GSL 非线性最小二乘拟合不会收敛

我对C++，尤其是GSL相对较新。尽管如此，我已经努力解决使用GSL提供的实现将非线性函数拟合到某些数据的问题。这个想法是有一个类（Clnm），它保存数据和模型系数等。Clnm类有一个方法Cnlm::fitModel_manu它接受初始值和指向要最小化的函数的函数指针，这些函数在fit_functions.cpp中提供。

有一个最小的工作示例，我首先使用公式和系数生成一些数据，如 GSL 参考手册提供的示例 （ Y = A exp（lambda*x）+b ，
{A，lambda，b}=<5.0，-0.1,1.0>）.这工作正常，我按预期获得数据。

使用此数据构造一个Cnlm对象。然后调用fitModel_manu方法。

实现工作正常，代码编译良好（使用 g++ 和 ISO C++11，g++ -std=c++0x ），但是即使我提供了正确的参数作为初始猜测，我似乎也无法获得收敛。

iteration: 0    c0 = 1  c1 = 5  c2 = -0.1
        |f(x)| =  1954.18
        status = success
iteration: 1    c0 = -15.513    c1 = 2170.38    c2 = 16.5136
        |f(x)| =  902.806
        status = success
iteration: 2    c0 = -15    c1 = 2170.38    c2 = 16
        |f(x)| =  901.11
status = cannot reach the specified tolerance in F
iteration: 3    c0 = -15    c1 = 2170.38    c2 = 16
        |f(x)| =  901.11 

我已经浏览了很多帖子，但我找不到解决我的问题的方法。

我已处在智慧的尽头。如果有人想尝试一下，我在下面提供了我的代码。也许其他人可以揭示一些信息？

提前感谢！

这是代码

标题nlls.h：

#ifndef NLLS_H_
#define NLLS_H_
#include<vector>
#include<string>
#include<gsl/gsl_blas.h>
#include<gsl/gsl_randist.h>
#include<gsl/gsl_rng.h>
#include<gsl/gsl_vector.h>
#include<gsl/gsl_multifit_nlin.h>
struct data {
    size_t n;
    double * x;
    double * y;
    double * sigma;
};
struct simulation {
    std::vector<double> x, y, weights, sigma, param;
    size_t p;
    size_t n;
};
// Class definition
class Cnlm {
public:
    Cnlm(simulation xy_data);
    const void printSummary();
    int fitModel_manu(std::vector<double> x_init,
            int (*f)(const gsl_vector *, void *, gsl_vector *),
            int (*df)(const gsl_vector *, void *, gsl_matrix *));
private:
    double m_sumsq, m_DOF, m_c;
    std::vector<double> m_param, m_ERR;
    struct resnorm {
        double chi, chi0;
    } m_resnorm;
    std::string m_solvername;
    unsigned niter, n_fun_eval, n_jacobian_eval;
    int m_info, m_status;
    simulation m_data;
};
void print_state(size_t iter, gsl_multifit_fdfsolver * s);
// function to simulate data
simulation expb_simulate(std::vector<double> x, std::vector<double> param,
        double si);
// fit functions
int expb_f(const gsl_vector * x, void *data, gsl_vector * f);
int expb_df(const gsl_vector * x, void *data, gsl_matrix * J);
#endif /* NLLS_H_ */

main.cpp ：

#include<iostream>
#include"nlls.h"
int main() {
    // simulate some data
    std::vector<double> in;
    for(unsigned i = 0; i < 30; i++){
        in.push_back(i+1);
    }
    std::vector<double> exp_par = {1, 5, -0.1};
    simulation exp_sim = expb_simulate(in, exp_par, 0.05);
    // create Clnm object
    Cnlm mynLM(exp_sim);
    // fit with initial parameters 
    std::vector<double> initial_x = {1, 5, -0.1};
    mynLM.fitModel_manu(initial_x, &expb_f, &expb_df);
    mynLM.printSummary();
    return 0;
}

class_functions.cpp ：

#include"nlls.h"
#include<iostream>
// constructor
Cnlm::Cnlm(simulation xy_data){
    m_data = xy_data;
}
int Cnlm::fitModel_manu(std::vector<double> x_init,  int (*f)(const gsl_vector * , void *, gsl_vector *), int (*df)(const gsl_vector * , void *, gsl_matrix * )){
    const size_t n = m_data.x.size();
    const size_t p = m_data.p;
    m_info = 0;
    unsigned iter = 0;
    //construct data struct to provide to gsl_multifit_function_fdf via function
    struct data d = { n, &m_data.y[0], &m_data.x[0], &m_data.sigma[0]}; // from simulated data
    gsl_vector_view w = gsl_vector_view_array(&m_data.weights[0], n);
    const gsl_multifit_fdfsolver_type * T = gsl_multifit_fdfsolver_lmsder;
    gsl_multifit_fdfsolver *s;
    gsl_matrix *J = gsl_matrix_alloc(n, p);
    gsl_matrix *covar = gsl_matrix_alloc (p, p);
    gsl_multifit_function_fdf FUN;
    gsl_vector *res_f;
    FUN.f = f;
    FUN.df = df;
    //FUN.df = NULL;
    FUN.n = n;
    FUN.p = p;
    FUN.params = &d;
    // initial values for determination of parameters
    gsl_vector_view x = gsl_vector_view_array (&x_init[0], p);
    // create new solver
    s = gsl_multifit_fdfsolver_alloc (T, n, p);
    /* initialize solver with starting point and weights */
    gsl_multifit_fdfsolver_wset (s, &FUN, &x.vector, &w.vector);
    /* compute initial residual norm */
    res_f = gsl_multifit_fdfsolver_residual(s);
    m_resnorm.chi0 = gsl_blas_dnrm2(res_f);
    print_state(iter, s);
    // solve by iteration
    do{
        iter++;
        m_status = gsl_multifit_fdfsolver_iterate (s);
        std::cout << "status = " << gsl_strerror (m_status) << std::endl;
        print_state (iter, s);
        if(m_status) break;
        m_status = gsl_multifit_test_delta (s->dx, s->x, 1e-4, 1e-4);
    }while (m_status == GSL_CONTINUE && iter < 500);
    // compute covariance matrix and best fit parameters
    gsl_multifit_fdfsolver_jac(s, J);
    gsl_multifit_covar (J, 0.0, covar);
    /* compute final residual norm */
    m_resnorm.chi = gsl_blas_dnrm2(res_f);
    m_solvername = gsl_multifit_fdfsolver_name(s);
    m_info = 0;
    niter = gsl_multifit_fdfsolver_niter(s);
    n_fun_eval = FUN.nevalf;
    n_jacobian_eval = FUN.nevaldf;
    m_DOF = n-p; //compute degrees of freedom
    m_c = GSL_MAX_DBL(1, m_resnorm.chi / sqrt(m_DOF));
    for(unsigned i = 0; i < p; i++){
        m_param.push_back(gsl_vector_get(s->x, i));
        m_ERR.push_back(gsl_matrix_get(covar,i,i));

    }
    gsl_multifit_fdfsolver_free (s);
    gsl_matrix_free (covar);
    gsl_matrix_free (J);
    return 0;
}
const void Cnlm::printSummary(){
    std::cout << "# Datan#txtytweighttsigman";
    for(unsigned i = 0; i < m_data.x.size(); i++){
        std::cout << "t" << m_data.x[i] << "t" << m_data.y[i]  << "t" << m_data.weights[i]  << "t" << m_data.sigma[i] << std::endl;
    }
    std::cout << "#n# Summaryn# -------------------------------------------n";
    std::cout << "# least squares fit estimates for Y = Vmax * X/(Km + X)n#n";
    std::cout << "# tVmax tKmn# valuet";
    for(unsigned i = 0; i < m_param.size(); i++){
        if(i == 0)  std::cout << "t" << m_param[i];
        else std::cout << "t" << m_param[i];
    }
    std::cout << std::endl;
    std::cout << "# errt";
    for(unsigned i = 0; i < m_ERR.size(); i++){
        if(i == 0)  std::cout << "t" << m_ERR[i];
        else std::cout << "t" << m_ERR[i];
    }
    std::cout << std::endl;
    std::cout << "#n# Chisq/DOF: " << pow(m_resnorm.chi, 2.0)/m_DOF << std::endl;
}

// General functions
void print_state (size_t iter, gsl_multifit_fdfsolver * s){
    std::cout << "iteration: " << iter;
    for(unsigned i = 0; i < s->x->size; i++){
        std::cout << "tc" << i << " = " << gsl_vector_get (s->x, i);
    }
    std::cout << "ntt|f(x)| =  " << gsl_blas_dnrm2 (s->f) << std::endl;
}

fit_functions.cpp ：

#include"nlls.h"

int expb_f (const gsl_vector * x, void *data, gsl_vector * f)
{
    size_t n = ((struct data *)data)->n;
    double *y = ((struct data *)data)->y;
    double A = gsl_vector_get (x, 0);
    double lambda = gsl_vector_get (x, 1);
    double b = gsl_vector_get (x, 2);
    size_t i;
    for (i = 0; i < n; i++)
    {
        /* Model Yi = A * exp(-lambda * i) + b */
        double t = i;
        double Yi = A * exp (-lambda * t) + b;
        gsl_vector_set (f, i, Yi - y[i]);
    }
    return GSL_SUCCESS;
}
int expb_df (const gsl_vector * x, void *data,  gsl_matrix * J)
{
    size_t n = ((struct data *)data)->n;
    double A = gsl_vector_get (x, 0);
    double lambda = gsl_vector_get (x, 1);
    size_t i;
    for (i = 0; i < n; i++)
    {
        /* Jacobian matrix J(i,j) = dfi / dxj, */
        /* where fi = (Yi - yi)/sigma[i],
         */
        /*
Yi = A * exp(-lambda * i) + b */
        /* and the xj are the parameters (A,lambda,b) */
        double t = i;
        double e = exp(-lambda * t);
        gsl_matrix_set (J, i, 0, e);
        gsl_matrix_set (J, i, 1, -t * A * e);
        gsl_matrix_set (J, i, 2, 1.0);
    }
    return GSL_SUCCESS;
}
simulation expb_simulate(std::vector<double> x, std::vector<double> param, double si){
    gsl_rng * r;
    const gsl_rng_type * type;
    gsl_rng_env_setup();
    unsigned n = x.size();
    simulation out;
    out.p = param.size();
    out.n = n;
    out.x.assign(x.begin(), x.end());
    out.sigma.assign(n, si);
    for(unsigned i = 0; i < out.p; i++){
        out.param.push_back(param[i]);
    }
    // start RNG
    type = gsl_rng_default;
    r = gsl_rng_alloc (type);
    // simulate data with some noise
    for (unsigned i = 0; i < n; i++)
    {
        double yi = out.param[0]+ out.param[1] * exp (out.param[2] * x[i]);
        double s = si;
        double dy = gsl_ran_gaussian(r, s);
        out.y.push_back(yi + dy);
        out.weights.push_back(1.0/(s*s));
    }
    gsl_rng_free (r);
    return out;
}