least_absolute_deviations_test.cc

Go to the documentation of this file.

// Copyright (c) 2018, ETH Zurich and UNC Chapel Hill.
// 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 ETH Zurich and UNC Chapel Hill 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 THE COPYRIGHT HOLDERS OR CONTRIBUTORS 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 ON ANY THEORY OF LIABILITY, WHETHER IN
// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
// POSSIBILITY OF SUCH DAMAGE.
//
// Author: Johannes L. Schoenberger (jsch-at-demuc-dot-de)
 
#define TEST_NAME "optim/least_absolute_deviations"
#include "util/testing.h"
 
#include <Eigen/Dense>
 
#include "optim/least_absolute_deviations.h"
#include "util/random.h"
 
using namespace colmap;
 
BOOST_AUTO_TEST_CASE(TestOverDetermined) {
  Eigen::SparseMatrix<double> A(4, 3);
  for (int i = 0; i < A.rows(); ++i) {
    for (int j = 0; j < A.cols(); ++j) {
      A.insert(i, j) = i * A.cols() + j + 1;
    }
  }
  A.coeffRef(0, 0) = 10;
 
  Eigen::VectorXd b(A.rows());
  for (int i = 0; i < b.size(); ++i) {
    b(i) = i + 1;
  }
 
  Eigen::VectorXd x = Eigen::VectorXd::Zero(A.cols());
 
  LeastAbsoluteDeviationsOptions options;
  BOOST_CHECK(SolveLeastAbsoluteDeviations(options, A, b, &x));
 
  // Reference solution obtained with Boyd's Matlab implementation.
  const Eigen::Vector3d x_ref(0, 0, 1 / 3.0);
  BOOST_CHECK(x.isApprox(x_ref));
 
  const Eigen::VectorXd residual = A * x - b;
  BOOST_CHECK_LE(residual.norm(), 1e-6);
}
 
BOOST_AUTO_TEST_CASE(TestWellDetermined) {
  Eigen::SparseMatrix<double> A(3, 3);
  for (int i = 0; i < A.rows(); ++i) {
    for (int j = 0; j < A.cols(); ++j) {
      A.insert(i, j) = i * A.cols() + j + 1;
    }
  }
  A.coeffRef(0, 0) = 10;
 
  Eigen::VectorXd b(A.rows());
  for (int i = 0; i < b.size(); ++i) {
    b(i) = i + 1;
  }
 
  Eigen::VectorXd x = Eigen::VectorXd::Zero(A.cols());
 
  LeastAbsoluteDeviationsOptions options;
  BOOST_CHECK(SolveLeastAbsoluteDeviations(options, A, b, &x));
 
  // Reference solution obtained with Boyd's Matlab implementation.
  const Eigen::Vector3d x_ref(0, 0, 1 / 3.0);
  BOOST_CHECK(x.isApprox(x_ref));
 
  const Eigen::VectorXd residual = A * x - b;
  BOOST_CHECK_LE(residual.norm(), 1e-6);
}
 
BOOST_AUTO_TEST_CASE(TestUnderDetermined) {
  // In this case, the system is rank-deficient and not positive semi-definite.
  Eigen::SparseMatrix<double> A(2, 3);
  Eigen::VectorXd b(A.rows());
  Eigen::VectorXd x = Eigen::VectorXd::Zero(A.cols());
  LeastAbsoluteDeviationsOptions options;
  BOOST_CHECK(!SolveLeastAbsoluteDeviations(options, A, b, &x));
}