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symbolic_expression_test.cc
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#include <algorithm>
#include <cmath>
#include <functional>
#include <map>
#include <memory>
#include <set>
#include <sstream>
#include <stdexcept>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
#include <gtest/gtest.h>
#include "drake/common/hash.h"
#include "drake/common/symbolic.h"
#include "drake/common/test_utilities/is_memcpy_movable.h"
#include "drake/common/test_utilities/symbolic_test_util.h"
using std::count_if;
using std::domain_error;
using std::equal_to;
using std::map;
using std::ostringstream;
using std::pair;
using std::runtime_error;
using std::set;
using std::string;
using std::unordered_map;
using std::unordered_set;
using std::vector;
namespace drake {
using test::IsMemcpyMovable;
namespace symbolic {
namespace {
using test::ExprEqual;
using test::ExprLess;
using test::ExprNotEqual;
using test::ExprNotLess;
using test::FormulaEqual;
template <typename T>
size_t get_std_hash(const T& item) {
return std::hash<T>{}(item);
}
// Checks if a given 'expressions' is ordered by Expression::Less.
void CheckOrdering(const vector<Expression>& expressions) {
for (size_t i{0}; i < expressions.size(); ++i) {
for (size_t j{0}; j < expressions.size(); ++j) {
if (i < j) {
EXPECT_PRED2(ExprLess, expressions[i], expressions[j])
<< "(Expressions[" << i << "] = " << expressions[i] << ")"
<< " is not less than "
<< "(Expressions[" << j << "] = " << expressions[j] << ")";
EXPECT_PRED2(ExprNotLess, expressions[j], expressions[i])
<< "(Expressions[" << j << "] = " << expressions[j] << ")"
<< " is less than "
<< "(Expressions[" << i << "] = " << expressions[i] << ")";
} else if (i > j) {
EXPECT_PRED2(ExprLess, expressions[j], expressions[i])
<< "(Expressions[" << j << "] = " << expressions[j] << ")"
<< " is not less than "
<< "(Expressions[" << i << "] = " << expressions[i] << ")";
EXPECT_PRED2(ExprNotLess, expressions[i], expressions[j])
<< "(Expressions[" << i << "] = " << expressions[i] << ")"
<< " is less than "
<< "(Expressions[" << j << "] = " << expressions[j] << ")";
} else {
EXPECT_PRED2(ExprNotLess, expressions[i], expressions[j])
<< "(Expressions[" << i << "] = " << expressions[i] << ")"
<< " is less than "
<< "(Expressions[" << j << "] = " << expressions[j] << ")";
EXPECT_PRED2(ExprNotLess, expressions[j], expressions[i])
<< "(Expressions[" << j << "] = " << expressions[j] << ")"
<< " is less than "
<< "(Expressions[" << i << "] = " << expressions[i] << ")";
}
}
}
}
// Provides common variables that are used by the following tests.
class SymbolicExpressionTest : public ::testing::Test {
protected:
const Variable var_a_{"a"};
const Variable var_x_{"x"};
const Variable var_y_{"y"};
const Variable var_z_{"z"};
const Expression a_{var_a_};
const Expression x_{var_x_};
const Expression y_{var_y_};
const Expression z_{var_z_};
const Expression x_plus_y_{x_ + y_};
const Expression x_plus_z_{x_ + z_};
const Expression zero_{0.0};
const Expression one_{1.0};
const Expression two_{2.0};
const Expression neg_one_{-1.0};
const Expression pi_{M_PI};
const Expression neg_pi_{-M_PI};
const Expression e_{M_E};
const Expression c1_{-10.0};
const Expression c2_{1.0};
const Expression c3_{3.14159};
const Expression c4_{-2.718};
const Expression e_constant_{1.0};
const Expression e_var_{var_x_};
const Expression e_add_{x_ + y_};
const Expression e_neg_{-x_}; // -1 * x_
const Expression e_mul_{x_ * y_};
const Expression e_div_{x_ / y_};
const Expression e_log_{log(x_)};
const Expression e_abs_{abs(x_)};
const Expression e_exp_{exp(x_)};
const Expression e_sqrt_{sqrt(x_)};
const Expression e_pow_{pow(x_, y_)};
const Expression e_sin_{sin(x_)};
const Expression e_cos_{cos(x_)};
const Expression e_tan_{tan(x_)};
const Expression e_asin_{asin(x_)};
const Expression e_acos_{acos(x_)};
const Expression e_atan_{atan(x_)};
const Expression e_atan2_{atan2(x_, y_)};
const Expression e_sinh_{sinh(x_)};
const Expression e_cosh_{cosh(x_)};
const Expression e_tanh_{tanh(x_)};
const Expression e_min_{min(x_, y_)};
const Expression e_max_{max(x_, y_)};
const Expression e_ceil_{ceil(x_)};
const Expression e_floor_{floor(x_)};
const Expression e_ite_{if_then_else(x_ < y_, x_, y_)};
const Expression e_nan_{Expression::NaN()};
const Expression e_uf_{uninterpreted_function("uf", {var_x_, var_y_})};
const vector<Expression> collection_{
e_constant_, e_var_, e_add_, e_neg_, e_mul_, e_div_, e_log_,
e_abs_, e_exp_, e_sqrt_, e_pow_, e_sin_, e_cos_, e_tan_,
e_asin_, e_acos_, e_atan_, e_atan2_, e_sinh_, e_cosh_, e_tanh_,
e_min_, e_max_, e_ceil_, e_floor_, e_ite_, e_nan_, e_uf_};
};
TEST_F(SymbolicExpressionTest, Dummy) {
EXPECT_TRUE(is_nan(dummy_value<Expression>::get()));
}
TEST_F(SymbolicExpressionTest, IsConstant1) {
EXPECT_TRUE(is_constant(e_constant_));
const vector<Expression>::difference_type cnt{
count_if(collection_.begin(), collection_.end(),
[](const Expression& e) { return is_constant(e); })};
EXPECT_EQ(cnt, 1);
}
TEST_F(SymbolicExpressionTest, IsConstant2) {
EXPECT_TRUE(is_constant(Expression{}, 0.0));
EXPECT_TRUE(is_constant(Expression::Zero(), 0.0));
EXPECT_TRUE(is_constant(Expression::One(), 1.0));
EXPECT_TRUE(is_constant(Expression::Pi(), M_PI));
EXPECT_TRUE(is_constant(Expression::E(), M_E));
}
TEST_F(SymbolicExpressionTest, IsZero) {
EXPECT_TRUE(is_zero(Expression{}));
EXPECT_TRUE(is_zero(Expression::Zero()));
}
TEST_F(SymbolicExpressionTest, IsOne) {
EXPECT_TRUE(is_one(Expression::One()));
}
TEST_F(SymbolicExpressionTest, IsNegOne) { EXPECT_TRUE(is_neg_one(neg_one_)); }
TEST_F(SymbolicExpressionTest, IsTwo) { EXPECT_TRUE(is_two(two_)); }
TEST_F(SymbolicExpressionTest, NaN) {
// It's OK to have NaN expression.
const Expression nan{NAN};
EXPECT_TRUE(is_nan(nan));
EXPECT_TRUE(nan.EqualTo(Expression::NaN()));
// It's OK to have an expression including NaN inside.
const Expression e1{1.0 + nan};
// It's OK to display an expression including NaN inside.
EXPECT_EQ(e1.to_string(), "(1 + NaN)");
// It throws when we evaluate an expression including NaN.
EXPECT_THROW(e1.Evaluate(), runtime_error);
}
TEST_F(SymbolicExpressionTest, IsVariable) {
EXPECT_TRUE(is_variable(e_var_));
const vector<Expression>::difference_type cnt{
count_if(collection_.begin(), collection_.end(),
[](const Expression& e) { return is_variable(e); })};
EXPECT_EQ(cnt, 1);
}
TEST_F(SymbolicExpressionTest, IsAddition) {
EXPECT_TRUE(is_addition(e_add_));
const vector<Expression>::difference_type cnt{
count_if(collection_.begin(), collection_.end(),
[](const Expression& e) { return is_addition(e); })};
EXPECT_EQ(cnt, 1);
}
TEST_F(SymbolicExpressionTest, IsMultiplication) {
EXPECT_TRUE(is_multiplication(e_mul_));
const vector<Expression>::difference_type cnt{
count_if(collection_.begin(), collection_.end(),
[](const Expression& e) { return is_multiplication(e); })};
EXPECT_EQ(cnt, 2);
}
TEST_F(SymbolicExpressionTest, IsDivision) {
EXPECT_TRUE(is_division(e_div_));
const vector<Expression>::difference_type cnt{
count_if(collection_.begin(), collection_.end(),
[](const Expression& e) { return is_division(e); })};
EXPECT_EQ(cnt, 1);
}
TEST_F(SymbolicExpressionTest, IsLog) {
EXPECT_TRUE(is_log(e_log_));
const vector<Expression>::difference_type cnt{
count_if(collection_.begin(), collection_.end(),
[](const Expression& e) { return is_log(e); })};
EXPECT_EQ(cnt, 1);
}
TEST_F(SymbolicExpressionTest, IsAbs) {
EXPECT_TRUE(is_abs(e_abs_));
const vector<Expression>::difference_type cnt{
count_if(collection_.begin(), collection_.end(),
[](const Expression& e) { return is_abs(e); })};
EXPECT_EQ(cnt, 1);
}
TEST_F(SymbolicExpressionTest, IsExp) {
EXPECT_TRUE(is_exp(e_exp_));
const vector<Expression>::difference_type cnt{
count_if(collection_.begin(), collection_.end(),
[](const Expression& e) { return is_exp(e); })};
EXPECT_EQ(cnt, 1);
}
TEST_F(SymbolicExpressionTest, IsSqrt) {
EXPECT_TRUE(is_sqrt(e_sqrt_));
const vector<Expression>::difference_type cnt{
count_if(collection_.begin(), collection_.end(),
[](const Expression& e) { return is_sqrt(e); })};
EXPECT_EQ(cnt, 1);
}
TEST_F(SymbolicExpressionTest, IsPow) {
EXPECT_TRUE(is_pow(e_pow_));
const vector<Expression>::difference_type cnt{
count_if(collection_.begin(), collection_.end(),
[](const Expression& e) { return is_pow(e); })};
EXPECT_EQ(cnt, 1);
}
TEST_F(SymbolicExpressionTest, IsSin) {
EXPECT_TRUE(is_sin(e_sin_));
const vector<Expression>::difference_type cnt{
count_if(collection_.begin(), collection_.end(),
[](const Expression& e) { return is_sin(e); })};
EXPECT_EQ(cnt, 1);
}
TEST_F(SymbolicExpressionTest, IsCos) {
EXPECT_TRUE(is_cos(e_cos_));
const vector<Expression>::difference_type cnt{
count_if(collection_.begin(), collection_.end(),
[](const Expression& e) { return is_cos(e); })};
EXPECT_EQ(cnt, 1);
}
TEST_F(SymbolicExpressionTest, IsTan) {
EXPECT_TRUE(is_tan(e_tan_));
const vector<Expression>::difference_type cnt{
count_if(collection_.begin(), collection_.end(),
[](const Expression& e) { return is_tan(e); })};
EXPECT_EQ(cnt, 1);
}
TEST_F(SymbolicExpressionTest, IsAsin) {
EXPECT_TRUE(is_asin(e_asin_));
const vector<Expression>::difference_type cnt{
count_if(collection_.begin(), collection_.end(),
[](const Expression& e) { return is_asin(e); })};
EXPECT_EQ(cnt, 1);
}
TEST_F(SymbolicExpressionTest, IsAcos) {
EXPECT_TRUE(is_acos(e_acos_));
const vector<Expression>::difference_type cnt{
count_if(collection_.begin(), collection_.end(),
[](const Expression& e) { return is_acos(e); })};
EXPECT_EQ(cnt, 1);
}
TEST_F(SymbolicExpressionTest, IsAtan) {
EXPECT_TRUE(is_atan(e_atan_));
const vector<Expression>::difference_type cnt{
count_if(collection_.begin(), collection_.end(),
[](const Expression& e) { return is_atan(e); })};
EXPECT_EQ(cnt, 1);
}
TEST_F(SymbolicExpressionTest, IsAtan2) {
EXPECT_TRUE(is_atan2(e_atan2_));
const vector<Expression>::difference_type cnt{
count_if(collection_.begin(), collection_.end(),
[](const Expression& e) { return is_atan2(e); })};
EXPECT_EQ(cnt, 1);
}
TEST_F(SymbolicExpressionTest, IsSinh) {
EXPECT_TRUE(is_sinh(e_sinh_));
const vector<Expression>::difference_type cnt{
count_if(collection_.begin(), collection_.end(),
[](const Expression& e) { return is_sinh(e); })};
EXPECT_EQ(cnt, 1);
}
TEST_F(SymbolicExpressionTest, IsCosh) {
EXPECT_TRUE(is_cosh(e_cosh_));
const vector<Expression>::difference_type cnt{
count_if(collection_.begin(), collection_.end(),
[](const Expression& e) { return is_cosh(e); })};
EXPECT_EQ(cnt, 1);
}
TEST_F(SymbolicExpressionTest, IsTanh) {
EXPECT_TRUE(is_tanh(e_tanh_));
const vector<Expression>::difference_type cnt{
count_if(collection_.begin(), collection_.end(),
[](const Expression& e) { return is_tanh(e); })};
EXPECT_EQ(cnt, 1);
}
TEST_F(SymbolicExpressionTest, IsMin) {
EXPECT_TRUE(is_min(e_min_));
const vector<Expression>::difference_type cnt{
count_if(collection_.begin(), collection_.end(),
[](const Expression& e) { return is_min(e); })};
EXPECT_EQ(cnt, 1);
}
TEST_F(SymbolicExpressionTest, IsMax) {
EXPECT_TRUE(is_max(e_max_));
const vector<Expression>::difference_type cnt{
count_if(collection_.begin(), collection_.end(),
[](const Expression& e) { return is_max(e); })};
EXPECT_EQ(cnt, 1);
}
TEST_F(SymbolicExpressionTest, IsCeil) {
EXPECT_TRUE(is_ceil(e_ceil_));
const vector<Expression>::difference_type cnt{
count_if(collection_.begin(), collection_.end(),
[](const Expression& e) { return is_ceil(e); })};
EXPECT_EQ(cnt, 1);
}
TEST_F(SymbolicExpressionTest, IsFloor) {
EXPECT_TRUE(is_floor(e_floor_));
const vector<Expression>::difference_type cnt{
count_if(collection_.begin(), collection_.end(),
[](const Expression& e) { return is_floor(e); })};
EXPECT_EQ(cnt, 1);
}
TEST_F(SymbolicExpressionTest, IsIfThenElse) {
EXPECT_TRUE(is_if_then_else(e_ite_));
const vector<Expression>::difference_type cnt{
count_if(collection_.begin(), collection_.end(),
[](const Expression& e) { return is_if_then_else(e); })};
EXPECT_EQ(cnt, 1);
}
TEST_F(SymbolicExpressionTest, IsNaN) {
EXPECT_TRUE(is_nan(e_nan_));
const vector<Expression>::difference_type cnt{
count_if(collection_.begin(), collection_.end(),
[](const Expression& e) { return is_nan(e); })};
EXPECT_EQ(cnt, 1);
}
TEST_F(SymbolicExpressionTest, IsUninterpretedFunction) {
EXPECT_TRUE(is_uninterpreted_function(e_uf_));
const vector<Expression>::difference_type cnt{count_if(
collection_.begin(), collection_.end(),
[](const Expression& e) { return is_uninterpreted_function(e); })};
EXPECT_EQ(cnt, 1);
}
TEST_F(SymbolicExpressionTest, GetConstantValue) {
EXPECT_EQ(get_constant_value(c1_), -10.0);
EXPECT_EQ(get_constant_value(c2_), 1.0);
EXPECT_EQ(get_constant_value(c3_), 3.14159);
EXPECT_EQ(get_constant_value(c4_), -2.718);
}
TEST_F(SymbolicExpressionTest, GetVariable) {
EXPECT_EQ(get_variable(x_), var_x_);
EXPECT_EQ(get_variable(y_), var_y_);
EXPECT_EQ(get_variable(z_), var_z_);
}
TEST_F(SymbolicExpressionTest, GetArgument) {
EXPECT_PRED2(ExprEqual, get_argument(e_log_), x_);
EXPECT_PRED2(ExprEqual, get_argument(e_abs_), x_);
EXPECT_PRED2(ExprEqual, get_argument(e_exp_), x_);
EXPECT_PRED2(ExprEqual, get_argument(e_sqrt_), x_);
EXPECT_PRED2(ExprEqual, get_argument(e_sin_), x_);
EXPECT_PRED2(ExprEqual, get_argument(e_cos_), x_);
EXPECT_PRED2(ExprEqual, get_argument(e_tan_), x_);
EXPECT_PRED2(ExprEqual, get_argument(e_asin_), x_);
EXPECT_PRED2(ExprEqual, get_argument(e_acos_), x_);
EXPECT_PRED2(ExprEqual, get_argument(e_atan_), x_);
EXPECT_PRED2(ExprEqual, get_argument(e_sinh_), x_);
EXPECT_PRED2(ExprEqual, get_argument(e_cosh_), x_);
EXPECT_PRED2(ExprEqual, get_argument(e_tanh_), x_);
EXPECT_PRED2(ExprEqual, get_argument(e_ceil_), x_);
EXPECT_PRED2(ExprEqual, get_argument(e_floor_), x_);
}
TEST_F(SymbolicExpressionTest, GetFirstArgument) {
EXPECT_PRED2(ExprEqual, get_first_argument(e_div_), x_);
EXPECT_PRED2(ExprEqual, get_first_argument(e_pow_), x_);
EXPECT_PRED2(ExprEqual, get_first_argument(e_atan2_), x_);
EXPECT_PRED2(ExprEqual, get_first_argument(e_min_), x_);
EXPECT_PRED2(ExprEqual, get_first_argument(e_max_), x_);
}
TEST_F(SymbolicExpressionTest, GetSecondArgument) {
EXPECT_PRED2(ExprEqual, get_second_argument(e_div_), y_);
EXPECT_PRED2(ExprEqual, get_second_argument(e_pow_), y_);
EXPECT_PRED2(ExprEqual, get_second_argument(e_atan2_), y_);
EXPECT_PRED2(ExprEqual, get_second_argument(e_min_), y_);
EXPECT_PRED2(ExprEqual, get_second_argument(e_max_), y_);
}
TEST_F(SymbolicExpressionTest, GetConstantTermInAddition) {
EXPECT_PRED2(ExprEqual, get_constant_in_addition(2 * x_ + 3 * y_), 0.0);
EXPECT_PRED2(ExprEqual, get_constant_in_addition(3 + 2 * x_ + 3 * y_), 3);
EXPECT_PRED2(ExprEqual, get_constant_in_addition(-2 + 2 * x_ + 3 * y_), -2);
}
TEST_F(SymbolicExpressionTest, GetTermsInAddition) {
const Expression e{3 + 2 * x_ + 3 * y_};
const map<Expression, double> terms{get_expr_to_coeff_map_in_addition(e)};
EXPECT_EQ(terms.at(x_), 2.0);
EXPECT_EQ(terms.at(y_), 3.0);
}
TEST_F(SymbolicExpressionTest, GetConstantFactorInMultiplication) {
EXPECT_PRED2(ExprEqual, get_constant_in_multiplication(e_neg_), -1.0);
EXPECT_PRED2(ExprEqual, get_constant_in_multiplication(x_ * y_ * y_), 1.0);
EXPECT_PRED2(ExprEqual, get_constant_in_multiplication(2 * x_ * y_ * y_),
2.0);
EXPECT_PRED2(ExprEqual, get_constant_in_multiplication(-3 * x_ * y_ * y_),
-3.0);
}
TEST_F(SymbolicExpressionTest, GetProductsInMultiplication) {
const Expression e{2 * x_ * y_ * y_ * pow(z_, y_)};
const map<Expression, Expression> products{
get_base_to_exponent_map_in_multiplication(e)};
EXPECT_PRED2(ExprEqual, products.at(x_), 1.0);
EXPECT_PRED2(ExprEqual, products.at(y_), 2.0);
EXPECT_PRED2(ExprEqual, products.at(z_), y_);
}
TEST_F(SymbolicExpressionTest, GetIfThenElse) {
const Formula conditional{x_ > y_};
const Expression e1{x_ + y_};
const Expression e2{x_ - y_};
const Expression e{if_then_else(conditional, e1, e2)};
EXPECT_PRED2(FormulaEqual, get_conditional_formula(e), conditional);
EXPECT_PRED2(ExprEqual, get_then_expression(e), e1);
EXPECT_PRED2(ExprEqual, get_else_expression(e), e2);
}
TEST_F(SymbolicExpressionTest, IsPolynomial) {
const vector<pair<Expression, bool>> test_vec{
{e_constant_, true}, {e_var_, true}, {e_neg_, true},
{e_add_, true}, {e_mul_, true}, {e_div_, false},
{e_log_, false}, {e_abs_, false}, {e_exp_, false},
{e_sqrt_, false}, {e_pow_, false}, {e_sin_, false},
{e_cos_, false}, {e_tan_, false}, {e_asin_, false},
{e_acos_, false}, {e_atan_, false}, {e_atan2_, false},
{e_sinh_, false}, {e_cosh_, false}, {e_tanh_, false},
{e_min_, false}, {e_max_, false}, {e_ceil_, false},
{e_floor_, false}, {e_ite_, false}, {e_nan_, false},
{e_uf_, false}};
for (const pair<Expression, bool>& p : test_vec) {
EXPECT_EQ(p.first.is_polynomial(), p.second);
}
// x^2 -> polynomial
EXPECT_TRUE(pow(x_, 2).is_polynomial());
// 3 + x + y + z -> polynomial
EXPECT_TRUE((3 + x_ + y_ + z_).is_polynomial());
// 1 + x^2 + y^2 -> polynomial
EXPECT_TRUE((1 + pow(x_, 2) + pow(y_, 2)).is_polynomial());
// x^2 * y^2 -> polynomial
EXPECT_TRUE((pow(x_, 2) * pow(y_, 2)).is_polynomial());
// (x + y + z)^3 -> polynomial
EXPECT_TRUE(pow(x_ + y_ + z_, 3).is_polynomial());
// (x + y + z)^3 / 10 -> polynomial
EXPECT_TRUE((pow(x_ + y_ + z_, 3) / 10).is_polynomial());
// (x^3)^(1/3) -> x -> polynomial
EXPECT_TRUE(pow(pow(x_, 3), 1 / 3).is_polynomial());
// x^-1 -> not polynomial
EXPECT_FALSE(pow(x_, -1).is_polynomial());
// x^2.1 -> not polynomial
EXPECT_FALSE(pow(x_, 2.1).is_polynomial());
// x^y -> not polynomial
EXPECT_FALSE(pow(x_, y_).is_polynomial());
// 3 + x^y -> not polynomial
EXPECT_FALSE((3 + pow(x_, y_)).is_polynomial());
// 3 + x^2.1 -> not polynomial
EXPECT_FALSE((3 + pow(x_, 2.1)).is_polynomial());
// x^y / 10 -> not polynomial
EXPECT_FALSE((pow(x_, y_) / 10).is_polynomial());
// x^2 * y^ 2.1 -> not polynomial
EXPECT_FALSE((pow(x_, 2) * pow(y_, 2.1)).is_polynomial());
// x^2 * y^ -1 -> not polynomial
EXPECT_FALSE((pow(x_, 2) * pow(y_, -1)).is_polynomial());
// x^2 * y^ 2 * x^y / 10 -> not polynomial
EXPECT_FALSE((pow(x_, 2) * pow(y_, 2) * pow(x_, y_) / 10).is_polynomial());
// (x + y + z)^3 / x -> not polynomial
EXPECT_FALSE((pow(x_ + y_ + z_, 3) / x_).is_polynomial());
// sqrt(x^2) -> |x| -> not polynomial
EXPECT_FALSE(sqrt(pow(x_, 2)).is_polynomial());
}
TEST_F(SymbolicExpressionTest, ToPolynomial1) {
Environment env{{var_x_, 1.0}, {var_y_, 2.0}, {var_z_, 3.0}};
const map<Polynomiald::VarType, double> eval_point{
{var_x_.get_id(), env[var_x_]},
{var_y_.get_id(), env[var_y_]},
{var_z_.get_id(), env[var_z_]}};
const Expression e0{42.0};
const Expression e1{pow(x_, 2)};
const Expression e2{3 + x_ + y_ + z_};
const Expression e3{1 + pow(x_, 2) + pow(y_, 2)};
const Expression e4{pow(x_, 2) * pow(y_, 2)};
const Expression e5{pow(x_ + y_ + z_, 3)};
const Expression e6{pow(x_ + y_ + z_, 3) / 10};
const Expression e7{-pow(y_, 3)};
const Expression e8{pow(pow(x_, 3), 1.0 / 3)};
EXPECT_NEAR(e0.Evaluate(env),
e0.ToPolynomial().EvaluateMultivariate(eval_point), 1e-8);
EXPECT_NEAR(e1.Evaluate(env),
e1.ToPolynomial().EvaluateMultivariate(eval_point), 1e-8);
EXPECT_NEAR(e2.Evaluate(env),
e2.ToPolynomial().EvaluateMultivariate(eval_point), 1e-8);
EXPECT_NEAR(e3.Evaluate(env),
e3.ToPolynomial().EvaluateMultivariate(eval_point), 1e-8);
EXPECT_NEAR(e4.Evaluate(env),
e4.ToPolynomial().EvaluateMultivariate(eval_point), 1e-8);
EXPECT_NEAR(e5.Evaluate(env),
e5.ToPolynomial().EvaluateMultivariate(eval_point), 1e-8);
EXPECT_NEAR(e6.Evaluate(env),
e6.ToPolynomial().EvaluateMultivariate(eval_point), 1e-8);
EXPECT_NEAR(e7.Evaluate(env),
e7.ToPolynomial().EvaluateMultivariate(eval_point), 1e-8);
EXPECT_NEAR(e8.Evaluate(env),
e8.ToPolynomial().EvaluateMultivariate(eval_point), 1e-8);
}
TEST_F(SymbolicExpressionTest, ToPolynomial2) {
const vector<Expression> test_vec{
e_log_, e_abs_, e_exp_, e_sqrt_, e_sin_,
e_cos_, e_tan_, e_asin_, e_acos_, e_atan_,
e_atan2_, e_sinh_, e_cosh_, e_tanh_, e_min_,
e_max_, e_ceil_, e_floor_, e_ite_, Expression::NaN(),
e_uf_};
for (const Expression& e : test_vec) {
EXPECT_FALSE(e.is_polynomial());
EXPECT_THROW(e.ToPolynomial(), runtime_error);
}
}
TEST_F(SymbolicExpressionTest, LessKind) {
CheckOrdering({e_constant_, e_var_, e_add_, e_neg_, e_mul_, e_div_,
e_log_, e_abs_, e_exp_, e_sqrt_, e_pow_, e_sin_,
e_cos_, e_tan_, e_asin_, e_acos_, e_atan_, e_atan2_,
e_sinh_, e_cosh_, e_tanh_, e_min_, e_max_, e_ceil_,
e_floor_, e_ite_, e_nan_, e_uf_});
}
TEST_F(SymbolicExpressionTest, LessConstant) { CheckOrdering({c1_, c2_, c3_}); }
TEST_F(SymbolicExpressionTest, LessVariable) { CheckOrdering({x_, y_, z_}); }
TEST_F(SymbolicExpressionTest, LessNeg) {
// Defined in the ascending order.
const Expression neg1{-c3_};
const Expression neg2{-c1_};
const Expression neg3{-x_}; // note: Constant kind < Variable kind
CheckOrdering({neg1, neg2, neg3});
}
TEST_F(SymbolicExpressionTest, LessAdd) {
const Expression add1{c1_ + x_ + y_};
const Expression add2{c1_ + 2 * x_ + y_};
const Expression add3{c1_ - 2 * y_ + z_};
const Expression add4{c1_ + y_ + z_};
const Expression add5{c1_ + 5 * y_ + z_};
const Expression add6{c3_ - 2 * x_ + y_};
const Expression add7{c3_ + x_ + y_};
const Expression add8{c3_ + y_ + 2 * z_};
const Expression add9{c3_ + y_ + 3 * z_};
CheckOrdering({add1, add2, add3, add4, add5, add6, add7, add8, add9});
}
TEST_F(SymbolicExpressionTest, LessSub) {
const Expression sub1{c1_ - x_ - y_};
const Expression sub2{c1_ - y_ - z_};
const Expression sub3{c3_ - x_ - y_};
const Expression sub4{c3_ - y_ - z_};
CheckOrdering({sub1, sub2, sub3, sub4});
}
TEST_F(SymbolicExpressionTest, LessMul) {
const Expression mul1{c1_ * x_ * y_};
const Expression mul2{c1_ * y_ * z_};
const Expression mul3{c3_ * x_ * y_};
const Expression mul4{c3_ * y_ * z_};
CheckOrdering({mul1, mul2, mul3, mul4});
}
TEST_F(SymbolicExpressionTest, LessDiv) {
const Expression div1{x_ / y_};
const Expression div2{x_ / z_};
const Expression div3{y_ / z_};
CheckOrdering({div1, div2, div3});
}
TEST_F(SymbolicExpressionTest, LessLog) {
const Expression log1{log(x_)};
const Expression log2{log(y_)};
const Expression log3{log(x_plus_y_)};
const Expression log4{log(x_plus_z_)};
CheckOrdering({log1, log2, log3, log4});
}
TEST_F(SymbolicExpressionTest, LessAbs) {
const Expression abs1{abs(x_)};
const Expression abs2{abs(y_)};
const Expression abs3{abs(x_plus_y_)};
const Expression abs4{abs(x_plus_z_)};
CheckOrdering({abs1, abs2, abs3, abs4});
}
TEST_F(SymbolicExpressionTest, LessExp) {
const Expression exp1{exp(x_)};
const Expression exp2{exp(y_)};
const Expression exp3{exp(x_plus_y_)};
const Expression exp4{exp(x_plus_z_)};
CheckOrdering({exp1, exp2, exp3, exp4});
}
TEST_F(SymbolicExpressionTest, LessSqrt) {
const Expression sqrt1{sqrt(x_)};
const Expression sqrt2{sqrt(y_)};
const Expression sqrt3{sqrt(x_plus_y_)};
const Expression sqrt4{sqrt(x_plus_z_)};
CheckOrdering({sqrt1, sqrt2, sqrt3, sqrt4});
}
TEST_F(SymbolicExpressionTest, LessSin) {
const Expression sin1{sin(x_)};
const Expression sin2{sin(y_)};
const Expression sin3{sin(x_plus_y_)};
const Expression sin4{sin(x_plus_z_)};
CheckOrdering({sin1, sin2, sin3, sin4});
}
TEST_F(SymbolicExpressionTest, LessCos) {
const Expression cos1{cos(x_)};
const Expression cos2{cos(y_)};
const Expression cos3{cos(x_plus_y_)};
const Expression cos4{cos(x_plus_z_)};
CheckOrdering({cos1, cos2, cos3, cos4});
}
TEST_F(SymbolicExpressionTest, LessTan) {
const Expression tan1{tan(x_)};
const Expression tan2{tan(y_)};
const Expression tan3{tan(x_plus_y_)};
const Expression tan4{tan(x_plus_z_)};
CheckOrdering({tan1, tan2, tan3, tan4});
}
TEST_F(SymbolicExpressionTest, LessAsin) {
const Expression asin1{asin(x_)};
const Expression asin2{asin(y_)};
const Expression asin3{asin(x_plus_y_)};
const Expression asin4{asin(x_plus_z_)};
CheckOrdering({asin1, asin2, asin3, asin4});
}
TEST_F(SymbolicExpressionTest, LessAcos) {
const Expression acos1{acos(x_)};
const Expression acos2{acos(y_)};
const Expression acos3{acos(x_plus_y_)};
const Expression acos4{acos(x_plus_z_)};
CheckOrdering({acos1, acos2, acos3, acos4});
}
TEST_F(SymbolicExpressionTest, LessAtan) {
const Expression atan1{atan(x_)};
const Expression atan2{atan(y_)};
const Expression atan3{atan(x_plus_y_)};
const Expression atan4{atan(x_plus_z_)};
CheckOrdering({atan1, atan2, atan3, atan4});
}
TEST_F(SymbolicExpressionTest, LessSinh) {
const Expression sinh1{sinh(x_)};
const Expression sinh2{sinh(y_)};
const Expression sinh3{sinh(x_plus_y_)};
const Expression sinh4{sinh(x_plus_z_)};
CheckOrdering({sinh1, sinh2, sinh3, sinh4});
}
TEST_F(SymbolicExpressionTest, LessCosh) {
const Expression cosh1{cosh(x_)};
const Expression cosh2{cosh(y_)};
const Expression cosh3{cosh(x_plus_y_)};
const Expression cosh4{cosh(x_plus_z_)};
CheckOrdering({cosh1, cosh2, cosh3, cosh4});
}
TEST_F(SymbolicExpressionTest, LessTanh) {
const Expression tanh1{tanh(x_)};
const Expression tanh2{tanh(y_)};
const Expression tanh3{tanh(x_plus_y_)};
const Expression tanh4{tanh(x_plus_z_)};
CheckOrdering({tanh1, tanh2, tanh3, tanh4});
}
TEST_F(SymbolicExpressionTest, LessPow) {
const Expression pow1{pow(x_, y_)};
const Expression pow2{pow(x_, z_)};
const Expression pow3{pow(y_, z_)};
CheckOrdering({pow1, pow2, pow3});
}
TEST_F(SymbolicExpressionTest, LessAtan2) {
const Expression atan2_1{atan2(x_, y_)};
const Expression atan2_2{atan2(x_, z_)};
const Expression atan2_3{atan2(y_, z_)};
CheckOrdering({atan2_1, atan2_2, atan2_3});
}
TEST_F(SymbolicExpressionTest, LessMin) {
const Expression min1{min(x_, y_)};
const Expression min2{min(x_, z_)};
const Expression min3{min(y_, z_)};
CheckOrdering({min1, min2, min3});
}
TEST_F(SymbolicExpressionTest, LessMax) {
const Expression max1{max(x_, y_)};
const Expression max2{max(x_, z_)};
const Expression max3{max(y_, z_)};
CheckOrdering({max1, max2, max3});
}
TEST_F(SymbolicExpressionTest, LessCeil) {
const Expression ceil1{ceil(x_)};
const Expression ceil2{ceil(y_)};
const Expression ceil3{ceil(x_plus_y_)};
const Expression ceil4{ceil(x_plus_z_)};
CheckOrdering({ceil1, ceil2, ceil3, ceil4});
}
TEST_F(SymbolicExpressionTest, LessFloor) {
const Expression floor1{floor(x_)};
const Expression floor2{floor(y_)};
const Expression floor3{floor(x_plus_y_)};
const Expression floor4{floor(x_plus_z_)};
CheckOrdering({floor1, floor2, floor3, floor4});
}
TEST_F(SymbolicExpressionTest, LessIfThenElse) {
const Formula f1{x_ < y_};
const Formula f2{y_ < z_};
const Expression ite1{if_then_else(f1, x_, y_)};
const Expression ite2{if_then_else(f1, x_, z_)};
const Expression ite3{if_then_else(f1, y_, z_)};
const Expression ite4{if_then_else(f2, y_, z_)};
const Expression ite5{if_then_else(f2, z_, x_)};
CheckOrdering({ite1, ite2, ite3, ite4, ite5});
}
TEST_F(SymbolicExpressionTest, LessUninterpretedFunction) {
const Expression uf1{uninterpreted_function("name1", {x_, y_ + z_})};
const Expression uf2{uninterpreted_function("name1", {x_, y_ * z_})};
const Expression uf3{uninterpreted_function("name1", {x_, y_ * z_, 3.0})};
const Expression uf4{uninterpreted_function("name2", {})};
const Expression uf5{uninterpreted_function("name2", {0.0, -1.0})};
const Expression uf6{uninterpreted_function("name2", {1.0, 0.0})};
CheckOrdering({uf1, uf2, uf3, uf4, uf5, uf6});
}
TEST_F(SymbolicExpressionTest, Variable) {
EXPECT_EQ(x_.to_string(), var_x_.get_name());
EXPECT_EQ(y_.to_string(), var_y_.get_name());
EXPECT_EQ(z_.to_string(), var_z_.get_name());
EXPECT_PRED2(ExprEqual, x_, x_);
EXPECT_PRED2(ExprNotEqual, x_, y_);
EXPECT_PRED2(ExprNotEqual, x_, z_);
EXPECT_PRED2(ExprNotEqual, y_, x_);
EXPECT_PRED2(ExprEqual, y_, y_);
EXPECT_PRED2(ExprNotEqual, y_, z_);
EXPECT_PRED2(ExprNotEqual, z_, x_);
EXPECT_PRED2(ExprNotEqual, z_, y_);
EXPECT_PRED2(ExprEqual, z_, z_);
}
TEST_F(SymbolicExpressionTest, Evaluate) {
EXPECT_THROW(x_plus_y_.Evaluate(), std::runtime_error);
}
TEST_F(SymbolicExpressionTest, Constant) {
EXPECT_EQ(c1_.Evaluate(), -10);
EXPECT_EQ(c2_.Evaluate(), 1);
EXPECT_EQ(c3_.Evaluate(), 3.14159);
EXPECT_EQ(c4_.Evaluate(), -2.718);
EXPECT_THROW(Expression{NAN}.Evaluate(), runtime_error);
}
TEST_F(SymbolicExpressionTest, StaticConstant) {
EXPECT_DOUBLE_EQ(Expression::Zero().Evaluate(), 0.0);
EXPECT_DOUBLE_EQ(Expression::One().Evaluate(), 1.0);
EXPECT_NEAR(Expression::Pi().Evaluate(), M_PI, 0.000001);
EXPECT_NEAR(Expression::E().Evaluate(), M_E, 0.000000001);
}
TEST_F(SymbolicExpressionTest, Hash) {
Expression x{var_x_};
const Expression x_prime(x);
EXPECT_EQ(get_std_hash(x), get_std_hash(x_prime));
x++;
EXPECT_NE(get_std_hash(x), get_std_hash(x_prime));
}
TEST_F(SymbolicExpressionTest, HashBinary) {
const Expression e1{x_plus_y_ + x_plus_z_};
const Expression e2{x_plus_y_ - x_plus_z_};
const Expression e3{x_plus_y_ * x_plus_z_};
const Expression e4{x_plus_y_ / x_plus_z_};
const Expression e5{pow(x_plus_y_, x_plus_z_)};
const Expression e6{atan2(x_plus_y_, x_plus_z_)};
const Expression e7{min(x_plus_y_, x_plus_z_)};
const Expression e8{max(x_plus_y_, x_plus_z_)};
// e1, ..., e8 share the same sub-expressions, but their hash values should be
// distinct.
unordered_set<size_t> hash_set;
const vector<Expression> exprs{e1, e2, e3, e4, e5, e6, e7, e8};
for (auto const& e : exprs) {
hash_set.insert(get_std_hash(e));
}
EXPECT_EQ(hash_set.size(), exprs.size());
}
TEST_F(SymbolicExpressionTest, HashUnary) {
const Expression e0{log(x_plus_y_)};
const Expression e1{abs(x_plus_y_)};
const Expression e2{exp(x_plus_y_)};
const Expression e3{sqrt(x_plus_y_)};
const Expression e4{sin(x_plus_y_)};
const Expression e5{cos(x_plus_y_)};
const Expression e6{tan(x_plus_y_)};
const Expression e7{asin(x_plus_y_)};
const Expression e8{acos(x_plus_y_)};
const Expression e9{atan(x_plus_y_)};
const Expression e10{sinh(x_plus_y_)};
const Expression e11{cosh(x_plus_y_)};
const Expression e12{tanh(x_plus_y_)};
const Expression e13{ceil(x_plus_y_)};
const Expression e14{floor(x_plus_y_)};
// e0, ..., e14 share the same sub-expression, but their hash values should be
// distinct.
unordered_set<size_t> hash_set;
const vector<Expression> exprs{e0, e1, e2, e3, e4, e5, e6, e7,
e8, e9, e10, e11, e12, e13, e14};
for (auto const& e : exprs) {
hash_set.insert(get_std_hash(e));
}
EXPECT_EQ(hash_set.size(), exprs.size());
}
// Confirm that numeric_limits is appropriately specialized for Expression.
// We'll just spot-test a few values, since our implementation is trivially
// forwarding to numeric_limits<double>.
TEST_F(SymbolicExpressionTest, NumericLimits) {
using std::numeric_limits;
using Limits = numeric_limits<Expression>;
const Expression num_eps = Limits::epsilon();
ASSERT_TRUE(is_constant(num_eps));
EXPECT_EQ(get_constant_value(num_eps), numeric_limits<double>::epsilon());
const Expression num_min = Limits::min();
ASSERT_TRUE(is_constant(num_min));
EXPECT_EQ(get_constant_value(num_min), numeric_limits<double>::min());
const Expression num_infinity = Limits::infinity();
EXPECT_EQ(num_infinity.to_string(), "inf");
}
TEST_F(SymbolicExpressionTest, UnaryPlus) {
EXPECT_PRED2(ExprEqual, c3_, +c3_);
EXPECT_PRED2(ExprEqual, Expression(var_x_), +var_x_);
}
TEST_F(SymbolicExpressionTest, UnaryMinus) {
EXPECT_PRED2(ExprEqual, -Expression(var_x_), -var_x_);
EXPECT_PRED2(ExprNotEqual, c3_, -c3_);
EXPECT_DOUBLE_EQ(c3_.Evaluate(), -(-c3_).Evaluate());
EXPECT_PRED2(ExprEqual, c3_, -(-c3_));
EXPECT_DOUBLE_EQ(c3_.Evaluate(), (-(-c3_)).Evaluate());
const Expression e{x_ + y_};
const Environment env{{var_x_, 1.0}, {var_y_, 2.0}};
EXPECT_EQ((-x_).Evaluate(env), -1.0);
EXPECT_PRED2(ExprEqual, x_, -(-x_));
// (x + y) and -(-(x + y)) are structurally equal (after simplification)
EXPECT_PRED2(ExprEqual, e, -(-e));
// and their evaluations should be the same.
EXPECT_DOUBLE_EQ(e.Evaluate(env), (-(-e)).Evaluate(env));
EXPECT_PRED2(ExprEqual, -(x_plus_y_ + x_plus_z_ + pi_),
-x_plus_y_ + (-x_plus_z_) + (-pi_));
EXPECT_EQ((-(x_)).to_string(), "(-1 * x)");
}
TEST_F(SymbolicExpressionTest, Add1) {
EXPECT_PRED2(ExprEqual, c3_ + zero_, c3_);
EXPECT_EQ((c3_ + zero_).to_string(), c3_.to_string());
EXPECT_PRED2(ExprEqual, zero_ + c3_, c3_);
EXPECT_EQ((zero_ + c3_).to_string(), c3_.to_string());
EXPECT_PRED2(ExprEqual, 0.0 + c3_, c3_);
EXPECT_EQ((0.0 + c3_).to_string(), c3_.to_string());
EXPECT_PRED2(ExprEqual, c3_ + 0.0, c3_);
EXPECT_EQ((c3_ + 0.0).to_string(), c3_.to_string());
EXPECT_PRED2(ExprEqual, c3_ + c4_, 3.14159 + -2.718);
EXPECT_EQ((c3_ + c4_).to_string(), Expression{3.14159 + -2.718}.to_string());
EXPECT_PRED2(ExprEqual, c3_ + x_, 3.14159 + x_);
EXPECT_EQ((c3_ + x_).to_string(), (3.14159 + x_).to_string());
EXPECT_PRED2(ExprEqual, x_ + c3_, x_ + 3.14159);
EXPECT_EQ((x_ + c3_).to_string(), (x_ + 3.14159).to_string());
}
TEST_F(SymbolicExpressionTest, Add2) {
Expression e1{x_ + y_};
Expression e2{e1 + e1};
const auto str_rep_e2(e2.to_string());
EXPECT_EQ(str_rep_e2, "(2 * x + 2 * y)");
EXPECT_PRED2(ExprEqual, e2, 2 * x_ + 2 * y_);
e1 += z_;
EXPECT_PRED2(ExprEqual, e1, x_ + y_ + z_);
EXPECT_EQ(e2.to_string(), str_rep_e2); // e2 doesn't change.
}
TEST_F(SymbolicExpressionTest, Add3) {
const Expression e1{2 + x_ + y_};
const Expression e2{3 + x_ + y_};
EXPECT_PRED2(ExprNotEqual, e1, e2);
}
TEST_F(SymbolicExpressionTest, Add4) {
const Expression e1{-2 - x_ + -3 * y_};
const Expression e2{-2 - x_ - 3 * y_};
EXPECT_EQ(e1.to_string(), "(-2 - x - 3 * y)");
EXPECT_EQ(e2.to_string(), "(-2 - x - 3 * y)");
}
TEST_F(SymbolicExpressionTest, Inc1) {
// Prefix increment
Expression x{var_x_};
Expression x_prime{var_x_};
EXPECT_PRED2(ExprEqual, x, x_prime);
EXPECT_PRED2(ExprEqual, x++, x_prime);
EXPECT_PRED2(ExprNotEqual, x, x_prime);
EXPECT_PRED2(ExprNotEqual, x, x_prime++);