unsupported/test/matrix_power.cpp

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Chen-Pang He <jdh8@ms63.hinet.net>
//
// 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 "matrix_functions.h"

template <typename T>
void test2dRotation(double tol)
{
  Matrix<T,2,2> A, B, C;
  T angle, c, s;

  A << 0, 1, -1, 0;
  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 = A.pow(std::ldexp(angle, 1) / M_PI);
    std::cout << "test2dRotation: i = " << i << "   error powerm = " << relerr(C, B) << '\n';
    VERIFY(C.isApprox(B, T(tol)));
  }
}

template <typename T>
void test2dHyperbolicRotation(double tol)
{
  Matrix<std::complex<T>,2,2> A, B, C;
  T angle, ch = std::cosh(1);
  std::complex<T> ish(0, std::sinh(1));

  A << ch, ish, -ish, ch;
  for (int i = 0; i <= 20; i++) {
    angle = std::ldexp(T(i-10), -1);
    ch = std::cosh(angle);
    ish = std::complex<T>(0, std::sinh(angle));
    B << ch, ish, -ish, ch;

    C = A.pow(angle);
    std::cout << "test2dHyperbolicRotation: i = " << i << "   error powerm = " << relerr(C, B) << '\n';
    VERIFY(C.isApprox(B, T(tol)));
  }
}

template <typename MatrixType>
void testIntPowers(const MatrixType& m, double tol)
{
  typedef typename MatrixType::RealScalar RealScalar;
  const MatrixType m1 = MatrixType::Random(m.rows(), m.cols());
  const MatrixType identity = MatrixType::Identity(m.rows(), m.cols());
  const PartialPivLU<MatrixType> solver(m1);
  MatrixType m2, m3, m4;

  m3 = m1.pow(0);
  m4 = m1.pow(0.);
  std::cout << "testIntPower: i = 0   error powerm = " << relerr(identity, m3) << "   " << relerr(identity, m4) << '\n';
  VERIFY(identity == m3 && identity == m4);

  m3 = m1.pow(1);
  m4 = m1.pow(1.);
  std::cout << "testIntPower: i = 1   error powerm = " << relerr(m1, m3) << "   " << relerr(m1, m4) << '\n';
  VERIFY(m1 == m3 && m1 == m4);

  m2 = m1 * m1;
  m3 = m1.pow(2);
  m4 = m1.pow(2.);
  std::cout << "testIntPower: i = 2   error powerm = " << relerr(m2, m3) << "   " << relerr(m2, m4) << '\n';
  VERIFY(m2.isApprox(m3, RealScalar(tol)) && m2.isApprox(m4, RealScalar(tol)));

  for (int i = 3; i <= 20; i++) {
    m2 *= m1;
    m3 = m1.pow(i);
    m4 = m1.pow(RealScalar(i));
    std::cout << "testIntPower: i = " << i << "   error powerm = " << relerr(m2, m3) << "   " << relerr (m2, m4) << '\n';
    VERIFY(m2.isApprox(m3, RealScalar(tol)) && m2.isApprox(m4, RealScalar(tol)));
  }

  m2 = solver.inverse();
  m3 = m1.pow(-1);
  m4 = m1.pow(-1.);
  std::cout << "testIntPower: i = -1   error powerm = " << relerr(m2, m3) << "   " << relerr (m2, m4) << '\n';
  VERIFY(m2.isApprox(m3, RealScalar(tol)) && m2.isApprox(m4, RealScalar(tol)));

  for (int i = -2; i >= -20; i--) {
    m2 = solver.solve(m2);
    m3 = m1.pow(i);
    m4 = m1.pow(RealScalar(i));
    std::cout << "testIntPower: i = " << i << "   error powerm = " << relerr(m2, m3) << "   " << relerr (m2, m4) << '\n';
    VERIFY(m2.isApprox(m3, RealScalar(tol)) && m2.isApprox(m4, RealScalar(tol)));
  }
}

template <typename MatrixType>
void testExponentLaws(const MatrixType& m, double tol)
{
  typedef typename MatrixType::RealScalar RealScalar;
  MatrixType m1, m2, m3, m4, m5;
  RealScalar x, y;

  for (int i = 0; i < g_repeat; i++) {
    generateTestMatrix<MatrixType>::run(m1, m.rows());
    x = internal::random<RealScalar>();
    y = internal::random<RealScalar>();
    m2 = m1.pow(x);
    m3 = m1.pow(y);

    m4 = m1.pow(x + y);
    m5 = m2 * m3;
    std::cout << "testExponentLaws: error powerm = " << relerr(m4, m5);
    VERIFY(m4.isApprox(m5, RealScalar(tol)));

    if (!NumTraits<typename MatrixType::Scalar>::IsComplex) {
      m4 = m1.pow(x * y);
      m5 = m2.pow(y);
      std::cout << "   " << relerr(m4, m5);
      VERIFY(m4.isApprox(m5, RealScalar(tol)));
    }

    m4 = (std::abs(x) * m1).pow(y);
    m5 = std::pow(std::abs(x), y) * m3;
    std::cout << "   " << relerr(m4, m5) << '\n';
    VERIFY(m4.isApprox(m5, RealScalar(tol)));
  }
}

template <typename MatrixType, typename VectorType>
void testMatrixVectorProduct(const MatrixType& m, const VectorType& v, double tol)
{
  typedef typename MatrixType::RealScalar RealScalar;
  MatrixType m1;
  VectorType v1, v2, v3;
  RealScalar pReal;
  signed char pInt;

  for (int i = 0; i < g_repeat; i++) {
    generateTestMatrix<MatrixType>::run(m1, m.rows());
    v1 = VectorType::Random(v.rows(), v.cols());
    pReal = internal::random<RealScalar>();
    pInt = rand();
    pInt >>= 2;

    v2 = m1.pow(pReal).eval() * v1;
    v3 = m1.pow(pReal) * v1;
    std::cout << "testMatrixVectorProduct: error powerm = " << relerr(v2, v3);
    VERIFY(v2.isApprox(v3, RealScalar(tol)));

    v2 = m1.pow(pInt).eval() * v1;
    v3 = m1.pow(pInt) * v1;
    std::cout << "   " << relerr(v2, v3) << '\n';
    VERIFY(v2.isApprox(v3, RealScalar(tol)) || v2 == v3);
  }
}

void test_matrix_power()
{
  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_9(test2dRotation<long double>(1e-13)); 
  CALL_SUBTEST_2(test2dHyperbolicRotation<double>(1e-14));
  CALL_SUBTEST_1(test2dHyperbolicRotation<float>(1e-5));
  CALL_SUBTEST_9(test2dHyperbolicRotation<long double>(1e-14));

  CALL_SUBTEST_2(testIntPowers(Matrix2d(), 1e-13));
  CALL_SUBTEST_7(testIntPowers(Matrix<double,3,3,RowMajor>(), 1e-13));
  CALL_SUBTEST_3(testIntPowers(Matrix4cd(), 1e-13));
  CALL_SUBTEST_4(testIntPowers(MatrixXd(8,8), 1e-13));
  CALL_SUBTEST_1(testIntPowers(Matrix2f(), 1e-4));
  CALL_SUBTEST_5(testIntPowers(Matrix3cf(), 1e-4));
  CALL_SUBTEST_8(testIntPowers(Matrix4f(), 1e-4));
  CALL_SUBTEST_6(testIntPowers(MatrixXf(8,8), 1e-4));

  CALL_SUBTEST_2(testExponentLaws(Matrix2d(), 1e-13));
  CALL_SUBTEST_7(testExponentLaws(Matrix<double,3,3,RowMajor>(), 1e-13));
  CALL_SUBTEST_3(testExponentLaws(Matrix4cd(), 1e-13));
  CALL_SUBTEST_4(testExponentLaws(MatrixXd(8,8), 1e-13));
  CALL_SUBTEST_1(testExponentLaws(Matrix2f(), 1e-4));
  CALL_SUBTEST_5(testExponentLaws(Matrix3cf(), 1e-4));
  CALL_SUBTEST_8(testExponentLaws(Matrix4f(), 1e-4));
  CALL_SUBTEST_6(testExponentLaws(MatrixXf(8,8), 1e-4));

  CALL_SUBTEST_2(testMatrixVectorProduct(Matrix2d(), Vector2d(), 1e-13));
  CALL_SUBTEST_7(testMatrixVectorProduct(Matrix<double,3,3,RowMajor>(), Vector3d(), 1e-13));
  CALL_SUBTEST_3(testMatrixVectorProduct(Matrix4cd(), Vector4cd(), 1e-13));
  CALL_SUBTEST_4(testMatrixVectorProduct(MatrixXd(8,8), MatrixXd(8,2), 1e-13));
  CALL_SUBTEST_1(testMatrixVectorProduct(Matrix2f(), Vector2f(), 1e-4));
  CALL_SUBTEST_5(testMatrixVectorProduct(Matrix3cf(), Vector3cf(), 1e-4));
  CALL_SUBTEST_8(testMatrixVectorProduct(Matrix4f(), Vector4f(), 1e-4));
  CALL_SUBTEST_6(testMatrixVectorProduct(MatrixXf(8,8), VectorXf(8), 1e-4));
  CALL_SUBTEST_10(testMatrixVectorProduct(Matrix<long double,Dynamic,Dynamic>(7,7), Matrix<long double,7,9>(), 1e-13));
}