text: // This file is part of Eigen, a lightweight C++ template library
  // for linear algebra. Eigen itself is part of the KDE project.
  //
  // Copyright (C) 2008 Daniel Gomez Ferro <dgomezferro@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 "sparse.h"
  
  template<typename SparseMatrixType> void sparse_product(const SparseMatrixType& ref)
  {
    const int rows = ref.rows();
    const int 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;
  
    // test matrix-matrix product
    {
      DenseMatrix refMat2 = DenseMatrix::Zero(rows, rows);
      DenseMatrix refMat3 = DenseMatrix::Zero(rows, rows);
      DenseMatrix refMat4 = DenseMatrix::Zero(rows, rows);
      DenseMatrix dm4 = DenseMatrix::Zero(rows, 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);
      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());
  
      // 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());
  
      // 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());
  
      VERIFY_IS_APPROX(m3=m3*m3, refMat3=refMat3*refMat3);
    }
  
    // test matrix - diagonal product
    if(false) // it compiles, but the precision is terrible. probably doesn't matter in this branch....
    {
      DenseMatrix refM2 = DenseMatrix::Zero(rows, rows);
      DenseMatrix refM3 = DenseMatrix::Zero(rows, rows);
      DiagonalMatrix<DenseVector> 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 marked<UpperTriangular|SelfAdjoint>()*b, refX=refS*b);
      VERIFY_IS_APPROX(x=mLo.template marked<LowerTriangular|SelfAdjoint>()*b, refX=refS*b);
      VERIFY_IS_APPROX(x=mS.template marked<SelfAdjoint>()*b, refX=refS*b);
    }
  
  }
  
  void test_eigen2_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)) );
    }
  }
  