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Diff for /OpenXM/src/asir-contrib/packages/doc/Attic/Matrix.texi between version 1.3 and 1.4

version 1.3, 2000/01/03 09:15:53 version 1.4, 2001/06/24 01:14:22
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 @c $OpenXM$  @c $OpenXM: OpenXM/src/asir-contrib/packages/doc/Matrix.texi,v 1.3 2000/01/03 09:15:53 okutani Exp $
 @node Matrix operations,,, $B$=$NB>$NH!?t(B  @node Matrix operations (library by Okutani),,, Top
 @section Matrix operations  @section 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.
   
   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.
   $B$9$Y$F$N4X?tL>$O(B omatrix_ $B$G;O$^$j$^$9(B.
   
 @menu  @menu
 * matrix_1::  * omatrix_1::
 * matrix_diag::  * omatrix_diag::
 * matrix_trans::  * omatrix_trans::
 * matrix_inverse::  * omatrix_inverse::
 * matrix_solve::  * omatrix_solve::
 * matrix_kernel::  * omatrix_kernel::
 @end menu  @end menu
   
 @node matrix_1,,, Matrix operations  @node omatrix_1,,, Matrix operations (library by Okutani)
 @subsection @code{matrix_1}  @subsection @code{omatrix_1}
 @findex matrix_1  @findex omatrix_1
 @table @t  @table @t
 @item matrix_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  $B@0?t(B
 @end table  @end table
 @itemize @bullet  @itemize @bullet
 @item  @code{matrix_1}$B$NNc(B.  @item  @code{omatrix_1}$B$NNc(B.
 @end itemize  @end itemize
 @example  @example
 [297] matrix_1(1);  [297] omatrix_1(1);
 [ 1 ]  [ 1 ]
   
 [298] matrix_1(2);  [298] omatrix_1(2);
 [ 1 0 ]  [ 1 0 ]
 [ 0 1 ]  [ 0 1 ]
   
 [299] matrix_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
   
 @node matrix_diag,,, Matrix operations  @node omatrix_diag,,, Matrix operations (library by Okutani)
 @subsection @code{matrix_diag}  @subsection @code{omatrix_diag}
 @findex matrix_diag  @findex omatrix_diag
 @table @t  @table @t
 @item matrix_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  $B%j%9%H(B
 @end table  @end table
 @itemize @bullet  @itemize @bullet
 @item  @code{matrix_diag}$B$NNc(B.  @item  @code{omatrix_diag}$B$NNc(B.
 @end itemize  @end itemize
 @example  @example
 [301] matrix_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 ]
   
 [302] matrix_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
   
 @node matrix_trans,,, Matrix operations  @node omatrix_trans,,, Matrix operations (library by Okutani)
 @subsection @code{matrix_trans}  @subsection @code{omatrix_trans}
 @findex matrix_trans  @findex omatrix_trans
 @table @t  @table @t
 @item matrix_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 $B%j%9%H(B
 @end table  @end table
 @itemize @bullet  @itemize @bullet
 @item  @code{matrix_trans}$B$NNc(B.  @item  @code{omatrix_trans}$B$NNc(B.
 @end itemize  @end itemize
 @example  @example
 [303] matrix_trans([[a,b],[c,d]]);  [303] omatrix_trans([[a,b],[c,d]]);
 [ a c ]  [ a c ]
 [ b d ]  [ b d ]
   
 [304] matrix_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
   
 @node matrix_inverse,,, Matrix operations  @node omatrix_inverse,,, Matrix operations (library by Okutani)
 @subsection @code{matrix_inverse}  @subsection @code{omatrix_inverse}
 @findex matrix_inverse  @findex omatrix_inverse
 @table @t  @table @t
 @item matrix_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 $BB?9`<0(B.
 @item @code{matrix_inverse}$B$NNc(B.  @item @code{omatrix_inverse}$B$NNc(B.
 @end itemize  @end itemize
 @example  @example
 [309] matrix_inverse([[1,1],[1,2]]);  [309] omatrix_inverse([[1,1],[1,2]]);
 [ 2 -1 ]  [ 2 -1 ]
 [ -1 1 ]  [ -1 1 ]
   
 [310] matrix_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
   
 @node matrix_solve,,, Matrix operations  @node omatrix_solve,,, Matrix operations (library by Okutani)
 @subsection @code{matrix_solve}  @subsection @code{omatrix_solve}
 @findex matrix_solve  @findex omatrix_solve
 @table @t  @table @t
 @item matrix_solve(@var{A},@var{X},@var{Y})  @item omatrix_solve(@var{A},@var{X},@var{Y})
 ::  @code{matrix_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 $BB?9`<0(B.
 @item  @code{matrix_solve}$B$NNc(B.  @item  @code{omatrix_solve}$B$NNc(B.
 @end itemize  @end itemize
 @example  @example
 [376] matrix_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]]
   
 [377] matrix_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
   
 @node matrix_kernel,,, Matrix operations  @node omatrix_kernel,,, Matrix operations (library by Okutani)
 @subsection @code{matrix_kernel}  @subsection @code{omatrix_kernel}
 @findex matrix_kernel  @findex omatrix_kernel
 @table @t  @table @t
 @item matrix_kernel(@var{A})  @item omatrix_kernel(@var{A})
 ::  @code{matrix_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 $BB?9`<0(B.
 @item  @code{matrix_kernel}$B$NNc(B.  @item  @code{omatrix_kernel}$B$NNc(B.
 @end itemize  @end itemize
 @example  @example
 [383] matrix_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]]]
   
 [384] matrix_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
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