matrix_exponential.cpp File Reference

#include "matrix_functions.h"

Functions
double	binom (int n, int k)
template<typename T >
T	expfn (T x, int)
template<typename T >
void	test2dRotation (double tol)
template<typename T >
void	test2dHyperbolicRotation (double tol)
template<typename T >
void	testPascal (double tol)
template<typename MatrixType >
void	randomTest (const MatrixType &m, double tol)
	EIGEN_DECLARE_TEST (matrix_exponential)

Function Documentation

binom()

double binom	(	int	n,
		int	k
	)

                           {
  double res = 1;
  for (int i = 0; i < k; i++) res = res * (n - k + i + 1) / (i + 1);
  return res;
}

References i, k, n, and res.

Referenced by testPascal().

EIGEN_DECLARE_TEST()

EIGEN_DECLARE_TEST

(

matrix_exponential

)

                                       {
  CALL_SUBTEST_2(test2dRotation<double>(1e-13));
  CALL_SUBTEST_1(test2dRotation<float>(2e-5));  // was 1e-5, relaxed for clang 2.8 / linux / x86-64
  CALL_SUBTEST_8(test2dRotation<long double>(1e-13));
  CALL_SUBTEST_2(test2dHyperbolicRotation<double>(1e-14));
  CALL_SUBTEST_1(test2dHyperbolicRotation<float>(1e-5));
  CALL_SUBTEST_8(test2dHyperbolicRotation<long 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_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_1(randomTest(Matrix4f(), 1e-4));
  CALL_SUBTEST_6(randomTest(MatrixXf(8, 8), 1e-4));
  CALL_SUBTEST_9(randomTest(Matrix<long double, Dynamic, Dynamic>(7, 7), 1e-13));
}

References CALL_SUBTEST_1, CALL_SUBTEST_2, CALL_SUBTEST_3, CALL_SUBTEST_4, CALL_SUBTEST_5, CALL_SUBTEST_6, CALL_SUBTEST_7, CALL_SUBTEST_8, CALL_SUBTEST_9, e(), and randomTest().

expfn()

template<typename T >

T expfn	(	T	x,
		int
	)

                  {
  return std::exp(x);
}

References Eigen::bfloat16_impl::exp(), and plotDoE::x.

Referenced by randomTest(), test2dHyperbolicRotation(), test2dRotation(), and testPascal().

randomTest()

template<typename MatrixType >

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)));
  }
}

References cols, Eigen::bfloat16_impl::exp(), expfn(), Eigen::g_repeat, i, m, m1, m2(), relerr(), rows, and VERIFY.

Referenced by EIGEN_DECLARE_TEST().

test2dHyperbolicRotation()

template<typename T >

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)));
  }
}

References Jeffery_Solution::angle(), Eigen::bfloat16_impl::cosh(), expfn(), i, relerr(), Eigen::bfloat16_impl::sinh(), and VERIFY.

test2dRotation()

template<typename T >

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 << std::cos(angle), std::sin(angle), -std::sin(angle), std::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)));
  }
}

References Jeffery_Solution::angle(), cos(), Eigen::bfloat16_impl::exp(), expfn(), i, Eigen::ArrayBase< Derived >::pow(), relerr(), sin(), and VERIFY.

testPascal()

template<typename T >

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)));
  }
}

References binom(), expfn(), i, j, relerr(), Eigen::PlainObjectBase< Derived >::setZero(), size, and VERIFY.