|
11947 | 11947 |
|
11948 | 11948 | \rSec3[linalg.helpers.mandates]{Mandates}
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11949 | 11949 |
|
| 11950 | +\pnum |
11950 | 11951 | \begin{note}
|
11951 | 11952 | These exposition-only helper functions use
|
11952 | 11953 | the less constraining input concepts even for the output arguments,
|
|
12005 | 12006 |
|
12006 | 12007 | \rSec3[linalg.helpers.precond]{Preconditions}
|
12007 | 12008 |
|
| 12009 | +\pnum |
12008 | 12010 | \begin{note}
|
12009 | 12011 | These exposition-only helper functions use
|
12010 | 12012 | the less constraining input concepts even for the output arguments,
|
|
12853 | 12855 | \end{itemdecl}
|
12854 | 12856 |
|
12855 | 12857 | \begin{itemdescr}
|
| 12858 | +\pnum |
12856 | 12859 | \begin{note}
|
12857 | 12860 | These functions correspond to the BLAS function \tcode{xROT}\supercite{blas1}.
|
12858 | 12861 | \end{note}
|
|
12884 | 12887 | \end{itemdecl}
|
12885 | 12888 |
|
12886 | 12889 | \begin{itemdescr}
|
| 12890 | +\pnum |
12887 | 12891 | \begin{note}
|
12888 | 12892 | These functions correspond to the BLAS function \tcode{xSWAP}\supercite{blas1}.
|
12889 | 12893 | \end{note}
|
|
12919 | 12923 | \end{itemdecl}
|
12920 | 12924 |
|
12921 | 12925 | \begin{itemdescr}
|
| 12926 | +\pnum |
12922 | 12927 | \begin{note}
|
12923 | 12928 | These functions correspond to the BLAS function \tcode{xSCAL}\supercite{blas1}.
|
12924 | 12929 | \end{note}
|
|
12940 | 12945 | \end{itemdecl}
|
12941 | 12946 |
|
12942 | 12947 | \begin{itemdescr}
|
| 12948 | +\pnum |
12943 | 12949 | \begin{note}
|
12944 | 12950 | These functions correspond to the BLAS function \tcode{xCOPY\supercite{blas1}}.
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12945 | 12951 | \end{note}
|
|
12976 | 12982 | \end{itemdecl}
|
12977 | 12983 |
|
12978 | 12984 | \begin{itemdescr}
|
| 12985 | +\pnum |
12979 | 12986 | \begin{note}
|
12980 | 12987 | These functions correspond to the BLAS function \tcode{xAXPY}\supercite{blas1}.
|
12981 | 12988 | \end{note}
|
|
13003 | 13010 |
|
13004 | 13011 | \rSec3[linalg.algs.blas1.dot]{Dot product of two vectors}
|
13005 | 13012 |
|
| 13013 | +\pnum |
13006 | 13014 | \begin{note}
|
13007 | 13015 | The functions in this section correspond to the BLAS
|
13008 | 13016 | functions \tcode{xDOT}, \tcode{xDOTU}, and \tcode{xDOTC}\supercite{blas1}.
|
|
13157 | 13165 | \end{itemdecl}
|
13158 | 13166 |
|
13159 | 13167 | \begin{itemdescr}
|
| 13168 | +\pnum |
13160 | 13169 | \begin{note}
|
13161 | 13170 | These functions correspond to the LAPACK function \tcode{xLASSQ}\supercite{lapack}.
|
13162 | 13171 | \end{note}
|
|
13203 | 13212 | \end{itemdecl}
|
13204 | 13213 |
|
13205 | 13214 | \begin{itemdescr}
|
| 13215 | +\pnum |
13206 | 13216 | \begin{note}
|
13207 | 13217 | These functions correspond to the BLAS function \tcode{xNRM2}\supercite{blas1}.
|
13208 | 13218 | \end{note}
|
|
13274 | 13284 | \end{itemdecl}
|
13275 | 13285 |
|
13276 | 13286 | \begin{itemdescr}
|
| 13287 | +\pnum |
13277 | 13288 | \begin{note}
|
13278 | 13289 | These functions correspond to the BLAS functions
|
13279 | 13290 | \tcode{SASUM}, \tcode{DASUM}, \tcode{SCASUM}, and \tcode{DZASUM}\supercite{blas1}.
|
|
13354 | 13365 | \end{itemdecl}
|
13355 | 13366 |
|
13356 | 13367 | \begin{itemdescr}
|
| 13368 | +\pnum |
13357 | 13369 | \begin{note}
|
13358 | 13370 | These functions correspond to the BLAS function \tcode{IxAMAX}\supercite{blas1}.
|
13359 | 13371 | \end{note}
|
|
13391 | 13403 |
|
13392 | 13404 | \rSec3[linalg.algs.blas1.matfrobnorm]{Frobenius norm of a matrix}
|
13393 | 13405 |
|
| 13406 | +\pnum |
13394 | 13407 | \begin{note}
|
13395 | 13408 | These functions exist in the BLAS standard\supercite{blas-std}
|
13396 | 13409 | but are not part of the reference implementation.
|
|
13461 | 13474 |
|
13462 | 13475 | \rSec3[linalg.algs.blas1.matonenorm]{One norm of a matrix}
|
13463 | 13476 |
|
| 13477 | +\pnum |
13464 | 13478 | \begin{note}
|
13465 | 13479 | These functions exist in the BLAS standard\supercite{blas-std}
|
13466 | 13480 | but are not part of the reference implementation.
|
|
13532 | 13546 |
|
13533 | 13547 | \rSec3[linalg.algs.blas1.matinfnorm]{Infinity norm of a matrix}
|
13534 | 13548 |
|
| 13549 | +\pnum |
13535 | 13550 | \begin{note}
|
13536 | 13551 | These functions exist in the BLAS standard\supercite{blas-std}
|
13537 | 13552 | but are not part of the reference implementation.
|
|
13608 | 13623 |
|
13609 | 13624 | \rSec3[linalg.algs.blas2.gemv]{General matrix-vector product}
|
13610 | 13625 |
|
| 13626 | +\pnum |
13611 | 13627 | \begin{note}
|
13612 | 13628 | These functions correspond to the BLAS function \tcode{xGEMV}.
|
13613 | 13629 | \end{note}
|
|
13708 | 13724 |
|
13709 | 13725 | \rSec3[linalg.algs.blas2.symv]{Symmetric matrix-vector product}
|
13710 | 13726 |
|
| 13727 | +\pnum |
13711 | 13728 | \begin{note}
|
13712 | 13729 | These functions correspond to the BLAS functions
|
13713 | 13730 | \tcode{xSYMV} and \tcode{xSPMV}\supercite{blas2}.
|
|
13796 | 13813 |
|
13797 | 13814 | \rSec3[linalg.algs.blas2.hemv]{Hermitian matrix-vector product}
|
13798 | 13815 |
|
| 13816 | +\pnum |
13799 | 13817 | \begin{note}
|
13800 | 13818 | These functions correspond to the BLAS functions
|
13801 | 13819 | \tcode{xHEMV} and \tcode{xHPMV}\supercite{blas2}.
|
|
13883 | 13901 |
|
13884 | 13902 | \rSec3[linalg.algs.blas2.trmv]{Triangular matrix-vector product}
|
13885 | 13903 |
|
| 13904 | +\pnum |
13886 | 13905 | \begin{note}
|
13887 | 13906 | These functions correspond to the BLAS functions
|
13888 | 13907 | \tcode{xTRMV} and \tcode{xTPMV}\supercite{blas2}.
|
|
14017 | 14036 |
|
14018 | 14037 | \rSec3[linalg.algs.blas2.trsv]{Solve a triangular linear system}
|
14019 | 14038 |
|
| 14039 | +\pnum |
14020 | 14040 | \begin{note}
|
14021 | 14041 | These functions correspond to the BLAS functions
|
14022 | 14042 | \tcode{xTRSV} and \tcode{xTPSV}\supercite{blas2}.
|
|
14387 | 14407 |
|
14388 | 14408 | \rSec3[linalg.algs.blas2.rank2]{Symmetric and Hermitian rank-2 matrix updates}
|
14389 | 14409 |
|
| 14410 | +\pnum |
14390 | 14411 | \begin{note}
|
14391 | 14412 | These functions correspond to the BLAS functions
|
14392 | 14413 | \tcode{xSYR2},\tcode{xSPR2}, \tcode{xHER2} and \tcode{xHPR2}\supercite{blas2}.
|
|
14473 | 14494 |
|
14474 | 14495 | \rSec3[linalg.algs.blas3.gemm]{General matrix-matrix product}
|
14475 | 14496 |
|
| 14497 | +\pnum |
14476 | 14498 | \begin{note}
|
14477 | 14499 | These functions correspond to the BLAS function \tcode{xGEMM}\supercite{blas3}.
|
14478 | 14500 | \end{note}
|
|
14536 | 14558 |
|
14537 | 14559 | \rSec3[linalg.algs.blas3.xxmm]{Symmetric, Hermitian, and triangular matrix-matrix product}
|
14538 | 14560 |
|
| 14561 | +\pnum |
14539 | 14562 | \begin{note}
|
14540 | 14563 | These functions correspond to the BLAS functions
|
14541 | 14564 | \tcode{xSYMM}, \tcode{xHEMM}, and \tcode{xTRMM}\supercite{blas3}.
|
|
14896 | 14919 |
|
14897 | 14920 | \rSec3[linalg.algs.blas3.rankk]{Rank-k update of a symmetric or Hermitian matrix}
|
14898 | 14921 |
|
| 14922 | +\pnum |
14899 | 14923 | \begin{note}
|
14900 | 14924 | These functions correspond to the BLAS functions
|
14901 | 14925 | \tcode{xSYRK} and \tcode{xHERK}\supercite{blas3}.
|
|
15005 | 15029 |
|
15006 | 15030 | \rSec3[linalg.algs.blas3.rank2k]{Rank-2k update of a symmetric or Hermitian matrix}
|
15007 | 15031 |
|
| 15032 | +\pnum |
15008 | 15033 | \begin{note}
|
15009 | 15034 | These functions correspond to the BLAS functions
|
15010 | 15035 | \tcode{xSYR2K} and \tcode{xHER2K}\supercite{blas3}.
|
|
15078 | 15103 |
|
15079 | 15104 | \rSec3[linalg.algs.blas3.trsm]{Solve multiple triangular linear systems}
|
15080 | 15105 |
|
| 15106 | +\pnum |
15081 | 15107 | \begin{note}
|
15082 | 15108 | These functions correspond to the BLAS function \tcode{xTRSM}\supercite{blas3}.
|
15083 | 15109 | \end{note}
|
|
15279 | 15305 |
|
15280 | 15306 | \rSec3[linalg.algs.blas3.inplacetrsm]{Solve multiple triangular linear systems in-place}
|
15281 | 15307 |
|
| 15308 | +\pnum |
15282 | 15309 | \begin{note}
|
15283 | 15310 | These functions correspond to the BLAS function \tcode{xTRSM}\supercite{blas3}.
|
15284 | 15311 | \end{note}
|
|
15390 | 15417 | \end{itemdecl}
|
15391 | 15418 |
|
15392 | 15419 | \begin{itemdescr}
|
15393 |
| - |
15394 | 15420 | \pnum
|
15395 | 15421 | These functions perform multiple in-place matrix solves,
|
15396 | 15422 | taking into account the \tcode{Triangle} and \tcode{DiagonalStorage} parameters
|
|
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