154*> 33 34 30 31 32 33 155*> 44 40 41 42 43 44 156*> 157*> 158*> Let TRANSR = 'N'. RFP holds AP as follows: 159*> For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last 160*> three columns of AP upper. The lower triangle A(3:4,0:1) consists of 161*> the transpose of the first two columns of AP upper. 162*> For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first 163*> three columns of AP lower. The upper triangle A(0:1,1:2) consists of 164*> the transpose of the last two columns of AP lower. 165*> This covers the case N odd and TRANSR = 'N'. 166*> 167*> RFP A RFP A 168*> 169*> 02 03 04 00 33 43 170*> 12 13 14 10 11 44 171*> 22 23 24 20 21 22 172*> 00 33 34 30 31 32 173*> 01 11 44 40 41 42 174*> 175*> Now let TRANSR = 'T'. RFP A in both UPLO cases is just the 176*> transpose of RFP A above. One therefore gets: 177*> 178*> RFP A RFP A 179*> 180*> 02 12 22 00 01 00 10 20 30 40 50 181*> 03 13 23 33 11 33 11 21 31 41 51 182*> 04 14 24 34 44 43 44 22 32 42 52 183*> \endverbatim 184*> 185* ===================================================================== 186 SUBROUTINE DTFTTP( TRANSR, UPLO, N, ARF, AP, INFO ) 187* 188* -- LAPACK computational routine -- 189* -- LAPACK is a software package provided by Univ. of Tennessee, -- 190* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 191* 192* .. Scalar Arguments .. 193 CHARACTER TRANSR, UPLO 194 INTEGER INFO, N 195* .. 196* .. Array Arguments .. 197 DOUBLE PRECISION AP( 0: * ), ARF( 0: * ) 198* .. 199* 200* ===================================================================== 201* 202* .. Parameters .. 203* .. 204* .. Local Scalars .. 205 LOGICAL LOWER, NISODD, NORMALTRANSR 206 INTEGER N1, N2, K, NT 207 INTEGER I, J, IJ 208 INTEGER IJP, JP, LDA, JS 209* .. 210* .. External Functions .. 211 LOGICAL LSAME 212 EXTERNAL LSAME 213* .. 214* .. External Subroutines .. 215 EXTERNAL XERBLA 216* .. 217* .. Executable Statements .. 218* 219* Test the input parameters. 220* 221 INFO = 0 222 NORMALTRANSR = LSAME( TRANSR, 'N' ) 223 LOWER = LSAME( UPLO, 'L' ) 224 IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'T' ) ) THEN 225 INFO = -1 226 ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN 227 INFO = -2 228 ELSE IF( N.LT.0 ) THEN 229 INFO = -3 230 END IF 231 IF( INFO.NE.0 ) THEN 232 CALL XERBLA( 'DTFTTP', -INFO ) 233 RETURN 234 END IF 235* 236* Quick return if possible 237* 238 IF( N.EQ.0 ) 239 $ RETURN 240* 241 IF( N.EQ.1 ) THEN 242 IF( NORMALTRANSR ) THEN 243 AP( 0 ) = ARF( 0 ) 244 ELSE 245 AP( 0 ) = ARF( 0 ) 246 END IF 247 RETURN 248 END IF 249* 250* Size of array ARF(0:NT-1) 251* 252 NT = N*( N+1 ) / 2 253* 254* Set N1 and N2 depending on LOWER 255* 256 IF( LOWER ) THEN 257 N2 = N / 2 258 N1 = N - N2 259 ELSE 260 N1 = N / 2 261 N2 = N - N1 262 END IF 263* 264* If N is odd, set NISODD = .TRUE. 265* If N is even, set K = N/2 and NISODD = .FALSE. 266* 267* set lda of ARF^C; ARF^C is (0:(N+1)/2-1,0:N-noe) 268* where noe = 0 if n is even, noe = 1 if n is odd 269* 270 IF( MOD( N, 2 ).EQ.0 ) THEN 271 K = N / 2 272 NISODD = .FALSE. 273 LDA = N + 1 274 ELSE 275 NISODD = .TRUE. 276 LDA = N 277 END IF 278* 279* ARF^C has lda rows and n+1-noe cols 280* 281 IF( .NOT.NORMALTRANSR ) 282 $ LDA = ( N+1 ) / 2 283* 284* start execution: there are eight cases 285* 286 IF( NISODD ) THEN 287* 288* N is odd 289* 290 IF( NORMALTRANSR ) THEN 291* 292* N is odd and TRANSR = 'N' 293* 294 IF( LOWER ) THEN 295* 296* SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) ) 297* T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0) 298* T1 -> a(0), T2 -> a(n), S -> a(n1); lda = n 299* 300 IJP = 0 301 JP = 0 302 DO J = 0, N2 303 DO I = J, N - 1 304 IJ = I + JP 305 AP( IJP ) = ARF( IJ ) 306 IJP = IJP + 1 307 END DO 308 JP = JP + LDA 309 END DO 310 DO I = 0, N2 - 1 311 DO J = 1 + I, N2 312 IJ = I + J*LDA 313 AP( IJP ) = ARF( IJ ) 314 IJP = IJP + 1 315 END DO 316 END DO 317* 318 ELSE 319* 320* SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1) 321* T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0) 322* T1 -> a(n2), T2 -> a(n1), S -> a(0) 323* 324 IJP = 0 325 DO J = 0, N1 - 1 326 IJ = N2 + J 327 DO I = 0, J 328 AP( IJP ) = ARF( IJ ) 329 IJP = IJP + 1 330 IJ = IJ + LDA 331 END DO 332 END DO 333 JS = 0 334 DO J = N1, N - 1 335 IJ = JS 336 DO IJ = JS, JS + J 337 AP( IJP ) = ARF( IJ ) 338 IJP = IJP + 1 339 END DO 340 JS = JS + LDA 341 END DO 342* 343 END IF 344* 345 ELSE 346* 347* N is odd and TRANSR = 'T' 348* 349 IF( LOWER ) THEN 350* 351* SRPA for LOWER, TRANSPOSE and N is odd 352* T1 -> A(0,0) , T2 -> A(1,0) , S -> A(0,n1) 353* T1 -> a(0+0) , T2 -> a(1+0) , S -> a(0+n1*n1); lda=n1 354* 355 IJP = 0 356 DO I = 0, N2 357 DO IJ = I*( LDA+1 ), N*LDA - 1, LDA 358 AP( IJP ) = ARF( IJ ) 359 IJP = IJP + 1 360 END DO 361 END DO 362 JS = 1 363 DO J = 0, N2 - 1 364 DO IJ = JS, JS + N2 - J - 1 365 AP( IJP ) = ARF( IJ ) 366 IJP = IJP + 1 367 END DO 368 JS = JS + LDA + 1 369 END DO 370* 371 ELSE 372* 373* SRPA for UPPER, TRANSPOSE and N is odd 374* T1 -> A(0,n1+1), T2 -> A(0,n1), S -> A(0,0) 375* T1 -> a(n2*n2), T2 -> a(n1*n2), S -> a(0); lda = n2 376* 377 IJP = 0 378 JS = N2*LDA 379 DO J = 0, N1 - 1 380 DO IJ = JS, JS + J 381 AP( IJP ) = ARF( IJ ) 382 IJP = IJP + 1 383 END DO 384 JS = JS + LDA 385 END DO 386 DO I = 0, N1 387 DO IJ = I, I + ( N1+I )*LDA, LDA 388 AP( IJP ) = ARF( IJ ) 389 IJP = IJP + 1 390 END DO 391 END DO 392* 393 END IF 394* 395 END IF 396* 397 ELSE 398* 399* N is even 400* 401 IF( NORMALTRANSR ) THEN 402* 403* N is even and TRANSR = 'N' 404* 405 IF( LOWER ) THEN 406* 407* SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) ) 408* T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0) 409* T1 -> a(1), T2 -> a(0), S -> a(k+1) 410* 411 IJP = 0 412 JP = 0 413 DO J = 0, K - 1 414 DO I = J, N - 1 415 IJ = 1 + I + JP 416 AP( IJP ) = ARF( IJ ) 417 IJP = IJP + 1 418 END DO 419 JP = JP + LDA 420 END DO 421 DO I = 0, K - 1 422 DO J = I, K - 1 423 IJ = I + J*LDA 424 AP( IJP ) = ARF( IJ ) 425 IJP = IJP + 1 426 END DO 427 END DO 428* 429 ELSE 430* 431* SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) ) 432* T1 -> a(k+1,0) , T2 -> a(k,0), S -> a(0,0) 433* T1 -> a(k+1), T2 -> a(k), S -> a(0) 434* 435 IJP = 0 436 DO J = 0, K - 1 437 IJ = K + 1 + J 438 DO I = 0, J 439 AP( IJP ) = ARF( IJ ) 440 IJP = IJP + 1 441 IJ = IJ + LDA 442 END DO 443 END DO 444 JS = 0 445 DO J = K, N - 1 446 IJ = JS 447 DO IJ = JS, JS + J 448 AP( IJP ) = ARF( IJ ) 449 IJP = IJP + 1 450 END DO 451 JS = JS + LDA 452 END DO 453* 454 END IF 455* 456 ELSE 457* 458* N is even and TRANSR = 'T' 459* 460 IF( LOWER ) THEN 461* 462* SRPA for LOWER, TRANSPOSE and N is even (see paper) 463* T1 -> B(0,1), T2 -> B(0,0), S -> B(0,k+1) 464* T1 -> a(0+k), T2 -> a(0+0), S -> a(0+k*(k+1)); lda=k 465* 466 IJP = 0 467 DO I = 0, K - 1 468 DO IJ = I + ( I+1 )*LDA, ( N+1 )*LDA - 1, LDA 469 AP( IJP ) = ARF( IJ ) 470 IJP = IJP + 1 471 END DO 472 END DO 473 JS = 0 474 DO J = 0, K - 1 475 DO IJ = JS, JS + K - J - 1 476 AP( IJP ) = ARF( IJ ) 477 IJP = IJP + 1 478 END DO 479 JS = JS + LDA + 1 480 END DO 481* 482 ELSE 483* 484* SRPA for UPPER, TRANSPOSE and N is even (see paper) 485* T1 -> B(0,k+1), T2 -> B(0,k), S -> B(0,0) 486* T1 -> a(0+k*(k+1)), T2 -> a(0+k*k), S -> a(0+0)); lda=k 487* 488 IJP = 0 489 JS = ( K+1 )*LDA 490 DO J = 0, K - 1 491 DO IJ = JS, JS + J 492 AP( IJP ) = ARF( IJ ) 493 IJP = IJP + 1 494 END DO 495 JS = JS + LDA 496 END DO 497 DO I = 0, K - 1 498 DO IJ = I, I + ( K+I )*LDA, LDA 499 AP( IJP ) = ARF( IJ ) 500 IJP = IJP + 1 501 END DO 502 END DO 503* 504 END IF 505* 506 END IF 507* 508 END IF 509* 510 RETURN 511* 512* End of DTFTTP 513* 514 END 515