text: // 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::Index Index;
    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());
    
    // regression test
    MatrixType tmp = m1 * m1.adjoint() * s1;
    VERIFY_IS_APPROX(tmp, m1 * m1.adjoint() * s1);
  }
  
  // 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;
  }
  
  void 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_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> >() );
  }
  