|
11474 | 11474 | the function satisfies the complexity requirements; and
|
11475 | 11475 | \item
|
11476 | 11476 | the function is logarithmically stable,
|
11477 |
| -as defined in Demmel 2007. |
| 11477 | +as defined in Demmel 2007\supercite{linalg-stable}. |
11478 | 11478 | Strassen's algorithm for matrix-matrix multiply
|
11479 | 11479 | is an example of a logarithmically stable algorithm.
|
11480 | 11480 | \end{itemize}
|
|
12855 | 12855 |
|
12856 | 12856 | \rSec3[linalg.algs.blas1.givens]{Givens rotations}
|
12857 | 12857 |
|
12858 |
| - |
12859 | 12858 | \rSec4[linalg.algs.blas1.givens.lartg]{Compute Givens rotation}
|
12860 | 12859 |
|
12861 | 12860 | \begin{itemdecl}
|
|
12897 | 12896 | whose first component $r$ is the Euclidean norm of the input vector, and
|
12898 | 12897 | whose second component is zero.
|
12899 | 12898 | \begin{note}
|
12900 |
| -These functions correspond to the LAPACK function \tcode{xLARTG}. |
| 12899 | +These functions correspond to the LAPACK function \tcode{xLARTG}\supercite{lapack}. |
12901 | 12900 | \end{note}
|
12902 | 12901 |
|
12903 | 12902 | \pnum
|
|
12927 | 12926 | \begin{itemdescr}
|
12928 | 12927 | \pnum
|
12929 | 12928 | \begin{note}
|
12930 |
| -These functions correspond to the BLAS function \tcode{xROT}. |
| 12929 | +These functions correspond to the BLAS function \tcode{xROT}\supercite{blas1}. |
12931 | 12930 | \end{note}
|
12932 | 12931 |
|
12933 | 12932 | \pnum
|
|
12959 | 12958 | \begin{itemdescr}
|
12960 | 12959 | \pnum
|
12961 | 12960 | \begin{note}
|
12962 |
| -These functions correspond to the BLAS function \tcode{xSWAP}. |
| 12961 | +These functions correspond to the BLAS function \tcode{xSWAP}\supercite{blas1}. |
12963 | 12962 | \end{note}
|
12964 | 12963 |
|
12965 | 12964 | \pnum
|
|
12995 | 12994 | \begin{itemdescr}
|
12996 | 12995 | \pnum
|
12997 | 12996 | \begin{note}
|
12998 |
| -These functions correspond to the BLAS function \tcode{xSCAL}. |
| 12997 | +These functions correspond to the BLAS function \tcode{xSCAL}\supercite{blas1}. |
12999 | 12998 | \end{note}
|
13000 | 12999 |
|
13001 | 13000 | \pnum
|
|
13017 | 13016 | \begin{itemdescr}
|
13018 | 13017 | \pnum
|
13019 | 13018 | \begin{note}
|
13020 |
| -These functions correspond to the BLAS function \tcode{xCOPY}. |
| 13019 | +These functions correspond to the BLAS function \tcode{xCOPY\supercite{blas1}}. |
13021 | 13020 | \end{note}
|
13022 | 13021 |
|
13023 | 13022 | \pnum
|
|
13054 | 13053 | \begin{itemdescr}
|
13055 | 13054 | \pnum
|
13056 | 13055 | \begin{note}
|
13057 |
| -These functions correspond to the BLAS function \tcode{xAXPY}. |
| 13056 | +These functions correspond to the BLAS function \tcode{xAXPY}\supercite{blas1}. |
13058 | 13057 | \end{note}
|
13059 | 13058 |
|
13060 | 13059 | \pnum
|
|
13083 | 13082 | \pnum
|
13084 | 13083 | \begin{note}
|
13085 | 13084 | The functions in this section correspond to the BLAS
|
13086 |
| -functions \tcode{xDOT}, \tcode{xDOTU}, and \tcode{xDOTC}. |
| 13085 | +functions \tcode{xDOT}, \tcode{xDOTU}, and \tcode{xDOTC}\supercite{blas1}. |
13087 | 13086 | \end{note}
|
13088 | 13087 |
|
13089 | 13088 | \pnum
|
|
13237 | 13236 | \begin{itemdescr}
|
13238 | 13237 | \pnum
|
13239 | 13238 | \begin{note}
|
13240 |
| -These functions correspond to the LAPACK function \tcode{xLASSQ}. |
| 13239 | +These functions correspond to the LAPACK function \tcode{xLASSQ}\supercite{lapack}. |
13241 | 13240 | \end{note}
|
13242 | 13241 |
|
13243 | 13242 | \pnum
|
|
13284 | 13283 | \begin{itemdescr}
|
13285 | 13284 | \pnum
|
13286 | 13285 | \begin{note}
|
13287 |
| -These functions correspond to the BLAS function \tcode{xNRM2}. |
| 13286 | +These functions correspond to the BLAS function \tcode{xNRM2}\supercite{blas1}. |
13288 | 13287 | \end{note}
|
13289 | 13288 |
|
13290 | 13289 | \pnum
|
|
13357 | 13356 | \pnum
|
13358 | 13357 | \begin{note}
|
13359 | 13358 | These functions correspond to the BLAS functions
|
13360 |
| -\tcode{SASUM}, \tcode{DASUM}, \tcode{SCASUM}, and \tcode{DZASUM}. |
| 13359 | +\tcode{SASUM}, \tcode{DASUM}, \tcode{SCASUM}, and \tcode{DZASUM}\supercite{blas1}. |
13361 | 13360 | \end{note}
|
13362 | 13361 |
|
13363 | 13362 | \pnum
|
|
13437 | 13436 | \begin{itemdescr}
|
13438 | 13437 | \pnum
|
13439 | 13438 | \begin{note}
|
13440 |
| -These functions correspond to the BLAS function \tcode{IxAMAX}. |
| 13439 | +These functions correspond to the BLAS function \tcode{IxAMAX}\supercite{blas1}. |
13441 | 13440 | \end{note}
|
13442 | 13441 |
|
13443 | 13442 | \pnum
|
|
13794 | 13793 | \pnum
|
13795 | 13794 | \begin{note}
|
13796 | 13795 | These functions correspond to the BLAS functions
|
13797 |
| -\tcode{xSYMV} and \tcode{xSPMV}. |
| 13796 | +\tcode{xSYMV} and \tcode{xSPMV}\supercite{blas2}. |
13798 | 13797 | \end{note}
|
13799 | 13798 |
|
13800 | 13799 | \pnum
|
|
13883 | 13882 | \pnum
|
13884 | 13883 | \begin{note}
|
13885 | 13884 | These functions correspond to the BLAS functions
|
13886 |
| -\tcode{xHEMV} and \tcode{xHPMV}. |
| 13885 | +\tcode{xHEMV} and \tcode{xHPMV}\supercite{blas2}. |
13887 | 13886 | \end{note}
|
13888 | 13887 |
|
13889 | 13888 | \pnum
|
|
13971 | 13970 | \pnum
|
13972 | 13971 | \begin{note}
|
13973 | 13972 | These functions correspond to the BLAS functions
|
13974 |
| -\tcode{xTRMV} and \tcode{xTPMV}. |
| 13973 | +\tcode{xTRMV} and \tcode{xTPMV}\supercite{blas2}. |
13975 | 13974 | \end{note}
|
13976 | 13975 |
|
13977 | 13976 | \pnum
|
|
14106 | 14105 | \pnum
|
14107 | 14106 | \begin{note}
|
14108 | 14107 | These functions correspond to the BLAS functions
|
14109 |
| -\tcode{xTRSV} and \tcode{xTPSV}. |
| 14108 | +\tcode{xTRSV} and \tcode{xTPSV}\supercite{blas2}. |
14110 | 14109 | \end{note}
|
14111 | 14110 |
|
14112 | 14111 | \pnum
|
|
14287 | 14286 | \begin{note}
|
14288 | 14287 | These functions correspond to the BLAS functions
|
14289 | 14288 | \tcode{xGER} (for real element types) and
|
14290 |
| -\tcode{xGERU} (for complex element types). |
| 14289 | +\tcode{xGERU} (for complex element types)\supercite{blas2}. |
14291 | 14290 | \end{note}
|
14292 | 14291 |
|
14293 | 14292 | \pnum
|
|
14322 | 14321 | \begin{note}
|
14323 | 14322 | These functions correspond to the BLAS functions
|
14324 | 14323 | \tcode{xGER} (for real element types) and
|
14325 |
| -\tcode{xGERC} (for complex element types). |
| 14324 | +\tcode{xGERC} (for complex element types)\supercite{blas2}. |
14326 | 14325 | \end{note}
|
14327 | 14326 |
|
14328 | 14327 | \pnum
|
|
14347 | 14346 | \pnum
|
14348 | 14347 | \begin{note}
|
14349 | 14348 | These functions correspond to the BLAS functions
|
14350 |
| -\tcode{xSYR}, \tcode{xSPR}, \tcode{xHER}, and \tcode{xHPR}. |
| 14349 | +\tcode{xSYR}, \tcode{xSPR}, \tcode{xHER}, and \tcode{xHPR}\supercite{blas2}. |
14351 | 14350 | They have overloads taking a scaling factor \tcode{alpha},
|
14352 | 14351 | because it would be impossible to express the update
|
14353 | 14352 | $A = A - x x^T$ otherwise.
|
|
14477 | 14476 | \pnum
|
14478 | 14477 | \begin{note}
|
14479 | 14478 | These functions correspond to the BLAS functions
|
14480 |
| -\tcode{xSYR2},\tcode{xSPR2}, \tcode{xHER2} and \tcode{xHPR2}. |
| 14479 | +\tcode{xSYR2},\tcode{xSPR2}, \tcode{xHER2} and \tcode{xHPR2}\supercite{blas2}. |
14481 | 14480 | \end{note}
|
14482 | 14481 |
|
14483 | 14482 | \pnum
|
|
14563 | 14562 |
|
14564 | 14563 | \pnum
|
14565 | 14564 | \begin{note}
|
14566 |
| -These functions correspond to the BLAS function \tcode{xGEMM}. |
| 14565 | +These functions correspond to the BLAS function \tcode{xGEMM}\supercite{blas3}. |
14567 | 14566 | \end{note}
|
14568 | 14567 |
|
14569 | 14568 | \pnum
|
|
14628 | 14627 | \pnum
|
14629 | 14628 | \begin{note}
|
14630 | 14629 | These functions correspond to the BLAS functions
|
14631 |
| -\tcode{xSYMM}, \tcode{xHEMM}, and \tcode{xTRMM}. |
| 14630 | +\tcode{xSYMM}, \tcode{xHEMM}, and \tcode{xTRMM}\supercite{blas3}. |
14632 | 14631 | \end{note}
|
14633 | 14632 |
|
14634 | 14633 | \pnum
|
|
14895 | 14894 | the \tcode{Triangle} and \tcode{Diagonal\-Storage} parameters
|
14896 | 14895 | that apply to the triangular matrix \tcode{A}\iref{linalg.general}.
|
14897 | 14896 | \begin{note}
|
14898 |
| -These functions correspond to the BLAS function \tcode{xTRMM}. |
| 14897 | +These functions correspond to the BLAS function \tcode{xTRMM}\supercite{blas3}. |
14899 | 14898 | \end{note}
|
14900 | 14899 |
|
14901 | 14900 | \begin{itemdecl}
|
|
14989 | 14988 | \pnum
|
14990 | 14989 | \begin{note}
|
14991 | 14990 | These functions correspond to the BLAS functions
|
14992 |
| -\tcode{xSYRK} and \tcode{xHERK}. |
| 14991 | +\tcode{xSYRK} and \tcode{xHERK}\supercite{blas3}. |
14993 | 14992 | \end{note}
|
14994 | 14993 |
|
14995 | 14994 | \pnum
|
|
15099 | 15098 | \pnum
|
15100 | 15099 | \begin{note}
|
15101 | 15100 | These functions correspond to the BLAS functions
|
15102 |
| -\tcode{xSYR2K} and \tcode{xHER2K}. |
| 15101 | +\tcode{xSYR2K} and \tcode{xHER2K}\supercite{blas3}. |
15103 | 15102 | \end{note}
|
15104 | 15103 |
|
15105 | 15104 | \pnum
|
|
15172 | 15171 |
|
15173 | 15172 | \pnum
|
15174 | 15173 | \begin{note}
|
15175 |
| -These functions correspond to the BLAS function \tcode{xTRSM}. |
| 15174 | +These functions correspond to the BLAS function \tcode{xTRSM}\supercite{blas3}. |
15176 | 15175 | \end{note}
|
15177 | 15176 |
|
15178 | 15177 | \begin{itemdecl}
|
|
15374 | 15373 |
|
15375 | 15374 | \pnum
|
15376 | 15375 | \begin{note}
|
15377 |
| -These functions correspond to the BLAS function \tcode{xTRSM}. |
| 15376 | +These functions correspond to the BLAS function \tcode{xTRSM}\supercite{blas3}. |
15378 | 15377 | \end{note}
|
15379 | 15378 |
|
15380 | 15379 | \begin{itemdecl}
|
|
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