ceres library multiple variables

ceres库里面给的例子都是一维情形，并不知道多维怎么写

1. 如果用autodiff，延展性会差一些

2. 采用analytic diff，需要自己求 jacobian，这样要注意维数是怎么分配的，参看下面的问题和解答

https://groups.google.com/forum/#!msg/ceres-solver/nVZdc4hu5zw/omW_02F9BwAJ

 

class QuadraticCostFunction : public ceres::SizedCostFunction < 4, 1, 1, 1, 1 >
{
public:
    virtual ~QuadraticCostFunction() {}
    virtual bool Evaluate(double const* const* parameters, double* residuals, double** jacobians) const
    {
        const double x1 = parameters[0][0];
        const double x2 = parameters[1][0];
        const double x3 = parameters[2][0];
        const double x4 = parameters[3][0];
        residuals[0] = x1 + 10.0*x2;
        residuals[1] = sqrt(5)*(x3 - x4);
        residuals[2] = pow((x2 - 2.0*x3), 2);
        residuals[3] = sqrt(10.0)*pow((x1 - x4), 2);

        if (jacobians != NULL && jacobians[0] != NULL)
        {
            jacobians[0][0] = 1.0;
            jacobians[0][1] = 10.0;
            jacobians[0][2] = 0.0;
            jacobians[0][3] = 0.0;

            jacobians[1][0] = 0.0;
            jacobians[1][1] = 0.0;
            jacobians[1][2] = sqrt(5.0);
            jacobians[1][3] = -sqrt(5.0);

            jacobians[2][0] = 0.0;
            jacobians[2][1] = 2.0*(x2 - 2.0*x3);
            jacobians[2][2] = -4.0*(x2 - 2.0*x3);
            jacobians[2][3] = 0.0;

            jacobians[3][0] = 2.0*sqrt(10)*(x1 - x4);
            jacobians[3][1] = 0.0;
            jacobians[3][2] = 0.0;
            jacobians[3][3] = -2.0*sqrt(10)*(x1 - x4);
        }
        return true;
    }
};

但是main函数里面如果是如下情形

double params[4] = { 0.0, 0.0, 0.0, 0.0 };
        Problem problem;
    CostFunction * cost_function = new QuadraticCostFunction;
    problem.AddResidualBlock(cost_function, NULL, params);
        Solver::Options options;
    options.linear_solver_type = ceres::DENSE_QR;
    options.minimizer_progress_to_stdout = true;
    Solver::Summary summary;
    Solve(options, &problem, &summary);

就要改成这样的定义方式

class QuadraticCostFunction : public ceres::SizedCostFunction < 4, 4 > /* I believe these entries are Num_residuals, size of x1, x2, x3 & x4... */
    {
public:
    virtual ~QuadraticCostFunction() {}
    virtual bool Evaluate(double const* const* parameters, double* residuals, double** jacobians) const
    {
        const double x1 = parameters[0][0];
        const double x2 = parameters[0][1];
        const double x3 = parameters[0][2];
        const double x4 = parameters[0][3];
        residuals[0] = x1 + 10.0*x2;
        residuals[1] = sqrt(5)*(x3 - x4);
        residuals[2] = pow((x2 - 2.0*x3), 2);
        residuals[3] = sqrt(10.0)*pow((x1 - x4), 2);

        if (jacobians != NULL && jacobians[0] != NULL)
        {
            jacobians[0][0] = 1.0;
            jacobians[0][1] = 10.0;
            jacobians[0][2] = 0.0;
            jacobians[0][3] = 0.0;
            //中间省略
            
            jacobians[0][15] = -2.0*sqrt(10)*(x1 - x4);
        }
        return true;
    }
};