Function triangular_square

dependence/eigen-3.4.0/test/triangular.cpp:40–175

template<typename MatrixType> void triangular_square(const MatrixType& m)
{
  typedef typename MatrixType::Scalar Scalar;
  typedef typename NumTraits<Scalar>::Real RealScalar;
  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;

  RealScalar largerEps = 10*test_precision<RealScalar>();

  Index rows = m.rows();
  Index cols = m.cols();

  MatrixType m1 = MatrixType::Random(rows, cols),
             m2 = MatrixType::Random(rows, cols),
             m3(rows, cols),
             m4(rows, cols),
             r1(rows, cols),
             r2(rows, cols);
  VectorType v2 = VectorType::Random(rows);

  MatrixType m1up = m1.template triangularView<Upper>();
  MatrixType m2up = m2.template triangularView<Upper>();

  if (rows*cols>1)
  {
    VERIFY(m1up.isUpperTriangular());
    VERIFY(m2up.transpose().isLowerTriangular());
    VERIFY(!m2.isLowerTriangular());
  }

//   VERIFY_IS_APPROX(m1up.transpose() * m2, m1.upper().transpose().lower() * m2);

  // test overloaded operator+=
  r1.setZero();
  r2.setZero();
  r1.template triangularView<Upper>() +=  m1;
  r2 += m1up;
  VERIFY_IS_APPROX(r1,r2);

  // test overloaded operator=
  m1.setZero();
  m1.template triangularView<Upper>() = m2.transpose() + m2;
  m3 = m2.transpose() + m2;
  VERIFY_IS_APPROX(m3.template triangularView<Lower>().transpose().toDenseMatrix(), m1);

  // test overloaded operator=
  m1.setZero();
  m1.template triangularView<Lower>() = m2.transpose() + m2;
  VERIFY_IS_APPROX(m3.template triangularView<Lower>().toDenseMatrix(), m1);

  VERIFY_IS_APPROX(m3.template triangularView<Lower>().conjugate().toDenseMatrix(),
                   m3.conjugate().template triangularView<Lower>().toDenseMatrix());

  m1 = MatrixType::Random(rows, cols);
  for (int i=0; i<rows; ++i)
    while (numext::abs2(m1(i,i))<RealScalar(1e-1)) m1(i,i) = internal::random<Scalar>();

  Transpose<MatrixType> trm4(m4);
  // test back and forward substitution with a vector as the rhs