test_covariance_matrix.cc

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/* Copyright (C) 2017
   Simon Pfreundschuh <simon.pfreundschuh@chalmers.se>
 
   This program is free software; 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, or (at your option) any
   later version.
 
   This program 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 General Public License for more details.
 
   You should have received a copy of the GNU General Public License
   along with this program; if not, write to the Free Software
   Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307,
   USA. */
 
#include <cstdlib>
#include <limits>
#include <random>
#include <utility>
 
#include "array.h"
#include "covariance_matrix.h"
#include "jacobian.h"
#include "lin_alg.h"
#include "test_utils.h"
#include "xml_io.h"
 
// Type alias describing a retrieval setup for testing.
using RetrievalData = std::tuple<ArrayOfRetrievalQuantity, ArrayOfArrayOfIndex>;
 
template <typename F>
std::shared_ptr<Matrix> create_covariance_matrix_1D(
    Index i, Index j, ArrayOfRetrievalQuantity jqs, F f) {
  if (i > j) {
    std::swap(i, j);
  }
 
  const RetrievalQuantity& q1 = jqs[i];
  const RetrievalQuantity& q2 = jqs[j];
 
  const Vector& gv1 = q1.Grids()[0];
  const Vector& gv2 = q2.Grids()[0];
 
  std::shared_ptr<Matrix> c =
      std::make_shared<Matrix>(gv1.nelem(), gv2.nelem());
 
  for (Index k = 0; k < gv1.nelem(); k++) {
    for (Index l = 0; l < gv2.nelem(); l++) {
      (*c)(k, l) = f(gv1[k], gv2[l]);
    }
  }
  return c;
}
 
template <typename F>
std::shared_ptr<Sparse> create_sparse_covariance_matrix_1D(
    Index i, Index j, ArrayOfRetrievalQuantity jqs, F f) {
  if (i > j) {
    std::swap(i, j);
  }
 
  const RetrievalQuantity& q1 = jqs[i];
  const RetrievalQuantity& q2 = jqs[j];
 
  const Vector& gv1 = q1.Grids()[0];
  const Vector& gv2 = q2.Grids()[0];
 
  std::shared_ptr<Sparse> s =
      std::make_shared<Sparse>(gv1.nelem(), gv2.nelem());
 
  Index nelem = gv1.nelem() * gv2.nelem();
  ArrayOfIndex row_indices{}, col_indices{};
  ArrayOfNumeric elements{};
  row_indices.reserve(nelem);
  col_indices.reserve(nelem);
  elements.reserve(nelem);
  for (Index k = 0; k < gv1.nelem(); k++) {
    for (Index l = 0; l < gv2.nelem(); l++) {
      row_indices.push_back(k);
      col_indices.push_back(l);
      elements.push_back(f(gv1[k], gv2[l]));
    }
  }
  s->insert_elements(nelem, row_indices, col_indices, Vector(elements));
  return s;
}
 
RetrievalData setup_retrieval_1D() {
  std::random_device rd;
  std::mt19937 gen(rd());
  std::uniform_int_distribution<> n_rqs_dist(2, 10), n_gs_dist(10, 100);
 
  Index n_rqs = n_rqs_dist(gen);
  Numeric g_begin = 0.0;
  Numeric g_end = 100.0;
  ArrayOfRetrievalQuantity rqs = ArrayOfRetrievalQuantity();
 
  for (Index i = 0; i < n_rqs; i++) {
    Index n_gs = n_gs_dist(gen);
    ArrayOfVector gvs(1);
    gvs[0] = Vector(n_gs);
    for (Index j = 0; j < n_gs; j++) {
      Numeric frac = static_cast<Numeric>(j) / static_cast<Numeric>(n_gs);
      gvs[0][j] = g_begin + (g_end - g_begin) * frac;
    }
    rqs.emplace_back("maintag", "subtag", "subsubtag", "mode", 1, 0.0, gvs);
  }
 
  ArrayOfArrayOfIndex jis(n_rqs);
  Index ji = 0;
  for (Index i = 0; i < n_rqs; i++) {
    Index n_grid_points = 1;
    const ArrayOfVector& gs = rqs[i].Grids();
    for (auto& g : gs) {
      n_grid_points *= g.nelem();
    }
    jis[i] = ArrayOfIndex{ji, ji + n_grid_points - 1};
    ji += n_grid_points;
  }
 
  return std::make_tuple(rqs, jis);
}
 
CovarianceMatrix random_covariance_matrix(const ArrayOfRetrievalQuantity& rqs,
                                          const ArrayOfArrayOfIndex& jis) {
  std::random_device rd;
  std::mt19937 gen(rd());
  std::uniform_real_distribution<> dis(0.0, 1.0);
  CovarianceMatrix covmat{};
 
  auto g = [](Numeric x, Numeric y) -> Numeric {
    if (x == y)
      return 1.0;
    else
      return 0.0;
  };
  auto g2 = [](Numeric x, Numeric y) -> Numeric {
    if (x == y)
      return 0.1;
    else
      return 0.0;
  };
 
  for (size_t i = 0; i < rqs.size(); i++) {
    Range range(jis[i][0], jis[i][1] - jis[i][0] + 1);
    auto inds = std::make_pair(i, i);
 
    Numeric p = dis(gen);
    if (p < 0.0) {
      std::shared_ptr<Matrix> m = create_covariance_matrix_1D(i, i, rqs, g);
      covmat.add_correlation(Block(range, range, inds, m));
    } else {
      std::shared_ptr<Sparse> m =
          create_sparse_covariance_matrix_1D(i, i, rqs, g);
      covmat.add_correlation(Block(range, range, inds, m));
    }
  }
 
  for (size_t i = 0; i < rqs.size(); i++) {
    for (size_t j = i + 1; j < rqs.size(); j++) {
      Range row_range(jis[i][0], jis[i][1] - jis[i][0] + 1);
      Range col_range(jis[j][0], jis[j][1] - jis[j][0] + 1);
      auto inds = std::make_pair(i, j);
      Numeric p = dis(gen);
      if (p > 0.8) {
        p = dis(gen);
        if (p < 0.0) {
          std::shared_ptr<Matrix> m = create_covariance_matrix_1D(i, j, rqs, g);
          covmat.add_correlation(Block(row_range, col_range, inds, m));
        } else {
          std::shared_ptr<Sparse> m =
              create_sparse_covariance_matrix_1D(i, j, rqs, g2);
          covmat.add_correlation(Block(row_range, col_range, inds, m));
        }
      }
    }
  }
  return covmat;
}
 
Numeric test_multiplication_by_vector(Index n_tests) {
  Numeric e = 0.0;
  for (Index i = 0; i < n_tests; i++) {
    ArrayOfArrayOfIndex jis;
    ArrayOfRetrievalQuantity rqs;
    std::tie(rqs, jis) = setup_retrieval_1D();
    CovarianceMatrix covmat(random_covariance_matrix(rqs, jis));
 
    Index n = covmat.ncols();
    Matrix A(covmat);
    Vector v(n), w(n), w_ref(n);
    random_fill_vector(v, 10.0, false);
 
    mult(w, covmat, v);
    mult(w_ref, A, v);
 
    e = std::max(e, get_maximum_error(w, w_ref, true));
  }
  return e;
}
 
Numeric test_multiplication_by_matrix(Index n_tests) {
  Numeric e = 0.0;
  for (Index i = 0; i < n_tests; i++) {
    ArrayOfArrayOfIndex jis;
    ArrayOfRetrievalQuantity rqs;
    std::tie(rqs, jis) = setup_retrieval_1D();
    CovarianceMatrix covmat(random_covariance_matrix(rqs, jis));
 
    Index n = covmat.ncols();
    Matrix A(covmat), B(n, n), C(n, n), C_ref(n, n);
    random_fill_matrix(B, 10.0, false);
 
    mult(C, covmat, B);
    mult(C_ref, A, B);
    e = std::max(e, get_maximum_error(C, C_ref, true));
 
    mult(C, B, covmat);
    mult(C_ref, B, A);
    e = std::max(e, get_maximum_error(C, C_ref, true));
  }
  return e;
}
 
Numeric test_inverse(Index n_tests) {
  Numeric e = 0.0;
  for (Index i = 0; i < n_tests; i++) {
    ArrayOfArrayOfIndex jis;
    ArrayOfRetrievalQuantity rqs;
    std::tie(rqs, jis) = setup_retrieval_1D();
    CovarianceMatrix covmat(random_covariance_matrix(rqs, jis));
 
    Index n = covmat.ncols();
    Matrix A(covmat), B(n, n), B_ref(n, n), C(n, n);
    random_fill_matrix(B, 10.0, false);
 
    covmat.compute_inverse();
    mult_inv(B, covmat, A);
    id_mat(B_ref);
    mult(C, covmat, B_ref);
    e = std::max(e, get_maximum_error(B, B_ref, true));
    id_mat(B_ref);
    mult_inv(B, A, covmat);
    e = std::max(e, get_maximum_error(B, B_ref, true));
  }
  return e;
}
 
Numeric test_addition(Index n_tests) {
  Numeric e = 0.0;
  for (Index i = 0; i < n_tests; i++) {
    ArrayOfArrayOfIndex jis;
    ArrayOfRetrievalQuantity rqs;
    std::tie(rqs, jis) = setup_retrieval_1D();
    CovarianceMatrix covmat(random_covariance_matrix(rqs, jis));
 
    Index n = covmat.ncols();
    Matrix A(covmat), B(n, n), B_ref(n, n), C(n, n);
    B = 0.0;
    B_ref = B;
 
    covmat.compute_inverse();
 
    B += covmat;
    B_ref += A;
    e = std::max(e, get_maximum_error(B, B_ref, true));
 
    add_inv(B, covmat);
    inv(C, A);
    B_ref += C;
    e = std::max(e, get_maximum_error(B, B_ref, true));
  }
  return e;
}
 
Numeric test_diagonal(Index n_tests) {
  Numeric e = 0.0;
  for (Index i = 0; i < n_tests; i++) {
    ArrayOfArrayOfIndex jis;
    ArrayOfRetrievalQuantity rqs;
    std::tie(rqs, jis) = setup_retrieval_1D();
    CovarianceMatrix covmat(random_covariance_matrix(rqs, jis));
 
    Vector diag_1 = covmat.diagonal();
    Vector diag_2 = Matrix(covmat).diagonal();
    e = std::max(e, get_maximum_error(diag_1, diag_2, true));
  }
  return e;
}
 
Numeric test_io(Index n_tests) {
  Numeric e(0.0);
  for (Index i = 0; i < n_tests; i++) {
    ArrayOfArrayOfIndex jis;
    ArrayOfRetrievalQuantity rqs;
    std::tie(rqs, jis) = setup_retrieval_1D();
    CovarianceMatrix covmat_1(random_covariance_matrix(rqs, jis)), covmat_2{};
    covmat_1.compute_inverse();
 
    xml_write_to_file("test.xml", covmat_1, FILE_TYPE_ASCII, 0, Verbosity());
    xml_read_from_file("test.xml", covmat_2, Verbosity());
 
    Matrix A(covmat_1), B(covmat_2), C(covmat_1);
    e = std::max(e, get_maximum_error(A, B, true));
 
    id_mat(C);
    mult_inv(A, covmat_1, C);
    mult_inv(B, covmat_2, C);
    e = std::max(e, get_maximum_error(A, B, true));
  }
  return 0.0;
}
 
template <typename MatrixType>
void covmat_seSet(CovarianceMatrix& covmat,
                  const MatrixType& block,
                  const Verbosity& /*v*/);
 
template <typename MatrixType>
void covmat_sxSet(CovarianceMatrix& covmat,
                  const MatrixType& block,
                  const Verbosity& /*v*/);
 
template <typename MatrixType>
void covmat_seAddBlock(CovarianceMatrix& covmat_se,
                       const MatrixType& block,
                       const Index& i,
                       const Index& j,
                       const Verbosity&);
 
template <typename MatrixType>
void covmat_seAddInverseBlock(CovarianceMatrix& covmat_se,
                              const MatrixType& block,
                              const Index& i,
                              const Index& j,
                              const Verbosity&);
 
template <typename MatrixType>
void covmat_sxAddBlock(CovarianceMatrix& covmat_se,
                       const ArrayOfRetrievalQuantity& jq,
                       const MatrixType& block,
                       const Index& i,
                       const Index& j,
                       const Verbosity&);
 
template <typename MatrixType>
void covmat_sxAddInverseBlock(CovarianceMatrix& covmat_se,
                              const ArrayOfRetrievalQuantity& jq,
                              const MatrixType& block,
                              const Index& i,
                              const Index& j,
                              const Verbosity&);
 
void test_workspace_methods() {
  CovarianceMatrix covmat{};
  Matrix A(10, 10);
  Sparse A_sparse(10, 10);
  Matrix B(20, 20);
  Matrix C(10, 20);
 
  // covmat_seSet
 
  covmat_seSet(covmat, A, Verbosity());
  assert(covmat.ncols() == 10);
 
  // covmat_seAddBlock
 
  covmat_seAddBlock(covmat, A_sparse, -1, -1, Verbosity());
  assert(covmat.ncols() == 20);
 
  try {
    covmat_seAddBlock(covmat, A, 3, 3, Verbosity());
    // This should fail.
    assert(false);
  } catch (const std::runtime_error&) {
  }
 
  covmat_seAddBlock(covmat, A, 0, 1, Verbosity());
 
  covmat_seAddBlock(covmat, A, 2, 2, Verbosity());
 
  try {
    covmat_seAddBlock(covmat, B, 1, 2, Verbosity());
    // This should fail.
    assert(false);
  } catch (const std::runtime_error&) {
  }
 
  covmat_seAddInverseBlock(covmat, A, 0, 1, Verbosity());
 
  try {
    covmat_seAddInverseBlock(covmat, B, 3, 3, Verbosity());
    // This should fail.
    assert(false);
  } catch (const std::runtime_error&) {
  }
 
  // covmat_sxSet
  covmat_sxSet(covmat, A, Verbosity());
  assert(covmat.ncols() == 10);
 
  // covmat_sxAddBlock
 
  A.resize(1000, 1000);
  A_sparse.resize(8000, 8000);
  C.resize(1000, 8000);
 
  ArrayOfVector grids_1{Vector(10), Vector(10), Vector(10)};
  ArrayOfVector grids_2{Vector(20), Vector(20), Vector(20)};
 
  RetrievalQuantity rq_1("mt", "st", "sst", "m", 1, 0.1, grids_1);
  RetrievalQuantity rq_2("mt", "st", "sst", "m", 1, 0.1, grids_2);
 
  ArrayOfRetrievalQuantity rqs{};
  rqs.push_back(rq_1);
  rqs.push_back(rq_2);
 
  covmat_sxAddBlock(covmat, rqs, A_sparse, -1, -1, Verbosity());
 
  try {
    covmat_sxAddBlock(covmat, rqs, A_sparse, 0, 1, Verbosity());
    // This should fail.
    assert(false);
  } catch (const std::runtime_error&) {
  }
 
  covmat_sxAddBlock(covmat, rqs, C, 0, 1, Verbosity());
  covmat_sxAddInverseBlock(covmat, rqs, A, 0, 0, Verbosity());
 
  try {
    covmat_sxAddInverseBlock(covmat, rqs, C, 1, 1, Verbosity());
    // This should fail.
    assert(false);
  } catch (const std::runtime_error&) {
  }
}
 
namespace {
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wunused-function"
#pragma GCC diagnostic ignored "-Wconversion"
 
#include "invlib/algebra.h"
#include "invlib/interfaces/arts_wrapper.h"
 
Numeric test_invlib_wrapper(Index n_tests) {
  Numeric e = 0.0;
  for (Index i = 0; i < n_tests; i++) {
    ArrayOfArrayOfIndex jis;
    ArrayOfRetrievalQuantity rqs;
    std::tie(rqs, jis) = setup_retrieval_1D();
    CovarianceMatrix covmat(random_covariance_matrix(rqs, jis));
    invlib::Matrix<ArtsCovarianceMatrixWrapper> wrapper(covmat);
    Index n = covmat.ncols();
 
    // Multiplication by Vector
    invlib::Vector<ArtsVector> v{}, w{}, w_ref{};
    v.resize(n);
    w.resize(n);
    w_ref.resize(n);
    random_fill_vector(v, 10.0, false);
 
    mult(w, covmat, v);
    w_ref = wrapper * v;
    e = std::max(e, get_maximum_error(w, w_ref, true));
 
    solve(w, covmat, v);
    w_ref = inv(wrapper) * v;
    e = std::max(e, get_maximum_error(w, w_ref, true));
    w_ref = inv(inv(wrapper)) * v;
 
    // Multiplication by Matrix
    invlib::Matrix<ArtsMatrix> A{static_cast<Matrix>(covmat)}, B{}, C{},
    C_ref{};
    B.resize(n, n);
    C.resize(n, n);
    C_ref.resize(n, n);
 
    random_fill_matrix(B, 10.0, false);
    mult(C, covmat, B);
    C_ref = wrapper * B;
    e = std::max(e, get_maximum_error(C, C_ref, true));
 
    // Inverse
    mult_inv(C, covmat, B);
    C_ref = invlib::inv(wrapper) * B;
    e = std::max(e, get_maximum_error(C, C_ref, true));
 
    // Addition to Matrix
    C += covmat;
    C_ref = C_ref + wrapper;
    e = std::max(e, get_maximum_error(C, C_ref, true));
 
    // Addition of Inverse to Matrix
    add_inv(C, covmat);
    C_ref = C_ref + inv(wrapper);
    e = std::max(e, get_maximum_error(C, C_ref, true));
  }
  return e;
}
 
#pragma GCC diagnostic pop
}  // namespace
 
int main() {
  Numeric e = 0.0, e_max = 0.0;
 
  std::cout << "Testing covariance matrix: " << std::endl;
  e = test_addition(10);
  std::cout << "\tAddition:                " << e << std::endl;
  e_max = std::max(e, e_max);
  if (e_max > 1e-5) {
    return -1;
  }
 
  e = test_multiplication_by_vector(10);
  std::cout << "\tVector Multiplication:   " << e << std::endl;
  e_max = std::max(e, e_max);
  if (e_max > 1e-5) {
    return -1;
  }
 
  e = test_multiplication_by_matrix(10);
  std::cout << "\tMatrix Multiplication:   " << e << std::endl;
  e_max = std::max(e, e_max);
  if (e_max > 1e-5) {
    return -1;
  }
 
  e = test_inverse(10);
  std::cout << "\tInverse:                 " << e << std::endl;
  e_max = std::max(e, e_max);
  if (e_max > 1e-5) {
    return -1;
  }
 
  e = test_io(10);
  std::cout << "\tXML IO:                  " << e << std::endl;
  e_max = std::max(e, e_max);
  if (e_max > 1e-5) {
    return -1;
  }
 
  e = test_invlib_wrapper(10);
  std::cout << "\tinvlib Wrapper:          " << e << std::endl;
  e_max = std::max(e, e_max);
  if (e_max > 1e-5) {
    return -1;
  }
 
  e = test_diagonal(10);
  std::cout << "\tdiagonal                 " << e << std::endl;
  e_max = std::max(e, e_max);
  if (e_max > 1e-5) {
    return -1;
  }
 
  std::cout << std::endl << "\tTesting workspace functions ... ";
  test_workspace_methods();
  std::cout << " DONE." << std::endl;
 
  return 0;
}