|
11405 | 11405 | the function satisfies the complexity requirements; and |
11406 | 11406 | \item |
11407 | 11407 | the function is logarithmically stable, |
11408 | | -as defined in Demmel 2007. |
| 11408 | +as defined in Demmel 2007\supercite{linalg-stable}. |
11409 | 11409 | Strassen's algorithm for matrix-matrix multiply |
11410 | 11410 | is an example of a logarithmically stable algorithm. |
11411 | 11411 | \end{itemize} |
|
12784 | 12784 |
|
12785 | 12785 | \rSec3[linalg.algs.blas1.givens]{Givens rotations} |
12786 | 12786 |
|
12787 | | - |
12788 | 12787 | \rSec4[linalg.algs.blas1.givens.lartg]{Compute Givens rotation} |
12789 | 12788 |
|
12790 | 12789 | \begin{itemdecl} |
|
12826 | 12825 | whose first component $r$ is the Euclidean norm of the input vector, and |
12827 | 12826 | whose second component is zero. |
12828 | 12827 | \begin{note} |
12829 | | -These functions correspond to the LAPACK function \tcode{xLARTG}. |
| 12828 | +These functions correspond to the LAPACK function \tcode{xLARTG}\supercite{lapack}. |
12830 | 12829 | \end{note} |
12831 | 12830 |
|
12832 | 12831 | \pnum |
|
12855 | 12854 |
|
12856 | 12855 | \begin{itemdescr} |
12857 | 12856 | \begin{note} |
12858 | | -These functions correspond to the BLAS function \tcode{xROT}. |
| 12857 | +These functions correspond to the BLAS function \tcode{xROT}\supercite{blas1}. |
12859 | 12858 | \end{note} |
12860 | 12859 |
|
12861 | 12860 | \pnum |
|
12886 | 12885 |
|
12887 | 12886 | \begin{itemdescr} |
12888 | 12887 | \begin{note} |
12889 | | -These functions correspond to the BLAS function \tcode{xSWAP}. |
| 12888 | +These functions correspond to the BLAS function \tcode{xSWAP}\supercite{blas1}. |
12890 | 12889 | \end{note} |
12891 | 12890 |
|
12892 | 12891 | \pnum |
|
12921 | 12920 |
|
12922 | 12921 | \begin{itemdescr} |
12923 | 12922 | \begin{note} |
12924 | | -These functions correspond to the BLAS function \tcode{xSCAL}. |
| 12923 | +These functions correspond to the BLAS function \tcode{xSCAL}\supercite{blas1}. |
12925 | 12924 | \end{note} |
12926 | 12925 |
|
12927 | 12926 | \pnum |
|
12942 | 12941 |
|
12943 | 12942 | \begin{itemdescr} |
12944 | 12943 | \begin{note} |
12945 | | -These functions correspond to the BLAS function \tcode{xCOPY}. |
| 12944 | +These functions correspond to the BLAS function \tcode{xCOPY\supercite{blas1}}. |
12946 | 12945 | \end{note} |
12947 | 12946 |
|
12948 | 12947 | \pnum |
|
12978 | 12977 |
|
12979 | 12978 | \begin{itemdescr} |
12980 | 12979 | \begin{note} |
12981 | | -These functions correspond to the BLAS function \tcode{xAXPY}. |
| 12980 | +These functions correspond to the BLAS function \tcode{xAXPY}\supercite{blas1}. |
12982 | 12981 | \end{note} |
12983 | 12982 |
|
12984 | 12983 | \pnum |
|
13006 | 13005 |
|
13007 | 13006 | \begin{note} |
13008 | 13007 | The functions in this section correspond to the BLAS |
13009 | | -functions \tcode{xDOT}, \tcode{xDOTU}, and \tcode{xDOTC}. |
| 13008 | +functions \tcode{xDOT}, \tcode{xDOTU}, and \tcode{xDOTC}\supercite{blas1}. |
13010 | 13009 | \end{note} |
13011 | 13010 |
|
13012 | 13011 | \pnum |
|
13159 | 13158 |
|
13160 | 13159 | \begin{itemdescr} |
13161 | 13160 | \begin{note} |
13162 | | -These functions correspond to the LAPACK function \tcode{xLASSQ}. |
| 13161 | +These functions correspond to the LAPACK function \tcode{xLASSQ}\supercite{lapack}. |
13163 | 13162 | \end{note} |
13164 | 13163 |
|
13165 | 13164 | \pnum |
|
13205 | 13204 |
|
13206 | 13205 | \begin{itemdescr} |
13207 | 13206 | \begin{note} |
13208 | | -These functions correspond to the BLAS function \tcode{xNRM2}. |
| 13207 | +These functions correspond to the BLAS function \tcode{xNRM2}\supercite{blas1}. |
13209 | 13208 | \end{note} |
13210 | 13209 |
|
13211 | 13210 | \pnum |
|
13277 | 13276 | \begin{itemdescr} |
13278 | 13277 | \begin{note} |
13279 | 13278 | These functions correspond to the BLAS functions |
13280 | | -\tcode{SASUM}, \tcode{DASUM}, \tcode{SCASUM}, and \tcode{DZASUM}. |
| 13279 | +\tcode{SASUM}, \tcode{DASUM}, \tcode{SCASUM}, and \tcode{DZASUM}\supercite{blas1}. |
13281 | 13280 | \end{note} |
13282 | 13281 |
|
13283 | 13282 | \pnum |
|
13356 | 13355 |
|
13357 | 13356 | \begin{itemdescr} |
13358 | 13357 | \begin{note} |
13359 | | -These functions correspond to the BLAS function \tcode{IxAMAX}. |
| 13358 | +These functions correspond to the BLAS function \tcode{IxAMAX}\supercite{blas1}. |
13360 | 13359 | \end{note} |
13361 | 13360 |
|
13362 | 13361 | \pnum |
|
13708 | 13707 |
|
13709 | 13708 | \begin{note} |
13710 | 13709 | These functions correspond to the BLAS functions |
13711 | | -\tcode{xSYMV} and \tcode{xSPMV}. |
| 13710 | +\tcode{xSYMV} and \tcode{xSPMV}\supercite{blas2}. |
13712 | 13711 | \end{note} |
13713 | 13712 |
|
13714 | 13713 | \pnum |
|
13796 | 13795 |
|
13797 | 13796 | \begin{note} |
13798 | 13797 | These functions correspond to the BLAS functions |
13799 | | -\tcode{xHEMV} and \tcode{xHPMV}. |
| 13798 | +\tcode{xHEMV} and \tcode{xHPMV}\supercite{blas2}. |
13800 | 13799 | \end{note} |
13801 | 13800 |
|
13802 | 13801 | \pnum |
|
13883 | 13882 |
|
13884 | 13883 | \begin{note} |
13885 | 13884 | These functions correspond to the BLAS functions |
13886 | | -\tcode{xTRMV} and \tcode{xTPMV}. |
| 13885 | +\tcode{xTRMV} and \tcode{xTPMV}\supercite{blas2}. |
13887 | 13886 | \end{note} |
13888 | 13887 |
|
13889 | 13888 | \pnum |
|
14017 | 14016 |
|
14018 | 14017 | \begin{note} |
14019 | 14018 | These functions correspond to the BLAS functions |
14020 | | -\tcode{xTRSV} and \tcode{xTPSV}. |
| 14019 | +\tcode{xTRSV} and \tcode{xTPSV}\supercite{blas2}. |
14021 | 14020 | \end{note} |
14022 | 14021 |
|
14023 | 14022 | \pnum |
|
14198 | 14197 | \begin{note} |
14199 | 14198 | These functions correspond to the BLAS functions |
14200 | 14199 | \tcode{xGER} (for real element types) and |
14201 | | -\tcode{xGERU} (for complex element types). |
| 14200 | +\tcode{xGERU} (for complex element types)\supercite{blas2}. |
14202 | 14201 | \end{note} |
14203 | 14202 |
|
14204 | 14203 | \pnum |
|
14233 | 14232 | \begin{note} |
14234 | 14233 | These functions correspond to the BLAS functions |
14235 | 14234 | \tcode{xGER} (for real element types) and |
14236 | | -\tcode{xGERC} (for complex element types). |
| 14235 | +\tcode{xGERC} (for complex element types)\supercite{blas2}. |
14237 | 14236 | \end{note} |
14238 | 14237 |
|
14239 | 14238 | \pnum |
|
14258 | 14257 | \pnum |
14259 | 14258 | \begin{note} |
14260 | 14259 | These functions correspond to the BLAS functions |
14261 | | -\tcode{xSYR}, \tcode{xSPR}, \tcode{xHER}, and \tcode{xHPR}. |
| 14260 | +\tcode{xSYR}, \tcode{xSPR}, \tcode{xHER}, and \tcode{xHPR}\supercite{blas2}. |
14262 | 14261 | They have overloads taking a scaling factor \tcode{alpha}, |
14263 | 14262 | because it would be impossible to express the update |
14264 | 14263 | $A = A - x x^T$ otherwise. |
|
14387 | 14386 |
|
14388 | 14387 | \begin{note} |
14389 | 14388 | These functions correspond to the BLAS functions |
14390 | | -\tcode{xSYR2},\tcode{xSPR2}, \tcode{xHER2} and \tcode{xHPR2}. |
| 14389 | +\tcode{xSYR2},\tcode{xSPR2}, \tcode{xHER2} and \tcode{xHPR2}\supercite{blas2}. |
14391 | 14390 | \end{note} |
14392 | 14391 |
|
14393 | 14392 | \pnum |
|
14472 | 14471 | \rSec3[linalg.algs.blas3.gemm]{General matrix-matrix product} |
14473 | 14472 |
|
14474 | 14473 | \begin{note} |
14475 | | -These functions correspond to the BLAS function \tcode{xGEMM}. |
| 14474 | +These functions correspond to the BLAS function \tcode{xGEMM}\supercite{blas3}. |
14476 | 14475 | \end{note} |
14477 | 14476 |
|
14478 | 14477 | \pnum |
|
14536 | 14535 |
|
14537 | 14536 | \begin{note} |
14538 | 14537 | These functions correspond to the BLAS functions |
14539 | | -\tcode{xSYMM}, \tcode{xHEMM}, and \tcode{xTRMM}. |
| 14538 | +\tcode{xSYMM}, \tcode{xHEMM}, and \tcode{xTRMM}\supercite{blas3}. |
14540 | 14539 | \end{note} |
14541 | 14540 |
|
14542 | 14541 | \pnum |
|
14803 | 14802 | the \tcode{Triangle} and \tcode{Diagonal\-Storage} parameters |
14804 | 14803 | that apply to the triangular matrix \tcode{A}\iref{linalg.general}. |
14805 | 14804 | \begin{note} |
14806 | | -These functions correspond to the BLAS function \tcode{xTRMM}. |
| 14805 | +These functions correspond to the BLAS function \tcode{xTRMM}\supercite{blas3}. |
14807 | 14806 | \end{note} |
14808 | 14807 |
|
14809 | 14808 | \begin{itemdecl} |
|
14896 | 14895 |
|
14897 | 14896 | \begin{note} |
14898 | 14897 | These functions correspond to the BLAS functions |
14899 | | -\tcode{xSYRK} and \tcode{xHERK}. |
| 14898 | +\tcode{xSYRK} and \tcode{xHERK}\supercite{blas3}. |
14900 | 14899 | \end{note} |
14901 | 14900 |
|
14902 | 14901 | \pnum |
|
15005 | 15004 |
|
15006 | 15005 | \begin{note} |
15007 | 15006 | These functions correspond to the BLAS functions |
15008 | | -\tcode{xSYR2K} and \tcode{xHER2K}. |
| 15007 | +\tcode{xSYR2K} and \tcode{xHER2K}\supercite{blas3}. |
15009 | 15008 | \end{note} |
15010 | 15009 |
|
15011 | 15010 | \pnum |
|
15077 | 15076 | \rSec3[linalg.algs.blas3.trsm]{Solve multiple triangular linear systems} |
15078 | 15077 |
|
15079 | 15078 | \begin{note} |
15080 | | -These functions correspond to the BLAS function \tcode{xTRSM}. |
| 15079 | +These functions correspond to the BLAS function \tcode{xTRSM}\supercite{blas3}. |
15081 | 15080 | \end{note} |
15082 | 15081 |
|
15083 | 15082 | \begin{itemdecl} |
|
15278 | 15277 | \rSec3[linalg.algs.blas3.inplacetrsm]{Solve multiple triangular linear systems in-place} |
15279 | 15278 |
|
15280 | 15279 | \begin{note} |
15281 | | -These functions correspond to the BLAS function \tcode{xTRSM}. |
| 15280 | +These functions correspond to the BLAS function \tcode{xTRSM}\supercite{blas3}. |
15282 | 15281 | \end{note} |
15283 | 15282 |
|
15284 | 15283 | \begin{itemdecl} |
|
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