eigen/test/product_extra.cpp

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2006-2008 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"

template <typename MatrixType>
void product_extra(const MatrixType& m) {
  typedef typename MatrixType::Scalar Scalar;
  typedef Matrix<Scalar, 1, Dynamic> RowVectorType;
  typedef Matrix<Scalar, Dynamic, 1> ColVectorType;
  typedef Matrix<Scalar, Dynamic, Dynamic, MatrixType::Flags & RowMajorBit> OtherMajorMatrixType;

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

  MatrixType m1 = MatrixType::Random(rows, cols), m2 = MatrixType::Random(rows, cols), m3(rows, cols),
             mzero = MatrixType::Zero(rows, cols), identity = MatrixType::Identity(rows, rows),
             square = MatrixType::Random(rows, rows), res = MatrixType::Random(rows, rows),
             square2 = MatrixType::Random(cols, cols), res2 = MatrixType::Random(cols, cols);
  RowVectorType v1 = RowVectorType::Random(rows), vrres(rows);
  ColVectorType vc2 = ColVectorType::Random(cols), vcres(cols);
  OtherMajorMatrixType tm1 = m1;

  Scalar s1 = internal::random<Scalar>(), s2 = internal::random<Scalar>(), s3 = internal::random<Scalar>();

  VERIFY_IS_APPROX(m3.noalias() = m1 * m2.adjoint(), m1 * m2.adjoint().eval());
  VERIFY_IS_APPROX(m3.noalias() = m1.adjoint() * square.adjoint(), m1.adjoint().eval() * square.adjoint().eval());
  VERIFY_IS_APPROX(m3.noalias() = m1.adjoint() * m2, m1.adjoint().eval() * m2);
  VERIFY_IS_APPROX(m3.noalias() = (s1 * m1.adjoint()) * m2, (s1 * m1.adjoint()).eval() * m2);
  VERIFY_IS_APPROX(m3.noalias() = ((s1 * m1).adjoint()) * m2, (numext::conj(s1) * m1.adjoint()).eval() * m2);
  VERIFY_IS_APPROX(m3.noalias() = (-m1.adjoint() * s1) * (s3 * m2), (-m1.adjoint() * s1).eval() * (s3 * m2).eval());
  VERIFY_IS_APPROX(m3.noalias() = (s2 * m1.adjoint() * s1) * m2, (s2 * m1.adjoint() * s1).eval() * m2);
  VERIFY_IS_APPROX(m3.noalias() = (-m1 * s2) * s1 * m2.adjoint(), (-m1 * s2).eval() * (s1 * m2.adjoint()).eval());

  // a very tricky case where a scale factor has to be automatically conjugated:
  VERIFY_IS_APPROX(m1.adjoint() * (s1 * m2).conjugate(), (m1.adjoint()).eval() * ((s1 * m2).conjugate()).eval());

  // test all possible conjugate combinations for the four matrix-vector product cases:

  VERIFY_IS_APPROX((-m1.conjugate() * s2) * (s1 * vc2), (-m1.conjugate() * s2).eval() * (s1 * vc2).eval());
  VERIFY_IS_APPROX((-m1 * s2) * (s1 * vc2.conjugate()), (-m1 * s2).eval() * (s1 * vc2.conjugate()).eval());
  VERIFY_IS_APPROX((-m1.conjugate() * s2) * (s1 * vc2.conjugate()),
                   (-m1.conjugate() * s2).eval() * (s1 * vc2.conjugate()).eval());

  VERIFY_IS_APPROX((s1 * vc2.transpose()) * (-m1.adjoint() * s2),
                   (s1 * vc2.transpose()).eval() * (-m1.adjoint() * s2).eval());
  VERIFY_IS_APPROX((s1 * vc2.adjoint()) * (-m1.transpose() * s2),
                   (s1 * vc2.adjoint()).eval() * (-m1.transpose() * s2).eval());
  VERIFY_IS_APPROX((s1 * vc2.adjoint()) * (-m1.adjoint() * s2),
                   (s1 * vc2.adjoint()).eval() * (-m1.adjoint() * s2).eval());

  VERIFY_IS_APPROX((-m1.adjoint() * s2) * (s1 * v1.transpose()),
                   (-m1.adjoint() * s2).eval() * (s1 * v1.transpose()).eval());
  VERIFY_IS_APPROX((-m1.transpose() * s2) * (s1 * v1.adjoint()),
                   (-m1.transpose() * s2).eval() * (s1 * v1.adjoint()).eval());
  VERIFY_IS_APPROX((-m1.adjoint() * s2) * (s1 * v1.adjoint()),
                   (-m1.adjoint() * s2).eval() * (s1 * v1.adjoint()).eval());

  VERIFY_IS_APPROX((s1 * v1) * (-m1.conjugate() * s2), (s1 * v1).eval() * (-m1.conjugate() * s2).eval());
  VERIFY_IS_APPROX((s1 * v1.conjugate()) * (-m1 * s2), (s1 * v1.conjugate()).eval() * (-m1 * s2).eval());
  VERIFY_IS_APPROX((s1 * v1.conjugate()) * (-m1.conjugate() * s2),
                   (s1 * v1.conjugate()).eval() * (-m1.conjugate() * s2).eval());

  VERIFY_IS_APPROX((-m1.adjoint() * s2) * (s1 * v1.adjoint()),
                   (-m1.adjoint() * s2).eval() * (s1 * v1.adjoint()).eval());

  // test the vector-matrix product with non aligned starts
  Index i = internal::random<Index>(0, m1.rows() - 2);
  Index j = internal::random<Index>(0, m1.cols() - 2);
  Index r = internal::random<Index>(1, m1.rows() - i);
  Index c = internal::random<Index>(1, m1.cols() - j);
  Index i2 = internal::random<Index>(0, m1.rows() - 1);
  Index j2 = internal::random<Index>(0, m1.cols() - 1);

  VERIFY_IS_APPROX(m1.col(j2).adjoint() * m1.block(0, j, m1.rows(), c),
                   m1.col(j2).adjoint().eval() * m1.block(0, j, m1.rows(), c).eval());
  VERIFY_IS_APPROX(m1.block(i, 0, r, m1.cols()) * m1.row(i2).adjoint(),
                   m1.block(i, 0, r, m1.cols()).eval() * m1.row(i2).adjoint().eval());

  // test negative strides
  {
    Map<MatrixType, Unaligned, Stride<Dynamic, Dynamic> > map1(&m1(rows - 1, cols - 1), rows, cols,
                                                               Stride<Dynamic, Dynamic>(-m1.outerStride(), -1));
    Map<MatrixType, Unaligned, Stride<Dynamic, Dynamic> > map2(&m2(rows - 1, cols - 1), rows, cols,
                                                               Stride<Dynamic, Dynamic>(-m2.outerStride(), -1));
    Map<RowVectorType, Unaligned, InnerStride<-1> > mapv1(&v1(v1.size() - 1), v1.size(), InnerStride<-1>(-1));
    Map<ColVectorType, Unaligned, InnerStride<-1> > mapvc2(&vc2(vc2.size() - 1), vc2.size(), InnerStride<-1>(-1));
    VERIFY_IS_APPROX(MatrixType(map1), m1.reverse());
    VERIFY_IS_APPROX(MatrixType(map2), m2.reverse());
    VERIFY_IS_APPROX(m3.noalias() = MatrixType(map1) * MatrixType(map2).adjoint(),
                     m1.reverse() * m2.reverse().adjoint());
    VERIFY_IS_APPROX(m3.noalias() = map1 * map2.adjoint(), m1.reverse() * m2.reverse().adjoint());
    VERIFY_IS_APPROX(map1 * vc2, m1.reverse() * vc2);
    VERIFY_IS_APPROX(m1 * mapvc2, m1 * mapvc2);
    VERIFY_IS_APPROX(map1.adjoint() * v1.transpose(), m1.adjoint().reverse() * v1.transpose());
    VERIFY_IS_APPROX(m1.adjoint() * mapv1.transpose(), m1.adjoint() * v1.reverse().transpose());
  }

  // regression test
  MatrixType tmp = m1 * m1.adjoint() * s1;
  VERIFY_IS_APPROX(tmp, m1 * m1.adjoint() * s1);

  // regression test for bug 1343, assignment to arrays
  Array<Scalar, Dynamic, 1> a1 = m1 * vc2;
  VERIFY_IS_APPROX(a1.matrix(), m1 * vc2);
  Array<Scalar, Dynamic, 1> a2 = s1 * (m1 * vc2);
  VERIFY_IS_APPROX(a2.matrix(), s1 * m1 * vc2);
  Array<Scalar, 1, Dynamic> a3 = v1 * m1;
  VERIFY_IS_APPROX(a3.matrix(), v1 * m1);
  Array<Scalar, Dynamic, Dynamic> a4 = m1 * m2.adjoint();
  VERIFY_IS_APPROX(a4.matrix(), m1 * m2.adjoint());
}

// Regression test for bug reported at http://forum.kde.org/viewtopic.php?f=74&t=96947
void mat_mat_scalar_scalar_product() {
  Eigen::Matrix2Xd dNdxy(2, 3);
  dNdxy << -0.5, 0.5, 0, -0.3, 0, 0.3;
  double det = 6.0, wt = 0.5;
  VERIFY_IS_APPROX(dNdxy.transpose() * dNdxy * det * wt, det * wt * dNdxy.transpose() * dNdxy);
}

template <typename MatrixType>
void zero_sized_objects(const MatrixType& m) {
  typedef typename MatrixType::Scalar Scalar;
  const int PacketSize = internal::packet_traits<Scalar>::size;
  const int PacketSize1 = PacketSize > 1 ? PacketSize - 1 : 1;
  Index rows = m.rows();
  Index cols = m.cols();

  {
    MatrixType res, a(rows, 0), b(0, cols);
    VERIFY_IS_APPROX((res = a * b), MatrixType::Zero(rows, cols));
    VERIFY_IS_APPROX((res = a * a.transpose()), MatrixType::Zero(rows, rows));
    VERIFY_IS_APPROX((res = b.transpose() * b), MatrixType::Zero(cols, cols));
    VERIFY_IS_APPROX((res = b.transpose() * a.transpose()), MatrixType::Zero(cols, rows));
  }

  {
    MatrixType res, a(rows, cols), b(cols, 0);
    res = a * b;
    VERIFY(res.rows() == rows && res.cols() == 0);
    b.resize(0, rows);
    res = b * a;
    VERIFY(res.rows() == 0 && res.cols() == cols);
  }

  {
    Matrix<Scalar, PacketSize, 0> a;
    Matrix<Scalar, 0, 1> b;
    Matrix<Scalar, PacketSize, 1> res;
    VERIFY_IS_APPROX((res = a * b), MatrixType::Zero(PacketSize, 1));
    VERIFY_IS_APPROX((res = a.lazyProduct(b)), MatrixType::Zero(PacketSize, 1));
  }

  {
    Matrix<Scalar, PacketSize1, 0> a;
    Matrix<Scalar, 0, 1> b;
    Matrix<Scalar, PacketSize1, 1> res;
    VERIFY_IS_APPROX((res = a * b), MatrixType::Zero(PacketSize1, 1));
    VERIFY_IS_APPROX((res = a.lazyProduct(b)), MatrixType::Zero(PacketSize1, 1));
  }

  {
    Matrix<Scalar, PacketSize, Dynamic> a(PacketSize, 0);
    Matrix<Scalar, Dynamic, 1> b(0, 1);
    Matrix<Scalar, PacketSize, 1> res;
    VERIFY_IS_APPROX((res = a * b), MatrixType::Zero(PacketSize, 1));
    VERIFY_IS_APPROX((res = a.lazyProduct(b)), MatrixType::Zero(PacketSize, 1));
  }

  {
    Matrix<Scalar, PacketSize1, Dynamic> a(PacketSize1, 0);
    Matrix<Scalar, Dynamic, 1> b(0, 1);
    Matrix<Scalar, PacketSize1, 1> res;
    VERIFY_IS_APPROX((res = a * b), MatrixType::Zero(PacketSize1, 1));
    VERIFY_IS_APPROX((res = a.lazyProduct(b)), MatrixType::Zero(PacketSize1, 1));
  }
}

template <int>
void bug_127() {
  // Bug 127
  //
  // a product of the form lhs*rhs with
  //
  // lhs:
  // rows = 1, cols = 4
  // RowsAtCompileTime = 1, ColsAtCompileTime = -1
  // MaxRowsAtCompileTime = 1, MaxColsAtCompileTime = 5
  //
  // rhs:
  // rows = 4, cols = 0
  // RowsAtCompileTime = -1, ColsAtCompileTime = -1
  // MaxRowsAtCompileTime = 5, MaxColsAtCompileTime = 1
  //
  // was failing on a runtime assertion, because it had been mis-compiled as a dot product because Product.h was using
  // the max-sizes to detect size 1 indicating vectors, and that didn't account for 0-sized object with max-size 1.

  Matrix<float, 1, Dynamic, RowMajor, 1, 5> a(1, 4);
  Matrix<float, Dynamic, Dynamic, ColMajor, 5, 1> b(4, 0);
  a* b;
}

template <int>
void bug_817() {
  ArrayXXf B = ArrayXXf::Random(10, 10), C;
  VectorXf x = VectorXf::Random(10);
  C = (x.transpose() * B.matrix());
  B = (x.transpose() * B.matrix());
  VERIFY_IS_APPROX(B, C);
}

template <int>
void unaligned_objects() {
  // Regression test for the bug reported here:
  // http://forum.kde.org/viewtopic.php?f=74&t=107541
  // Recall the matrix*vector kernel avoid unaligned loads by loading two packets and then reassemble then.
  // There was a mistake in the computation of the valid range for fully unaligned objects: in some rare cases,
  // memory was read outside the allocated matrix memory. Though the values were not used, this might raise segfault.
  for (int m = 450; m < 460; ++m) {
    for (int n = 8; n < 12; ++n) {
      MatrixXf M(m, n);
      VectorXf v1(n), r1(500);
      RowVectorXf v2(m), r2(16);

      M.setRandom();
      v1.setRandom();
      v2.setRandom();
      for (int o = 0; o < 4; ++o) {
        r1.segment(o, m).noalias() = M * v1;
        VERIFY_IS_APPROX(r1.segment(o, m), M * MatrixXf(v1));
        r2.segment(o, n).noalias() = v2 * M;
        VERIFY_IS_APPROX(r2.segment(o, n), MatrixXf(v2) * M);
      }
    }
  }
}

template <typename T>
EIGEN_DONT_INLINE Index test_compute_block_size(Index m, Index n, Index k) {
  Index mc(m), nc(n), kc(k);
  internal::computeProductBlockingSizes<T, T>(kc, mc, nc);
  return kc + mc + nc;
}

template <typename T>
Index compute_block_size() {
  Index ret = 0;
  ret += test_compute_block_size<T>(0, 1, 1);
  ret += test_compute_block_size<T>(1, 0, 1);
  ret += test_compute_block_size<T>(1, 1, 0);
  ret += test_compute_block_size<T>(0, 0, 1);
  ret += test_compute_block_size<T>(0, 1, 0);
  ret += test_compute_block_size<T>(1, 0, 0);
  ret += test_compute_block_size<T>(0, 0, 0);
  return ret;
}

template <typename>
void aliasing_with_resize() {
  Index m = internal::random<Index>(10, 50);
  Index n = internal::random<Index>(10, 50);
  MatrixXd A, B, C(m, n), D(m, m);
  VectorXd a, b, c(n);
  C.setRandom();
  D.setRandom();
  c.setRandom();
  double s = internal::random<double>(1, 10);

  A = C;
  B = A * A.transpose();
  A = A * A.transpose();
  VERIFY_IS_APPROX(A, B);

  A = C;
  B = (A * A.transpose()) / s;
  A = (A * A.transpose()) / s;
  VERIFY_IS_APPROX(A, B);

  A = C;
  B = (A * A.transpose()) + D;
  A = (A * A.transpose()) + D;
  VERIFY_IS_APPROX(A, B);

  A = C;
  B = D + (A * A.transpose());
  A = D + (A * A.transpose());
  VERIFY_IS_APPROX(A, B);

  A = C;
  B = s * (A * A.transpose());
  A = s * (A * A.transpose());
  VERIFY_IS_APPROX(A, B);

  A = C;
  a = c;
  b = (A * a) / s;
  a = (A * a) / s;
  VERIFY_IS_APPROX(a, b);
}

template <int>
void bug_1308() {
  int n = 10;
  MatrixXd r(n, n);
  VectorXd v = VectorXd::Random(n);
  r = v * RowVectorXd::Ones(n);
  VERIFY_IS_APPROX(r, v.rowwise().replicate(n));
  r = VectorXd::Ones(n) * v.transpose();
  VERIFY_IS_APPROX(r, v.rowwise().replicate(n).transpose());

  Matrix4d ones44 = Matrix4d::Ones();
  Matrix4d m44 = Matrix4d::Ones() * Matrix4d::Ones();
  VERIFY_IS_APPROX(m44, Matrix4d::Constant(4));
  VERIFY_IS_APPROX(m44.noalias() = ones44 * Matrix4d::Ones(), Matrix4d::Constant(4));
  VERIFY_IS_APPROX(m44.noalias() = ones44.transpose() * Matrix4d::Ones(), Matrix4d::Constant(4));
  VERIFY_IS_APPROX(m44.noalias() = Matrix4d::Ones() * ones44, Matrix4d::Constant(4));
  VERIFY_IS_APPROX(m44.noalias() = Matrix4d::Ones() * ones44.transpose(), Matrix4d::Constant(4));

  typedef Matrix<double, 4, 4, RowMajor> RMatrix4d;
  RMatrix4d r44 = Matrix4d::Ones() * Matrix4d::Ones();
  VERIFY_IS_APPROX(r44, Matrix4d::Constant(4));
  VERIFY_IS_APPROX(r44.noalias() = ones44 * Matrix4d::Ones(), Matrix4d::Constant(4));
  VERIFY_IS_APPROX(r44.noalias() = ones44.transpose() * Matrix4d::Ones(), Matrix4d::Constant(4));
  VERIFY_IS_APPROX(r44.noalias() = Matrix4d::Ones() * ones44, Matrix4d::Constant(4));
  VERIFY_IS_APPROX(r44.noalias() = Matrix4d::Ones() * ones44.transpose(), Matrix4d::Constant(4));
  VERIFY_IS_APPROX(r44.noalias() = ones44 * RMatrix4d::Ones(), Matrix4d::Constant(4));
  VERIFY_IS_APPROX(r44.noalias() = ones44.transpose() * RMatrix4d::Ones(), Matrix4d::Constant(4));
  VERIFY_IS_APPROX(r44.noalias() = RMatrix4d::Ones() * ones44, Matrix4d::Constant(4));
  VERIFY_IS_APPROX(r44.noalias() = RMatrix4d::Ones() * ones44.transpose(), Matrix4d::Constant(4));

  //   RowVector4d r4;
  m44.setOnes();
  r44.setZero();
  VERIFY_IS_APPROX(r44.noalias() += m44.row(0).transpose() * RowVector4d::Ones(), ones44);
  r44.setZero();
  VERIFY_IS_APPROX(r44.noalias() += m44.col(0) * RowVector4d::Ones(), ones44);
  r44.setZero();
  VERIFY_IS_APPROX(r44.noalias() += Vector4d::Ones() * m44.row(0), ones44);
  r44.setZero();
  VERIFY_IS_APPROX(r44.noalias() += Vector4d::Ones() * m44.col(0).transpose(), ones44);
}

EIGEN_DECLARE_TEST(product_extra) {
  for (int i = 0; i < g_repeat; i++) {
    CALL_SUBTEST_1(product_extra(
        MatrixXf(internal::random<int>(1, EIGEN_TEST_MAX_SIZE), internal::random<int>(1, EIGEN_TEST_MAX_SIZE))));
    CALL_SUBTEST_2(product_extra(
        MatrixXd(internal::random<int>(1, EIGEN_TEST_MAX_SIZE), internal::random<int>(1, EIGEN_TEST_MAX_SIZE))));
    CALL_SUBTEST_2(mat_mat_scalar_scalar_product());
    CALL_SUBTEST_3(product_extra(MatrixXcf(internal::random<int>(1, EIGEN_TEST_MAX_SIZE / 2),
                                           internal::random<int>(1, EIGEN_TEST_MAX_SIZE / 2))));
    CALL_SUBTEST_4(product_extra(MatrixXcd(internal::random<int>(1, EIGEN_TEST_MAX_SIZE / 2),
                                           internal::random<int>(1, EIGEN_TEST_MAX_SIZE / 2))));
    CALL_SUBTEST_1(zero_sized_objects(
        MatrixXf(internal::random<int>(1, EIGEN_TEST_MAX_SIZE), internal::random<int>(1, EIGEN_TEST_MAX_SIZE))));
  }
  CALL_SUBTEST_5(bug_127<0>());
  CALL_SUBTEST_5(bug_817<0>());
  CALL_SUBTEST_5(bug_1308<0>());
  CALL_SUBTEST_6(unaligned_objects<0>());
  CALL_SUBTEST_7(compute_block_size<float>());
  CALL_SUBTEST_7(compute_block_size<double>());
  CALL_SUBTEST_7(compute_block_size<std::complex<double> >());
  CALL_SUBTEST_8(aliasing_with_resize<void>());
}