1 files changed, 149 insertions, 0 deletions
diff --git a/unsupported/test/matrix_exponential.cpp b/unsupported/test/matrix_exponential.cpp
new file mode 100644
index 000000000..695472f91
--- /dev/null
+++ b/unsupported/test/matrix_exponential.cpp
@@ -0,0 +1,149 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Jitse Niesen <jitse@maths.leeds.ac.uk>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <unsupported/Eigen/MatrixFunctions>
+
+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;
+}
+
+template <typename Derived, typename OtherDerived>
+double relerr(const MatrixBase<Derived>& A, const MatrixBase<OtherDerived>& B)
+{
+  return std::sqrt((A - B).cwiseAbs2().sum() / (std::min)(A.cwiseAbs2().sum(), B.cwiseAbs2().sum()));
+}
+
+template <typename T>
+T expfn(T x, int)
+{
+  return std::exp(x);
+}
+
+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)));
+  }
+}
+
+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)));
+  }
+}
+
+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)));
+  }
+}
+
+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), m3(rows, cols),
+             identity = MatrixType::Identity(rows, rows);
+
+  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 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));
+}