examples/derivatives.jtc

   1 // use jtc's introspection abilities to calculate symbolic derivatives
   2 // of simple functions.
   3
   4 derive_expr = func(expr, var)
   5 {
   6     expansion = expand_node(expr)
   7     if(size(expansion) == 1)
   8     {
   9         if(type(expansion[0]) == "string")
  10         {
  11             if(expansion[0] == var)
  12             {
  13                 return "1"
  14             }
  15             else
  16             {
  17                 return "0"
  18             }
  19         }
  20         else
  21         {
  22             return derive(expansion[0], var)
  23         }
  24     }
  25     else if(expansion[0] == "(")
  26     {
  27         return derive_expr(expansion[1], var)
  28     }
  29     else
  30     {
  31         dleft = derive_expr(expansion[0], var)
  32         dright = derive_expr(expansion[2], var)
  33         left = tostring(expansion[0])
  34         right = tostring(expansion[2])
  35         if(expansion[1] == "+")
  36         {
  37             return "(" + dleft + "+" + dright + ")"
  38         }
  39         else if(expansion[1] == "-")
  40         {
  41             return "(" + dleft + "-" + dright + ")"
  42         }
  43         else if(expansion[1] == "*")
  44         {
  45             return "(" + left + "*" + dright + "+" + dleft + "*" + right + ")"
  46         }
  47         else if(expansion[1] == "/")
  48         {
  49             return "(" + dleft + "*" + right + "-" + dright + "*" + left + ")/(" + right + "*" + right + ")"
  50         }
  51     }
  52 }
  53
  54 derive = func(fun, var)
  55 {
  56     expansion = expand_node(fun)
  57     vars = tostring(expansion[1])
  58     if(var == nil)
  59     {
  60         var = tostring(expand_node(expansion[1])[1])
  61     }
  62     expr = expand_node(expansion[2])[1]
  63     source = "func"+vars+" return "+derive_expr(expr, var)+""
  64     return eval(parse_expression(source))
  65 }
  66
  67 f = func(x) return x*x
  68 df = derive(f)
  69
  70 g = func(x, y) return x*y
  71 dg = derive(g "y")
  72
  73 print(tostring(df) "\n")
  74 print(tostring(dg) "\n")