Class: CAS::Piecewise

Inherits:
BinaryOp show all
Defined in:
lib/functions/fnc-piecewise.rb,
lib/Mr.CAS/graphviz.rb

Overview

Piecewise function. The function returns when called a result that dependes upon the evaluation of a condition. In practice:

“`

 /
|  f(x)   if condition(x) is True

<

|  g(x)   otherwise
 \

“`

From this class other classes will inherit like `CAS::Max` and `CAS::Min` classes

Direct Known Subclasses

Max, Min, MinMax

Instance Attribute Summary collapse

Attributes inherited from BinaryOp

#x, #y

Attributes inherited from Op

#x

Instance Method Summary collapse

Methods inherited from BinaryOp

#args, #depend?, #inspect, #simplify, #subs, #subs_lhs, #subs_rhs

Methods inherited from Op

#!=, #*, #**, #+, #-, #[email protected], #/, #args, #as_proc, #depend?, #equal, #greater, #greater_equal, init_simplify_dict, #inspect, #limit, numeric_to_const, #simplify, simplify_dict, #simplify_dictionary, #smaller, #smaller_equal, #subs, #to_c_lib

Constructor Details

#initialize(x, y, condition) ⇒ Piecewise

Initialize a new piecewise function. It requires first the function that returns when condition is true, than the function when condition is false, and finally the condition that must be of class `CAS::Condition`

* **argument**: `CAS::Op` first function
* **argument**: `CAS::Op` second function
* **argument**: `CAS::Condition` evaluated condition
* **returns**: `CAS::Piecewise` new instance


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# File 'lib/functions/fnc-piecewise.rb', line 56

def initialize(x, y, condition)
  CAS::Help.assert(condition, CAS::Condition)

  super(x, y)
  @condition = condition
end

Instance Attribute Details

#condition ⇒ Object (readonly)

Returns the value of attribute condition


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# File 'lib/functions/fnc-piecewise.rb', line 46

def condition
  @condition
end

Instance Method Details

#==(op) ⇒ Object

Checks if two `CAS::Piecewise` are equal. Checks equality on all functions+ and conditions

* **argument**: `CAS::Op` to be checked against
* **returns**: `TrueClass` or `FalseClass`


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# File 'lib/functions/fnc-piecewise.rb', line 99

def ==(op)
  CAS::Help.assert(op, CAS::Op)
  if self.class != op.class
    return false
  else
    return ((@x == op.x) and (@y == op.y) and (@condition == op.condition))
  end
end

#call(fd) ⇒ Object

Executes the condition. If it is `true` it returns the first function, else it returns the value of the second function.

* **argument**: `Hash` with value tables
* **returns**: `Numeric` the result of the call


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# File 'lib/functions/fnc-piecewise.rb', line 89

def call(fd)
  CAS::Help.assert(fd, Hash)
  (@condition.call(fd) ? @x.call(fd) : @y.call(fd))
end

#diff(v) ⇒ Object

Derivative of a function is performed as derivative of the two internal functions while condition is unchanged

warning

Piecewise functions are in general not differentiable. Thus differentiability

is left to the user

“`

    /                                     /
d  |  f(x)   if condition(x) is True     | f'(x)   if condition(x) is True

– < = < dx | g(x) otherwise | g'(x) otherwise

\                                     \

“`

* **argument**: `CAS::Op` argument of derivative
* **returns**: `CAS::Piecewise` with derivated functions and unchanged condition


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# File 'lib/functions/fnc-piecewise.rb', line 79

def diff(v)
  CAS::Help.assert(v, CAS::Op)
  return CAS::Piecewise.new(@x.diff(v).simplify, @y.diff(v).simplify, @condition)
end

#dot_graph ⇒ Object

Convert piecewise function into a dot graphviz representation

* **returns**: `String`


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# File 'lib/Mr.CAS/graphviz.rb', line 94

def dot_graph
  cls = "#{self.class.to_s.gsub("CAS::", "")}_#{self.object_id}"
  "#{cls} -> #{@x.dot_graph}\n  #{cls} -> #{@y.dot_graph}\n  #{cls} -> #{@condition.dot_graph}"
end

#to_code ⇒ Object

Convert the piecewise funtion to a String of Ruby code

* **returns**: `String` of code


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# File 'lib/functions/fnc-piecewise.rb', line 111

def to_code
  "(#{@condition.to_code} ? (#{@x.to_code}) : (#{@y.to_code}))"
end

#to_latex ⇒ Object

Convert piecewise function into LaTeX representation

* **returns**: `String` of LaTeX code


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# File 'lib/functions/fnc-piecewise.rb', line 125

def to_latex
  "\\left\\{ \\begin{array}{lr} #{@x.to_latex} & #{@condition.to_latex} \\\\ #{@y.to_latex} \\end{array} \\right."
end

#to_s ⇒ Object

Convert the piecewise function into a String

* **returns**: `String`


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# File 'lib/functions/fnc-piecewise.rb', line 118

def to_s
  "(#{@condition} ? #{@x} : #{@y})"
end