test/inverse.cpp

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// 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 <Eigen/LU>

template <typename MatrixType>
void inverse_for_fixed_size(const MatrixType&, std::enable_if_t<MatrixType::SizeAtCompileTime == Dynamic>* = 0) {}

template <typename MatrixType>
void inverse_for_fixed_size(const MatrixType& m1, std::enable_if_t<MatrixType::SizeAtCompileTime != Dynamic>* = 0) {
  using std::abs;

  MatrixType m2, identity = MatrixType::Identity();

  typedef typename MatrixType::Scalar Scalar;
  typedef typename NumTraits<Scalar>::Real RealScalar;
  typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> VectorType;

  // computeInverseAndDetWithCheck tests
  // First: an invertible matrix
  bool invertible;
  Scalar det;

  m2.setZero();
  m1.computeInverseAndDetWithCheck(m2, det, invertible);
  VERIFY(invertible);
  VERIFY_IS_APPROX(identity, m1 * m2);
  VERIFY_IS_APPROX(det, m1.determinant());

  m2.setZero();
  m1.computeInverseWithCheck(m2, invertible);
  VERIFY(invertible);
  VERIFY_IS_APPROX(identity, m1 * m2);

  // Second: a rank one matrix (not invertible, except for 1x1 matrices)
  VectorType v3 = VectorType::Random();
  MatrixType m3 = v3 * v3.transpose(), m4;
  m3.computeInverseAndDetWithCheck(m4, det, invertible);
  VERIFY(m1.rows() == 1 ? invertible : !invertible);
  VERIFY_IS_MUCH_SMALLER_THAN(abs(det - m3.determinant()), RealScalar(1));
  m3.computeInverseWithCheck(m4, invertible);
  VERIFY(m1.rows() == 1 ? invertible : !invertible);

  // check with submatrices
  {
    Matrix<Scalar, MatrixType::RowsAtCompileTime + 1, MatrixType::RowsAtCompileTime + 1, MatrixType::Options> m5;
    m5.setRandom();
    m5.topLeftCorner(m1.rows(), m1.rows()) = m1;
    m2 = m5.template topLeftCorner<MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime>().inverse();
    VERIFY_IS_APPROX((m5.template topLeftCorner<MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime>()),
                     m2.inverse());
  }
}

template <typename MatrixType>
void inverse(const MatrixType& m) {
  /* this test covers the following files:
     Inverse.h
  */
  Index rows = m.rows();
  Index cols = m.cols();

  typedef typename MatrixType::Scalar Scalar;

  MatrixType m1(rows, cols), m2(rows, cols), identity = MatrixType::Identity(rows, rows);
  createRandomPIMatrixOfRank(rows, rows, rows, m1);
  m2 = m1.inverse();
  VERIFY_IS_APPROX(m1, m2.inverse());

  VERIFY_IS_APPROX((Scalar(2) * m2).inverse(), m2.inverse() * Scalar(0.5));

  VERIFY_IS_APPROX(identity, m1.inverse() * m1);
  VERIFY_IS_APPROX(identity, m1 * m1.inverse());

  VERIFY_IS_APPROX(m1, m1.inverse().inverse());

  // since for the general case we implement separately row-major and col-major, test that
  VERIFY_IS_APPROX(MatrixType(m1.transpose().inverse()), MatrixType(m1.inverse().transpose()));

  inverse_for_fixed_size(m1);

  // check in-place inversion
  if (MatrixType::RowsAtCompileTime >= 2 && MatrixType::RowsAtCompileTime <= 4) {
    // in-place is forbidden
    VERIFY_RAISES_ASSERT(m1 = m1.inverse());
  } else {
    m2 = m1.inverse();
    m1 = m1.inverse();
    VERIFY_IS_APPROX(m1, m2);
  }
}

template <typename Scalar>
void inverse_zerosized() {
  Matrix<Scalar, Dynamic, Dynamic> A(0, 0);
  {
    Matrix<Scalar, 0, 1> b, x;
    x = A.inverse() * b;
  }
  {
    Matrix<Scalar, Dynamic, Dynamic> b(0, 1), x;
    x = A.inverse() * b;
    VERIFY_IS_EQUAL(x.rows(), 0);
    VERIFY_IS_EQUAL(x.cols(), 1);
  }
}

EIGEN_DECLARE_TEST(inverse) {
  int s = 0;
  for (int i = 0; i < g_repeat; i++) {
    CALL_SUBTEST_1(inverse(Matrix<double, 1, 1>()));
    CALL_SUBTEST_2(inverse(Matrix2d()));
    CALL_SUBTEST_3(inverse(Matrix3f()));
    CALL_SUBTEST_4(inverse(Matrix4f()));
    CALL_SUBTEST_4(inverse(Matrix<float, 4, 4, DontAlign>()));

    s = internal::random<int>(50, 320);
    CALL_SUBTEST_5(inverse(MatrixXf(s, s)));
    TEST_SET_BUT_UNUSED_VARIABLE(s)
    CALL_SUBTEST_5(inverse_zerosized<float>());
    CALL_SUBTEST_5(inverse(MatrixXf(0, 0)));
    CALL_SUBTEST_5(inverse(MatrixXf(1, 1)));

    s = internal::random<int>(25, 100);
    CALL_SUBTEST_6(inverse(MatrixXcd(s, s)));
    TEST_SET_BUT_UNUSED_VARIABLE(s)

    CALL_SUBTEST_7(inverse(Matrix4d()));
    CALL_SUBTEST_7(inverse(Matrix<double, 4, 4, DontAlign>()));

    CALL_SUBTEST_8(inverse(Matrix4cd()));
  }
}