test/sparse_permutations.cpp

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2011 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/.

#include "sparse.h"

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;
  
  double density = (std::max)(8./(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;

  res = mat*p;
  res_d = mat_d*p;
  VERIFY(res.isApprox(res_d) && "mat*p");

  res = p*mat;
  res_d = p*mat_d;
  VERIFY(res.isApprox(res_d) && "p*mat");

  res = mat*p.inverse();
  res_d = mat*p.inverse();
  VERIFY(res.isApprox(res_d) && "mat*inv(p)");

  res = p.inverse()*mat;
  res_d = p.inverse()*mat_d;
  VERIFY(res.isApprox(res_d) && "inv(p)*mat");

  res = mat.twistedBy(p);
  res_d = (p * mat_d) * p.inverse();
  VERIFY(res.isApprox(res_d) && "p*mat*inv(p)");

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


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

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

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

  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");

  
  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");
  
  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");
  
  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");
  
  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)) ));
}

void 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) ));
  }
}