version 1.2, 1999/11/29 05:01:42 |
version 1.5, 2001/06/24 10:26:43 |
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@c $OpenXM$ |
@c $OpenXM: OpenXM/src/asir-contrib/packages/doc/Matrix.texi,v 1.4 2001/06/24 01:14:22 takayama Exp $ |
@node Matrix operations,,, $B$=$NB>$NH!?t(B |
@node Matrix operations (library by Okutani),,, Top |
@section Matrix operations |
@chapter Matrix operations (library by Okutani) |
$B%U%!%$%k(B @file{gr} $B$,I,MW$G$9(B. |
$B%U%!%$%k(B @file{gr} $B$,I,MW$G$9(B. |
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Yukio Okutani $B;a$K$h$k(B Risa/Asir $B8@8l$G=q$+$l$?9TNs7W;;MQ$N%i%$%V%i%j$G$9(B. |
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$B$9$Y$F$N4X?tL>$O(B omatrix_ $B$G;O$^$j$^$9(B. |
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@menu |
@menu |
* mat_1:: |
* omatrix_1:: |
* mat_diag:: |
* omatrix_diag:: |
* mat_trans:: |
* omatrix_trans:: |
* mat_inverse:: |
* omatrix_inverse:: |
* mat_solve:: |
* omatrix_solve:: |
* mat_kernel:: |
* omatrix_kernel:: |
@end menu |
@end menu |
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@node mat_1,,, Matrix operations |
@node omatrix_1,,, Matrix operations (library by Okutani) |
@subsection @code{mat_1} |
@subsection @code{omatrix_1} |
@findex mat_1 |
@findex omatrix_1 |
@table @t |
@table @t |
@item mat_1(@var{N}) |
@item omatrix_1(@var{N}) |
:: @var{N} $B<!C10L9TNs$r@8@.$7$^$9(B. |
:: @var{N} $B<!C10L9TNs$r@8@.$7$^$9(B. |
@end table |
@end table |
@table @var |
@table @var |
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$B@0?t(B |
$B@0?t(B |
@end table |
@end table |
@itemize @bullet |
@itemize @bullet |
@item @code{mat_1}$B$NNc(B. |
@item @code{omatrix_1}$B$NNc(B. |
@end itemize |
@end itemize |
@example |
@example |
[297] mat_1(1); |
[297] omatrix_1(1); |
[ 1 ] |
[ 1 ] |
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[298] mat_1(2); |
[298] omatrix_1(2); |
[ 1 0 ] |
[ 1 0 ] |
[ 0 1 ] |
[ 0 1 ] |
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[299] mat_1(3); |
[299] omatrix_1(3); |
[ 1 0 0 ] |
[ 1 0 0 ] |
[ 0 1 0 ] |
[ 0 1 0 ] |
[ 0 0 1 ] |
[ 0 0 1 ] |
@end example |
@end example |
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@node mat_diag,,, Matrix operations |
@node omatrix_diag,,, Matrix operations (library by Okutani) |
@subsection @code{mat_diag} |
@subsection @code{omatrix_diag} |
@findex mat_diag |
@findex omatrix_diag |
@table @t |
@table @t |
@item mat_diag(@var{L}) |
@item omatrix_diag(@var{L}) |
:: $B%j%9%H(B @var{L} $B$NMWAG$rBP3Q@.J,$H$9$kBP3Q9TNs$r@8@.$7$^$9(B. |
:: $B%j%9%H(B @var{L} $B$NMWAG$rBP3Q@.J,$H$9$kBP3Q9TNs$r@8@.$7$^$9(B. |
@end table |
@end table |
@table @var |
@table @var |
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$B%j%9%H(B |
$B%j%9%H(B |
@end table |
@end table |
@itemize @bullet |
@itemize @bullet |
@item @code{mat_diag}$B$NNc(B. |
@item @code{omatrix_diag}$B$NNc(B. |
@end itemize |
@end itemize |
@example |
@example |
[301] mat_diag([1,2,3]); |
[301] omatrix_diag([1,2,3]); |
[ 1 0 0 ] |
[ 1 0 0 ] |
[ 0 2 0 ] |
[ 0 2 0 ] |
[ 0 0 3 ] |
[ 0 0 3 ] |
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[302] mat_diag([a,b,c]); |
[302] omatrix_diag([a,b,c]); |
[ a 0 0 ] |
[ a 0 0 ] |
[ 0 b 0 ] |
[ 0 b 0 ] |
[ 0 0 c ] |
[ 0 0 c ] |
@end example |
@end example |
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@node mat_trans,,, Matrix operations |
@node omatrix_trans,,, Matrix operations (library by Okutani) |
@subsection @code{mat_trans} |
@subsection @code{omatrix_trans} |
@findex mat_trans |
@findex omatrix_trans |
@table @t |
@table @t |
@item mat_trans(@var{A}) |
@item omatrix_trans(@var{A}) |
:: $B9TNs(B @var{A} $B$NE>CV9TNs$r5a$a$^$9(B. |
:: $B9TNs(B @var{A} $B$NE>CV9TNs$r5a$a$^$9(B. |
@end table |
@end table |
@table @var |
@table @var |
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$B9TNs(B or $B%j%9%H(B |
$B9TNs(B or $B%j%9%H(B |
@end table |
@end table |
@itemize @bullet |
@itemize @bullet |
@item @code{mat_trans}$B$NNc(B. |
@item @code{omatrix_trans}$B$NNc(B. |
@end itemize |
@end itemize |
@example |
@example |
[303] mat_trans([[a,b],[c,d]]); |
[303] omatrix_trans([[a,b],[c,d]]); |
[ a c ] |
[ a c ] |
[ b d ] |
[ b d ] |
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[304] mat_trans([[1,2,3],[4,5,6],[7,8,9]]); |
[304] omatrix_trans([[1,2,3],[4,5,6],[7,8,9]]); |
[ 1 4 7 ] |
[ 1 4 7 ] |
[ 2 5 8 ] |
[ 2 5 8 ] |
[ 3 6 9 ] |
[ 3 6 9 ] |
@end example |
@end example |
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@node mat_inverse,,, Matrix operations |
@node omatrix_inverse,,, Matrix operations (library by Okutani) |
@subsection @code{mat_inverse} |
@subsection @code{omatrix_inverse} |
@findex mat_inverse |
@findex omatrix_inverse |
@table @t |
@table @t |
@item mat_inverse(@var{A}) |
@item omatrix_inverse(@var{A}) |
:: $B9TNs(B @var{A} $B$N5U9TNs$r5a$a$^$9(B. |
:: $B9TNs(B @var{A} $B$N5U9TNs$r5a$a$^$9(B. |
@end table |
@end table |
@table @var |
@table @var |
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@end table |
@end table |
@itemize @bullet |
@itemize @bullet |
@item $B9TNs(B @var{A} $B$N@.J,$OM-M}?t(B or $BB?9`<0(B. |
@item $B9TNs(B @var{A} $B$N@.J,$OM-M}?t(B or $BB?9`<0(B. |
@item @code{mat_inverse}$B$NNc(B. |
@item @code{omatrix_inverse}$B$NNc(B. |
@end itemize |
@end itemize |
@example |
@example |
[309] mat_inverse([[1,1],[1,2]]); |
[309] omatrix_inverse([[1,1],[1,2]]); |
[ 2 -1 ] |
[ 2 -1 ] |
[ -1 1 ] |
[ -1 1 ] |
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[310] mat_inverse([[a,b],[c,d]]); |
[310] omatrix_inverse([[a,b],[c,d]]); |
[ (d)/(d*a-c*b) (-b)/(d*a-c*b) ] |
[ (d)/(d*a-c*b) (-b)/(d*a-c*b) ] |
[ (-c)/(d*a-c*b) (a)/(d*a-c*b) ] |
[ (-c)/(d*a-c*b) (a)/(d*a-c*b) ] |
@end example |
@end example |
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@node mat_solve,,, Matrix operations |
@node omatrix_solve,,, Matrix operations (library by Okutani) |
@subsection @code{mat_solve} |
@subsection @code{omatrix_solve} |
@findex mat_solve |
@findex omatrix_solve |
@table @t |
@table @t |
@item mat_solve(@var{A},@var{X},@var{Y}) |
@item omatrix_solve(@var{A},@var{X},@var{Y}) |
:: @code{mat_solve}$B$OJ}Dx<0(B A*X=Y $B$N2r$r5a$a$^$9(B. |
:: @code{omatrix_solve}$B$OJ}Dx<0(B A*X=Y $B$N2r$r5a$a$^$9(B. |
@end table |
@end table |
@table @var |
@table @var |
@item return |
@item return |
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@end table |
@end table |
@itemize @bullet |
@itemize @bullet |
@item $B9TNs(B @var{A} $B$N@.J,$OM-M}?t(B or $BB?9`<0(B. |
@item $B9TNs(B @var{A} $B$N@.J,$OM-M}?t(B or $BB?9`<0(B. |
@item @code{mat_solve}$B$NNc(B. |
@item @code{omatrix_solve}$B$NNc(B. |
@end itemize |
@end itemize |
@example |
@example |
[376] mat_solve([[1,-1],[2,3]],[x,y],[1,1]); |
[376] omatrix_solve([[1,-1],[2,3]],[x,y],[1,1]); |
[[x,4/5],[y,-1/5]] |
[[x,4/5],[y,-1/5]] |
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[377] mat_solve([[a,b],[c,d]],[x,y],[1,1]); |
[377] omatrix_solve([[a,b],[c,d]],[x,y],[1,1]); |
[[x,(-b+d)/(d*a-c*b)],[y,(a-c)/(d*a-c*b)]] |
[[x,(-b+d)/(d*a-c*b)],[y,(a-c)/(d*a-c*b)]] |
@end example |
@end example |
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@node mat_kernel,,, Matrix operations |
@node omatrix_kernel,,, Matrix operations (library by Okutani) |
@subsection @code{mat_kernel} |
@subsection @code{omatrix_kernel} |
@findex mat_kernel |
@findex omatrix_kernel |
@table @t |
@table @t |
@item mat_kernel(@var{A}) |
@item omatrix_kernel(@var{A}) |
:: @code{mat_kernel}$B$O9TNs(B A $B$N(B kernel $B$N4pDl$r5a$a$^$9(B. |
:: @code{omatrix_kernel}$B$O9TNs(B A $B$N(B kernel $B$N4pDl$r5a$a$^$9(B. |
@end table |
@end table |
@table @var |
@table @var |
@item return |
@item return |
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@end table |
@end table |
@itemize @bullet |
@itemize @bullet |
@item $B9TNs(B @var{A} $B$N@.J,$OM-M}?t(B or $BB?9`<0(B. |
@item $B9TNs(B @var{A} $B$N@.J,$OM-M}?t(B or $BB?9`<0(B. |
@item @code{mat_kernel}$B$NNc(B. |
@item @code{omatrix_kernel}$B$NNc(B. |
@end itemize |
@end itemize |
@example |
@example |
[383] mat_kernel([[1,2,3,4],[1,0,1,0]]); |
[383] omatrix_kernel([[1,2,3,4],[1,0,1,0]]); |
[2,[[1,0,-1,1/2],[0,1,0,-1/2]]] |
[2,[[1,0,-1,1/2],[0,1,0,-1/2]]] |
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[384] mat_kernel([[1,2,3,4],[1,0,1,0],[0,0,0,1]]); |
[384] omatrix_kernel([[1,2,3,4],[1,0,1,0],[0,0,0,1]]); |
[1,[[1,1,-1,0]]] |
[1,[[1,1,-1,0]]] |
@end example |
@end example |