test/sparse_permutations.cpp

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2011-2015 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// 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/.

static long int nb_transposed_copies;
#define EIGEN_SPARSE_TRANSPOSED_COPY_PLUGIN \
  { nb_transposed_copies++; }
#define VERIFY_TRANSPOSITION_COUNT(XPR, N)                                                                  \
  {                                                                                                         \
    nb_transposed_copies = 0;                                                                               \
    XPR;                                                                                                    \
    if (nb_transposed_copies != N) std::cerr << "nb_transposed_copies == " << nb_transposed_copies << "\n"; \
    VERIFY((#XPR) && nb_transposed_copies == N);                                                            \
  }

static long int nb_temporaries;
#define EIGEN_SPARSE_CREATE_TEMPORARY_PLUGIN \
  { nb_temporaries++; }
#define VERIFY_TEMPORARY_COUNT(XPR, N)                                                    \
  {                                                                                       \
    nb_temporaries = 0;                                                                   \
    XPR;                                                                                  \
    if (nb_temporaries != N) std::cerr << "nb_temporaries == " << nb_temporaries << "\n"; \
    VERIFY((#XPR) && nb_temporaries == N);                                                \
  }

#include "sparse.h"

template <typename T>
bool is_sorted(const T& mat) {
  for (Index k = 0; k < mat.outerSize(); ++k) {
    Index prev = -1;
    for (typename T::InnerIterator it(mat, k); it; ++it) {
      if (prev >= it.index()) return false;
      prev = it.index();
    }
  }
  return true;
}

template <typename T>
typename internal::nested_eval<T, 1>::type eval(const T& xpr) {
  VERIFY(int(internal::nested_eval<T, 1>::type::Flags & RowMajorBit) ==
         int(internal::evaluator<T>::Flags & RowMajorBit));
  return xpr;
}

template <int OtherStorage, typename SparseMatrixType>
void sparse_permutations(const SparseMatrixType& ref) {
  const Index rows = ref.rows();
  const Index cols = ref.cols();
  typedef typename SparseMatrixType::Scalar Scalar;
  typedef typename SparseMatrixType::StorageIndex StorageIndex;
  typedef SparseMatrix<Scalar, OtherStorage, StorageIndex> OtherSparseMatrixType;
  typedef Matrix<Scalar, Dynamic, Dynamic> DenseMatrix;
  typedef Matrix<StorageIndex, Dynamic, 1> VectorI;
  //   bool IsRowMajor1 = SparseMatrixType::IsRowMajor;
  //   bool IsRowMajor2 = OtherSparseMatrixType::IsRowMajor;

  double density = (std::max)(8. / static_cast<double>(rows * cols), 0.01);

  SparseMatrixType mat(rows, cols), up(rows, cols), lo(rows, cols);
  OtherSparseMatrixType res;
  DenseMatrix mat_d = DenseMatrix::Zero(rows, cols), up_sym_d, lo_sym_d, res_d;

  initSparse<Scalar>(density, mat_d, mat, 0);

  up = mat.template triangularView<Upper>();
  lo = mat.template triangularView<Lower>();

  up_sym_d = mat_d.template selfadjointView<Upper>();
  lo_sym_d = mat_d.template selfadjointView<Lower>();

  VERIFY_IS_APPROX(mat, mat_d);
  VERIFY_IS_APPROX(up, DenseMatrix(mat_d.template triangularView<Upper>()));
  VERIFY_IS_APPROX(lo, DenseMatrix(mat_d.template triangularView<Lower>()));

  PermutationMatrix<Dynamic> p, p_null;
  VectorI pi;
  randomPermutationVector(pi, cols);
  p.indices() = pi;

  VERIFY(is_sorted(::eval(mat * p)));
  VERIFY(is_sorted(res = mat * p));
  VERIFY_TRANSPOSITION_COUNT(::eval(mat * p), 0);
  VERIFY_TEMPORARY_COUNT(::eval(mat * p), 1)
  res_d = mat_d * p;
  VERIFY(res.isApprox(res_d) && "mat*p");

  VERIFY(is_sorted(::eval(p * mat)));
  VERIFY(is_sorted(res = p * mat));
  VERIFY_TRANSPOSITION_COUNT(::eval(p * mat), 0);
  VERIFY_TEMPORARY_COUNT(::eval(p * mat), 1);
  res_d = p * mat_d;
  VERIFY(res.isApprox(res_d) && "p*mat");

  VERIFY(is_sorted((mat * p).eval()));
  VERIFY(is_sorted(res = mat * p.inverse()));
  VERIFY_TRANSPOSITION_COUNT(::eval(mat * p.inverse()), 0);
  VERIFY_TEMPORARY_COUNT(::eval(mat * p.inverse()), 1);
  res_d = mat * p.inverse();
  VERIFY(res.isApprox(res_d) && "mat*inv(p)");

  VERIFY(is_sorted((p * mat + p * mat).eval()));
  VERIFY(is_sorted(res = p.inverse() * mat));
  VERIFY_TRANSPOSITION_COUNT(::eval(p.inverse() * mat), 0);
  VERIFY_TEMPORARY_COUNT(::eval(p.inverse() * mat), 1);
  res_d = p.inverse() * mat_d;
  VERIFY(res.isApprox(res_d) && "inv(p)*mat");

  //

  VERIFY(is_sorted((p * mat * p.inverse()).eval()));
  VERIFY(is_sorted(res = mat.twistedBy(p)));
  VERIFY_TRANSPOSITION_COUNT(::eval(p * mat * p.inverse()), 0);
  res_d = (p * mat_d) * p.inverse();
  VERIFY(res.isApprox(res_d) && "p*mat*inv(p)");

  VERIFY(is_sorted(res = mat.template selfadjointView<Upper>().twistedBy(p_null)));
  res_d = up_sym_d;
  VERIFY(res.isApprox(res_d) && "full selfadjoint upper to full");

  VERIFY(is_sorted(res = mat.template selfadjointView<Lower>().twistedBy(p_null)));
  res_d = lo_sym_d;
  VERIFY(res.isApprox(res_d) && "full selfadjoint lower to full");

  VERIFY(is_sorted(res = up.template selfadjointView<Upper>().twistedBy(p_null)));
  res_d = up_sym_d;
  VERIFY(res.isApprox(res_d) && "upper selfadjoint to full");

  VERIFY(is_sorted(res = lo.template selfadjointView<Lower>().twistedBy(p_null)));
  res_d = lo_sym_d;
  VERIFY(res.isApprox(res_d) && "lower selfadjoint full");

  VERIFY(is_sorted(res = mat.template selfadjointView<Upper>()));
  res_d = up_sym_d;
  VERIFY(res.isApprox(res_d) && "full selfadjoint upper to full");

  VERIFY(is_sorted(res = mat.template selfadjointView<Lower>()));
  res_d = lo_sym_d;
  VERIFY(res.isApprox(res_d) && "full selfadjoint lower to full");

  VERIFY(is_sorted(res = up.template selfadjointView<Upper>()));
  res_d = up_sym_d;
  VERIFY(res.isApprox(res_d) && "upper selfadjoint to full");

  VERIFY(is_sorted(res = lo.template selfadjointView<Lower>()));
  res_d = lo_sym_d;
  VERIFY(res.isApprox(res_d) && "lower selfadjoint full");

  res.template selfadjointView<Upper>() = mat.template selfadjointView<Upper>();
  res_d = up_sym_d.template triangularView<Upper>();
  VERIFY(res.isApprox(res_d) && "full selfadjoint upper to upper");

  res.template selfadjointView<Lower>() = mat.template selfadjointView<Upper>();
  res_d = up_sym_d.template triangularView<Lower>();
  VERIFY(res.isApprox(res_d) && "full selfadjoint upper to lower");

  res.template selfadjointView<Upper>() = mat.template selfadjointView<Lower>();
  res_d = lo_sym_d.template triangularView<Upper>();
  VERIFY(res.isApprox(res_d) && "full selfadjoint lower to upper");

  res.template selfadjointView<Lower>() = mat.template selfadjointView<Lower>();
  res_d = lo_sym_d.template triangularView<Lower>();
  VERIFY(res.isApprox(res_d) && "full selfadjoint lower to lower");

  res.template selfadjointView<Upper>() = mat.template selfadjointView<Upper>().twistedBy(p);
  res_d = ((p * up_sym_d) * p.inverse()).eval().template triangularView<Upper>();
  VERIFY(res.isApprox(res_d) && "full selfadjoint upper twisted to upper");

  res.template selfadjointView<Upper>() = mat.template selfadjointView<Lower>().twistedBy(p);
  res_d = ((p * lo_sym_d) * p.inverse()).eval().template triangularView<Upper>();
  VERIFY(res.isApprox(res_d) && "full selfadjoint lower twisted to upper");

  res.template selfadjointView<Lower>() = mat.template selfadjointView<Lower>().twistedBy(p);
  res_d = ((p * lo_sym_d) * p.inverse()).eval().template triangularView<Lower>();
  VERIFY(res.isApprox(res_d) && "full selfadjoint lower twisted to lower");

  res.template selfadjointView<Lower>() = mat.template selfadjointView<Upper>().twistedBy(p);
  res_d = ((p * up_sym_d) * p.inverse()).eval().template triangularView<Lower>();
  VERIFY(res.isApprox(res_d) && "full selfadjoint upper twisted to lower");

  res.template selfadjointView<Upper>() = up.template selfadjointView<Upper>().twistedBy(p);
  res_d = ((p * up_sym_d) * p.inverse()).eval().template triangularView<Upper>();
  VERIFY(res.isApprox(res_d) && "upper selfadjoint twisted to upper");

  res.template selfadjointView<Upper>() = lo.template selfadjointView<Lower>().twistedBy(p);
  res_d = ((p * lo_sym_d) * p.inverse()).eval().template triangularView<Upper>();
  VERIFY(res.isApprox(res_d) && "lower selfadjoint twisted to upper");

  res.template selfadjointView<Lower>() = lo.template selfadjointView<Lower>().twistedBy(p);
  res_d = ((p * lo_sym_d) * p.inverse()).eval().template triangularView<Lower>();
  VERIFY(res.isApprox(res_d) && "lower selfadjoint twisted to lower");

  res.template selfadjointView<Lower>() = up.template selfadjointView<Upper>().twistedBy(p);
  res_d = ((p * up_sym_d) * p.inverse()).eval().template triangularView<Lower>();
  VERIFY(res.isApprox(res_d) && "upper selfadjoint twisted to lower");

  VERIFY(is_sorted(res = mat.template selfadjointView<Upper>().twistedBy(p)));
  res_d = (p * up_sym_d) * p.inverse();
  VERIFY(res.isApprox(res_d) && "full selfadjoint upper twisted to full");

  VERIFY(is_sorted(res = mat.template selfadjointView<Lower>().twistedBy(p)));
  res_d = (p * lo_sym_d) * p.inverse();
  VERIFY(res.isApprox(res_d) && "full selfadjoint lower twisted to full");

  VERIFY(is_sorted(res = up.template selfadjointView<Upper>().twistedBy(p)));
  res_d = (p * up_sym_d) * p.inverse();
  VERIFY(res.isApprox(res_d) && "upper selfadjoint twisted to full");

  VERIFY(is_sorted(res = lo.template selfadjointView<Lower>().twistedBy(p)));
  res_d = (p * lo_sym_d) * p.inverse();
  VERIFY(res.isApprox(res_d) && "lower selfadjoint twisted to full");
}

template <typename Scalar>
void sparse_permutations_all(int size) {
  CALL_SUBTEST((sparse_permutations<ColMajor>(SparseMatrix<Scalar, ColMajor>(size, size))));
  CALL_SUBTEST((sparse_permutations<ColMajor>(SparseMatrix<Scalar, RowMajor>(size, size))));
  CALL_SUBTEST((sparse_permutations<RowMajor>(SparseMatrix<Scalar, ColMajor>(size, size))));
  CALL_SUBTEST((sparse_permutations<RowMajor>(SparseMatrix<Scalar, RowMajor>(size, size))));
}

EIGEN_DECLARE_TEST(sparse_permutations) {
  for (int i = 0; i < g_repeat; i++) {
    int s = Eigen::internal::random<int>(1, 50);
    CALL_SUBTEST_1((sparse_permutations_all<double>(s)));
    CALL_SUBTEST_2((sparse_permutations_all<std::complex<double> >(s)));
  }

  VERIFY((internal::is_same<
          internal::permutation_matrix_product<SparseMatrix<double>, OnTheRight, false, SparseShape>::ReturnType,
          internal::nested_eval<Product<SparseMatrix<double>, PermutationMatrix<Dynamic, Dynamic>, AliasFreeProduct>,
                                1>::type>::value));

  VERIFY((internal::is_same<
          internal::permutation_matrix_product<SparseMatrix<double>, OnTheLeft, false, SparseShape>::ReturnType,
          internal::nested_eval<Product<PermutationMatrix<Dynamic, Dynamic>, SparseMatrix<double>, AliasFreeProduct>,
                                1>::type>::value));
}