text: // This file is part of Eigen, a lightweight C++ template library
  // for linear algebra.
  //
  // Copyright (C) 2008 Daniel Gomez Ferro <dgomezferro@gmail.com>
  //
  // Eigen is free software; you can redistribute it and/or
  // modify it under the terms of the GNU Lesser General Public
  // License as published by the Free Software Foundation; either
  // version 3 of the License, or (at your option) any later version.
  //
  // Alternatively, you can redistribute it and/or
  // modify it under the terms of the GNU General Public License as
  // published by the Free Software Foundation; either version 2 of
  // the License, or (at your option) any later version.
  //
  // Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
  // WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
  // FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
  // GNU General Public License for more details.
  //
  // You should have received a copy of the GNU Lesser General Public
  // License and a copy of the GNU General Public License along with
  // Eigen. If not, see <http://www.gnu.org/licenses/>.
  
  #include "sparse.h"
  
  template<typename SparseMatrixType> void sparse_product(const SparseMatrixType& ref)
  {
    typedef typename SparseMatrixType::Index Index;
    const Index rows = ref.rows();
    const Index cols = ref.cols();
    typedef typename SparseMatrixType::Scalar Scalar;
    enum { Flags = SparseMatrixType::Flags };
  
    double density = std::max(8./(rows*cols), 0.01);
    typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
    typedef Matrix<Scalar,Dynamic,1> DenseVector;
  
    Scalar s1 = ei_random<Scalar>();
    Scalar s2 = ei_random<Scalar>();
  
    // test matrix-matrix product
    {
      DenseMatrix refMat2 = DenseMatrix::Zero(rows, rows);
      DenseMatrix refMat3 = DenseMatrix::Zero(rows, rows);
      DenseMatrix refMat4 = DenseMatrix::Zero(rows, rows);
      DenseMatrix refMat5 = DenseMatrix::Random(rows, rows);
      DenseMatrix dm4 = DenseMatrix::Zero(rows, rows);
      DenseVector dv1 = DenseVector::Random(rows);
      SparseMatrixType m2(rows, rows);
      SparseMatrixType m3(rows, rows);
      SparseMatrixType m4(rows, rows);
      initSparse<Scalar>(density, refMat2, m2);
      initSparse<Scalar>(density, refMat3, m3);
      initSparse<Scalar>(density, refMat4, m4);
  
      int c = ei_random<int>(0,rows-1);
  
      VERIFY_IS_APPROX(m4=m2*m3, refMat4=refMat2*refMat3);
      VERIFY_IS_APPROX(m4=m2.transpose()*m3, refMat4=refMat2.transpose()*refMat3);
      VERIFY_IS_APPROX(m4=m2.transpose()*m3.transpose(), refMat4=refMat2.transpose()*refMat3.transpose());
      VERIFY_IS_APPROX(m4=m2*m3.transpose(), refMat4=refMat2*refMat3.transpose());
  
      VERIFY_IS_APPROX(m4 = m2*m3/s1, refMat4 = refMat2*refMat3/s1);
      VERIFY_IS_APPROX(m4 = m2*m3*s1, refMat4 = refMat2*refMat3*s1);
      VERIFY_IS_APPROX(m4 = s2*m2*m3*s1, refMat4 = s2*refMat2*refMat3*s1);
  
      // sparse * dense
      VERIFY_IS_APPROX(dm4=m2*refMat3, refMat4=refMat2*refMat3);
      VERIFY_IS_APPROX(dm4=m2*refMat3.transpose(), refMat4=refMat2*refMat3.transpose());
      VERIFY_IS_APPROX(dm4=m2.transpose()*refMat3, refMat4=refMat2.transpose()*refMat3);
      VERIFY_IS_APPROX(dm4=m2.transpose()*refMat3.transpose(), refMat4=refMat2.transpose()*refMat3.transpose());
  
      VERIFY_IS_APPROX(dm4=m2*(refMat3+refMat3), refMat4=refMat2*(refMat3+refMat3));
      VERIFY_IS_APPROX(dm4=m2.transpose()*(refMat3+refMat5)*0.5, refMat4=refMat2.transpose()*(refMat3+refMat5)*0.5);
  
      // dense * sparse
      VERIFY_IS_APPROX(dm4=refMat2*m3, refMat4=refMat2*refMat3);
      VERIFY_IS_APPROX(dm4=refMat2*m3.transpose(), refMat4=refMat2*refMat3.transpose());
      VERIFY_IS_APPROX(dm4=refMat2.transpose()*m3, refMat4=refMat2.transpose()*refMat3);
      VERIFY_IS_APPROX(dm4=refMat2.transpose()*m3.transpose(), refMat4=refMat2.transpose()*refMat3.transpose());
  
      // sparse * dense and dense * sparse outer product
      VERIFY_IS_APPROX(m4=m2.col(c)*dv1.transpose(), refMat4=refMat2.col(c)*dv1.transpose());
      VERIFY_IS_APPROX(m4=dv1*m2.col(c).transpose(), refMat4=dv1*refMat2.col(c).transpose());
  
      VERIFY_IS_APPROX(m3=m3*m3, refMat3=refMat3*refMat3);
    }
  
    // test matrix - diagonal product
    {
      DenseMatrix refM2 = DenseMatrix::Zero(rows, rows);
      DenseMatrix refM3 = DenseMatrix::Zero(rows, rows);
      DiagonalMatrix<Scalar,Dynamic> d1(DenseVector::Random(rows));
      SparseMatrixType m2(rows, rows);
      SparseMatrixType m3(rows, rows);
      initSparse<Scalar>(density, refM2, m2);
      initSparse<Scalar>(density, refM3, m3);
      VERIFY_IS_APPROX(m3=m2*d1, refM3=refM2*d1);
      VERIFY_IS_APPROX(m3=m2.transpose()*d1, refM3=refM2.transpose()*d1);
      VERIFY_IS_APPROX(m3=d1*m2, refM3=d1*refM2);
      VERIFY_IS_APPROX(m3=d1*m2.transpose(), refM3=d1 * refM2.transpose());
    }
  
    // test self adjoint products
    {
      DenseMatrix b = DenseMatrix::Random(rows, rows);
      DenseMatrix x = DenseMatrix::Random(rows, rows);
      DenseMatrix refX = DenseMatrix::Random(rows, rows);
      DenseMatrix refUp = DenseMatrix::Zero(rows, rows);
      DenseMatrix refLo = DenseMatrix::Zero(rows, rows);
      DenseMatrix refS = DenseMatrix::Zero(rows, rows);
      SparseMatrixType mUp(rows, rows);
      SparseMatrixType mLo(rows, rows);
      SparseMatrixType mS(rows, rows);
      do {
        initSparse<Scalar>(density, refUp, mUp, ForceRealDiag|/*ForceNonZeroDiag|*/MakeUpperTriangular);
      } while (refUp.isZero());
      refLo = refUp.transpose().conjugate();
      mLo = mUp.transpose().conjugate();
      refS = refUp + refLo;
      refS.diagonal() *= 0.5;
      mS = mUp + mLo;
      for (int k=0; k<mS.outerSize(); ++k)
        for (typename SparseMatrixType::InnerIterator it(mS,k); it; ++it)
          if (it.index() == k)
            it.valueRef() *= 0.5;
  
      VERIFY_IS_APPROX(refS.adjoint(), refS);
      VERIFY_IS_APPROX(mS.transpose().conjugate(), mS);
      VERIFY_IS_APPROX(mS, refS);
      VERIFY_IS_APPROX(x=mS*b, refX=refS*b);
  
      VERIFY_IS_APPROX(x=mUp.template selfadjointView<Upper>()*b, refX=refS*b);
      VERIFY_IS_APPROX(x=mLo.template selfadjointView<Lower>()*b, refX=refS*b);
      VERIFY_IS_APPROX(x=mS.template selfadjointView<Upper|Lower>()*b, refX=refS*b);
    }
  }
  
  void test_sparse_product()
  {
    for(int i = 0; i < g_repeat; i++) {
      CALL_SUBTEST_1( sparse_product(SparseMatrix<double>(8, 8)) );
      CALL_SUBTEST_2( sparse_product(SparseMatrix<std::complex<double> >(16, 16)) );
      CALL_SUBTEST_1( sparse_product(SparseMatrix<double>(33, 33)) );
  
      CALL_SUBTEST_3( sparse_product(DynamicSparseMatrix<double>(8, 8)) );
    }
  }
  