class Keisan::Functions::ExpressionFunction

Attributes

arguments[R]
expression[R]

Public Class Methods

new(name, arguments, expression, transient_definitions) click to toggle source
Calls superclass method Keisan::Function::new
# File lib/keisan/functions/expression_function.rb, line 6
def initialize(name, arguments, expression, transient_definitions)
  super(name, arguments.count)
  if expression.is_a?(::String)
    @expression = AST::parse(expression)
  else
    @expression = expression.deep_dup
  end
  @arguments = arguments
  @transient_definitions = transient_definitions
end

Public Instance Methods

call(context, *args) click to toggle source
# File lib/keisan/functions/expression_function.rb, line 17
def call(context, *args)
  validate_arguments!(args.count)

  local = local_context_for(context)
  arguments.each.with_index do |arg_name, i|
    local.register_variable!(arg_name, args[i])
  end

  expression.value(local)
end
differentiate(ast_function, variable, context = nil) click to toggle source

Multi-argument functions work as follows: Given f(x, y), in general we will take the derivative with respect to t, and x = x(t), y = y(t). For instance d/dt f(2*t, t+1). In this case, chain rule gives derivative: dx(t)/dt * f_x(x(t), y(t)) + dy(t)/dt * f_y(x(t), y(t)), where f_x and f_y are the x and y partial derivatives respectively.

# File lib/keisan/functions/expression_function.rb, line 72
def differentiate(ast_function, variable, context = nil)
  validate_arguments!(ast_function.children.count)

  local = local_context_for(context)

  argument_values = ast_function.children.map {|child| child.evaluated(local)}

  argument_derivatives = ast_function.children.map do |child|
    child.differentiated(variable, context)
  end

  partial_derivatives = calculate_partial_derivatives(context)

  AST::Plus.new(
    argument_derivatives.map.with_index {|argument_derivative, i|
      partial_derivative = partial_derivatives[i]
      argument_variables.each.with_index {|argument_variable, j|
        partial_derivative = partial_derivative.replaced(argument_variable, argument_values[j])
      }
      AST::Times.new([argument_derivative, partial_derivative])
    }
  )
end
evaluate(ast_function, context = nil) click to toggle source
# File lib/keisan/functions/expression_function.rb, line 36
def evaluate(ast_function, context = nil)
  validate_arguments!(ast_function.children.count)

  context ||= Context.new
  local = local_context_for(context)

  argument_values = ast_function.children.map {|child| child.evaluate(context)}

  arguments.each.with_index do |arg_name, i|
    local.register_variable!(arg_name, argument_values[i].evaluate(context))
  end

  expression.evaluated(local)
end
simplify(ast_function, context = nil) click to toggle source
# File lib/keisan/functions/expression_function.rb, line 51
def simplify(ast_function, context = nil)
  validate_arguments!(ast_function.children.count)

  ast_function.instance_variable_set(
    :@children,
    ast_function.children.map {|child| child.evaluate(context)}
  )

  if ast_function.children.all? {|child| child.is_a?(AST::ConstantLiteral)}
    value(ast_function, context).to_node.simplify(context)
  else
    ast_function
  end
end
value(ast_function, context = nil) click to toggle source
# File lib/keisan/functions/expression_function.rb, line 28
def value(ast_function, context = nil)
  validate_arguments!(ast_function.children.count)

  context ||= Context.new
  argument_values = ast_function.children.map {|child| child.value(context)}
  call(context, *argument_values)
end

Private Instance Methods

argument_variables() click to toggle source
# File lib/keisan/functions/expression_function.rb, line 98
def argument_variables
  @argument_variables ||= arguments.map {|argument| AST::Variable.new(argument)}
end
calculate_partial_derivatives(context) click to toggle source
# File lib/keisan/functions/expression_function.rb, line 102
def calculate_partial_derivatives(context)
  argument_variables.map.with_index do |variable, i|
    partial_derivative = expression.differentiated(variable, context)
  end
end
local_context_for(context = nil) click to toggle source
# File lib/keisan/functions/expression_function.rb, line 108
def local_context_for(context = nil)
  context ||= Context.new
  context.spawn_child(definitions: @transient_definitions, shadowed: @arguments, transient: true)
end