ceres-solver/internal/ceres/compressed_col_sparse_matrix_utils_test.cc

// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2015 Google Inc. All rights reserved.
// http://ceres-solver.org/
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// Author: sameeragarwal@google.com (Sameer Agarwal)

#include "ceres/compressed_col_sparse_matrix_utils.h"

#include <algorithm>
#include <numeric>

#include "Eigen/SparseCore"
#include "ceres/internal/export.h"
#include "ceres/triplet_sparse_matrix.h"
#include "glog/logging.h"
#include "gtest/gtest.h"

namespace ceres {
namespace internal {

using std::vector;

TEST(_, BlockPermutationToScalarPermutation) {
  vector<int> blocks;
  //  Block structure
  //  0  --1-  ---2---  ---3---  4
  // [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
  blocks.push_back(1);
  blocks.push_back(2);
  blocks.push_back(3);
  blocks.push_back(3);
  blocks.push_back(1);

  // Block ordering
  // [1, 0, 2, 4, 5]
  vector<int> block_ordering;
  block_ordering.push_back(1);
  block_ordering.push_back(0);
  block_ordering.push_back(2);
  block_ordering.push_back(4);
  block_ordering.push_back(3);

  // Expected ordering
  // [1, 2, 0, 3, 4, 5, 9, 6, 7, 8]
  vector<int> expected_scalar_ordering;
  expected_scalar_ordering.push_back(1);
  expected_scalar_ordering.push_back(2);
  expected_scalar_ordering.push_back(0);
  expected_scalar_ordering.push_back(3);
  expected_scalar_ordering.push_back(4);
  expected_scalar_ordering.push_back(5);
  expected_scalar_ordering.push_back(9);
  expected_scalar_ordering.push_back(6);
  expected_scalar_ordering.push_back(7);
  expected_scalar_ordering.push_back(8);

  vector<int> scalar_ordering;
  BlockOrderingToScalarOrdering(blocks, block_ordering, &scalar_ordering);
  EXPECT_EQ(scalar_ordering.size(), expected_scalar_ordering.size());
  for (int i = 0; i < expected_scalar_ordering.size(); ++i) {
    EXPECT_EQ(scalar_ordering[i], expected_scalar_ordering[i]);
  }
}

static void FillBlock(const vector<int>& row_blocks,
                      const vector<int>& col_blocks,
                      const int row_block_id,
                      const int col_block_id,
                      vector<Eigen::Triplet<double>>* triplets) {
  const int row_offset =
      std::accumulate(&row_blocks[0], &row_blocks[row_block_id], 0);
  const int col_offset =
      std::accumulate(&col_blocks[0], &col_blocks[col_block_id], 0);
  for (int r = 0; r < row_blocks[row_block_id]; ++r) {
    for (int c = 0; c < col_blocks[col_block_id]; ++c) {
      triplets->push_back(
          Eigen::Triplet<double>(row_offset + r, col_offset + c, 1.0));
    }
  }
}

TEST(_, ScalarMatrixToBlockMatrix) {
  // Block sparsity.
  //
  //     [1 2 3 2]
  // [1]  x   x
  // [2]    x   x
  // [2]  x x
  // num_nonzeros = 1 + 3 + 4 + 4 + 1 + 2 = 15

  vector<int> col_blocks;
  col_blocks.push_back(1);
  col_blocks.push_back(2);
  col_blocks.push_back(3);
  col_blocks.push_back(2);

  vector<int> row_blocks;
  row_blocks.push_back(1);
  row_blocks.push_back(2);
  row_blocks.push_back(2);

  const int num_rows =
      std::accumulate(row_blocks.begin(), row_blocks.end(), 0.0);
  const int num_cols =
      std::accumulate(col_blocks.begin(), col_blocks.end(), 0.0);

  vector<Eigen::Triplet<double>> triplets;
  FillBlock(row_blocks, col_blocks, 0, 0, &triplets);
  FillBlock(row_blocks, col_blocks, 2, 0, &triplets);
  FillBlock(row_blocks, col_blocks, 1, 1, &triplets);
  FillBlock(row_blocks, col_blocks, 2, 1, &triplets);
  FillBlock(row_blocks, col_blocks, 0, 2, &triplets);
  FillBlock(row_blocks, col_blocks, 1, 3, &triplets);
  Eigen::SparseMatrix<double> sparse_matrix(num_rows, num_cols);
  sparse_matrix.setFromTriplets(triplets.begin(), triplets.end());

  vector<int> expected_compressed_block_rows;
  expected_compressed_block_rows.push_back(0);
  expected_compressed_block_rows.push_back(2);
  expected_compressed_block_rows.push_back(1);
  expected_compressed_block_rows.push_back(2);
  expected_compressed_block_rows.push_back(0);
  expected_compressed_block_rows.push_back(1);

  vector<int> expected_compressed_block_cols;
  expected_compressed_block_cols.push_back(0);
  expected_compressed_block_cols.push_back(2);
  expected_compressed_block_cols.push_back(4);
  expected_compressed_block_cols.push_back(5);
  expected_compressed_block_cols.push_back(6);

  vector<int> compressed_block_rows;
  vector<int> compressed_block_cols;
  CompressedColumnScalarMatrixToBlockMatrix(sparse_matrix.innerIndexPtr(),
                                            sparse_matrix.outerIndexPtr(),
                                            row_blocks,
                                            col_blocks,
                                            &compressed_block_rows,
                                            &compressed_block_cols);

  EXPECT_EQ(compressed_block_rows, expected_compressed_block_rows);
  EXPECT_EQ(compressed_block_cols, expected_compressed_block_cols);
}

class SolveUpperTriangularTest : public ::testing::Test {
 protected:
  void SetUp() override {
    cols.resize(5);
    rows.resize(7);
    values.resize(7);

    cols[0] = 0;
    rows[0] = 0;
    values[0] = 0.50754;

    cols[1] = 1;
    rows[1] = 1;
    values[1] = 0.80483;

    cols[2] = 2;
    rows[2] = 1;
    values[2] = 0.14120;
    rows[3] = 2;
    values[3] = 0.3;

    cols[3] = 4;
    rows[4] = 0;
    values[4] = 0.77696;
    rows[5] = 1;
    values[5] = 0.41860;
    rows[6] = 3;
    values[6] = 0.88979;

    cols[4] = 7;
  }

  vector<int> cols;
  vector<int> rows;
  vector<double> values;
};

TEST_F(SolveUpperTriangularTest, SolveInPlace) {
  double rhs_and_solution[] = {1.0, 1.0, 2.0, 2.0};
  const double expected[] = {-1.4706, -1.0962, 6.6667, 2.2477};

  SolveUpperTriangularInPlace<int>(
      cols.size() - 1, &rows[0], &cols[0], &values[0], rhs_and_solution);

  for (int i = 0; i < 4; ++i) {
    EXPECT_NEAR(rhs_and_solution[i], expected[i], 1e-4) << i;
  }
}

TEST_F(SolveUpperTriangularTest, TransposeSolveInPlace) {
  double rhs_and_solution[] = {1.0, 1.0, 2.0, 2.0};
  double expected[] = {1.970288, 1.242498, 6.081864, -0.057255};

  SolveUpperTriangularTransposeInPlace<int>(
      cols.size() - 1, &rows[0], &cols[0], &values[0], rhs_and_solution);

  for (int i = 0; i < 4; ++i) {
    EXPECT_NEAR(rhs_and_solution[i], expected[i], 1e-4) << i;
  }
}

TEST_F(SolveUpperTriangularTest, RTRSolveWithSparseRHS) {
  double solution[4];
  // clang-format off
  double expected[] = { 6.8420e+00,   1.0057e+00,  -1.4907e-16,  -1.9335e+00,
                        1.0057e+00,   2.2275e+00,  -1.9493e+00,  -6.5693e-01,
                        -1.4907e-16,  -1.9493e+00,   1.1111e+01,   9.7381e-17,
                        -1.9335e+00,  -6.5693e-01,   9.7381e-17,   1.2631e+00 };
  // clang-format on

  for (int i = 0; i < 4; ++i) {
    SolveRTRWithSparseRHS<int>(
        cols.size() - 1, &rows[0], &cols[0], &values[0], i, solution);
    for (int j = 0; j < 4; ++j) {
      EXPECT_NEAR(solution[j], expected[4 * i + j], 1e-3) << i;
    }
  }
}

}  // namespace internal
}  // namespace ceres