> 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/normalprior.md).

# NormalPrior

```cpp
class NormalPrior
```

```cpp
class NormalPrior: public CostFunction {
 public:
  // Check that the number of rows in the vector b are the same as the
  // number of columns in the matrix A, crash otherwise.
  NormalPrior(const Matrix& A, const Vector& b);

  virtual bool Evaluate(double const* const* parameters,
                        double* residuals,
                        double** jacobians) const;
 };
```

实现以下形式的成本函数

$$
\operatorname{cost}(x)=|A(x-b)|^{2}
$$

其中，矩阵 $$A$$ 和向量 $$b$$ 是固定的，$$x$$ 是变量。如果用户想要实现以下形式的成本函数

$$
\operatorname{cost}(x)=(x-\mu)^{T} S^{-1}(x-\mu)
$$

where, $$\mu$$ is a vector and $$S$$ is a covariance matrix, then, $$A=S^{-1 / 2}$$ , i.e the matrix $$A$$ is the square root of the inverse of the covariance, also known as the stiffness matrix. There are however no restrictions on the shape of $$A$$ . It is free to be rectangular, which would be the case if the covariance matrix $$S$$ is rank deficient.