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Add support for general matrix functions.

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This does the job but it is only a first version. Further plans:
improved docs, more tests, improve code by refactoring, add convenience
functions for sine, cosine, sinh, cosh, and (eventually) add the matrix
logarithm.
This commit is contained in:
Jitse Niesen
2009-12-21 18:53:00 +00:00
parent 9f1fa6ea5e
commit f54a2a0484
5 changed files with 549 additions and 9 deletions
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49
unsupported/test/matrixExponential.cpp
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@@ -33,6 +33,18 @@ double binom(int n, int k)
return res;
}
template <typename Derived, typename OtherDerived>
double relerr(const MatrixBase<Derived>& A, const MatrixBase<OtherDerived>& B)
{
return std::sqrt((A - B).cwise().abs2().sum() / std::min(A.cwise().abs2().sum(), B.cwise().abs2().sum()));
}
template <typename T>
T expfn(T x, int)
{
return std::exp(x);
}
template <typename T>
void test2dRotation(double tol)
{
@@ -44,7 +56,13 @@ void test2dRotation(double tol)
{
angle = static_cast<T>(pow(10, i / 5. - 2));
B << cos(angle), sin(angle), -sin(angle), cos(angle);
ei_matrix_function(angle*A, expfn, &C);
std::cout << "test2dRotation: i = " << i << " error funm = " << relerr(C, B);
VERIFY(C.isApprox(B, static_cast<T>(tol)));
ei_matrix_exponential(angle*A, &C);
std::cout << " error expm = " << relerr(C, B) << "\n";
VERIFY(C.isApprox(B, static_cast<T>(tol)));
}
}
@@ -63,7 +81,13 @@ void test2dHyperbolicRotation(double tol)
sh = std::sinh(angle);
A << 0, angle*imagUnit, -angle*imagUnit, 0;
B << ch, sh*imagUnit, -sh*imagUnit, ch;
ei_matrix_function(A, expfn, &C);
std::cout << "test2dHyperbolicRotation: i = " << i << " error funm = " << relerr(C, B);
VERIFY(C.isApprox(B, static_cast<T>(tol)));
ei_matrix_exponential(A, &C);
std::cout << " error expm = " << relerr(C, B) << "\n";
VERIFY(C.isApprox(B, static_cast<T>(tol)));
}
}
@@ -81,7 +105,13 @@ void testPascal(double tol)
for (int i=0; i<size; i++)
for (int j=0; j<=i; j++)
B(i,j) = static_cast<T>(binom(i,j));
ei_matrix_function(A, expfn, &C);
std::cout << "testPascal: size = " << size << " error funm = " << relerr(C, B);
VERIFY(C.isApprox(B, static_cast<T>(tol)));
ei_matrix_exponential(A, &C);
std::cout << " error expm = " << relerr(C, B) << "\n";
VERIFY(C.isApprox(B, static_cast<T>(tol)));
}
}
@@ -101,26 +131,33 @@ void randomTest(const MatrixType& m, double tol)
for(int i = 0; i < g_repeat; i++) {
m1 = MatrixType::Random(rows, cols);
ei_matrix_function(m1, expfn, &m2);
ei_matrix_function(-m1, expfn, &m3);
std::cout << "randomTest: error funm = " << relerr(identity, m2 * m3);
VERIFY(identity.isApprox(m2 * m3, static_cast<RealScalar>(tol)));
ei_matrix_exponential(m1, &m2);
ei_matrix_exponential(-m1, &m3);
VERIFY(identity.isApprox(m2 * m3, static_cast<RealScalar>(tol)));
std::cout << " error expm = " << relerr(identity, m2 * m3) << "\n";
VERIFY(identity.isApprox(m2 * m3, static_cast<RealScalar>(tol)));
}
}
void test_matrixExponential()
{
CALL_SUBTEST_2(test2dRotation<double>(1e-14));
CALL_SUBTEST_2(test2dRotation<double>(1e-13));
CALL_SUBTEST_1(test2dRotation<float>(1e-5));
CALL_SUBTEST_2(test2dHyperbolicRotation<double>(1e-14));
CALL_SUBTEST_1(test2dHyperbolicRotation<float>(1e-5));
CALL_SUBTEST_1(testPascal<float>(1e-5));
CALL_SUBTEST_2(testPascal<double>(1e-14));
CALL_SUBTEST_6(testPascal<float>(1e-6));
CALL_SUBTEST_5(testPascal<double>(1e-15));
CALL_SUBTEST_2(randomTest(Matrix2d(), 1e-13));
CALL_SUBTEST_2(randomTest(Matrix<double,3,3,RowMajor>(), 1e-13));
CALL_SUBTEST_7(randomTest(Matrix<double,3,3,RowMajor>(), 1e-13));
CALL_SUBTEST_3(randomTest(Matrix4cd(), 1e-13));
CALL_SUBTEST_4(randomTest(MatrixXd(8,8), 1e-13));
CALL_SUBTEST_1(randomTest(Matrix2f(), 1e-4));
CALL_SUBTEST_5(randomTest(Matrix3cf(), 1e-4));
CALL_SUBTEST_5(randomTest(Matrix3cf(), 1e-4));
CALL_SUBTEST_1(randomTest(Matrix4f(), 1e-4));
CALL_SUBTEST_6(randomTest(MatrixXf(8,8), 1e-4));
}