// 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)) );
  }
}