eigen/test/sparse_product.cpp

// 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>
//
// 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)
{
  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;
  Scalar eps = 1e-6;

  // 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());
  }
  */
  
  // 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);
//     std::cerr << "foo\n" << (m2*d1).toDense() << "\n\n" << refM2*d1 << "\n\n";
    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);
//     std::cerr << "foo\n" << (d1*m2.transpose()).toDense() << "\n\n" << d1 * refM2.transpose() << "\n\n";
    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_sparse_product()
{
  for(int i = 0; i < g_repeat; i++) {
    CALL_SUBTEST( sparse_product(SparseMatrix<double>(8, 8)) );
    CALL_SUBTEST( sparse_product(SparseMatrix<std::complex<double> >(16, 16)) );
    CALL_SUBTEST( sparse_product(SparseMatrix<double>(33, 33)) );
    
    CALL_SUBTEST( sparse_product(DynamicSparseMatrix<double>(8, 8)) );
  }
}