| version 1.5, 2002/08/08 05:24:37 |
version 1.10, 2005/02/10 04:59:21 |
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| @comment $OpenXM: OpenXM/src/asir-doc/parts/builtin/array.texi,v 1.4 2000/11/13 00:16:36 noro Exp $ |
@comment $OpenXM: OpenXM/src/asir-doc/parts/builtin/array.texi,v 1.9 2003/12/18 10:26:20 ohara Exp $ |
| \BJP |
\BJP |
| @node $BG[Ns(B,,, $BAH$_9~$_H!?t(B |
@node $BG[Ns(B,,, $BAH$_9~$_H!?t(B |
| @section $BG[Ns(B |
@section $BG[Ns(B |
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| |
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| @menu |
@menu |
| * newvect:: |
* newvect:: |
| * newbytearray:: |
* ltov:: |
| * vtol:: |
* vtol:: |
| |
* newbytearray:: |
| * newmat:: |
* newmat:: |
| * size:: |
* size:: |
| * det invmat:: |
* det nd_det invmat:: |
| |
|
| * qsort:: |
* qsort:: |
| @end menu |
@end menu |
| |
|
| Line 144 separated simply by a `blank space', while those of a |
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| Line 146 separated simply by a `blank space', while those of a |
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| @table @t |
@table @t |
| \JP @item $B;2>H(B |
\JP @item $B;2>H(B |
| \EG @item References |
\EG @item References |
| @fref{newmat}, @fref{size}, @fref{vtol}. |
@fref{newmat}, @fref{size}, @fref{ltov}, @fref{vtol}. |
| @end table |
@end table |
| |
|
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\JP @node ltov,,, $BG[Ns(B |
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\EG @node ltov,,, Arrays |
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@subsection @code{ltov} |
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@findex ltov |
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|
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@table @t |
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@item ltov(@var{list}) |
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\JP :: $B%j%9%H$r%Y%/%H%k$KJQ49$9$k(B. |
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\EG :: Converts a list into a vector. |
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@end table |
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|
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@table @var |
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@item return |
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\JP $B%Y%/%H%k(B |
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\EG vector |
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@item list |
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\JP $B%j%9%H(B |
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\EG list |
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@end table |
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|
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@itemize @bullet |
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\BJP |
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@item |
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$B%j%9%H(B @var{list} $B$rF1$8D9$5$N%Y%/%H%k$KJQ49$9$k(B. |
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@item |
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$B$3$N4X?t$O(B @code{newvect(length(@var{list}), @var{list})} $B$KEy$7$$(B. |
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\E |
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\BEG |
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@item |
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Converts a list @var{list} into a vector of same length. |
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See also @code{newvect()}. |
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\E |
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@end itemize |
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|
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@example |
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[3] A=[1,2,3]; |
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[4] ltov(A); |
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[ 1 2 3 ] |
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@end example |
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|
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@table @t |
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\JP @item $B;2>H(B |
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\EG @item References |
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@fref{newvect}, @fref{vtol}. |
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@end table |
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| \JP @node vtol,,, $BG[Ns(B |
\JP @node vtol,,, $BG[Ns(B |
| \EG @node vtol,,, Arrays |
\EG @node vtol,,, Arrays |
| @subsection @code{vtol} |
@subsection @code{vtol} |
| Line 194 A conversion from a list to a vector is done by @code{ |
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| Line 242 A conversion from a list to a vector is done by @code{ |
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| @table @t |
@table @t |
| \JP @item $B;2>H(B |
\JP @item $B;2>H(B |
| \EG @item References |
\EG @item References |
| @fref{newvect}. |
@fref{newvect}, @fref{ltov}. |
| @end table |
@end table |
| |
|
| \JP @node newbytearray,,, $BG[Ns(B |
\JP @node newbytearray,,, $BG[Ns(B |
| Line 259 similar to that of @code{newvect}. |
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| Line 307 similar to that of @code{newvect}. |
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| @findex newmat |
@findex newmat |
| |
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| @table @t |
@table @t |
| @item newmat(@var{row},@var{col} [,@var{[[a,b,}...@var{],[c,d,}...@var{],}...@var{]}]) |
@item newmat(@var{row},@var{col} [,[[@var{a},@var{b},...],[@var{c},@var{d},...],...]]) |
| \JP :: @var{row} $B9T(B @var{col} $BNs$N9TNs$r@8@.$9$k(B. |
\JP :: @var{row} $B9T(B @var{col} $BNs$N9TNs$r@8@.$9$k(B. |
| \EG :: Creates a new matrix with @var{row} rows and @var{col} columns. |
\EG :: Creates a new matrix with @var{row} rows and @var{col} columns. |
| @end table |
@end table |
| Line 268 similar to that of @code{newvect}. |
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| Line 316 similar to that of @code{newvect}. |
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| @item return |
@item return |
| \JP $B9TNs(B |
\JP $B9TNs(B |
| \EG matrix |
\EG matrix |
| @item row,col |
@item row col |
| \JP $B<+A3?t(B |
\JP $B<+A3?t(B |
| \EG non-negative integer |
\EG non-negative integer |
| @item a,b,c,d |
@item a b c d |
| \JP $BG$0U(B |
\JP $BG$0U(B |
| \EG arbitrary |
\EG arbitrary |
| @end table |
@end table |
| Line 337 return to toplevel |
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| Line 385 return to toplevel |
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| @table @t |
@table @t |
| \JP @item $B;2>H(B |
\JP @item $B;2>H(B |
| \EG @item References |
\EG @item References |
| @fref{newvect}, @fref{size}, @fref{det invmat}. |
@fref{newvect}, @fref{size}, @fref{det nd_det invmat}. |
| @end table |
@end table |
| |
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| \JP @node size,,, $BG[Ns(B |
\JP @node size,,, $BG[Ns(B |
| Line 371 or a list containing row size and column size of the g |
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| Line 419 or a list containing row size and column size of the g |
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| @itemize @bullet |
@itemize @bullet |
| \BJP |
\BJP |
| @item |
@item |
| @var{vect} $BKt$O(B, @var{mat} $B$N%5%$%:$r%j%9%H$G=PNO$9$k(B. |
@var{vect} $B$ND9$5(B, $B$^$?$O(B @var{mat} $B$NBg$-$5$r%j%9%H$G=PNO$9$k(B. |
| @item |
@item |
| @var{list} $B$N%5%$%:$O(B @code{length()}$B$r(B, $BM-M}<0$K8=$l$kC19`<0$N?t$O(B @code{nmono()} $B$rMQ$$$k(B. |
@var{vect} $B$ND9$5$O(B @code{length()} $B$G5a$a$k$3$H$b$G$-$k(B. |
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@item |
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@var{list} $B$ND9$5$O(B @code{length()}$B$r(B, $BM-M}<0$K8=$l$kC19`<0$N?t$O(B @code{nmono()} $B$rMQ$$$k(B. |
| \E |
\E |
| \BEG |
\BEG |
| @item |
@item |
| Line 392 in a rational expression. |
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| Line 442 in a rational expression. |
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| [ 0 0 0 0 ] |
[ 0 0 0 0 ] |
| [1] size(A); |
[1] size(A); |
| [4] |
[4] |
| [2] B = newmat(2,3,[[1,2,3],[4,5,6]]); |
[2] length(A); |
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4 |
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[3] B = newmat(2,3,[[1,2,3],[4,5,6]]); |
| [ 1 2 3 ] |
[ 1 2 3 ] |
| [ 4 5 6 ] |
[ 4 5 6 ] |
| [3] size(B); |
[4] size(B); |
| [2,3] |
[2,3] |
| @end example |
@end example |
| |
|
| Line 405 in a rational expression. |
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| Line 457 in a rational expression. |
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| @fref{car cdr cons append reverse length}, @fref{nmono}. |
@fref{car cdr cons append reverse length}, @fref{nmono}. |
| @end table |
@end table |
| |
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| \JP @node det invmat,,, $BG[Ns(B |
\JP @node det nd_det invmat,,, $BG[Ns(B |
| \EG @node det invmat,,, Arrays |
\EG @node det nd_det invmat,,, Arrays |
| @subsection @code{det},@code{invmat} |
@subsection @code{det},@code{invmat} |
| @findex det |
@findex det |
| @findex invmat |
@findex invmat |
| |
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| @table @t |
@table @t |
| @item det(@var{mat}[,@var{mod}]) |
@item det(@var{mat}[,@var{mod}]) |
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@itemx nd_det(@var{mat}[,@var{mod}]) |
| \JP :: @var{mat} $B$N9TNs<0$r5a$a$k(B. |
\JP :: @var{mat} $B$N9TNs<0$r5a$a$k(B. |
| \EG :: Determinant of @var{mat}. |
\EG :: Determinant of @var{mat}. |
| @item invmat(@var{mat}) |
@item invmat(@var{mat}) |
| \JP :: @var{mat} $B$N9TNs<0$r5a$a$k(B. |
\JP :: @var{mat} $B$N5U9TNs$r5a$a$k(B. |
| \EG :: Inverse matrix of @var{mat}. |
\EG :: Inverse matrix of @var{mat}. |
| @end table |
@end table |
| |
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| Line 435 in a rational expression. |
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| Line 488 in a rational expression. |
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| @itemize @bullet |
@itemize @bullet |
| \BJP |
\BJP |
| @item |
@item |
| @code{det} $B$O9TNs(B @var{mat} $B$N9TNs<0$r5a$a$k(B. |
@code{det} $B$*$h$S(B @code{nd_det} $B$O9TNs(B @var{mat} $B$N9TNs<0$r5a$a$k(B. |
| @code{invmat} $B$O9TNs(B @var{mat} $B$N5U9TNs$r5a$a$k(B. $B5U9TNs$O(B @code{[$BJ,Jl(B, $BJ,;R(B]} |
@code{invmat} $B$O9TNs(B @var{mat} $B$N5U9TNs$r5a$a$k(B. $B5U9TNs$O(B @code{[$BJ,Jl(B, $BJ,;R(B]} |
| $B$N7A$GJV$5$l(B, @code{$BJ,Jl(B}$B$,9TNs(B, @code{$BJ,Jl(B/$BJ,;R(B} $B$,5U9TNs$H$J$k(B. |
$B$N7A$GJV$5$l(B, @code{$BJ,Jl(B}$B$,9TNs(B, @code{$BJ,Jl(B/$BJ,;R(B} $B$,5U9TNs$H$J$k(B. |
| @item |
@item |
| Line 443 in a rational expression. |
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| Line 496 in a rational expression. |
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| @item |
@item |
| $BJ,?t$J$7$N%,%&%9>C5nK!$K$h$C$F$$$k$?$a(B, $BB?JQ?tB?9`<0$r@.J,$H$9$k(B |
$BJ,?t$J$7$N%,%&%9>C5nK!$K$h$C$F$$$k$?$a(B, $BB?JQ?tB?9`<0$r@.J,$H$9$k(B |
| $B9TNs$KBP$7$F$O>.9TNs<0E83+$K$h$kJ}K!$N$[$&$,8zN($,$h$$>l9g$b$"$k(B. |
$B9TNs$KBP$7$F$O>.9TNs<0E83+$K$h$kJ}K!$N$[$&$,8zN($,$h$$>l9g$b$"$k(B. |
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@item |
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@code{nd_det} $B$OM-M}?t$^$?$OM-8BBN>e$NB?9`<09TNs$N9TNs<0(B |
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$B7W;;@lMQ$G$"$k(B. $B%"%k%4%j%:%`$O$d$O$jJ,?t$J$7$N%,%&%9>C5nK!$@$,(B, |
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$B%G!<%?9=B$$*$h$S>h=|;;$N9)IW$K$h$j(B, $B0lHL$K(B @code{det} $B$h$j9bB.$K(B |
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$B7W;;$G$-$k(B. |
| \E |
\E |
| \BEG |
\BEG |
| @item |
@item |
| @code{det} computes the determinant of matrix @var{mat}. |
@code{det} and @code{nd_det} compute the determinant of matrix @var{mat}. |
| @code{invmat} computes the inverse matrix of matrix @var{mat}. |
@code{invmat} computes the inverse matrix of matrix @var{mat}. |
| @code{invmat} returns a list @code{[num,den]}, where @code{num} |
@code{invmat} returns a list @code{[num,den]}, where @code{num} |
| is a matrix and @code{num/den} represents the inverse matrix. |
is a matrix and @code{num/den} represents the inverse matrix. |
| Line 456 is more efficient than the fraction free Gaussian algo |
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| Line 514 is more efficient than the fraction free Gaussian algo |
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| The fraction free Gaussian algorithm is employed. For matrices with |
The fraction free Gaussian algorithm is employed. For matrices with |
| multi-variate polynomial entries, minor expansion algorithm sometimes |
multi-variate polynomial entries, minor expansion algorithm sometimes |
| is more efficient than the fraction free Gaussian algorithm. |
is more efficient than the fraction free Gaussian algorithm. |
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@item |
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@code{nd_det} can be used for computing the determinant of a matrix with |
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polynomial entries over the rationals or finite fields. The algorithm |
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is an improved vesion of the fraction free Gaussian algorithm |
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and it computes the determinant faster than @code{det}. |
| \E |
\E |
| @end itemize |
@end itemize |
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| Line 471 is more efficient than the fraction free Gaussian algo |
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| Line 534 is more efficient than the fraction free Gaussian algo |
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| [ 1 u u^2 u^3 u^4 ] |
[ 1 u u^2 u^3 u^4 ] |
| [ 1 v v^2 v^3 v^4 ] |
[ 1 v v^2 v^3 v^4 ] |
| [95] fctr(det(A)); |
[95] fctr(det(A)); |
| [[1,1],[u-v,1],[-z+v,1],[-z+u,1],[-y+u,1],[y-v,1],[-y+z,1],[-x+u,1],[-x+z,1], |
[[1,1],[u-v,1],[-z+v,1],[-z+u,1],[-y+u,1],[y-v,1],[-y+z,1],[-x+u,1], |
| [-x+v,1],[-x+y,1]] |
[-x+z,1],[-x+v,1],[-x+y,1]] |
| [96] A = newmat(3,3)$ |
[96] A = newmat(3,3)$ |
| [97] for(I=0;I<3;I++)for(J=0,B=A[I],W=V[I];J<3;J++)B[J]=W^J; |
[97] for(I=0;I<3;I++)for(J=0,B=A[I],W=V[I];J<3;J++)B[J]=W^J; |
| [98] A; |
[98] A; |
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