test/redux.cpp

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2015 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// 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/.

#define TEST_ENABLE_TEMPORARY_TRACKING
#define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 8
// ^^ see bug 1449

#include "main.h"

template <typename MatrixType>
void matrixRedux(const MatrixType& m) {
  typedef typename MatrixType::Scalar Scalar;
  typedef typename MatrixType::RealScalar RealScalar;

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

  MatrixType m1 = MatrixType::Random(rows, cols);

  // The entries of m1 are uniformly distributed in [-1,1), so m1.prod() is very small. This may lead to test
  // failures if we underflow into denormals. Thus, we scale so that entries are close to 1.
  MatrixType m1_for_prod = MatrixType::Ones(rows, cols) + RealScalar(0.2) * m1;

  Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> m2(rows, rows);
  m2.setRandom();
  // Prevent overflows for integer types.
  if (Eigen::NumTraits<Scalar>::IsInteger) {
    Scalar kMaxVal = Scalar(10000);
    m1.array() = m1.array() - kMaxVal * (m1.array() / kMaxVal);
    m2.array() = m2.array() - kMaxVal * (m2.array() / kMaxVal);
  }

  VERIFY_IS_MUCH_SMALLER_THAN(MatrixType::Zero(rows, cols).sum(), Scalar(1));
  VERIFY_IS_APPROX(
      MatrixType::Ones(rows, cols).sum(),
      Scalar(float(
          rows *
          cols)));  // the float() here to shut up excessive MSVC warning about int->complex conversion being lossy
  Scalar s(0), p(1), minc(numext::real(m1.coeff(0))), maxc(numext::real(m1.coeff(0)));
  for (int j = 0; j < cols; j++)
    for (int i = 0; i < rows; i++) {
      s += m1(i, j);
      p *= m1_for_prod(i, j);
      minc = (std::min)(numext::real(minc), numext::real(m1(i, j)));
      maxc = (std::max)(numext::real(maxc), numext::real(m1(i, j)));
    }
  const Scalar mean = s / Scalar(RealScalar(rows * cols));

  VERIFY_IS_APPROX(m1.sum(), s);
  VERIFY_IS_APPROX(m1.mean(), mean);
  VERIFY_IS_APPROX(m1_for_prod.prod(), p);
  VERIFY_IS_APPROX(m1.real().minCoeff(), numext::real(minc));
  VERIFY_IS_APPROX(m1.real().maxCoeff(), numext::real(maxc));

  // test that partial reduction works if nested expressions is forced to evaluate early
  VERIFY_IS_APPROX((m1.matrix() * m1.matrix().transpose()).cwiseProduct(m2.matrix()).rowwise().sum().sum(),
                   (m1.matrix() * m1.matrix().transpose()).eval().cwiseProduct(m2.matrix()).rowwise().sum().sum());

  // test slice vectorization assuming assign is ok
  Index r0 = internal::random<Index>(0, rows - 1);
  Index c0 = internal::random<Index>(0, cols - 1);
  Index r1 = internal::random<Index>(r0 + 1, rows) - r0;
  Index c1 = internal::random<Index>(c0 + 1, cols) - c0;
  VERIFY_IS_APPROX(m1.block(r0, c0, r1, c1).sum(), m1.block(r0, c0, r1, c1).eval().sum());
  VERIFY_IS_APPROX(m1.block(r0, c0, r1, c1).mean(), m1.block(r0, c0, r1, c1).eval().mean());
  VERIFY_IS_APPROX(m1_for_prod.block(r0, c0, r1, c1).prod(), m1_for_prod.block(r0, c0, r1, c1).eval().prod());
  VERIFY_IS_APPROX(m1.block(r0, c0, r1, c1).real().minCoeff(), m1.block(r0, c0, r1, c1).real().eval().minCoeff());
  VERIFY_IS_APPROX(m1.block(r0, c0, r1, c1).real().maxCoeff(), m1.block(r0, c0, r1, c1).real().eval().maxCoeff());

  // regression for bug 1090
  const int R1 = MatrixType::RowsAtCompileTime >= 2 ? MatrixType::RowsAtCompileTime / 2 : 6;
  const int C1 = MatrixType::ColsAtCompileTime >= 2 ? MatrixType::ColsAtCompileTime / 2 : 6;
  if (R1 <= rows - r0 && C1 <= cols - c0) {
    VERIFY_IS_APPROX((m1.template block<R1, C1>(r0, c0).sum()), m1.block(r0, c0, R1, C1).sum());
  }

  // test empty objects
  VERIFY_IS_APPROX(m1.block(r0, c0, 0, 0).sum(), Scalar(0));
  VERIFY_IS_APPROX(m1.block(r0, c0, 0, 0).prod(), Scalar(1));

  // test nesting complex expression
  VERIFY_EVALUATION_COUNT((m1.matrix() * m1.matrix().transpose()).sum(),
                          (MatrixType::IsVectorAtCompileTime && MatrixType::SizeAtCompileTime != 1 ? 0 : 1));
  VERIFY_EVALUATION_COUNT(((m1.matrix() * m1.matrix().transpose()) + m2).sum(),
                          (MatrixType::IsVectorAtCompileTime && MatrixType::SizeAtCompileTime != 1 ? 0 : 1));
}

template <typename VectorType>
void vectorRedux(const VectorType& w) {
  using std::abs;
  typedef typename VectorType::Scalar Scalar;
  typedef typename NumTraits<Scalar>::Real RealScalar;
  Index size = w.size();

  VectorType v = VectorType::Random(size);
  VectorType v_for_prod = VectorType::Ones(size) + Scalar(0.2) * v;  // see comment above declaration of m1_for_prod

  for (int i = 1; i < size; i++) {
    Scalar s(0), p(1);
    RealScalar minc(numext::real(v.coeff(0))), maxc(numext::real(v.coeff(0)));
    for (int j = 0; j < i; j++) {
      s += v[j];
      p *= v_for_prod[j];
      minc = (std::min)(minc, numext::real(v[j]));
      maxc = (std::max)(maxc, numext::real(v[j]));
    }
    VERIFY_IS_MUCH_SMALLER_THAN(abs(s - v.head(i).sum()), Scalar(1));
    VERIFY_IS_APPROX(p, v_for_prod.head(i).prod());
    VERIFY_IS_APPROX(minc, v.real().head(i).minCoeff());
    VERIFY_IS_APPROX(maxc, v.real().head(i).maxCoeff());
  }

  for (int i = 0; i < size - 1; i++) {
    Scalar s(0), p(1);
    RealScalar minc(numext::real(v.coeff(i))), maxc(numext::real(v.coeff(i)));
    for (int j = i; j < size; j++) {
      s += v[j];
      p *= v_for_prod[j];
      minc = (std::min)(minc, numext::real(v[j]));
      maxc = (std::max)(maxc, numext::real(v[j]));
    }
    VERIFY_IS_MUCH_SMALLER_THAN(abs(s - v.tail(size - i).sum()), Scalar(1));
    VERIFY_IS_APPROX(p, v_for_prod.tail(size - i).prod());
    VERIFY_IS_APPROX(minc, v.real().tail(size - i).minCoeff());
    VERIFY_IS_APPROX(maxc, v.real().tail(size - i).maxCoeff());
  }

  for (int i = 0; i < size / 2; i++) {
    Scalar s(0), p(1);
    RealScalar minc(numext::real(v.coeff(i))), maxc(numext::real(v.coeff(i)));
    for (int j = i; j < size - i; j++) {
      s += v[j];
      p *= v_for_prod[j];
      minc = (std::min)(minc, numext::real(v[j]));
      maxc = (std::max)(maxc, numext::real(v[j]));
    }
    VERIFY_IS_MUCH_SMALLER_THAN(abs(s - v.segment(i, size - 2 * i).sum()), Scalar(1));
    VERIFY_IS_APPROX(p, v_for_prod.segment(i, size - 2 * i).prod());
    VERIFY_IS_APPROX(minc, v.real().segment(i, size - 2 * i).minCoeff());
    VERIFY_IS_APPROX(maxc, v.real().segment(i, size - 2 * i).maxCoeff());
  }

  // test empty objects
  VERIFY_IS_APPROX(v.head(0).sum(), Scalar(0));
  VERIFY_IS_APPROX(v.tail(0).prod(), Scalar(1));
  VERIFY_RAISES_ASSERT(v.head(0).mean());
  VERIFY_RAISES_ASSERT(v.head(0).minCoeff());
  VERIFY_RAISES_ASSERT(v.head(0).maxCoeff());
}

EIGEN_DECLARE_TEST(redux) {
  // the max size cannot be too large, otherwise reduxion operations obviously generate large errors.
  int maxsize = (std::min)(100, EIGEN_TEST_MAX_SIZE);
  TEST_SET_BUT_UNUSED_VARIABLE(maxsize);
  for (int i = 0; i < g_repeat; i++) {
    CALL_SUBTEST_1(matrixRedux(Matrix<float, 1, 1>()));
    CALL_SUBTEST_1(matrixRedux(Array<float, 1, 1>()));
    CALL_SUBTEST_2(matrixRedux(Matrix2f()));
    CALL_SUBTEST_2(matrixRedux(Array2f()));
    CALL_SUBTEST_2(matrixRedux(Array22f()));
    CALL_SUBTEST_3(matrixRedux(Matrix4d()));
    CALL_SUBTEST_3(matrixRedux(Array4d()));
    CALL_SUBTEST_3(matrixRedux(Array44d()));
    CALL_SUBTEST_4(matrixRedux(MatrixXcf(internal::random<int>(1, maxsize), internal::random<int>(1, maxsize))));
    CALL_SUBTEST_4(matrixRedux(ArrayXXcf(internal::random<int>(1, maxsize), internal::random<int>(1, maxsize))));
    CALL_SUBTEST_5(matrixRedux(MatrixXd(internal::random<int>(1, maxsize), internal::random<int>(1, maxsize))));
    CALL_SUBTEST_5(matrixRedux(ArrayXXd(internal::random<int>(1, maxsize), internal::random<int>(1, maxsize))));
    CALL_SUBTEST_6(matrixRedux(MatrixXi(internal::random<int>(1, maxsize), internal::random<int>(1, maxsize))));
    CALL_SUBTEST_6(matrixRedux(ArrayXXi(internal::random<int>(1, maxsize), internal::random<int>(1, maxsize))));
  }
  for (int i = 0; i < g_repeat; i++) {
    CALL_SUBTEST_7(vectorRedux(Vector4f()));
    CALL_SUBTEST_7(vectorRedux(Array4f()));
    CALL_SUBTEST_5(vectorRedux(VectorXd(internal::random<int>(1, maxsize))));
    CALL_SUBTEST_5(vectorRedux(ArrayXd(internal::random<int>(1, maxsize))));
    CALL_SUBTEST_8(vectorRedux(VectorXf(internal::random<int>(1, maxsize))));
    CALL_SUBTEST_8(vectorRedux(ArrayXf(internal::random<int>(1, maxsize))));
  }
}