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Annotation of OpenXM/src/asir-contrib/packages/doc/Matrix-ja.texi, Revision 1.2

1.2     ! takayama    1: @c $OpenXM: OpenXM/src/asir-contrib/packages/doc/Matrix-ja.texi,v 1.1 2002/07/29 02:56:27 takayama Exp $
1.1       takayama    2: @node Matrix operations (library by Okutani),,, Top
                      3: @chapter Matrix operations (library by Okutani)
1.2     ! takayama    4: $B%U%!%$%k(B @file{gr}, @file{Matrix} $B$,I,MW$G$9(B.
1.1       takayama    5:
                      6: 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.
                      7: $B$9$Y$F$N4X?tL>$O(B omatrix_ $B$G;O$^$j$^$9(B.
                      8:
                      9: @menu
                     10: * omatrix_1::
                     11: * omatrix_diag::
                     12: * omatrix_trans::
                     13: * omatrix_inverse::
                     14: * omatrix_solve::
                     15: * omatrix_kernel::
                     16: @end menu
                     17:
                     18: @node omatrix_1,,, Matrix operations (library by Okutani)
                     19: @subsection @code{omatrix_1}
                     20: @findex omatrix_1
                     21: @table @t
                     22: @item omatrix_1(@var{N})
                     23: ::  @var{N} $B<!C10L9TNs$r@8@.$7$^$9(B.
                     24: @end table
                     25: @table @var
                     26: @item return
                     27: $B9TNs(B
                     28: @item N
                     29: $B@0?t(B
                     30: @end table
                     31: @itemize @bullet
                     32: @item  @code{omatrix_1}$B$NNc(B.
                     33: @end itemize
                     34: @example
                     35: [297] omatrix_1(1);
                     36: [ 1 ]
                     37:
                     38: [298] omatrix_1(2);
                     39: [ 1 0 ]
                     40: [ 0 1 ]
                     41:
                     42: [299] omatrix_1(3);
                     43: [ 1 0 0 ]
                     44: [ 0 1 0 ]
                     45: [ 0 0 1 ]
                     46: @end example
                     47:
                     48: @node omatrix_diag,,, Matrix operations (library by Okutani)
                     49: @subsection @code{omatrix_diag}
                     50: @findex omatrix_diag
                     51: @table @t
                     52: @item omatrix_diag(@var{L})
                     53: ::  $B%j%9%H(B @var{L} $B$NMWAG$rBP3Q@.J,$H$9$kBP3Q9TNs$r@8@.$7$^$9(B.
                     54: @end table
                     55: @table @var
                     56: @item return
                     57: $B9TNs(B
                     58: @item L
                     59: $B%j%9%H(B
                     60: @end table
                     61: @itemize @bullet
                     62: @item  @code{omatrix_diag}$B$NNc(B.
                     63: @end itemize
                     64: @example
                     65: [301] omatrix_diag([1,2,3]);
                     66: [ 1 0 0 ]
                     67: [ 0 2 0 ]
                     68: [ 0 0 3 ]
                     69:
                     70: [302] omatrix_diag([a,b,c]);
                     71: [ a 0 0 ]
                     72: [ 0 b 0 ]
                     73: [ 0 0 c ]
                     74: @end example
                     75:
                     76: @node omatrix_trans,,, Matrix operations (library by Okutani)
                     77: @subsection @code{omatrix_trans}
                     78: @findex omatrix_trans
                     79: @table @t
                     80: @item omatrix_trans(@var{A})
                     81: ::  $B9TNs(B @var{A} $B$NE>CV9TNs$r5a$a$^$9(B.
                     82: @end table
                     83: @table @var
                     84: @item return
                     85: $B9TNs(B
                     86: @item A
                     87: $B9TNs(B or $B%j%9%H(B
                     88: @end table
                     89: @itemize @bullet
                     90: @item  @code{omatrix_trans}$B$NNc(B.
                     91: @end itemize
                     92: @example
                     93: [303] omatrix_trans([[a,b],[c,d]]);
                     94: [ a c ]
                     95: [ b d ]
                     96:
                     97: [304] omatrix_trans([[1,2,3],[4,5,6],[7,8,9]]);
                     98: [ 1 4 7 ]
                     99: [ 2 5 8 ]
                    100: [ 3 6 9 ]
                    101: @end example
                    102:
                    103: @node omatrix_inverse,,, Matrix operations (library by Okutani)
                    104: @subsection @code{omatrix_inverse}
                    105: @findex omatrix_inverse
                    106: @table @t
                    107: @item omatrix_inverse(@var{A})
                    108: ::  $B9TNs(B @var{A} $B$N5U9TNs$r5a$a$^$9(B.
                    109: @end table
                    110: @table @var
                    111: @item return
                    112: $B9TNs(B
                    113: @item A
                    114: $B9TNs(B or $B%j%9%H(B
                    115: @end table
                    116: @itemize @bullet
                    117: @item $B9TNs(B @var{A} $B$N@.J,$OM-M}?t(B or $BB?9`<0(B.
1.2     ! takayama  118: @item $B0[$J$k%"%k%4%j%:%`$rMQ$$$F5U9TNs$r7W;;$9$k(B
        !           119: @code{omatrix_inverse2}, @code{omatrix_inverse3}
        !           120: $B$b$"$k(B.
1.1       takayama  121: @item @code{omatrix_inverse}$B$NNc(B.
                    122: @end itemize
                    123: @example
                    124: [309] omatrix_inverse([[1,1],[1,2]]);
                    125: [ 2 -1 ]
                    126: [ -1 1 ]
                    127:
                    128: [310] omatrix_inverse([[a,b],[c,d]]);
                    129: [ (d)/(d*a-c*b) (-b)/(d*a-c*b) ]
                    130: [ (-c)/(d*a-c*b) (a)/(d*a-c*b) ]
                    131: @end example
                    132:
                    133: @node omatrix_solve,,, Matrix operations (library by Okutani)
                    134: @subsection @code{omatrix_solve}
                    135: @findex omatrix_solve
                    136: @table @t
                    137: @item omatrix_solve(@var{A},@var{X},@var{Y})
                    138: ::  @code{omatrix_solve}$B$OJ}Dx<0(B A*X=Y $B$N2r$r5a$a$^$9(B.
                    139: @end table
                    140: @table @var
                    141: @item return
                    142: $B%j%9%H(B
                    143: @item A
                    144: $B9TNs(B or $B%j%9%H(B
                    145: @item X
                    146: $B%Y%/%H%k(B or $B%j%9%H(B
                    147: @item Y
                    148: $B%Y%/%H%k(B or $B%j%9%H(B
                    149: @end table
                    150: @itemize @bullet
                    151: @item $B9TNs(B @var{A} $B$N@.J,$OM-M}?t(B or $BB?9`<0(B.
                    152: @item  @code{omatrix_solve}$B$NNc(B.
                    153: @end itemize
                    154: @example
                    155: [376] omatrix_solve([[1,-1],[2,3]],[x,y],[1,1]);
                    156: [[x,4/5],[y,-1/5]]
                    157:
                    158: [377] omatrix_solve([[a,b],[c,d]],[x,y],[1,1]);
                    159: [[x,(-b+d)/(d*a-c*b)],[y,(a-c)/(d*a-c*b)]]
                    160: @end example
                    161:
                    162: @node omatrix_kernel,,, Matrix operations (library by Okutani)
                    163: @subsection @code{omatrix_kernel}
                    164: @findex omatrix_kernel
                    165: @table @t
                    166: @item omatrix_kernel(@var{A})
                    167: ::  @code{omatrix_kernel}$B$O9TNs(B A $B$N(B kernel $B$N4pDl$r5a$a$^$9(B.
                    168: @end table
                    169: @table @var
                    170: @item return
                    171: $B%j%9%H(B
                    172: @item A
                    173: $B9TNs(B or $B%j%9%H(B
                    174: @end table
                    175: @itemize @bullet
                    176: @item $B9TNs(B @var{A} $B$N@.J,$OM-M}?t(B or $BB?9`<0(B.
                    177: @item  @code{omatrix_kernel}$B$NNc(B.
                    178: @end itemize
                    179: @example
                    180: [383] omatrix_kernel([[1,2,3,4],[1,0,1,0]]);
                    181: [2,[[1,0,-1,1/2],[0,1,0,-1/2]]]
                    182:
                    183: [384] omatrix_kernel([[1,2,3,4],[1,0,1,0],[0,0,0,1]]);
                    184: [1,[[1,1,-1,0]]]
                    185: @end example