// Copyright (c) 2015-2016, ETH Zurich, Wyss Zurich, Zurich Eye
// All rights reserved.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are met:
//     * Redistributions of source code must retain the above copyright
//       notice, this list of conditions and the following disclaimer.
//     * Redistributions in binary form must reproduce the above copyright
//       notice, this list of conditions and the following disclaimer in the
//       documentation and/or other materials provided with the distribution.
//     * Neither the name of the ETH Zurich, Wyss Zurich, Zurich Eye nor the
//       names of its contributors may be used to endorse or promote products
//       derived from this software without specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
// ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
// WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
// DISCLAIMED. IN NO EVENT SHALL ETH Zurich, Wyss Zurich, Zurich Eye BE LIABLE FOR ANY
// DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
// (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
// LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
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#include <ze/common/matrix.hpp>

#include <Eigen/SVD>
#include <Eigen/LU>

namespace ze {

std::tuple<int, real_t, VectorX> directLinearTransform(const MatrixX& A, real_t rank_tol)
{
  int n = A.rows();
  int p = A.cols();
  int m = std::min(n,p);
  Eigen::JacobiSVD<MatrixX> svd(A, Eigen::ComputeFullV);
  VectorX s = svd.singularValues();
  MatrixX V = svd.matrixV();

  // Find rank
  int rank = 0;
  for (int i = 0; i < m; ++i)
  {
    if (s(i) > rank_tol)
    {
      ++rank;
    }
  }

  // Return rank, error, and corresponding column of V
  real_t error = (m < p) ? 0.0 : s(m-1);
  return std::make_tuple(rank, error, V.col(p-1));
}

} // namespace ze
