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symbolic_polynomial_matrix_test.cc
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symbolic_polynomial_matrix_test.cc
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#include <gtest/gtest.h>
#include "drake/common/eigen_types.h"
#include "drake/common/symbolic.h"
#include "drake/common/test_utilities/symbolic_test_util.h"
namespace drake {
namespace symbolic {
namespace {
using test::ExprEqual;
class SymbolicPolynomialMatrixTest : public ::testing::Test {
protected:
const Variable var_x_{"x"};
const Variable var_y_{"y"};
const Variable var_z_{"z"};
const Monomial m_x_{var_x_};
const Monomial m_y_{var_y_};
const Monomial m_z_{var_z_};
MatrixX<Polynomial> M_poly_dynamic_{2, 2};
Eigen::Matrix<Polynomial, 2, 2> M_poly_static_;
MatrixX<Monomial> M_monomial_dynamic_{2, 2};
Eigen::Matrix<Monomial, 2, 2> M_monomial_static_;
MatrixX<double> M_double_dynamic_{2, 2};
Eigen::Matrix<double, 2, 2> M_double_static_;
VectorX<Polynomial> v_poly_dynamic_{2};
Eigen::Matrix<Polynomial, 2, 1> v_poly_static_;
VectorX<Monomial> v_monomial_dynamic_{2};
Eigen::Matrix<Monomial, 2, 1> v_monomial_static_;
VectorX<double> v_double_dynamic_{2};
Eigen::Matrix<double, 2, 1> v_double_static_;
void SetUp() override {
// clang-format off
M_poly_dynamic_ << Polynomial{}, (m_x_ + m_y_), // [0 x + y]
(2 + m_x_ * m_y_), Polynomial{m_z_}; // [2 + xy z ]
M_poly_static_ << Polynomial{}, (m_x_ + m_y_), // [0 x + y]
(2 + m_x_ * m_y_), Polynomial{m_z_}; // [2 + xy z ]
M_monomial_dynamic_ << Monomial{}, m_x_, // [1 x ]
(m_x_ * m_y_), (m_x_ * m_x_ * m_z_); // [xy x²z]
M_monomial_static_ << Monomial{}, m_x_, // [1 x ]
(m_x_ * m_y_), (m_x_ * m_x_ * m_z_); // [xy x²z]
M_double_dynamic_ << -2.0, 4.0, // [-2.0 4.0]
5.0, -9.0; // [ 5.0 -9.0]
M_double_static_ << -2.0, 4.0, // [-2.0 4.0]
5.0, -9.0; // [ 5.0 -9.0]
v_poly_dynamic_ << (m_x_ + m_y_), // [x+y ]
(3 + m_x_ * m_y_ * m_z_); // [3 + xyz]
v_poly_static_ << (m_x_ + m_y_), // [x+y ]
(3 + m_x_ * m_y_ * m_z_); // [3 + xyz]
v_monomial_dynamic_ << (m_x_ * m_y_), // [xy ]
(m_x_ * m_y_ * m_z_); // [xyz]
v_monomial_static_ << (m_x_ * m_y_), // [xy ]
(m_x_ * m_y_ * m_z_); // [xyz]
v_double_dynamic_ << -1.1, // [-1.1]
5.2; // [ 5.2]
v_double_static_ << -1.1, // [-1.1]
5.2; // [ 5.2]
// clang-format on
}
};
// Compares m1 and m2 after expanding both of them.
::testing::AssertionResult CompareMatricesWithExpansion(
const Eigen::Ref<const MatrixX<Expression>>& m1,
const Eigen::Ref<const MatrixX<Expression>>& m2) {
const MatrixX<Expression> m1_expanded{
m1.unaryExpr([](const Expression& e) { return e.Expand(); })};
const MatrixX<Expression> m2_expanded{
m2.unaryExpr([](const Expression& e) { return e.Expand(); })};
if (m1_expanded == m2_expanded) {
return ::testing::AssertionSuccess()
<< "m1 and m2 are equal after expansion where m1 = \n"
<< m1 << "\n"
<< "and m2 = " << m2;
} else {
return ::testing::AssertionFailure()
<< "m1 and m2 are not equal after expansion where m1 = \n"
<< m1 << "\n"
<< "m2 = " << m2 << "\n"
<< "m1_expanded = \n"
<< m1_expanded << "\n"
<< "m2_expanded = \n"
<< m2_expanded;
}
}
template <typename Matrix1, typename Matrix2>
::testing::AssertionResult CheckAddition(const Matrix1& M1, const Matrix2& M2) {
return CompareMatricesWithExpansion(
(M1 + M2).template cast<Expression>(),
M1.template cast<Expression>() + M2.template cast<Expression>());
}
template <typename Matrix1, typename Matrix2>
::testing::AssertionResult CheckSubtraction(const Matrix1& M1,
const Matrix2& M2) {
return CompareMatricesWithExpansion(
(M1 - M2).template cast<Expression>(),
M1.template cast<Expression>() - M2.template cast<Expression>());
}
template <typename Matrix1, typename Matrix2>
::testing::AssertionResult CheckMultiplication(const Matrix1& M1,
const Matrix2& M2) {
return CompareMatricesWithExpansion(
(M1 * M2).template cast<Expression>(),
M1.template cast<Expression>() * M2.template cast<Expression>());
}
template <typename Vector1, typename Vector2>
bool CheckDotProduct(const Vector1& v1, const Vector2& v2) {
const Expression e1{v1.dot(v2).ToExpression()};
const Expression e2{v1.template cast<Expression>()
.dot(v2.template cast<Expression>())
.Expand()};
return e1.EqualTo(e2);
}
TEST_F(SymbolicPolynomialMatrixTest, PolynomialPolynomial) {
// Checks Dynamic op Dynamic where op = {+, -, *, ·}.
EXPECT_TRUE(CheckAddition(M_poly_dynamic_, M_poly_dynamic_));
EXPECT_TRUE(CheckSubtraction(M_poly_dynamic_, M_poly_dynamic_));
EXPECT_TRUE(CheckMultiplication(M_poly_dynamic_, M_poly_dynamic_));
EXPECT_TRUE(CheckDotProduct(v_poly_dynamic_, v_poly_dynamic_));
// Checks Static op Dynamic where op = {+, -, *, ·}.
EXPECT_TRUE(CheckAddition(M_poly_static_, M_poly_dynamic_));
EXPECT_TRUE(CheckSubtraction(M_poly_static_, M_poly_dynamic_));
EXPECT_TRUE(CheckMultiplication(M_poly_static_, M_poly_dynamic_));
EXPECT_TRUE(CheckDotProduct(v_poly_static_, v_poly_dynamic_));
// Checks Dynamic op Static where op = {+, -, *}.
EXPECT_TRUE(CheckAddition(M_poly_dynamic_, M_poly_static_));
EXPECT_TRUE(CheckSubtraction(M_poly_dynamic_, M_poly_static_));
EXPECT_TRUE(CheckMultiplication(M_poly_dynamic_, M_poly_static_));
EXPECT_TRUE(CheckDotProduct(v_poly_dynamic_, v_poly_static_));
// Checks Static op Static where op = {+, -, *, ·}.
EXPECT_TRUE(CheckAddition(M_poly_static_, M_poly_static_));
EXPECT_TRUE(CheckSubtraction(M_poly_static_, M_poly_static_));
EXPECT_TRUE(CheckMultiplication(M_poly_static_, M_poly_static_));
EXPECT_TRUE(CheckDotProduct(v_poly_static_, v_poly_static_));
}
TEST_F(SymbolicPolynomialMatrixTest, PolynomialMonomial) {
// Checks Dynamic op Dynamic where op = {+, -, *, ·}.
EXPECT_TRUE(CheckAddition(M_poly_dynamic_, M_monomial_dynamic_));
EXPECT_TRUE(CheckSubtraction(M_poly_dynamic_, M_monomial_dynamic_));
EXPECT_TRUE(CheckMultiplication(M_poly_dynamic_, M_monomial_dynamic_));
EXPECT_TRUE(CheckDotProduct(v_poly_dynamic_, v_monomial_dynamic_));
// Checks Static op Dynamic where op = {+, -, *, ·}.
EXPECT_TRUE(CheckAddition(M_poly_static_, M_monomial_dynamic_));
EXPECT_TRUE(CheckSubtraction(M_poly_static_, M_monomial_dynamic_));
EXPECT_TRUE(CheckMultiplication(M_poly_static_, M_monomial_dynamic_));
EXPECT_TRUE(CheckDotProduct(v_poly_static_, v_monomial_dynamic_));
// Checks Dynamic op Static where op = {+, -, *}.
EXPECT_TRUE(CheckAddition(M_poly_dynamic_, M_monomial_static_));
EXPECT_TRUE(CheckSubtraction(M_poly_dynamic_, M_monomial_static_));
EXPECT_TRUE(CheckMultiplication(M_poly_dynamic_, M_monomial_static_));
EXPECT_TRUE(CheckDotProduct(v_poly_dynamic_, v_monomial_static_));
// Checks Static op Static where op = {+, -, *, ·}.
EXPECT_TRUE(CheckAddition(M_poly_static_, M_monomial_static_));
EXPECT_TRUE(CheckSubtraction(M_poly_static_, M_monomial_static_));
EXPECT_TRUE(CheckMultiplication(M_poly_static_, M_monomial_static_));
EXPECT_TRUE(CheckDotProduct(v_poly_static_, v_monomial_static_));
}
TEST_F(SymbolicPolynomialMatrixTest, PolynomialDouble) {
// Checks Dynamic op Dynamic where op = {+, -, *, ·}.
EXPECT_TRUE(CheckAddition(M_poly_dynamic_, M_double_dynamic_));
EXPECT_TRUE(CheckSubtraction(M_poly_dynamic_, M_double_dynamic_));
EXPECT_TRUE(CheckMultiplication(M_poly_dynamic_, M_double_dynamic_));
EXPECT_TRUE(CheckDotProduct(v_poly_dynamic_, v_double_dynamic_));
// Checks Static op Dynamic where op = {+, -, *, ·}.
EXPECT_TRUE(CheckAddition(M_poly_static_, M_double_dynamic_));
EXPECT_TRUE(CheckSubtraction(M_poly_static_, M_double_dynamic_));
EXPECT_TRUE(CheckMultiplication(M_poly_static_, M_double_dynamic_));
EXPECT_TRUE(CheckDotProduct(v_poly_static_, v_double_dynamic_));
// Checks Dynamic op Static where op = {+, -, *}.
EXPECT_TRUE(CheckAddition(M_poly_dynamic_, M_double_static_));
EXPECT_TRUE(CheckSubtraction(M_poly_dynamic_, M_double_static_));
EXPECT_TRUE(CheckMultiplication(M_poly_dynamic_, M_double_static_));
EXPECT_TRUE(CheckDotProduct(v_poly_dynamic_, v_double_static_));
// Checks Static op Static where op = {+, -, *, ·}.
EXPECT_TRUE(CheckAddition(M_poly_static_, M_double_static_));
EXPECT_TRUE(CheckSubtraction(M_poly_static_, M_double_static_));
EXPECT_TRUE(CheckMultiplication(M_poly_static_, M_double_static_));
EXPECT_TRUE(CheckDotProduct(v_poly_static_, v_double_static_));
}
TEST_F(SymbolicPolynomialMatrixTest, MonomialPolynomial) {
// Checks Dynamic op Dynamic where op = {+, -, *, ·}.
EXPECT_TRUE(CheckAddition(M_monomial_dynamic_, M_poly_dynamic_));
EXPECT_TRUE(CheckSubtraction(M_monomial_dynamic_, M_poly_dynamic_));
EXPECT_TRUE(CheckMultiplication(M_monomial_dynamic_, M_poly_dynamic_));
EXPECT_TRUE(CheckDotProduct(v_monomial_dynamic_, v_poly_dynamic_));
// Checks Static op Dynamic where op = {+, -, *, ·}.
EXPECT_TRUE(CheckAddition(M_monomial_static_, M_poly_dynamic_));
EXPECT_TRUE(CheckSubtraction(M_monomial_static_, M_poly_dynamic_));
EXPECT_TRUE(CheckMultiplication(M_monomial_static_, M_poly_dynamic_));
EXPECT_TRUE(CheckDotProduct(v_monomial_static_, v_poly_dynamic_));
// Checks Dynamic op Static where op = {+, -, *}.
EXPECT_TRUE(CheckAddition(M_monomial_dynamic_, M_poly_static_));
EXPECT_TRUE(CheckSubtraction(M_monomial_dynamic_, M_poly_static_));
EXPECT_TRUE(CheckMultiplication(M_monomial_dynamic_, M_poly_static_));
EXPECT_TRUE(CheckDotProduct(v_monomial_dynamic_, v_poly_static_));
// Checks Static op Static where op = {+, -, *, ·}.
EXPECT_TRUE(CheckAddition(M_monomial_static_, M_poly_static_));
EXPECT_TRUE(CheckSubtraction(M_monomial_static_, M_poly_static_));
EXPECT_TRUE(CheckMultiplication(M_monomial_static_, M_poly_static_));
EXPECT_TRUE(CheckDotProduct(v_monomial_static_, v_poly_static_));
}
TEST_F(SymbolicPolynomialMatrixTest, MonomialMonomial) {
// Checks Dynamic op Dynamic where op = {+, -, *, ·}.
EXPECT_TRUE(CheckAddition(M_monomial_dynamic_, M_monomial_dynamic_));
EXPECT_TRUE(CheckSubtraction(M_monomial_dynamic_, M_monomial_dynamic_));
EXPECT_TRUE(CheckMultiplication(M_monomial_dynamic_, M_monomial_dynamic_));
EXPECT_TRUE(CheckDotProduct(v_monomial_dynamic_, v_monomial_dynamic_));
// Checks Static op Dynamic where op = {+, -, *, ·}.
EXPECT_TRUE(CheckAddition(M_monomial_static_, M_monomial_dynamic_));
EXPECT_TRUE(CheckSubtraction(M_monomial_static_, M_monomial_dynamic_));
EXPECT_TRUE(CheckMultiplication(M_monomial_static_, M_monomial_dynamic_));
EXPECT_TRUE(CheckDotProduct(v_monomial_static_, v_monomial_dynamic_));
// Checks Dynamic op Static where op = {+, -, *}.
EXPECT_TRUE(CheckAddition(M_monomial_dynamic_, M_monomial_static_));
EXPECT_TRUE(CheckSubtraction(M_monomial_dynamic_, M_monomial_static_));
EXPECT_TRUE(CheckMultiplication(M_monomial_dynamic_, M_monomial_static_));
EXPECT_TRUE(CheckDotProduct(v_monomial_dynamic_, v_monomial_static_));
// Checks Static op Static where op = {+, -, *, ·}.
EXPECT_TRUE(CheckAddition(M_monomial_static_, M_monomial_static_));
EXPECT_TRUE(CheckSubtraction(M_monomial_static_, M_monomial_static_));
EXPECT_TRUE(CheckMultiplication(M_monomial_static_, M_monomial_static_));
EXPECT_TRUE(CheckDotProduct(v_monomial_static_, v_monomial_static_));
}
TEST_F(SymbolicPolynomialMatrixTest, MonomialDouble) {
// Checks Dynamic op Dynamic where op = {+, -, *, ·}.
EXPECT_TRUE(CheckAddition(M_monomial_dynamic_, M_double_dynamic_));
EXPECT_TRUE(CheckSubtraction(M_monomial_dynamic_, M_double_dynamic_));
EXPECT_TRUE(CheckMultiplication(M_monomial_dynamic_, M_double_dynamic_));
EXPECT_TRUE(CheckDotProduct(v_monomial_dynamic_, v_double_dynamic_));
// Checks Static op Dynamic where op = {+, -, *, ·}.
EXPECT_TRUE(CheckAddition(M_monomial_static_, M_double_dynamic_));
EXPECT_TRUE(CheckSubtraction(M_monomial_static_, M_double_dynamic_));
EXPECT_TRUE(CheckMultiplication(M_monomial_static_, M_double_dynamic_));
EXPECT_TRUE(CheckDotProduct(v_monomial_static_, v_double_dynamic_));
// Checks Dynamic op Static where op = {+, -, *}.
EXPECT_TRUE(CheckAddition(M_monomial_dynamic_, M_double_static_));
EXPECT_TRUE(CheckSubtraction(M_monomial_dynamic_, M_double_static_));
EXPECT_TRUE(CheckMultiplication(M_monomial_dynamic_, M_double_static_));
EXPECT_TRUE(CheckDotProduct(v_monomial_dynamic_, v_double_static_));
// Checks Static op Static where op = {+, -, *, ·}.
EXPECT_TRUE(CheckAddition(M_monomial_static_, M_double_static_));
EXPECT_TRUE(CheckSubtraction(M_monomial_static_, M_double_static_));
EXPECT_TRUE(CheckMultiplication(M_monomial_static_, M_double_static_));
EXPECT_TRUE(CheckDotProduct(v_monomial_static_, v_double_static_));
}
TEST_F(SymbolicPolynomialMatrixTest, doublePolynomial) {
// Checks Dynamic op Dynamic where op = {+, -, *, ·}.
EXPECT_TRUE(CheckAddition(M_double_dynamic_, M_poly_dynamic_));
EXPECT_TRUE(CheckSubtraction(M_double_dynamic_, M_poly_dynamic_));
EXPECT_TRUE(CheckMultiplication(M_double_dynamic_, M_poly_dynamic_));
EXPECT_TRUE(CheckDotProduct(v_double_dynamic_, v_poly_dynamic_));
// Checks Static op Dynamic where op = {+, -, *, ·}.
EXPECT_TRUE(CheckAddition(M_double_static_, M_poly_dynamic_));
EXPECT_TRUE(CheckSubtraction(M_double_static_, M_poly_dynamic_));
EXPECT_TRUE(CheckMultiplication(M_double_static_, M_poly_dynamic_));
EXPECT_TRUE(CheckDotProduct(v_double_static_, v_poly_dynamic_));
// Checks Dynamic op Static where op = {+, -, *}.
EXPECT_TRUE(CheckAddition(M_double_dynamic_, M_poly_static_));
EXPECT_TRUE(CheckSubtraction(M_double_dynamic_, M_poly_static_));
EXPECT_TRUE(CheckMultiplication(M_double_dynamic_, M_poly_static_));
EXPECT_TRUE(CheckDotProduct(v_double_dynamic_, v_poly_static_));
// Checks Static op Static where op = {+, -, *, ·}.
EXPECT_TRUE(CheckAddition(M_double_static_, M_poly_static_));
EXPECT_TRUE(CheckSubtraction(M_double_static_, M_poly_static_));
EXPECT_TRUE(CheckMultiplication(M_double_static_, M_poly_static_));
EXPECT_TRUE(CheckDotProduct(v_double_static_, v_poly_static_));
}
TEST_F(SymbolicPolynomialMatrixTest, doubleMonomial) {
// Checks Dynamic op Dynamic where op = {+, -, *, ·}.
EXPECT_TRUE(CheckAddition(M_double_dynamic_, M_monomial_dynamic_));
EXPECT_TRUE(CheckSubtraction(M_double_dynamic_, M_monomial_dynamic_));
EXPECT_TRUE(CheckMultiplication(M_double_dynamic_, M_monomial_dynamic_));
EXPECT_TRUE(CheckDotProduct(v_double_dynamic_, v_monomial_dynamic_));
// Checks Static op Dynamic where op = {+, -, *, ·}.
EXPECT_TRUE(CheckAddition(M_double_static_, M_monomial_dynamic_));
EXPECT_TRUE(CheckSubtraction(M_double_static_, M_monomial_dynamic_));
EXPECT_TRUE(CheckMultiplication(M_double_static_, M_monomial_dynamic_));
EXPECT_TRUE(CheckDotProduct(v_double_static_, v_monomial_dynamic_));
// Checks Dynamic op Static where op = {+, -, *}.
EXPECT_TRUE(CheckAddition(M_double_dynamic_, M_monomial_static_));
EXPECT_TRUE(CheckSubtraction(M_double_dynamic_, M_monomial_static_));
EXPECT_TRUE(CheckMultiplication(M_double_dynamic_, M_monomial_static_));
EXPECT_TRUE(CheckDotProduct(v_double_dynamic_, v_monomial_static_));
// Checks Static op Static where op = {+, -, *, ·}.
EXPECT_TRUE(CheckAddition(M_double_static_, M_monomial_static_));
EXPECT_TRUE(CheckSubtraction(M_double_static_, M_monomial_static_));
EXPECT_TRUE(CheckMultiplication(M_double_static_, M_monomial_static_));
EXPECT_TRUE(CheckDotProduct(v_double_static_, v_monomial_static_));
}
TEST_F(SymbolicPolynomialMatrixTest, EvaluateMatrix) {
const Environment env{{{var_x_, 1.0}, {var_y_, 2.0}, {var_z_, 3.0}}};
EXPECT_EQ(Evaluate(M_poly_dynamic_, env),
Evaluate(M_poly_dynamic_.cast<Expression>(), env));
EXPECT_EQ(Evaluate(M_poly_static_, env),
Evaluate(M_poly_static_.cast<Expression>(), env));
EXPECT_EQ(Evaluate(v_poly_dynamic_, env),
Evaluate(v_poly_dynamic_.cast<Expression>(), env));
EXPECT_EQ(Evaluate(v_poly_static_, env),
Evaluate(v_poly_static_.cast<Expression>(), env));
}
TEST_F(SymbolicPolynomialMatrixTest, Jacobian) {
const Vector3<Variable> vars{var_x_, var_y_, var_z_};
{
const MatrixX<Polynomial> result{Jacobian(v_poly_dynamic_, vars)};
for (int i = 0; i < v_poly_dynamic_.size(); ++i) {
for (int j = 0; j < vars.size(); ++j) {
const Polynomial p1{v_poly_dynamic_(i).Differentiate(vars(j))};
const Polynomial& p2{result(i, j)};
EXPECT_TRUE(p1.EqualTo(p2));
}
}
}
{
const MatrixX<Polynomial> result{Jacobian(v_poly_static_, vars)};
for (int i = 0; i < v_poly_static_.size(); ++i) {
for (int j = 0; j < vars.size(); ++j) {
const Polynomial p1{v_poly_static_(i).Differentiate(vars(j))};
const Polynomial& p2{result(i, j)};
EXPECT_TRUE(p1.EqualTo(p2));
}
}
}
}
} // namespace
} // namespace symbolic
} // namespace drake