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lammps/lib/colvars/lepton/src/ParsedExpression.cpp
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ParsedExpression.cpp
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/* -------------------------------------------------------------------------- *
* Lepton *
* -------------------------------------------------------------------------- *
* This is part of the Lepton expression parser originating from *
* Simbios, the NIH National Center for Physics-Based Simulation of *
* Biological Structures at Stanford, funded under the NIH Roadmap for *
* Medical Research, grant U54 GM072970. See https://simtk.org. *
* *
* Portions copyright (c) 2009 Stanford University and the Authors. *
* Authors: Peter Eastman *
* Contributors: *
* *
* Permission is hereby granted, free of charge, to any person obtaining a *
* copy of this software and associated documentation files (the "Software"), *
* to deal in the Software without restriction, including without limitation *
* the rights to use, copy, modify, merge, publish, distribute, sublicense, *
* and/or sell copies of the Software, and to permit persons to whom the *
* Software is furnished to do so, subject to the following conditions: *
* *
* The above copyright notice and this permission notice shall be included in *
* all copies or substantial portions of the Software. *
* *
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR *
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, *
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL *
* THE AUTHORS, CONTRIBUTORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, *
* DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR *
* OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE *
* USE OR OTHER DEALINGS IN THE SOFTWARE. *
* -------------------------------------------------------------------------- */
#include "lepton/ParsedExpression.h"
#include "lepton/CompiledExpression.h"
#include "lepton/ExpressionProgram.h"
#include "lepton/Operation.h"
#include <limits>
#include <vector>
using namespace Lepton;
using namespace std;
ParsedExpression::ParsedExpression() : rootNode(ExpressionTreeNode()) {
}
ParsedExpression::ParsedExpression(const ExpressionTreeNode& rootNode) : rootNode(rootNode) {
}
const ExpressionTreeNode& ParsedExpression::getRootNode() const {
if (&rootNode.getOperation() == NULL)
throw Exception("Illegal call to an initialized ParsedExpression");
return rootNode;
}
double ParsedExpression::evaluate() const {
return evaluate(getRootNode(), map<string, double>());
}
double ParsedExpression::evaluate(const map<string, double>& variables) const {
return evaluate(getRootNode(), variables);
}
double ParsedExpression::evaluate(const ExpressionTreeNode& node, const map<string, double>& variables) {
int numArgs = (int) node.getChildren().size();
vector<double> args(max(numArgs, 1));
for (int i = 0; i < numArgs; i++)
args[i] = evaluate(node.getChildren()[i], variables);
return node.getOperation().evaluate(&args[0], variables);
}
ParsedExpression ParsedExpression::optimize() const {
ExpressionTreeNode result = precalculateConstantSubexpressions(getRootNode());
while (true) {
ExpressionTreeNode simplified = substituteSimplerExpression(result);
if (simplified == result)
break;
result = simplified;
}
return ParsedExpression(result);
}
ParsedExpression ParsedExpression::optimize(const map<string, double>& variables) const {
ExpressionTreeNode result = preevaluateVariables(getRootNode(), variables);
result = precalculateConstantSubexpressions(result);
while (true) {
ExpressionTreeNode simplified = substituteSimplerExpression(result);
if (simplified == result)
break;
result = simplified;
}
return ParsedExpression(result);
}
ExpressionTreeNode ParsedExpression::preevaluateVariables(const ExpressionTreeNode& node, const map<string, double>& variables) {
if (node.getOperation().getId() == Operation::VARIABLE) {
const Operation::Variable& var = dynamic_cast<const Operation::Variable&>(node.getOperation());
map<string, double>::const_iterator iter = variables.find(var.getName());
if (iter == variables.end())
return node;
return ExpressionTreeNode(new Operation::Constant(iter->second));
}
vector<ExpressionTreeNode> children(node.getChildren().size());
for (int i = 0; i < (int) children.size(); i++)
children[i] = preevaluateVariables(node.getChildren()[i], variables);
return ExpressionTreeNode(node.getOperation().clone(), children);
}
ExpressionTreeNode ParsedExpression::precalculateConstantSubexpressions(const ExpressionTreeNode& node) {
vector<ExpressionTreeNode> children(node.getChildren().size());
for (int i = 0; i < (int) children.size(); i++)
children[i] = precalculateConstantSubexpressions(node.getChildren()[i]);
ExpressionTreeNode result = ExpressionTreeNode(node.getOperation().clone(), children);
if (node.getOperation().getId() == Operation::VARIABLE || node.getOperation().getId() == Operation::CUSTOM)
return result;
for (int i = 0; i < (int) children.size(); i++)
if (children[i].getOperation().getId() != Operation::CONSTANT)
return result;
return ExpressionTreeNode(new Operation::Constant(evaluate(result, map<string, double>())));
}
ExpressionTreeNode ParsedExpression::substituteSimplerExpression(const ExpressionTreeNode& node) {
vector<ExpressionTreeNode> children(node.getChildren().size());
for (int i = 0; i < (int) children.size(); i++)
children[i] = substituteSimplerExpression(node.getChildren()[i]);
switch (node.getOperation().getId()) {
case Operation::ADD:
{
double first = getConstantValue(children[0]);
double second = getConstantValue(children[1]);
if (first == 0.0) // Add 0
return children[1];
if (second == 0.0) // Add 0
return children[0];
if (first == first) // Add a constant
return ExpressionTreeNode(new Operation::AddConstant(first), children[1]);
if (second == second) // Add a constant
return ExpressionTreeNode(new Operation::AddConstant(second), children[0]);
if (children[1].getOperation().getId() == Operation::NEGATE) // a+(-b) = a-b
return ExpressionTreeNode(new Operation::Subtract(), children[0], children[1].getChildren()[0]);
if (children[0].getOperation().getId() == Operation::NEGATE) // (-a)+b = b-a
return ExpressionTreeNode(new Operation::Subtract(), children[1], children[0].getChildren()[0]);
break;
}
case Operation::SUBTRACT:
{
if (children[0] == children[1])
return ExpressionTreeNode(new Operation::Constant(0.0)); // Subtracting anything from itself is 0
double first = getConstantValue(children[0]);
if (first == 0.0) // Subtract from 0
return ExpressionTreeNode(new Operation::Negate(), children[1]);
double second = getConstantValue(children[1]);
if (second == 0.0) // Subtract 0
return children[0];
if (second == second) // Subtract a constant
return ExpressionTreeNode(new Operation::AddConstant(-second), children[0]);
if (children[1].getOperation().getId() == Operation::NEGATE) // a-(-b) = a+b
return ExpressionTreeNode(new Operation::Add(), children[0], children[1].getChildren()[0]);
break;
}
case Operation::MULTIPLY:
{
double first = getConstantValue(children[0]);
double second = getConstantValue(children[1]);
if (first == 0.0 || second == 0.0) // Multiply by 0
return ExpressionTreeNode(new Operation::Constant(0.0));
if (first == 1.0) // Multiply by 1
return children[1];
if (second == 1.0) // Multiply by 1
return children[0];
if (children[0].getOperation().getId() == Operation::CONSTANT) { // Multiply by a constant
if (children[1].getOperation().getId() == Operation::MULTIPLY_CONSTANT) // Combine two multiplies into a single one
return ExpressionTreeNode(new Operation::MultiplyConstant(first*dynamic_cast<const Operation::MultiplyConstant*>(&children[1].getOperation())->getValue()), children[1].getChildren()[0]);
return ExpressionTreeNode(new Operation::MultiplyConstant(first), children[1]);
}
if (children[1].getOperation().getId() == Operation::CONSTANT) { // Multiply by a constant
if (children[0].getOperation().getId() == Operation::MULTIPLY_CONSTANT) // Combine two multiplies into a single one
return ExpressionTreeNode(new Operation::MultiplyConstant(second*dynamic_cast<const Operation::MultiplyConstant*>(&children[0].getOperation())->getValue()), children[0].getChildren()[0]);
return ExpressionTreeNode(new Operation::MultiplyConstant(second), children[0]);
}
if (children[0].getOperation().getId() == Operation::NEGATE && children[1].getOperation().getId() == Operation::NEGATE) // The two negations cancel
return ExpressionTreeNode(new Operation::Multiply(), children[0].getChildren()[0], children[1].getChildren()[0]);
if (children[0].getOperation().getId() == Operation::NEGATE && children[1].getOperation().getId() == Operation::MULTIPLY_CONSTANT) // Negate the constant
return ExpressionTreeNode(new Operation::Multiply(), children[0].getChildren()[0], ExpressionTreeNode(new Operation::MultiplyConstant(-dynamic_cast<const Operation::MultiplyConstant*>(&children[1].getOperation())->getValue()), children[1].getChildren()[0]));
if (children[1].getOperation().getId() == Operation::NEGATE && children[0].getOperation().getId() == Operation::MULTIPLY_CONSTANT) // Negate the constant
return ExpressionTreeNode(new Operation::Multiply(), ExpressionTreeNode(new Operation::MultiplyConstant(-dynamic_cast<const Operation::MultiplyConstant*>(&children[0].getOperation())->getValue()), children[0].getChildren()[0]), children[1].getChildren()[0]);
if (children[0].getOperation().getId() == Operation::NEGATE) // Pull the negation out so it can possibly be optimized further
return ExpressionTreeNode(new Operation::Negate(), ExpressionTreeNode(new Operation::Multiply(), children[0].getChildren()[0], children[1]));
if (children[1].getOperation().getId() == Operation::NEGATE) // Pull the negation out so it can possibly be optimized further
return ExpressionTreeNode(new Operation::Negate(), ExpressionTreeNode(new Operation::Multiply(), children[0], children[1].getChildren()[0]));
if (children[1].getOperation().getId() == Operation::RECIPROCAL) // a*(1/b) = a/b
return ExpressionTreeNode(new Operation::Divide(), children[0], children[1].getChildren()[0]);
if (children[0].getOperation().getId() == Operation::RECIPROCAL) // (1/a)*b = b/a
return ExpressionTreeNode(new Operation::Divide(), children[1], children[0].getChildren()[0]);
if (children[0] == children[1])
return ExpressionTreeNode(new Operation::Square(), children[0]); // x*x = square(x)
if (children[0].getOperation().getId() == Operation::SQUARE && children[0].getChildren()[0] == children[1])
return ExpressionTreeNode(new Operation::Cube(), children[1]); // x*x*x = cube(x)
if (children[1].getOperation().getId() == Operation::SQUARE && children[1].getChildren()[0] == children[0])
return ExpressionTreeNode(new Operation::Cube(), children[0]); // x*x*x = cube(x)
break;
}
case Operation::DIVIDE:
{
if (children[0] == children[1])
return ExpressionTreeNode(new Operation::Constant(1.0)); // Dividing anything from itself is 0
double numerator = getConstantValue(children[0]);
if (numerator == 0.0) // 0 divided by something
return ExpressionTreeNode(new Operation::Constant(0.0));
if (numerator == 1.0) // 1 divided by something
return ExpressionTreeNode(new Operation::Reciprocal(), children[1]);
double denominator = getConstantValue(children[1]);
if (denominator == 1.0) // Divide by 1
return children[0];
if (children[1].getOperation().getId() == Operation::CONSTANT) {
if (children[0].getOperation().getId() == Operation::MULTIPLY_CONSTANT) // Combine a multiply and a divide into one multiply
return ExpressionTreeNode(new Operation::MultiplyConstant(dynamic_cast<const Operation::MultiplyConstant*>(&children[0].getOperation())->getValue()/denominator), children[0].getChildren()[0]);
return ExpressionTreeNode(new Operation::MultiplyConstant(1.0/denominator), children[0]); // Replace a divide with a multiply
}
if (children[0].getOperation().getId() == Operation::NEGATE && children[1].getOperation().getId() == Operation::NEGATE) // The two negations cancel
return ExpressionTreeNode(new Operation::Divide(), children[0].getChildren()[0], children[1].getChildren()[0]);
if (children[1].getOperation().getId() == Operation::NEGATE && children[0].getOperation().getId() == Operation::MULTIPLY_CONSTANT) // Negate the constant
return ExpressionTreeNode(new Operation::Divide(), ExpressionTreeNode(new Operation::MultiplyConstant(-dynamic_cast<const Operation::MultiplyConstant*>(&children[0].getOperation())->getValue()), children[0].getChildren()[0]), children[1].getChildren()[0]);
if (children[0].getOperation().getId() == Operation::NEGATE) // Pull the negation out so it can possibly be optimized further
return ExpressionTreeNode(new Operation::Negate(), ExpressionTreeNode(new Operation::Divide(), children[0].getChildren()[0], children[1]));
if (children[1].getOperation().getId() == Operation::NEGATE) // Pull the negation out so it can possibly be optimized further
return ExpressionTreeNode(new Operation::Negate(), ExpressionTreeNode(new Operation::Divide(), children[0], children[1].getChildren()[0]));
if (children[1].getOperation().getId() == Operation::RECIPROCAL) // a/(1/b) = a*b
return ExpressionTreeNode(new Operation::Multiply(), children[0], children[1].getChildren()[0]);
break;
}
case Operation::POWER:
{
double base = getConstantValue(children[0]);
if (base == 0.0) // 0 to any power is 0
return ExpressionTreeNode(new Operation::Constant(0.0));
if (base == 1.0) // 1 to any power is 1
return ExpressionTreeNode(new Operation::Constant(1.0));
double exponent = getConstantValue(children[1]);
if (exponent == 0.0) // x^0 = 1
return ExpressionTreeNode(new Operation::Constant(1.0));
if (exponent == 1.0) // x^1 = x
return children[0];
if (exponent == -1.0) // x^-1 = recip(x)
return ExpressionTreeNode(new Operation::Reciprocal(), children[0]);
if (exponent == 2.0) // x^2 = square(x)
return ExpressionTreeNode(new Operation::Square(), children[0]);
if (exponent == 3.0) // x^3 = cube(x)
return ExpressionTreeNode(new Operation::Cube(), children[0]);
if (exponent == 0.5) // x^0.5 = sqrt(x)
return ExpressionTreeNode(new Operation::Sqrt(), children[0]);
if (exponent == exponent) // Constant power
return ExpressionTreeNode(new Operation::PowerConstant(exponent), children[0]);
break;
}
case Operation::NEGATE:
{
if (children[0].getOperation().getId() == Operation::MULTIPLY_CONSTANT) // Combine a multiply and a negate into a single multiply
return ExpressionTreeNode(new Operation::MultiplyConstant(-dynamic_cast<const Operation::MultiplyConstant*>(&children[0].getOperation())->getValue()), children[0].getChildren()[0]);
if (children[0].getOperation().getId() == Operation::CONSTANT) // Negate a constant
return ExpressionTreeNode(new Operation::Constant(-getConstantValue(children[0])));
if (children[0].getOperation().getId() == Operation::NEGATE) // The two negations cancel
return children[0].getChildren()[0];
break;
}
case Operation::MULTIPLY_CONSTANT:
{
if (children[0].getOperation().getId() == Operation::MULTIPLY_CONSTANT) // Combine two multiplies into a single one
return ExpressionTreeNode(new Operation::MultiplyConstant(dynamic_cast<const Operation::MultiplyConstant*>(&node.getOperation())->getValue()*dynamic_cast<const Operation::MultiplyConstant*>(&children[0].getOperation())->getValue()), children[0].getChildren()[0]);
if (children[0].getOperation().getId() == Operation::CONSTANT) // Multiply two constants
return ExpressionTreeNode(new Operation::Constant(dynamic_cast<const Operation::MultiplyConstant*>(&node.getOperation())->getValue()*getConstantValue(children[0])));
if (children[0].getOperation().getId() == Operation::NEGATE) // Combine a multiply and a negate into a single multiply
return ExpressionTreeNode(new Operation::MultiplyConstant(-dynamic_cast<const Operation::MultiplyConstant*>(&node.getOperation())->getValue()), children[0].getChildren()[0]);
break;
}
default:
{
// If operation ID is not one of the above,
// we don't substitute a simpler expression.
break;
}
}
return ExpressionTreeNode(node.getOperation().clone(), children);
}
ParsedExpression ParsedExpression::differentiate(const string& variable) const {
return differentiate(getRootNode(), variable);
}
ExpressionTreeNode ParsedExpression::differentiate(const ExpressionTreeNode& node, const string& variable) {
vector<ExpressionTreeNode> childDerivs(node.getChildren().size());
for (int i = 0; i < (int) childDerivs.size(); i++)
childDerivs[i] = differentiate(node.getChildren()[i], variable);
return node.getOperation().differentiate(node.getChildren(),childDerivs, variable);
}
double ParsedExpression::getConstantValue(const ExpressionTreeNode& node) {
if (node.getOperation().getId() == Operation::CONSTANT)
return dynamic_cast<const Operation::Constant&>(node.getOperation()).getValue();
return numeric_limits<double>::quiet_NaN();
}
ExpressionProgram ParsedExpression::createProgram() const {
return ExpressionProgram(*this);
}
CompiledExpression ParsedExpression::createCompiledExpression() const {
return CompiledExpression(*this);
}
ParsedExpression ParsedExpression::renameVariables(const map<string, string>& replacements) const {
return ParsedExpression(renameNodeVariables(getRootNode(), replacements));
}
ExpressionTreeNode ParsedExpression::renameNodeVariables(const ExpressionTreeNode& node, const map<string, string>& replacements) {
if (node.getOperation().getId() == Operation::VARIABLE) {
map<string, string>::const_iterator replace = replacements.find(node.getOperation().getName());
if (replace != replacements.end())
return ExpressionTreeNode(new Operation::Variable(replace->second));
}
vector<ExpressionTreeNode> children;
for (int i = 0; i < (int) node.getChildren().size(); i++)
children.push_back(renameNodeVariables(node.getChildren()[i], replacements));
return ExpressionTreeNode(node.getOperation().clone(), children);
}
ostream& Lepton::operator<<(ostream& out, const ExpressionTreeNode& node) {
if (node.getOperation().isInfixOperator() && node.getChildren().size() == 2) {
out << "(" << node.getChildren()[0] << ")" << node.getOperation().getName() << "(" << node.getChildren()[1] << ")";
}
else if (node.getOperation().isInfixOperator() && node.getChildren().size() == 1) {
out << "(" << node.getChildren()[0] << ")" << node.getOperation().getName();
}
else {
out << node.getOperation().getName();
if (node.getChildren().size() > 0) {
out << "(";
for (int i = 0; i < (int) node.getChildren().size(); i++) {
if (i > 0)
out << ", ";
out << node.getChildren()[i];
}
out << ")";
}
}
return out;
}
ostream& Lepton::operator<<(ostream& out, const ParsedExpression& exp) {
out << exp.getRootNode();
return out;
}
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