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Annotation of OpenXM/src/asir-contrib/packages/doc/Matrix.texi, Revision 1.1.1.1

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