Return to Matrix.texi CVS log

Up to [local] / OpenXM / src / asir-contrib / packages / doc

Annotation of OpenXM/src/asir-contrib/packages/doc/Matrix.texi, Revision 1.1

1.1     ! takayama    1: @c $OpenXM: OpenXM/src/asir99/lib/contrib/packages/doc/Matrix.texi,v 1.2 1999/11/21 10:58:55 okutani Exp $
        !             2: @node Matrix operations,,, $B$=$NB>$NH!?t(B
        !             3: @section Matrix operations
        !             4: $B%U%!%$%k(B @file{gr} $B$,I,MW$G$9(B.
        !             5: @menu
        !             6: * mat_1::
        !             7: * mat_diag::
        !             8: * mat_trans::
        !             9: * mat_inverse::
        !            10: * mat_solve::
        !            11: * mat_kernel::
        !            12: @end menu
        !            13:
        !            14: @node mat_1,,, Matrix operations
        !            15: @subsection @code{mat_1}
        !            16: @findex mat_1
        !            17: @table @t
        !            18: @item mat_1(@var{N})
        !            19: ::  @var{N} $B<!C10L9TNs$r@8@.$7$^$9(B.
        !            20: @end table
        !            21: @table @var
        !            22: @item return
        !            23: $B9TNs(B
        !            24: @item N
        !            25: $B@0?t(B
        !            26: @end table
        !            27: @itemize @bullet
        !            28: @item  @code{mat_1}$B$NNc(B.
        !            29: @end itemize
        !            30: @example
        !            31: [297] mat_1(1);
        !            32: [ 1 ]
        !            33:
        !            34: [298] mat_1(2);
        !            35: [ 1 0 ]
        !            36: [ 0 1 ]
        !            37:
        !            38: [299] mat_1(3);
        !            39: [ 1 0 0 ]
        !            40: [ 0 1 0 ]
        !            41: [ 0 0 1 ]
        !            42: @end example
        !            43:
        !            44: @node mat_diag,,, Matrix operations
        !            45: @subsection @code{mat_diag}
        !            46: @findex mat_diag
        !            47: @table @t
        !            48: @item mat_diag(@var{L})
        !            49: ::  $B%j%9%H(B @var{L} $B$NMWAG$rBP3Q@.J,$H$9$kBP3Q9TNs$r@8@.$7$^$9(B.
        !            50: @end table
        !            51: @table @var
        !            52: @item return
        !            53: $B9TNs(B
        !            54: @item L
        !            55: $B%j%9%H(B
        !            56: @end table
        !            57: @itemize @bullet
        !            58: @item  @code{mat_diag}$B$NNc(B.
        !            59: @end itemize
        !            60: @example
        !            61: [301] mat_diag([1,2,3]);
        !            62: [ 1 0 0 ]
        !            63: [ 0 2 0 ]
        !            64: [ 0 0 3 ]
        !            65:
        !            66: [302] mat_diag([a,b,c]);
        !            67: [ a 0 0 ]
        !            68: [ 0 b 0 ]
        !            69: [ 0 0 c ]
        !            70: @end example
        !            71:
        !            72: @node mat_trans,,, Matrix operations
        !            73: @subsection @code{mat_trans}
        !            74: @findex mat_trans
        !            75: @table @t
        !            76: @item mat_trans(@var{A})
        !            77: ::  $B9TNs(B @var{A} $B$NE>CV9TNs$r5a$a$^$9(B.
        !            78: @end table
        !            79: @table @var
        !            80: @item return
        !            81: $B9TNs(B
        !            82: @item A
        !            83: $B9TNs(B or $B%j%9%H(B
        !            84: @end table
        !            85: @itemize @bullet
        !            86: @item  @code{mat_trans}$B$NNc(B.
        !            87: @end itemize
        !            88: @example
        !            89: [303] mat_trans([[a,b],[c,d]]);
        !            90: [ a c ]
        !            91: [ b d ]
        !            92:
        !            93: [304] mat_trans([[1,2,3],[4,5,6],[7,8,9]]);
        !            94: [ 1 4 7 ]
        !            95: [ 2 5 8 ]
        !            96: [ 3 6 9 ]
        !            97: @end example
        !            98:
        !            99: @node mat_inverse,,, Matrix operations
        !           100: @subsection @code{mat_inverse}
        !           101: @findex mat_inverse
        !           102: @table @t
        !           103: @item mat_inverse(@var{A})
        !           104: ::  $B9TNs(B @var{A} $B$N5U9TNs$r5a$a$^$9(B.
        !           105: @end table
        !           106: @table @var
        !           107: @item return
        !           108: $B9TNs(B
        !           109: @item A
        !           110: $B9TNs(B or $B%j%9%H(B
        !           111: @end table
        !           112: @itemize @bullet
        !           113: @item $B9TNs(B @var{A} $B$N@.J,$OM-M}?t(B or $BB?9`<0(B.
        !           114: @item @code{mat_inverse}$B$NNc(B.
        !           115: @end itemize
        !           116: @example
        !           117: [309] mat_inverse([[1,1],[1,2]]);
        !           118: [ 2 -1 ]
        !           119: [ -1 1 ]
        !           120:
        !           121: [310] mat_inverse([[a,b],[c,d]]);
        !           122: [ (d)/(d*a-c*b) (-b)/(d*a-c*b) ]
        !           123: [ (-c)/(d*a-c*b) (a)/(d*a-c*b) ]
        !           124: @end example
        !           125:
        !           126: @node mat_solve,,, Matrix operations
        !           127: @subsection @code{mat_solve}
        !           128: @findex mat_solve
        !           129: @table @t
        !           130: @item mat_solve(@var{A},@var{X},@var{Y})
        !           131: ::  @code{mat_solve}$B$OJ}Dx<0(B A*X=Y $B$N2r$r5a$a$^$9(B.
        !           132: @end table
        !           133: @table @var
        !           134: @item return
        !           135: $B%j%9%H(B
        !           136: @item A
        !           137: $B9TNs(B or $B%j%9%H(B
        !           138: @item X
        !           139: $B%Y%/%H%k(B or $B%j%9%H(B
        !           140: @item Y
        !           141: $B%Y%/%H%k(B or $B%j%9%H(B
        !           142: @end table
        !           143: @itemize @bullet
        !           144: @item $B9TNs(B @var{A} $B$N@.J,$OM-M}?t(B or $BB?9`<0(B.
        !           145: @item  @code{mat_solve}$B$NNc(B.
        !           146: @end itemize
        !           147: @example
        !           148: [376] mat_solve([[1,-1],[2,3]],[x,y],[1,1]);
        !           149: [[x,4/5],[y,-1/5]]
        !           150:
        !           151: [377] mat_solve([[a,b],[c,d]],[x,y],[1,1]);
        !           152: [[x,(-b+d)/(d*a-c*b)],[y,(a-c)/(d*a-c*b)]]
        !           153: @end example
        !           154:
        !           155: @node mat_kernel,,, Matrix operations
        !           156: @subsection @code{mat_kernel}
        !           157: @findex mat_kernel
        !           158: @table @t
        !           159: @item mat_kernel(@var{A})
        !           160: ::  @code{mat_kernel}$B$O9TNs(B A $B$N(B kernel $B$N4pDl$r5a$a$^$9(B.
        !           161: @end table
        !           162: @table @var
        !           163: @item return
        !           164: $B%j%9%H(B
        !           165: @item A
        !           166: $B9TNs(B or $B%j%9%H(B
        !           167: @end table
        !           168: @itemize @bullet
        !           169: @item $B9TNs(B @var{A} $B$N@.J,$OM-M}?t(B or $BB?9`<0(B.
        !           170: @item  @code{mat_kernel}$B$NNc(B.
        !           171: @end itemize
        !           172: @example
        !           173: [383] mat_kernel([[1,2,3,4],[1,0,1,0]]);
        !           174: [2,[[1,0,-1,1/2],[0,1,0,-1/2]]]
        !           175:
        !           176: [384] mat_kernel([[1,2,3,4],[1,0,1,0],[0,0,0,1]]);
        !           177: [1,[[1,1,-1,0]]]
        !           178: @end example