internal/ceres/compressed_col_sparse_matrix_utils_test.cc

// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2013 Google Inc. All rights reserved.
// http://code.google.com/p/ceres-solver/
//
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// modification, are permitted provided that the following conditions are met:
//
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//   this list of conditions and the following disclaimer.
// * Redistributions in binary form must reproduce the above copyright notice,
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//   and/or other materials provided with the distribution.
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// Author: sameeragarwal@google.com (Sameer Agarwal)

#include <algorithm>
#include "ceres/compressed_col_sparse_matrix_utils.h"
#include "ceres/internal/port.h"
#include "ceres/suitesparse.h"
#include "ceres/triplet_sparse_matrix.h"
#include "glog/logging.h"
#include "gtest/gtest.h"

namespace ceres {
namespace internal {

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]);
  }
}

// Helper function to fill the sparsity pattern of a TripletSparseMatrix.
int FillBlock(const vector<int>& row_blocks,
              const vector<int>& col_blocks,
              const int row_block_id,
              const int col_block_id,
              int* rows,
              int* cols) {
  int row_pos = 0;
  for (int i = 0; i < row_block_id; ++i) {
    row_pos += row_blocks[i];
  }

  int col_pos = 0;
  for (int i = 0; i < col_block_id; ++i) {
    col_pos += col_blocks[i];
  }

  int offset = 0;
  for (int r = 0; r < row_blocks[row_block_id]; ++r) {
    for (int c = 0; c < col_blocks[col_block_id]; ++c, ++offset) {
      rows[offset] = row_pos + r;
      cols[offset] = col_pos + c;
    }
  }
  return offset;
}

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);

  TripletSparseMatrix tsm(5, 8, 18);
  int* rows = tsm.mutable_rows();
  int* cols = tsm.mutable_cols();
  fill(tsm.mutable_values(), tsm.mutable_values() + 18, 1.0);
  int offset = 0;

#define CERES_TEST_FILL_BLOCK(row_block_id, col_block_id) \
  offset += FillBlock(row_blocks, col_blocks, \
                      row_block_id, col_block_id, \
                      rows + offset, cols + offset);

  CERES_TEST_FILL_BLOCK(0, 0);
  CERES_TEST_FILL_BLOCK(2, 0);
  CERES_TEST_FILL_BLOCK(1, 1);
  CERES_TEST_FILL_BLOCK(2, 1);
  CERES_TEST_FILL_BLOCK(0, 2);
  CERES_TEST_FILL_BLOCK(1, 3);
#undef CERES_TEST_FILL_BLOCK

  tsm.set_num_nonzeros(offset);

  SuiteSparse ss;
  scoped_ptr<cholmod_sparse> ccsm(ss.CreateSparseMatrix(&tsm));

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

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

  vector<int> block_rows;
  vector<int> block_cols;
  CompressedColumnScalarMatrixToBlockMatrix(
      reinterpret_cast<const int*>(ccsm->i),
      reinterpret_cast<const int*>(ccsm->p),
      row_blocks,
      col_blocks,
      &block_rows,
      &block_cols);

  EXPECT_EQ(block_cols.size(), expected_block_cols.size());
  EXPECT_EQ(block_rows.size(), expected_block_rows.size());

  for (int i = 0; i < expected_block_cols.size(); ++i) {
    EXPECT_EQ(block_cols[i], expected_block_cols[i]);
  }

  for (int i = 0; i < expected_block_rows.size(); ++i) {
    EXPECT_EQ(block_rows[i], expected_block_rows[i]);
  }

  ss.Free(ccsm.release());
}

class SolveUpperTriangularTest : public ::testing::Test {
 protected:
  void SetUp() {
    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];
  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 };

  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