> For the complete documentation index, see [llms.txt](https://ceres-solver-tutorial-cn.gitbook.io/ceres/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://ceres-solver-tutorial-cn.gitbook.io/ceres/modeling-non-linear-least-squares/main-class-interface/costfunction.md).

# CostFunction

对于目标函数中的每个项，都有一个`CostFunction` 负责计算残差向量和 Jacobian 矩阵。考虑其中一项残差 $$f(x\_1,x\_2,...,x\_k)$$ ，其取决于参数块 $$\[x\_1,x\_2,...,x\_k]$$。给定参数 $$\[x\_1,x\_2,...,x\_k]$$，`CostFunction` 负责计算向量函数 $$f(x\_1,x\_2,...,x\_k)$$ 和它对每个变量的 Jacobian 矩阵。

$$
J\_i=D\_if(x\_1,...,x\_k) \ \forall \in {1,...,k}
$$

```cpp
class CostFunction
```

Code Impl

```cpp
class CostFunction {
 public:
  virtual bool Evaluate(double const* const* parameters,
                        double* residuals,
                        double** jacobians) const = 0;
  const std::vector<int32>& parameter_block_sizes();
  int num_residuals() const;

 protected:
  std::vector<int32>* mutable_parameter_block_sizes();
  void set_num_residuals(int num_residuals);
};
```

`CostFunction` 输入参数块的数量和大小以及输出的数量分别存储在 `CostFunction::parameter_block_sizes_` 和 `CostFunction::num_residuals_`中。从该类继承的用户代码应使用相应的函数方法设置这两个成员。当使用 `Problem::AddResidualBlock()` 添加时，`Problem` 将验证这些信息。

```cpp
bool CostFunction::Evaluate(double const *const *parameters, 
                            double *residuals, 
                            double **jacobians) const
```

上述函数用于计算残差向量和 Jacobian 矩阵。该函数为纯虚函数，需要在子类进行重写，因为 Ceres 不知道你的残差是如何计算的。对其中的参数做出一些解释和强调。

* `parameters` 是一个数组，其大小为 `CostFunction::parameter_block_sizes_.size()`。
* `parameters[i]` 也是一个数组，其大小为 `CostFunction::parameter_block_sizes_[i]`
* 从上面了两条可以看出 `parameters` 其实是一个二维数组。
* `parameters` 永远不能为 `nullptr`。
* `residuals` 是一个数组，长度为 `num_residuals`。
* `residuals` 永远不能为 `nullptr`。
* `jacobians` 是一个数组，长度为 `CostFunction::parameter_block_sizes_.size()`。
* `jacobians[i]` 是一个 row-major 数组，长度为 `num_residuals x parameter_block_sizes_[i]`。
* 如果 `jacobians[i]` 不为 `nullptr` 的话，需要用户手动计算残差相对于 `parameters[i]` 的 Jacobian 矩阵，并存储在数组中，例如 `jacobians[i][r * parameter_block_sizes_[i] + c]` = $$\frac{\partial \text{residual\[r]}}{\partial \text{paramters\[i]\[c]}}$$。
* 如果 `jacobians[i]` 为 `nullptr`，那么它的计算过程可以跳过，这种情况发生在当参数块被设定为常数的时候。
* 返回值表示残差和 Jacobian 的计算是否成功。这可用于检查 jacobian 计算中是否有数值问题。


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