text: // Ceres Solver - A fast non-linear least squares minimizer
  // Copyright 2017 Google Inc. All rights reserved.
  // http://ceres-solver.org/
  //
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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
  // CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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  // INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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  //
  // Author: fredp@google.com (Fred Pighin)
  //
  // TODO(sameeragarwal): More comprehensive testing with larger and
  // more badly conditioned problem.
  
  #include <memory>
  #include "gtest/gtest.h"
  #include "ceres/conjugate_gradients_solver.h"
  #include "ceres/linear_solver.h"
  #include "ceres/triplet_sparse_matrix.h"
  #include "ceres/internal/eigen.h"
  #include "ceres/types.h"
  
  namespace ceres {
  namespace internal {
  
  TEST(ConjugateGradientTest, Solves3x3IdentitySystem) {
    double diagonal[] = { 1.0, 1.0, 1.0 };
    std::unique_ptr<TripletSparseMatrix>
        A(TripletSparseMatrix::CreateSparseDiagonalMatrix(diagonal, 3));
    Vector b(3);
    Vector x(3);
  
    b(0) = 1.0;
    b(1) = 2.0;
    b(2) = 3.0;
  
    x(0) = 1;
    x(1) = 1;
    x(2) = 1;
  
    LinearSolver::Options options;
    options.max_num_iterations = 10;
  
    LinearSolver::PerSolveOptions per_solve_options;
    per_solve_options.r_tolerance = 1e-9;
  
    ConjugateGradientsSolver solver(options);
    LinearSolver::Summary summary =
        solver.Solve(A.get(), b.data(), per_solve_options, x.data());
  
    EXPECT_EQ(summary.termination_type, LINEAR_SOLVER_SUCCESS);
    ASSERT_EQ(summary.num_iterations, 1);
  
    ASSERT_DOUBLE_EQ(1, x(0));
    ASSERT_DOUBLE_EQ(2, x(1));
    ASSERT_DOUBLE_EQ(3, x(2));
  }
  
  
  TEST(ConjuateGradientTest, Solves3x3SymmetricSystem) {
    std::unique_ptr<TripletSparseMatrix> A(new TripletSparseMatrix(3, 3, 9));
    Vector b(3);
    Vector x(3);
  
    //      | 2  -1  0|
    //  A = |-1   2 -1| is symmetric positive definite.
    //      | 0  -1  2|
    int* Ai = A->mutable_rows();
    int* Aj = A->mutable_cols();
    double* Ax = A->mutable_values();
    int counter = 0;
    for (int i = 0; i < 3; ++i) {
      for (int j = 0; j < 3; ++j) {
        Ai[counter] = i;
        Aj[counter] = j;
        ++counter;
      }
    }
    Ax[0] = 2.;
    Ax[1] = -1.;
    Ax[2] = 0;
    Ax[3] = -1.;
    Ax[4] = 2;
    Ax[5] = -1;
    Ax[6] = 0;
    Ax[7] = -1;
    Ax[8] = 2;
    A->set_num_nonzeros(9);
  
    b(0) = -1;
    b(1) = 0;
    b(2) = 3;
  
    x(0) = 1;
    x(1) = 1;
    x(2) = 1;
  
    LinearSolver::Options options;
    options.max_num_iterations = 10;
  
    LinearSolver::PerSolveOptions per_solve_options;
    per_solve_options.r_tolerance = 1e-9;
  
    ConjugateGradientsSolver solver(options);
    LinearSolver::Summary summary =
        solver.Solve(A.get(), b.data(), per_solve_options, x.data());
  
    EXPECT_EQ(summary.termination_type, LINEAR_SOLVER_SUCCESS);
  
    ASSERT_DOUBLE_EQ(0, x(0));
    ASSERT_DOUBLE_EQ(1, x(1));
    ASSERT_DOUBLE_EQ(2, x(2));
  }
  
  }  // namespace internal
  }  // namespace ceres
  