void test2dRotation(double tol)
{
Matrix<T,2,2> A, B, C;
T angle;
A << 0, 1, -1, 0;
for (int i=0; i<=20; i++)
{
angle = static_cast<T>(pow(10, i / 5. - 2));
B << cos(angle), sin(angle), -sin(angle), cos(angle);
C = (angle*A).matrixFunction(expfn);
std::cout << "test2dRotation: i = " << i << " error funm = " << relerr(C, B);
VERIFY(C.isApprox(B, static_cast<T>(tol)));
C = (angle*A).exp();
std::cout << " error expm = " << relerr(C, B) << "\n";
VERIFY(C.isApprox(B, static_cast<T>(tol)));
}
}
void testPascal(double tol)
{
for (int size=1; size<20; size++)
{
Matrix<T,Dynamic,Dynamic> A(size,size), B(size,size), C(size,size);
A.setZero();
for (int i=0; i<size-1; i++)
A(i+1,i) = static_cast<T>(i+1);
B.setZero();
for (int i=0; i<size; i++)
for (int j=0; j<=i; j++)
B(i,j) = static_cast<T>(binom(i,j));
C = A.matrixFunction(expfn);
std::cout << "testPascal: size = " << size << " error funm = " << relerr(C, B);
VERIFY(C.isApprox(B, static_cast<T>(tol)));
C = A.exp();
std::cout << " error expm = " << relerr(C, B) << "\n";
VERIFY(C.isApprox(B, static_cast<T>(tol)));
}
}
void test2dHyperbolicRotation(double tol)
{
Matrix<std::complex<T>,2,2> A, B, C;
std::complex<T> imagUnit(0,1);
T angle, ch, sh;
for (int i=0; i<=20; i++)
{
angle = static_cast<T>((i-10) / 2.0);
ch = std::cosh(angle);
sh = std::sinh(angle);
A << 0, angle*imagUnit, -angle*imagUnit, 0;
B << ch, sh*imagUnit, -sh*imagUnit, ch;
C = A.matrixFunction(expfn);
std::cout << "test2dHyperbolicRotation: i = " << i << " error funm = " << relerr(C, B);
VERIFY(C.isApprox(B, static_cast<T>(tol)));
C = A.exp();
std::cout << " error expm = " << relerr(C, B) << "\n";
VERIFY(C.isApprox(B, static_cast<T>(tol)));
}
}
void randomTest(const MatrixType& m, double tol)
{
/* this test covers the following files:
Inverse.h
*/
typename MatrixType::Index rows = m.rows();
typename MatrixType::Index cols = m.cols();
MatrixType m1(rows, cols), m2(rows, cols), identity = MatrixType::Identity(rows, cols);
typedef typename NumTraits<typename internal::traits<MatrixType>::Scalar>::Real RealScalar;
for(int i = 0; i < g_repeat; i++) {
m1 = MatrixType::Random(rows, cols);
m2 = m1.matrixFunction(expfn) * (-m1).matrixFunction(expfn);
std::cout << "randomTest: error funm = " << relerr(identity, m2);
VERIFY(identity.isApprox(m2, static_cast<RealScalar>(tol)));
m2 = m1.exp() * (-m1).exp();
std::cout << " error expm = " << relerr(identity, m2) << "\n";
VERIFY(identity.isApprox(m2, static_cast<RealScalar>(tol)));
}
}
void test2dRotation(double tol)
{
Matrix<T,2,2> A, B, C;
T angle, c, s;
A << 0, 1, -1, 0;
MatrixPower<Matrix<T,2,2> > Apow(A);
for (int i=0; i<=20; ++i) {
angle = pow(10, (i-10) / 5.);
c = std::cos(angle);
s = std::sin(angle);
B << c, s, -s, c;
C = Apow(std::ldexp(angle,1) / M_PI);
std::cout << "test2dRotation: i = " << i << " error powerm = " << relerr(C,B) << '\n';
VERIFY(C.isApprox(B, static_cast<T>(tol)));
}
}
void test2dHyperbolicRotation(double tol)
{
Matrix<std::complex<T>,2,2> A, B, C;
T angle, ch = std::cosh((T)1);
std::complex<T> ish(0, std::sinh((T)1));
A << ch, ish, -ish, ch;
MatrixPower<Matrix<std::complex<T>,2,2> > Apow(A);
for (int i=0; i<=20; ++i) {
angle = std::ldexp(static_cast<T>(i-10), -1);
ch = std::cosh(angle);
ish = std::complex<T>(0, std::sinh(angle));
B << ch, ish, -ish, ch;
C = Apow(angle);
std::cout << "test2dHyperbolicRotation: i = " << i << " error powerm = " << relerr(C,B) << '\n';
VERIFY(C.isApprox(B, static_cast<T>(tol)));
}
}
void testTriangularProduct(const MatrixType& m, const VectorType& v, double tol)
{
typedef typename MatrixType::RealScalar RealScalar;
MatrixType m1;
VectorType v1, v2, v3;
RealScalar p;
for (int i=0; i < g_repeat; ++i) {
generateTriangularMatrix<MatrixType>::run(m1, m.rows());
MatrixPowerTriangular<MatrixType> mpow(m1);
v1 = VectorType::Random(v.rows(), v.cols());
p = internal::random<RealScalar>();
v2.noalias() = mpow(p) * v1;
v3.noalias() = mpow(p).eval() * v1;
std::cout << "testTriangularProduct: error powerm = " << relerr(v2, v3) << '\n';
VERIFY(v2.isApprox(v3, static_cast<RealScalar>(tol)));
}
}