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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b ZTPTTF 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download ZTPTTF + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztpttf.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ztpttf.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztpttf.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE ZTPTTF( TRANSR, UPLO, N, AP, ARF, INFO ) 00022 * 00023 * .. Scalar Arguments .. 00024 * CHARACTER TRANSR, UPLO 00025 * INTEGER INFO, N 00026 * .. 00027 * .. Array Arguments .. 00028 * COMPLEX*16 AP( 0: * ), ARF( 0: * ) 00029 * 00030 * 00031 *> \par Purpose: 00032 * ============= 00033 *> 00034 *> \verbatim 00035 *> 00036 *> ZTPTTF copies a triangular matrix A from standard packed format (TP) 00037 *> to rectangular full packed format (TF). 00038 *> \endverbatim 00039 * 00040 * Arguments: 00041 * ========== 00042 * 00043 *> \param[in] TRANSR 00044 *> \verbatim 00045 *> TRANSR is CHARACTER*1 00046 *> = 'N': ARF in Normal format is wanted; 00047 *> = 'C': ARF in Conjugate-transpose format is wanted. 00048 *> \endverbatim 00049 *> 00050 *> \param[in] UPLO 00051 *> \verbatim 00052 *> UPLO is CHARACTER*1 00053 *> = 'U': A is upper triangular; 00054 *> = 'L': A is lower triangular. 00055 *> \endverbatim 00056 *> 00057 *> \param[in] N 00058 *> \verbatim 00059 *> N is INTEGER 00060 *> The order of the matrix A. N >= 0. 00061 *> \endverbatim 00062 *> 00063 *> \param[in] AP 00064 *> \verbatim 00065 *> AP is COMPLEX*16 array, dimension ( N*(N+1)/2 ), 00066 *> On entry, the upper or lower triangular matrix A, packed 00067 *> columnwise in a linear array. The j-th column of A is stored 00068 *> in the array AP as follows: 00069 *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; 00070 *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. 00071 *> \endverbatim 00072 *> 00073 *> \param[out] ARF 00074 *> \verbatim 00075 *> ARF is COMPLEX*16 array, dimension ( N*(N+1)/2 ), 00076 *> On exit, the upper or lower triangular matrix A stored in 00077 *> RFP format. For a further discussion see Notes below. 00078 *> \endverbatim 00079 *> 00080 *> \param[out] INFO 00081 *> \verbatim 00082 *> INFO is INTEGER 00083 *> = 0: successful exit 00084 *> < 0: if INFO = -i, the i-th argument had an illegal value 00085 *> \endverbatim 00086 * 00087 * Authors: 00088 * ======== 00089 * 00090 *> \author Univ. of Tennessee 00091 *> \author Univ. of California Berkeley 00092 *> \author Univ. of Colorado Denver 00093 *> \author NAG Ltd. 00094 * 00095 *> \date November 2011 00096 * 00097 *> \ingroup complex16OTHERcomputational 00098 * 00099 *> \par Further Details: 00100 * ===================== 00101 *> 00102 *> \verbatim 00103 *> 00104 *> We first consider Standard Packed Format when N is even. 00105 *> We give an example where N = 6. 00106 *> 00107 *> AP is Upper AP is Lower 00108 *> 00109 *> 00 01 02 03 04 05 00 00110 *> 11 12 13 14 15 10 11 00111 *> 22 23 24 25 20 21 22 00112 *> 33 34 35 30 31 32 33 00113 *> 44 45 40 41 42 43 44 00114 *> 55 50 51 52 53 54 55 00115 *> 00116 *> 00117 *> Let TRANSR = 'N'. RFP holds AP as follows: 00118 *> For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last 00119 *> three columns of AP upper. The lower triangle A(4:6,0:2) consists of 00120 *> conjugate-transpose of the first three columns of AP upper. 00121 *> For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first 00122 *> three columns of AP lower. The upper triangle A(0:2,0:2) consists of 00123 *> conjugate-transpose of the last three columns of AP lower. 00124 *> To denote conjugate we place -- above the element. This covers the 00125 *> case N even and TRANSR = 'N'. 00126 *> 00127 *> RFP A RFP A 00128 *> 00129 *> -- -- -- 00130 *> 03 04 05 33 43 53 00131 *> -- -- 00132 *> 13 14 15 00 44 54 00133 *> -- 00134 *> 23 24 25 10 11 55 00135 *> 00136 *> 33 34 35 20 21 22 00137 *> -- 00138 *> 00 44 45 30 31 32 00139 *> -- -- 00140 *> 01 11 55 40 41 42 00141 *> -- -- -- 00142 *> 02 12 22 50 51 52 00143 *> 00144 *> Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate- 00145 *> transpose of RFP A above. One therefore gets: 00146 *> 00147 *> 00148 *> RFP A RFP A 00149 *> 00150 *> -- -- -- -- -- -- -- -- -- -- 00151 *> 03 13 23 33 00 01 02 33 00 10 20 30 40 50 00152 *> -- -- -- -- -- -- -- -- -- -- 00153 *> 04 14 24 34 44 11 12 43 44 11 21 31 41 51 00154 *> -- -- -- -- -- -- -- -- -- -- 00155 *> 05 15 25 35 45 55 22 53 54 55 22 32 42 52 00156 *> 00157 *> 00158 *> We next consider Standard Packed Format when N is odd. 00159 *> We give an example where N = 5. 00160 *> 00161 *> AP is Upper AP is Lower 00162 *> 00163 *> 00 01 02 03 04 00 00164 *> 11 12 13 14 10 11 00165 *> 22 23 24 20 21 22 00166 *> 33 34 30 31 32 33 00167 *> 44 40 41 42 43 44 00168 *> 00169 *> 00170 *> Let TRANSR = 'N'. RFP holds AP as follows: 00171 *> For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last 00172 *> three columns of AP upper. The lower triangle A(3:4,0:1) consists of 00173 *> conjugate-transpose of the first two columns of AP upper. 00174 *> For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first 00175 *> three columns of AP lower. The upper triangle A(0:1,1:2) consists of 00176 *> conjugate-transpose of the last two columns of AP lower. 00177 *> To denote conjugate we place -- above the element. This covers the 00178 *> case N odd and TRANSR = 'N'. 00179 *> 00180 *> RFP A RFP A 00181 *> 00182 *> -- -- 00183 *> 02 03 04 00 33 43 00184 *> -- 00185 *> 12 13 14 10 11 44 00186 *> 00187 *> 22 23 24 20 21 22 00188 *> -- 00189 *> 00 33 34 30 31 32 00190 *> -- -- 00191 *> 01 11 44 40 41 42 00192 *> 00193 *> Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate- 00194 *> transpose of RFP A above. One therefore gets: 00195 *> 00196 *> 00197 *> RFP A RFP A 00198 *> 00199 *> -- -- -- -- -- -- -- -- -- 00200 *> 02 12 22 00 01 00 10 20 30 40 50 00201 *> -- -- -- -- -- -- -- -- -- 00202 *> 03 13 23 33 11 33 11 21 31 41 51 00203 *> -- -- -- -- -- -- -- -- -- 00204 *> 04 14 24 34 44 43 44 22 32 42 52 00205 *> \endverbatim 00206 *> 00207 * ===================================================================== 00208 SUBROUTINE ZTPTTF( TRANSR, UPLO, N, AP, ARF, INFO ) 00209 * 00210 * -- LAPACK computational routine (version 3.4.0) -- 00211 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00212 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00213 * November 2011 00214 * 00215 * .. Scalar Arguments .. 00216 CHARACTER TRANSR, UPLO 00217 INTEGER INFO, N 00218 * .. 00219 * .. Array Arguments .. 00220 COMPLEX*16 AP( 0: * ), ARF( 0: * ) 00221 * 00222 * ===================================================================== 00223 * 00224 * .. Parameters .. 00225 * .. 00226 * .. Local Scalars .. 00227 LOGICAL LOWER, NISODD, NORMALTRANSR 00228 INTEGER N1, N2, K, NT 00229 INTEGER I, J, IJ 00230 INTEGER IJP, JP, LDA, JS 00231 * .. 00232 * .. External Functions .. 00233 LOGICAL LSAME 00234 EXTERNAL LSAME 00235 * .. 00236 * .. External Subroutines .. 00237 EXTERNAL XERBLA 00238 * .. 00239 * .. Intrinsic Functions .. 00240 INTRINSIC DCONJG, MOD 00241 * .. 00242 * .. Executable Statements .. 00243 * 00244 * Test the input parameters. 00245 * 00246 INFO = 0 00247 NORMALTRANSR = LSAME( TRANSR, 'N' ) 00248 LOWER = LSAME( UPLO, 'L' ) 00249 IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'C' ) ) THEN 00250 INFO = -1 00251 ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN 00252 INFO = -2 00253 ELSE IF( N.LT.0 ) THEN 00254 INFO = -3 00255 END IF 00256 IF( INFO.NE.0 ) THEN 00257 CALL XERBLA( 'ZTPTTF', -INFO ) 00258 RETURN 00259 END IF 00260 * 00261 * Quick return if possible 00262 * 00263 IF( N.EQ.0 ) 00264 $ RETURN 00265 * 00266 IF( N.EQ.1 ) THEN 00267 IF( NORMALTRANSR ) THEN 00268 ARF( 0 ) = AP( 0 ) 00269 ELSE 00270 ARF( 0 ) = DCONJG( AP( 0 ) ) 00271 END IF 00272 RETURN 00273 END IF 00274 * 00275 * Size of array ARF(0:NT-1) 00276 * 00277 NT = N*( N+1 ) / 2 00278 * 00279 * Set N1 and N2 depending on LOWER 00280 * 00281 IF( LOWER ) THEN 00282 N2 = N / 2 00283 N1 = N - N2 00284 ELSE 00285 N1 = N / 2 00286 N2 = N - N1 00287 END IF 00288 * 00289 * If N is odd, set NISODD = .TRUE. 00290 * If N is even, set K = N/2 and NISODD = .FALSE. 00291 * 00292 * set lda of ARF^C; ARF^C is (0:(N+1)/2-1,0:N-noe) 00293 * where noe = 0 if n is even, noe = 1 if n is odd 00294 * 00295 IF( MOD( N, 2 ).EQ.0 ) THEN 00296 K = N / 2 00297 NISODD = .FALSE. 00298 LDA = N + 1 00299 ELSE 00300 NISODD = .TRUE. 00301 LDA = N 00302 END IF 00303 * 00304 * ARF^C has lda rows and n+1-noe cols 00305 * 00306 IF( .NOT.NORMALTRANSR ) 00307 $ LDA = ( N+1 ) / 2 00308 * 00309 * start execution: there are eight cases 00310 * 00311 IF( NISODD ) THEN 00312 * 00313 * N is odd 00314 * 00315 IF( NORMALTRANSR ) THEN 00316 * 00317 * N is odd and TRANSR = 'N' 00318 * 00319 IF( LOWER ) THEN 00320 * 00321 * SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) ) 00322 * T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0) 00323 * T1 -> a(0), T2 -> a(n), S -> a(n1); lda = n 00324 * 00325 IJP = 0 00326 JP = 0 00327 DO J = 0, N2 00328 DO I = J, N - 1 00329 IJ = I + JP 00330 ARF( IJ ) = AP( IJP ) 00331 IJP = IJP + 1 00332 END DO 00333 JP = JP + LDA 00334 END DO 00335 DO I = 0, N2 - 1 00336 DO J = 1 + I, N2 00337 IJ = I + J*LDA 00338 ARF( IJ ) = DCONJG( AP( IJP ) ) 00339 IJP = IJP + 1 00340 END DO 00341 END DO 00342 * 00343 ELSE 00344 * 00345 * SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1) 00346 * T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0) 00347 * T1 -> a(n2), T2 -> a(n1), S -> a(0) 00348 * 00349 IJP = 0 00350 DO J = 0, N1 - 1 00351 IJ = N2 + J 00352 DO I = 0, J 00353 ARF( IJ ) = DCONJG( AP( IJP ) ) 00354 IJP = IJP + 1 00355 IJ = IJ + LDA 00356 END DO 00357 END DO 00358 JS = 0 00359 DO J = N1, N - 1 00360 IJ = JS 00361 DO IJ = JS, JS + J 00362 ARF( IJ ) = AP( IJP ) 00363 IJP = IJP + 1 00364 END DO 00365 JS = JS + LDA 00366 END DO 00367 * 00368 END IF 00369 * 00370 ELSE 00371 * 00372 * N is odd and TRANSR = 'C' 00373 * 00374 IF( LOWER ) THEN 00375 * 00376 * SRPA for LOWER, TRANSPOSE and N is odd 00377 * T1 -> A(0,0) , T2 -> A(1,0) , S -> A(0,n1) 00378 * T1 -> a(0+0) , T2 -> a(1+0) , S -> a(0+n1*n1); lda=n1 00379 * 00380 IJP = 0 00381 DO I = 0, N2 00382 DO IJ = I*( LDA+1 ), N*LDA - 1, LDA 00383 ARF( IJ ) = DCONJG( AP( IJP ) ) 00384 IJP = IJP + 1 00385 END DO 00386 END DO 00387 JS = 1 00388 DO J = 0, N2 - 1 00389 DO IJ = JS, JS + N2 - J - 1 00390 ARF( IJ ) = AP( IJP ) 00391 IJP = IJP + 1 00392 END DO 00393 JS = JS + LDA + 1 00394 END DO 00395 * 00396 ELSE 00397 * 00398 * SRPA for UPPER, TRANSPOSE and N is odd 00399 * T1 -> A(0,n1+1), T2 -> A(0,n1), S -> A(0,0) 00400 * T1 -> a(n2*n2), T2 -> a(n1*n2), S -> a(0); lda = n2 00401 * 00402 IJP = 0 00403 JS = N2*LDA 00404 DO J = 0, N1 - 1 00405 DO IJ = JS, JS + J 00406 ARF( IJ ) = AP( IJP ) 00407 IJP = IJP + 1 00408 END DO 00409 JS = JS + LDA 00410 END DO 00411 DO I = 0, N1 00412 DO IJ = I, I + ( N1+I )*LDA, LDA 00413 ARF( IJ ) = DCONJG( AP( IJP ) ) 00414 IJP = IJP + 1 00415 END DO 00416 END DO 00417 * 00418 END IF 00419 * 00420 END IF 00421 * 00422 ELSE 00423 * 00424 * N is even 00425 * 00426 IF( NORMALTRANSR ) THEN 00427 * 00428 * N is even and TRANSR = 'N' 00429 * 00430 IF( LOWER ) THEN 00431 * 00432 * SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) ) 00433 * T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0) 00434 * T1 -> a(1), T2 -> a(0), S -> a(k+1) 00435 * 00436 IJP = 0 00437 JP = 0 00438 DO J = 0, K - 1 00439 DO I = J, N - 1 00440 IJ = 1 + I + JP 00441 ARF( IJ ) = AP( IJP ) 00442 IJP = IJP + 1 00443 END DO 00444 JP = JP + LDA 00445 END DO 00446 DO I = 0, K - 1 00447 DO J = I, K - 1 00448 IJ = I + J*LDA 00449 ARF( IJ ) = DCONJG( AP( IJP ) ) 00450 IJP = IJP + 1 00451 END DO 00452 END DO 00453 * 00454 ELSE 00455 * 00456 * SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) ) 00457 * T1 -> a(k+1,0) , T2 -> a(k,0), S -> a(0,0) 00458 * T1 -> a(k+1), T2 -> a(k), S -> a(0) 00459 * 00460 IJP = 0 00461 DO J = 0, K - 1 00462 IJ = K + 1 + J 00463 DO I = 0, J 00464 ARF( IJ ) = DCONJG( AP( IJP ) ) 00465 IJP = IJP + 1 00466 IJ = IJ + LDA 00467 END DO 00468 END DO 00469 JS = 0 00470 DO J = K, N - 1 00471 IJ = JS 00472 DO IJ = JS, JS + J 00473 ARF( IJ ) = AP( IJP ) 00474 IJP = IJP + 1 00475 END DO 00476 JS = JS + LDA 00477 END DO 00478 * 00479 END IF 00480 * 00481 ELSE 00482 * 00483 * N is even and TRANSR = 'C' 00484 * 00485 IF( LOWER ) THEN 00486 * 00487 * SRPA for LOWER, TRANSPOSE and N is even (see paper) 00488 * T1 -> B(0,1), T2 -> B(0,0), S -> B(0,k+1) 00489 * T1 -> a(0+k), T2 -> a(0+0), S -> a(0+k*(k+1)); lda=k 00490 * 00491 IJP = 0 00492 DO I = 0, K - 1 00493 DO IJ = I + ( I+1 )*LDA, ( N+1 )*LDA - 1, LDA 00494 ARF( IJ ) = DCONJG( AP( IJP ) ) 00495 IJP = IJP + 1 00496 END DO 00497 END DO 00498 JS = 0 00499 DO J = 0, K - 1 00500 DO IJ = JS, JS + K - J - 1 00501 ARF( IJ ) = AP( IJP ) 00502 IJP = IJP + 1 00503 END DO 00504 JS = JS + LDA + 1 00505 END DO 00506 * 00507 ELSE 00508 * 00509 * SRPA for UPPER, TRANSPOSE and N is even (see paper) 00510 * T1 -> B(0,k+1), T2 -> B(0,k), S -> B(0,0) 00511 * T1 -> a(0+k*(k+1)), T2 -> a(0+k*k), S -> a(0+0)); lda=k 00512 * 00513 IJP = 0 00514 JS = ( K+1 )*LDA 00515 DO J = 0, K - 1 00516 DO IJ = JS, JS + J 00517 ARF( IJ ) = AP( IJP ) 00518 IJP = IJP + 1 00519 END DO 00520 JS = JS + LDA 00521 END DO 00522 DO I = 0, K - 1 00523 DO IJ = I, I + ( K+I )*LDA, LDA 00524 ARF( IJ ) = DCONJG( AP( IJP ) ) 00525 IJP = IJP + 1 00526 END DO 00527 END DO 00528 * 00529 END IF 00530 * 00531 END IF 00532 * 00533 END IF 00534 * 00535 RETURN 00536 * 00537 * End of ZTPTTF 00538 * 00539 END