text: // 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:
  //
  // * 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 Google Inc. 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
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  // ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
  // LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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  //
  // Author: sameeragarwal@google.com (Sameer Agarwal)
  
  #include <limits>
  #include <vector>
  
  #include "ceres/block_random_access_diagonal_matrix.h"
  #include "ceres/internal/eigen.h"
  #include "glog/logging.h"
  #include "gtest/gtest.h"
  #include "Eigen/Cholesky"
  
  namespace ceres {
  namespace internal {
  
  class BlockRandomAccessDiagonalMatrixTest : public ::testing::Test {
   public:
    void SetUp() {
      std::vector<int> blocks;
      blocks.push_back(3);
      blocks.push_back(4);
      blocks.push_back(5);
      const int num_rows = 3 + 4 + 5;
      num_nonzeros_ =  3 * 3 + 4 * 4 + 5 * 5;
  
      m_.reset(new BlockRandomAccessDiagonalMatrix(blocks));
  
      EXPECT_EQ(m_->num_rows(), num_rows);
      EXPECT_EQ(m_->num_cols(), num_rows);
  
      for (int i = 0; i < blocks.size(); ++i) {
        const int row_block_id = i;
        int col_block_id;
        int row;
        int col;
        int row_stride;
        int col_stride;
  
        for (int j = 0; j < blocks.size(); ++j) {
          col_block_id = j;
          CellInfo* cell =  m_->GetCell(row_block_id, col_block_id,
                                      &row, &col,
                                      &row_stride, &col_stride);
          // Off diagonal entries are not present.
          if (i != j) {
            EXPECT_TRUE(cell == NULL);
            continue;
          }
  
          EXPECT_TRUE(cell != NULL);
          EXPECT_EQ(row, 0);
          EXPECT_EQ(col, 0);
          EXPECT_EQ(row_stride, blocks[row_block_id]);
          EXPECT_EQ(col_stride, blocks[col_block_id]);
  
          // Write into the block
          MatrixRef(cell->values, row_stride, col_stride).block(
              row, col, blocks[row_block_id], blocks[col_block_id]) =
              (row_block_id + 1) * (col_block_id +1) *
              Matrix::Ones(blocks[row_block_id], blocks[col_block_id])
              + Matrix::Identity(blocks[row_block_id], blocks[row_block_id]);
        }
      }
    }
  
   protected:
    int num_nonzeros_;
    scoped_ptr<BlockRandomAccessDiagonalMatrix> m_;
  };
  
  TEST_F(BlockRandomAccessDiagonalMatrixTest, MatrixContents) {
    const TripletSparseMatrix* tsm = m_->matrix();
    EXPECT_EQ(tsm->num_nonzeros(), num_nonzeros_);
    EXPECT_EQ(tsm->max_num_nonzeros(), num_nonzeros_);
  
    Matrix dense;
    tsm->ToDenseMatrix(&dense);
  
    double kTolerance = 1e-14;
  
    // (0,0)
    EXPECT_NEAR((dense.block(0, 0, 3, 3) -
                 (Matrix::Ones(3, 3) + Matrix::Identity(3, 3))).norm(),
                0.0,
                kTolerance);
  
    // (1,1)
    EXPECT_NEAR((dense.block(3, 3, 4, 4) -
                 (2 * 2 * Matrix::Ones(4, 4) + Matrix::Identity(4, 4))).norm(),
                0.0,
                kTolerance);
  
    // (1,1)
    EXPECT_NEAR((dense.block(7, 7, 5, 5) -
                 (3 * 3 * Matrix::Ones(5, 5) + Matrix::Identity(5, 5))).norm(),
                0.0,
                kTolerance);
  
    // There is nothing else in the matrix besides these four blocks.
    EXPECT_NEAR(dense.norm(),
                sqrt(6 * 1.0 + 3 * 4.0 +
                     12 * 16.0 + 4 * 25.0 +
                     20 * 81.0 + 5 * 100.0), kTolerance);
  }
  
  TEST_F(BlockRandomAccessDiagonalMatrixTest, RightMultiply) {
    double kTolerance = 1e-14;
    const TripletSparseMatrix* tsm = m_->matrix();
    Matrix dense;
    tsm->ToDenseMatrix(&dense);
    Vector x = Vector::Random(dense.rows());
    Vector expected_y = dense * x;
    Vector actual_y = Vector::Zero(dense.rows());
    m_->RightMultiply(x.data(),  actual_y.data());
    EXPECT_NEAR((expected_y - actual_y).norm(), 0, kTolerance);
  }
  
  TEST_F(BlockRandomAccessDiagonalMatrixTest, Invert) {
    double kTolerance = 1e-14;
    const TripletSparseMatrix* tsm = m_->matrix();
    Matrix dense;
    tsm->ToDenseMatrix(&dense);
    Matrix expected_inverse =
        dense.llt().solve(Matrix::Identity(dense.rows(), dense.rows()));
  
    m_->Invert();
    tsm->ToDenseMatrix(&dense);
  
    EXPECT_NEAR((expected_inverse - dense).norm(), 0.0, kTolerance);
  }
  
  }  // namespace internal
  }  // namespace ceres
  