test/vectorwiseop.cpp

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2011 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

#include "main.h"

template <typename ArrayType>
void vectorwiseop_array(const ArrayType& m) {
  typedef typename ArrayType::Scalar Scalar;
  typedef Array<Scalar, ArrayType::RowsAtCompileTime, 1> ColVectorType;
  typedef Array<Scalar, 1, ArrayType::ColsAtCompileTime> RowVectorType;

  Index rows = m.rows();
  Index cols = m.cols();
  Index r = internal::random<Index>(0, rows - 1), c = internal::random<Index>(0, cols - 1);

  ArrayType m1 = ArrayType::Random(rows, cols), m2(rows, cols), m3(rows, cols);

  ColVectorType colvec = ColVectorType::Random(rows);
  RowVectorType rowvec = RowVectorType::Random(cols);

  // test addition
  m2 = m1;
  m2.colwise() += colvec;
  VERIFY_IS_APPROX(m2, m1.colwise() + colvec);
  VERIFY_IS_APPROX(m2.col(c), m1.col(c) + colvec);

  m2 = m1;
  m2.rowwise() += rowvec;
  VERIFY_IS_APPROX(m2, m1.rowwise() + rowvec);
  VERIFY_IS_APPROX(m2.row(r), m1.row(r) + rowvec);

  // test subtraction
  m2 = m1;
  m2.colwise() -= colvec;
  VERIFY_IS_APPROX(m2, m1.colwise() - colvec);
  VERIFY_IS_APPROX(m2.col(c), m1.col(c) - colvec);

  m2 = m1;
  m2.rowwise() -= rowvec;
  VERIFY_IS_APPROX(m2, m1.rowwise() - rowvec);
  VERIFY_IS_APPROX(m2.row(r), m1.row(r) - rowvec);

  // test multiplication
  m2 = m1;
  m2.colwise() *= colvec;
  VERIFY_IS_APPROX(m2, m1.colwise() * colvec);
  VERIFY_IS_APPROX(m2.col(c), m1.col(c) * colvec);

  m2 = m1;
  m2.rowwise() *= rowvec;
  VERIFY_IS_APPROX(m2, m1.rowwise() * rowvec);
  VERIFY_IS_APPROX(m2.row(r), m1.row(r) * rowvec);

  // test quotient
  m2 = m1;
  m2.colwise() /= colvec;
  VERIFY_IS_APPROX(m2, m1.colwise() / colvec);
  VERIFY_IS_APPROX(m2.col(c), m1.col(c) / colvec);

  m2 = m1;
  m2.rowwise() /= rowvec;
  VERIFY_IS_APPROX(m2, m1.rowwise() / rowvec);
  VERIFY_IS_APPROX(m2.row(r), m1.row(r) / rowvec);

  m2 = m1;
  // yes, there might be an aliasing issue there but ".rowwise() /="
  // is supposed to evaluate " m2.colwise().sum()" into a temporary to avoid
  // evaluating the reduction multiple times
  if (ArrayType::RowsAtCompileTime > 2 || ArrayType::RowsAtCompileTime == Dynamic) {
    m2.rowwise() /= m2.colwise().sum();
    VERIFY_IS_APPROX(m2, m1.rowwise() / m1.colwise().sum());
  }

  // all/any
  Array<bool, Dynamic, Dynamic> mb(rows, cols);
  mb = (m1.real() <= 0.7).colwise().all();
  VERIFY((mb.col(c) == (m1.real().col(c) <= 0.7).all()).all());
  mb = (m1.real() <= 0.7).rowwise().all();
  VERIFY((mb.row(r) == (m1.real().row(r) <= 0.7).all()).all());

  mb = (m1.real() >= 0.7).colwise().any();
  VERIFY((mb.col(c) == (m1.real().col(c) >= 0.7).any()).all());
  mb = (m1.real() >= 0.7).rowwise().any();
  VERIFY((mb.row(r) == (m1.real().row(r) >= 0.7).any()).all());
}

template <typename MatrixType>
void vectorwiseop_matrix(const MatrixType& m) {
  typedef typename MatrixType::Scalar Scalar;
  typedef typename NumTraits<Scalar>::Real RealScalar;
  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> ColVectorType;
  typedef Matrix<Scalar, 1, MatrixType::ColsAtCompileTime> RowVectorType;
  typedef Matrix<RealScalar, MatrixType::RowsAtCompileTime, 1> RealColVectorType;
  typedef Matrix<RealScalar, 1, MatrixType::ColsAtCompileTime> RealRowVectorType;
  typedef Matrix<Scalar, Dynamic, Dynamic> MatrixX;

  Index rows = m.rows();
  Index cols = m.cols();
  Index r = internal::random<Index>(0, rows - 1), c = internal::random<Index>(0, cols - 1);

  MatrixType m1 = MatrixType::Random(rows, cols), m2(rows, cols), m3(rows, cols);

  ColVectorType colvec = ColVectorType::Random(rows);
  RowVectorType rowvec = RowVectorType::Random(cols);
  RealColVectorType rcres;
  RealRowVectorType rrres;

  // test broadcast assignment
  m2 = m1;
  m2.colwise() = colvec;
  for (Index j = 0; j < cols; ++j) VERIFY_IS_APPROX(m2.col(j), colvec);
  m2.rowwise() = rowvec;
  for (Index i = 0; i < rows; ++i) VERIFY_IS_APPROX(m2.row(i), rowvec);

  // test addition
  m2 = m1;
  m2.colwise() += colvec;
  VERIFY_IS_APPROX(m2, m1.colwise() + colvec);
  VERIFY_IS_APPROX(m2.col(c), m1.col(c) + colvec);

  m2 = m1;
  m2.rowwise() += rowvec;
  VERIFY_IS_APPROX(m2, m1.rowwise() + rowvec);
  VERIFY_IS_APPROX(m2.row(r), m1.row(r) + rowvec);

  // test subtraction
  m2 = m1;
  m2.colwise() -= colvec;
  VERIFY_IS_APPROX(m2, m1.colwise() - colvec);
  VERIFY_IS_APPROX(m2.col(c), m1.col(c) - colvec);

  m2 = m1;
  m2.rowwise() -= rowvec;
  VERIFY_IS_APPROX(m2, m1.rowwise() - rowvec);
  VERIFY_IS_APPROX(m2.row(r), m1.row(r) - rowvec);

  // ------ partial reductions ------

#define TEST_PARTIAL_REDUX_BASIC(FUNC, ROW, COL, PREPROCESS)                              \
  {                                                                                       \
    ROW = m1 PREPROCESS.colwise().FUNC;                                                   \
    for (Index k = 0; k < cols; ++k) VERIFY_IS_APPROX(ROW(k), m1.col(k) PREPROCESS.FUNC); \
    COL = m1 PREPROCESS.rowwise().FUNC;                                                   \
    for (Index k = 0; k < rows; ++k) VERIFY_IS_APPROX(COL(k), m1.row(k) PREPROCESS.FUNC); \
  }

  TEST_PARTIAL_REDUX_BASIC(sum(), rowvec, colvec, EIGEN_EMPTY);
  TEST_PARTIAL_REDUX_BASIC(prod(), rowvec, colvec, EIGEN_EMPTY);
  TEST_PARTIAL_REDUX_BASIC(mean(), rowvec, colvec, EIGEN_EMPTY);
  TEST_PARTIAL_REDUX_BASIC(minCoeff(), rrres, rcres, .real());
  TEST_PARTIAL_REDUX_BASIC(maxCoeff(), rrres, rcres, .real());
  TEST_PARTIAL_REDUX_BASIC(norm(), rrres, rcres, EIGEN_EMPTY);
  TEST_PARTIAL_REDUX_BASIC(squaredNorm(), rrres, rcres, EIGEN_EMPTY);
  TEST_PARTIAL_REDUX_BASIC(redux(internal::scalar_sum_op<Scalar, Scalar>()), rowvec, colvec, EIGEN_EMPTY);

  VERIFY_IS_APPROX(m1.cwiseAbs().colwise().sum(), m1.colwise().template lpNorm<1>());
  VERIFY_IS_APPROX(m1.cwiseAbs().rowwise().sum(), m1.rowwise().template lpNorm<1>());
  VERIFY_IS_APPROX(m1.cwiseAbs().colwise().maxCoeff(), m1.colwise().template lpNorm<Infinity>());
  VERIFY_IS_APPROX(m1.cwiseAbs().rowwise().maxCoeff(), m1.rowwise().template lpNorm<Infinity>());

  // regression for bug 1158
  VERIFY_IS_APPROX(m1.cwiseAbs().colwise().sum().x(), m1.col(0).cwiseAbs().sum());

  // test normalized
  m2 = m1.colwise().normalized();
  VERIFY_IS_APPROX(m2.col(c), m1.col(c).normalized());
  m2 = m1.rowwise().normalized();
  VERIFY_IS_APPROX(m2.row(r), m1.row(r).normalized());

  // test normalize
  m2 = m1;
  m2.colwise().normalize();
  VERIFY_IS_APPROX(m2.col(c), m1.col(c).normalized());
  m2 = m1;
  m2.rowwise().normalize();
  VERIFY_IS_APPROX(m2.row(r), m1.row(r).normalized());

  // test with partial reduction of products
  Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> m1m1 = m1 * m1.transpose();
  VERIFY_IS_APPROX((m1 * m1.transpose()).colwise().sum(), m1m1.colwise().sum());
  Matrix<Scalar, 1, MatrixType::RowsAtCompileTime> tmp(rows);
  VERIFY_EVALUATION_COUNT(tmp = (m1 * m1.transpose()).colwise().sum(), 1);

  m2 = m1.rowwise() - (m1.colwise().sum() / RealScalar(m1.rows())).eval();
  m1 = m1.rowwise() - (m1.colwise().sum() / RealScalar(m1.rows()));
  VERIFY_IS_APPROX(m1, m2);
  VERIFY_EVALUATION_COUNT(m2 = (m1.rowwise() - m1.colwise().sum() / RealScalar(m1.rows())),
                          (MatrixType::RowsAtCompileTime != 1 ? 1 : 0));

  // test empty expressions
  VERIFY_IS_APPROX(m1.matrix().middleCols(0, 0).rowwise().sum().eval(), MatrixX::Zero(rows, 1));
  VERIFY_IS_APPROX(m1.matrix().middleRows(0, 0).colwise().sum().eval(), MatrixX::Zero(1, cols));
  VERIFY_IS_APPROX(m1.matrix().middleCols(0, fix<0>).rowwise().sum().eval(), MatrixX::Zero(rows, 1));
  VERIFY_IS_APPROX(m1.matrix().middleRows(0, fix<0>).colwise().sum().eval(), MatrixX::Zero(1, cols));

  VERIFY_IS_APPROX(m1.matrix().middleCols(0, 0).rowwise().prod().eval(), MatrixX::Ones(rows, 1));
  VERIFY_IS_APPROX(m1.matrix().middleRows(0, 0).colwise().prod().eval(), MatrixX::Ones(1, cols));
  VERIFY_IS_APPROX(m1.matrix().middleCols(0, fix<0>).rowwise().prod().eval(), MatrixX::Ones(rows, 1));
  VERIFY_IS_APPROX(m1.matrix().middleRows(0, fix<0>).colwise().prod().eval(), MatrixX::Ones(1, cols));
  VERIFY_IS_APPROX(m1.matrix().middleCols(0, 0).rowwise().squaredNorm().eval(), MatrixX::Zero(rows, 1));

  VERIFY_IS_EQUAL(m1.real().middleRows(0, 0).rowwise().maxCoeff().eval().rows(), 0);
  VERIFY_IS_EQUAL(m1.real().middleCols(0, 0).colwise().maxCoeff().eval().cols(), 0);
  VERIFY_IS_EQUAL(m1.real().middleRows(0, fix<0>).rowwise().maxCoeff().eval().rows(), 0);
  VERIFY_IS_EQUAL(m1.real().middleCols(0, fix<0>).colwise().maxCoeff().eval().cols(), 0);
}

EIGEN_DECLARE_TEST(vectorwiseop) {
  CALL_SUBTEST_1(vectorwiseop_array(Array22cd()));
  CALL_SUBTEST_2(vectorwiseop_array(Array<double, 3, 2>()));
  CALL_SUBTEST_3(vectorwiseop_array(ArrayXXf(3, 4)));
  CALL_SUBTEST_4(vectorwiseop_matrix(Matrix4cf()));
  CALL_SUBTEST_5(vectorwiseop_matrix(Matrix4f()));
  CALL_SUBTEST_5(vectorwiseop_matrix(Vector4f()));
  CALL_SUBTEST_5(vectorwiseop_matrix(Matrix<float, 4, 5>()));
  CALL_SUBTEST_6(vectorwiseop_matrix(
      MatrixXd(internal::random<int>(1, EIGEN_TEST_MAX_SIZE), internal::random<int>(1, EIGEN_TEST_MAX_SIZE))));
  CALL_SUBTEST_7(vectorwiseop_matrix(VectorXd(internal::random<int>(1, EIGEN_TEST_MAX_SIZE))));
  CALL_SUBTEST_7(vectorwiseop_matrix(RowVectorXd(internal::random<int>(1, EIGEN_TEST_MAX_SIZE))));
}