@c $OpenXM: OpenXM/src/asir-contrib/packages/doc/Matrix.texi,v 1.5 2001/06/24 10:26:43 takayama Exp $
@node Matrix operations (library by Okutani),,, Top
@chapter Matrix operations (library by Okutani)
ファイル @file{gr} が必要です.  

Yukio Okutani 氏による Risa/Asir 言語で書かれた行列計算用のライブラリです.
すべての関数名は omatrix_ で始まります. 

@menu
* omatrix_1::
* omatrix_diag::
* omatrix_trans::
* omatrix_inverse::
* omatrix_solve::
* omatrix_kernel::
@end menu

@node omatrix_1,,, Matrix operations (library by Okutani)
@subsection @code{omatrix_1}
@findex omatrix_1
@table @t
@item omatrix_1(@var{N})
::  @var{N} 次単位行列を生成します.
@end table
@table @var
@item return
行列
@item N
整数
@end table
@itemize @bullet
@item  @code{omatrix_1}の例.
@end itemize
@example
[297] omatrix_1(1);
[ 1 ]

[298] omatrix_1(2);
[ 1 0 ]
[ 0 1 ]

[299] omatrix_1(3);
[ 1 0 0 ]
[ 0 1 0 ]
[ 0 0 1 ]
@end example

@node omatrix_diag,,, Matrix operations (library by Okutani)
@subsection @code{omatrix_diag}
@findex omatrix_diag
@table @t
@item omatrix_diag(@var{L})
::  リスト @var{L} の要素を対角成分とする対角行列を生成します.
@end table
@table @var
@item return
行列
@item L
リスト
@end table
@itemize @bullet
@item  @code{omatrix_diag}の例.
@end itemize
@example
[301] omatrix_diag([1,2,3]);
[ 1 0 0 ]
[ 0 2 0 ]
[ 0 0 3 ]

[302] omatrix_diag([a,b,c]);
[ a 0 0 ]
[ 0 b 0 ]
[ 0 0 c ]
@end example

@node omatrix_trans,,, Matrix operations (library by Okutani)
@subsection @code{omatrix_trans}
@findex omatrix_trans
@table @t
@item omatrix_trans(@var{A})
::  行列 @var{A} の転置行列を求めます.
@end table
@table @var
@item return
行列
@item A
行列 or リスト
@end table
@itemize @bullet
@item  @code{omatrix_trans}の例.
@end itemize
@example
[303] omatrix_trans([[a,b],[c,d]]);
[ a c ]
[ b d ]

[304] omatrix_trans([[1,2,3],[4,5,6],[7,8,9]]);
[ 1 4 7 ]
[ 2 5 8 ]
[ 3 6 9 ]
@end example

@node omatrix_inverse,,, Matrix operations (library by Okutani)
@subsection @code{omatrix_inverse}
@findex omatrix_inverse
@table @t
@item omatrix_inverse(@var{A})
::  行列 @var{A} の逆行列を求めます.
@end table
@table @var
@item return
行列
@item A
行列 or リスト
@end table
@itemize @bullet
@item 行列 @var{A} の成分は有理数 or 多項式.
@item @code{omatrix_inverse}の例.
@end itemize
@example
[309] omatrix_inverse([[1,1],[1,2]]);
[ 2 -1 ]
[ -1 1 ]

[310] omatrix_inverse([[a,b],[c,d]]);
[ (d)/(d*a-c*b) (-b)/(d*a-c*b) ]
[ (-c)/(d*a-c*b) (a)/(d*a-c*b) ]
@end example

@node omatrix_solve,,, Matrix operations (library by Okutani)
@subsection @code{omatrix_solve}
@findex omatrix_solve
@table @t
@item omatrix_solve(@var{A},@var{X},@var{Y})
::  @code{omatrix_solve}は方程式 A*X=Y の解を求めます.
@end table
@table @var
@item return
リスト
@item A
行列 or リスト
@item X
ベクトル or リスト
@item Y
ベクトル or リスト
@end table
@itemize @bullet
@item 行列 @var{A} の成分は有理数 or 多項式.
@item  @code{omatrix_solve}の例.
@end itemize
@example
[376] omatrix_solve([[1,-1],[2,3]],[x,y],[1,1]);
[[x,4/5],[y,-1/5]]

[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)]]
@end example

@node omatrix_kernel,,, Matrix operations (library by Okutani)
@subsection @code{omatrix_kernel}
@findex omatrix_kernel
@table @t
@item omatrix_kernel(@var{A})
::  @code{omatrix_kernel}は行列 A の kernel の基底を求めます.
@end table
@table @var
@item return
リスト
@item A
行列 or リスト
@end table
@itemize @bullet
@item 行列 @var{A} の成分は有理数 or 多項式.
@item  @code{omatrix_kernel}の例.
@end itemize
@example
[383] omatrix_kernel([[1,2,3,4],[1,0,1,0]]);
[2,[[1,0,-1,1/2],[0,1,0,-1/2]]]

[384] omatrix_kernel([[1,2,3,4],[1,0,1,0],[0,0,0,1]]);
[1,[[1,1,-1,0]]]
@end example