/*
Author: Juan Rada-Vilela, Ph.D.
Copyright (C) 2010-2014 FuzzyLite Limited
All rights reserved
This file is part of fuzzylite.
fuzzylite is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License as published by the Free
Software Foundation, either version 3 of the License, or (at your option)
any later version.
fuzzylite is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License
for more details.
You should have received a copy of the GNU Lesser General Public License
along with fuzzylite. If not, see .
fuzzyliteâ„¢ is a trademark of FuzzyLite Limited.
*/
#include "fl/term/Function.h"
#include "fl/Engine.h"
#include "fl/factory/FactoryManager.h"
#include "fl/factory/FunctionFactory.h"
#include "fl/rule/Rule.h"
#include "fl/variable/InputVariable.h"
#include "fl/variable/OutputVariable.h"
#include
#include
#include
#include
#include
namespace fl {
/**
* Parsing elements
*/
Function::Element::Element(const std::string& name, const std::string& description, Type type)
: name(name), description(description), type(type), unary(fl::null), binary(fl::null), arity(0),
precedence(0), associativity(-1) {
}
Function::Element::Element(const std::string& name, const std::string& description,
Type type, Unary unary, int precedence, int associativity)
: name(name), description(description), type(type), unary(unary), binary(fl::null), arity(1),
precedence(precedence), associativity(associativity) {
}
Function::Element::Element(const std::string& name, const std::string& description,
Type type, Binary binary, int precedence, int associativity)
: name(name), description(description), type(type), unary(fl::null), binary(binary), arity(2),
precedence(precedence), associativity(associativity) {
}
Function::Element::~Element() {
}
bool Function::Element::isOperator() const {
return type == OPERATOR;
}
bool Function::Element::isFunction() const {
return type == FUNCTION;
}
Function::Element* Function::Element::clone() const {
return new Element(*this);
}
std::string Function::Element::toString() const {
std::ostringstream ss;
if (type == OPERATOR) {
ss << "Operator (name=" << name << ", "
<< "description=" << description << ", "
<< "precedence=" << precedence << ", "
<< "arity=" << arity << ", "
<< "associativity=" << associativity << ", ";
if (arity == 1) ss << "pointer=" << unary;
else if (arity == 2) ss << "pointer=" << binary;
else ss << "pointer=error";
ss << ")";
} else if (type == FUNCTION) {
ss << "Function (name=" << name << ", "
<< "description=" << description << ", "
<< "arity=" << arity << ", "
<< "associativity=" << associativity << ", ";
if (arity == 1) ss << "pointer=" << unary;
else if (arity == 2) ss << "pointer=" << binary;
else ss << "pointer=error";
ss << ")";
}
return ss.str();
}
/******************************
* Tree Node Elements
******************************/
Function::Node::Node(Element* element, Node* left, Node* right)
: element(element), left(left), right(right), variable(""), value(fl::nan) {
}
Function::Node::Node(const std::string& variable)
: element(fl::null), left(fl::null), right(fl::null), variable(variable), value(fl::nan) {
}
Function::Node::Node(scalar value)
: element(fl::null), left(fl::null), right(fl::null), variable(""), value(value) {
}
Function::Node::Node(const Node& other)
: element(fl::null), left(fl::null), right(fl::null), variable(""), value(fl::nan) {
copyFrom(other);
}
Function::Node& Function::Node::operator=(const Node& other) {
if (this != &other) {
element.reset(fl::null);
left.reset(fl::null);
right.reset(fl::null);
copyFrom(other);
}
return *this;
}
void Function::Node::copyFrom(const Node& other) {
if (other.element.get()) element.reset(other.element->clone());
if (other.left.get()) left.reset(other.left->clone());
if (other.right.get()) right.reset(other.right->clone());
variable = other.variable;
value = other.value;
}
Function::Node::~Node() {
}
scalar Function::Node::evaluate(const std::map* variables) const {
scalar result = fl::nan;
if (element.get()) {
if (element->unary) {
result = element->unary(left->evaluate(variables));
} else if (element->binary) {
result = element->binary(right->evaluate(variables), left->evaluate(variables));
} else {
std::ostringstream ex;
ex << "[function error] arity <" << element->arity << "> of "
<< (element->isOperator() ? "operator" : "function") <<
" <" << element->name << "> is fl::null";
throw fl::Exception(ex.str(), FL_AT);
}
} else if (not variable.empty()) {
if (not variables) {
throw fl::Exception("[function error] "
"expected a map of variables, but none was provided", FL_AT);
}
std::map::const_iterator it = variables->find(variable);
if (it != variables->end()) result = it->second;
else throw fl::Exception("[function error] "
"unknown variable <" + variable + ">", FL_AT);
} else {
result = value;
}
return result;
}
Function::Node* Function::Node::clone() const {
return new Node(*this);
}
std::string Function::Node::toString() const {
std::ostringstream ss;
if (element.get()) ss << element->name;
else if (not variable.empty()) ss << variable;
else ss << fl::Op::str(value);
return ss.str();
}
std::string Function::Node::toPrefix(const Node* node) const {
if (not node) node = this;
if (not fl::Op::isNaN(node->value)) { //is terminal
return fl::Op::str(node->value);
}
if (not node->variable.empty()) {
return node->variable;
}
std::ostringstream ss;
ss << node->toString();
if (node->left.get())
ss << " " << this->toPrefix(node->left.get());
if (node->right.get())
ss << " " << this->toPrefix(node->right.get());
return ss.str();
}
std::string Function::Node::toInfix(const Node* node) const {
if (not node) node = this;
if (not fl::Op::isNaN(node->value)) { //is proposition
return fl::Op::str(node->value);
}
if (not node->variable.empty()) {
return node->variable;
}
std::ostringstream ss;
if (node->left.get())
ss << this->toInfix(node->left.get()) << " ";
ss << node->toString();
if (node->right.get())
ss << " " << this->toInfix(node->right.get());
return ss.str();
}
std::string Function::Node::toPostfix(const Node* node) const {
if (not node) node = this;
if (not fl::Op::isNaN(node->value)) { //is proposition
return fl::Op::str(node->value);
}
if (not node->variable.empty()) {
return node->variable;
}
std::ostringstream ss;
if (node->left.get())
ss << this->toPostfix(node->left.get()) << " ";
if (node->right.get())
ss << this->toPostfix(node->right.get()) << " ";
ss << node->toString();
return ss.str();
}
/**********************************
* Function class.
**********************************/
Function::Function(const std::string& name,
const std::string& formula, const Engine* engine)
: Term(name), _root(fl::null), _formula(formula), _engine(engine) {
}
Function::Function(const Function& other) : Term(other),
_root(fl::null), _formula(other._formula), _engine(other._engine) {
if (other._root.get()) _root.reset(other._root->clone());
variables = other.variables;
}
Function& Function::operator=(const Function& other) {
if (this != &other) {
_root.reset(fl::null);
Term::operator=(other);
_formula = other._formula;
_engine = other._engine;
if (other._root.get()) _root.reset(other._root->clone());
variables = other.variables;
}
return *this;
}
Function::~Function() {
}
std::string Function::className() const {
return "Function";
}
scalar Function::membership(scalar x) const {
if (not this->_root.get()) {
throw fl::Exception("[function error] function <" + _formula + "> not loaded.", FL_AT);
}
if (this->_engine) {
for (int i = 0; i < this->_engine->numberOfInputVariables(); ++i) {
InputVariable* input = this->_engine->getInputVariable(i);
this->variables[input->getName()] = input->getInputValue();
}
for (int i = 0; i < this->_engine->numberOfOutputVariables(); ++i) {
OutputVariable* output = this->_engine->getOutputVariable(i);
this->variables[output->getName()] = output->getOutputValue();
}
}
this->variables["x"] = x;
return this->evaluate(&this->variables);
}
scalar Function::evaluate(const std::map* localVariables) const {
if (not this->_root.get())
throw fl::Exception("[function error] evaluation failed because the function is not loaded", FL_AT);
if (localVariables)
return this->_root->evaluate(localVariables);
return this->_root->evaluate(&this->variables);
}
std::string Function::parameters() const {
return _formula;
}
void Function::configure(const std::string& parameters) {
load(parameters);
}
Function* Function::create(const std::string& name,
const std::string& infix, const Engine* engine) {
FL_unique_ptr result(new Function(name));
result->load(infix, engine);
return result.release();
}
bool Function::isLoaded() const {
return this->_root.get() != fl::null;
}
void Function::unload() {
this->_root.reset(fl::null);
this->variables.clear();
}
void Function::load() {
load(this->_formula);
}
void Function::load(const std::string& formula) {
load(formula, this->_engine);
}
void Function::load(const std::string& formula,
const Engine* engine) {
unload();
this->_formula = formula;
this->_engine = engine;
this->_root.reset(parse(formula));
membership(0.0); //make sure function evaluates without throwing exception.
}
void Function::setFormula(const std::string& formula) {
this->_formula = formula;
}
std::string Function::getFormula() const {
return this->_formula;
}
void Function::setEngine(const Engine* engine) {
this->_engine = engine;
}
const Engine* Function::getEngine() const {
return this->_engine;
}
Function::Node* Function::root() const {
return this->_root.get();
}
Function* Function::clone() const {
return new Function(*this);
}
Term* Function::constructor() {
return new Function;
}
std::string Function::space(const std::string& formula) const {
std::vector chars;
chars.push_back("(");
chars.push_back(")");
chars.push_back(",");
std::vector operators = fl::FactoryManager::instance()->function()->availableOperators();
for (std::size_t i = 0; i < operators.size(); ++i) {
if (not (operators.at(i) == fl::Rule::andKeyword() or
operators.at(i) == fl::Rule::orKeyword())) {
chars.push_back(operators.at(i));
}
}
std::string result = formula;
for (std::size_t i = 0; i < chars.size(); ++i) {
result = fl::Op::findReplace(result, chars.at(i), " " + chars.at(i) + " ");
}
return result;
}
/****************************************
* The Glorious Parser
* Shunting-yard algorithm
* TODO: Maybe change it for http://en.wikipedia.org/wiki/Operator-precedence_parser
***************************************/
std::string Function::toPostfix(const std::string& formula) const {
std::string spacedFormula = space(formula);
std::queue queue;
std::stack stack;
std::stringstream tokenizer(spacedFormula);
std::string token;
FunctionFactory* factory = fl::FactoryManager::instance()->function();
while (tokenizer >> token) {
Element* element = factory->getObject(token);
bool isOperand = not element and token != "(" and token != ")" and token != ",";
if (isOperand) {
queue.push(token);
} else if (element and element->isFunction()) {
stack.push(token);
} else if (token == ",") {
while (not stack.empty() and stack.top() != "(") {
queue.push(stack.top());
stack.pop();
}
if (stack.empty() or stack.top() != "(") {
std::ostringstream ex;
ex << "[parsing error] mismatching parentheses in: " << formula;
throw fl::Exception(ex.str(), FL_AT);
}
} else if (element and element->isOperator()) {
Element* op1 = element;
for (;;) {
Element* op2 = fl::null;
if (not stack.empty()) op2 = factory->getObject(stack.top());
if (not op2) break;
if ((op1->associativity < 0 and op1->precedence == op2->precedence)
or op1->precedence < op2->precedence) {
queue.push(stack.top());
stack.pop();
} else
break;
}
stack.push(token);
} else if (token == "(") {
stack.push(token);
} else if (token == ")") {
while (not stack.empty() and stack.top() != "(") {
queue.push(stack.top());
stack.pop();
}
if (stack.empty() or stack.top() != "(") {
std::ostringstream ex;
ex << "[parsing error] mismatching parentheses in: " << formula;
throw fl::Exception(ex.str(), FL_AT);
}
stack.pop(); //get rid of "("
Element* top = fl::null;
if (not stack.empty()) top = factory->getObject(stack.top());
if (top and top->isFunction()) {
queue.push(stack.top());
stack.pop();
}
} else {
std::ostringstream ex;
ex << "[parsing error] unexpected error with token <" << token << ">";
throw fl::Exception(ex.str(), FL_AT);
}
}
while (not stack.empty()) {
if (stack.top() == "(" or stack.top() == ")") {
std::ostringstream ex;
ex << "[parsing error] mismatching parentheses in: " << formula;
throw fl::Exception(ex.str(), FL_AT);
}
queue.push(stack.top());
stack.pop();
}
std::stringstream ssPostfix;
while (not queue.empty()) {
ssPostfix << queue.front();
queue.pop();
if (not queue.empty()) ssPostfix << " ";
}
// FL_DBG("postfix=" << ssPostfix.str());
return ssPostfix.str();
}
// bool FunctionFactory::isOperand(const std::string& name) const {
// //An operand is not a parenthesis...
// if (name == "(" or name == ")" or name == ",") return false;
// //nor an operator...
// if (isOperator(name)) return false;
// //nor a function...
// if (isFunction(name)) return false;
// //...it is everything else :)
// return true;
// }
Function::Node* Function::parse(const std::string& formula) {
if (formula.empty())
throw fl::Exception("[function error] formula is empty", FL_AT);
std::string postfix = toPostfix(formula);
std::stack stack;
std::istringstream tokenizer(postfix);
std::string token;
FunctionFactory* factory = fl::FactoryManager::instance()->function();
while (tokenizer >> token) {
Element* element = factory->getObject(token);
bool isOperand = not element and token != "(" and token != ")" and token != ",";
if (element) {
if (element->arity > (int) stack.size()) {
std::ostringstream ss;
ss << "[function error] " << (element->isOperator() ? "operator" : "function") <<
" <" << element->name << "> has arity <" << element->arity << ">, "
"but found <" << stack.size() << "> element" <<
(stack.size() == 1 ? "" : "s");
throw fl::Exception(ss.str(), FL_AT);
}
Node* node = new Node(element->clone());
node->left.reset(stack.top());
stack.pop();
if (element->arity == 2) {
node->right.reset(stack.top());
stack.pop();
}
stack.push(node);
} else if (isOperand) {
Node* node;
try {
scalar value = fl::Op::toScalar(token);
node = new Node(value);
} catch (std::exception& ex) {
(void) ex;
node = new Node(token);
}
stack.push(node);
}
}
if (stack.size() != 1)
throw fl::Exception("[function error] ill-formed formula <" + formula + ">", FL_AT);
return stack.top();
}
void Function::main() {
Function f;
std::string text = "3+4*2/(1-5)^2^3";
FL_LOG(f.toPostfix(text));
FL_LOG("P: " << f.parse(text)->toInfix());
FL_LOG(">" << f.parse(text)->evaluate());
//3 4 2 * 1 5 - 2 3 ^ ^ / +
f.variables["y"] = 1.0;
text = "sin(y*x)^2/x";
FL_LOG("pre: " << f.parse(text)->toPrefix());
FL_LOG("in: " << f.parse(text)->toInfix());
FL_LOG("pos: " << f.parse(text)->toPostfix());
f.load(text);
FL_LOG("Result: " << f.membership(1));
//y x * sin 2 ^ x /
text = "(Temperature is High and Oxygen is Low) or "
"(Temperature is Low and (Oxygen is Low or Oxygen is High))";
FL_LOG(f.toPostfix(text));
f.variables["pi"] = 3.14;
text = "-5 *4/sin(-pi/2)";
FL_LOG(f.toPostfix(text));
try {
FL_LOG(f.parse(text)->evaluate());
} catch (std::exception& e) {
FL_LOG(e.what());
}
f.variables["pi"] = 3.14;
text = "~5 *4/sin(~pi/2)";
FL_LOG(f.toPostfix(text));
try {
FL_LOG(f.parse(text)->evaluate(&f.variables));
} catch (std::exception& e) {
FL_LOG(e.what());
}
}
}