c - 基本GSL示例程序中的错误-简单的非线性拟合

Question

我刚刚在 Windows 盒子上设置了 GSL，我正在尝试学习如何使用非线性拟合函数。我做的第一件事就是直接从他们的网站上获取一个示例:https://www.gnu.org/software/gsl/manual/html_node/Example-programs-for-Nonlinear-Least_002dSquares-Fitting.html

在这里:

#include <stdlib.h>
#include <stdio.h>
#include <stdlib.h>
#include <stdio.h>
#include <gsl/gsl_rng.h>
#include <gsl/gsl_randist.h>
#include <gsl/gsl_vector.h>
#include <gsl/gsl_blas.h>
#include <gsl/gsl_multifit_nlin.h>
#define N 40
#define FIT(i) gsl_vector_get(s->x, i)
#define ERR(i) sqrt(gsl_matrix_get(covar,i,i))

struct data {
    size_t n;
    double * y;
    double * sigma;
};

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 *sigma = ((struct data *) data)->sigma;

    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])/sigma[i]);
    }

    return GSL_SUCCESS;
}

int expb_df (const gsl_vector * x, void *data, gsl_matrix * J)
{
    size_t n = ((struct data *)data)->n;
    double *sigma = ((struct data *) data)->sigma;

    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 s = sigma[i];
        double e = exp(-lambda * t);
        gsl_matrix_set (J, i, 0, e/s);
        gsl_matrix_set (J, i, 1, -t * A * e/s);
        gsl_matrix_set (J, i, 2, 1/s);
    }
    return GSL_SUCCESS;
}

int expb_fdf (const gsl_vector * x, void *data, gsl_vector * f, gsl_matrix * J)
{
    expb_f (x, data, f);
    expb_df (x, data, J);

    return GSL_SUCCESS;
}


void print_state (size_t iter, gsl_multifit_fdfsolver * s);

int main (void)
{
    const gsl_multifit_fdfsolver_type *T;
    gsl_multifit_fdfsolver *s;
    int status;
    unsigned int i, iter = 0;
    const size_t n = N;
    const size_t p = 3;

    gsl_matrix *covar = gsl_matrix_alloc (p, p);
    double y[N], sigma[N];
    struct data d = { n, y, sigma};
    gsl_multifit_function_fdf f;
    double x_init[3] = { 1.0, 0.0, 0.0 };
    gsl_vector_view x = gsl_vector_view_array (x_init, p);
    const gsl_rng_type * type;
    gsl_rng * r;

    gsl_rng_env_setup();

    type = gsl_rng_default;
    r = gsl_rng_alloc (type);

    f.f = &expb_f;
    f.df = &expb_df;
    f.fdf = &expb_fdf;
    f.n = n;
    f.p = p;
    f.params = &d;

  /* This is the data to be fitted */

    for (i = 0; i < n; i++)
    {
        double t = i;
        y[i] = 1.0 + 5 * exp (-0.1 * t) + gsl_ran_gaussian (r, 0.1);
        sigma[i] = 0.1;
        printf ("data: %u %g %g\n", i, y[i], sigma[i]);
    };
    T = gsl_multifit_fdfsolver_lmsder;
    s = gsl_multifit_fdfsolver_alloc (T, n, p);
    gsl_multifit_fdfsolver_set (s, &f, &x.vector);

    print_state (iter, s);

    do
    {
        iter++;
        status = gsl_multifit_fdfsolver_iterate (s);

        printf ("status = %s\n", gsl_strerror (status));

        print_state (iter, s);

        if (status)
        break;

        status = gsl_multifit_test_delta (s->dx, s->x,
                                        1e-4, 1e-4);
    }
    while (status == GSL_CONTINUE && iter < 500);
    gsl_multifit_covar (s->J, 0.0, covar);
    {
        double chi = gsl_blas_dnrm2(s->f);
        double dof = n - p;
        double c = GSL_MAX_DBL(1, chi / sqrt(dof));

        printf("chisq/dof = %g\n",  pow(chi, 2.0) / dof);

        printf ("A      = %.5f +/- %.5f\n", FIT(0), c*ERR(0));
        printf ("lambda = %.5f +/- %.5f\n", FIT(1), c*ERR(1));
        printf ("b      = %.5f +/- %.5f\n", FIT(2), c*ERR(2));
    }

    printf ("status = %s\n", gsl_strerror (status));

    gsl_multifit_fdfsolver_free (s);
    gsl_matrix_free (covar);
    gsl_rng_free (r);
    return 0;
}

void print_state (size_t iter, gsl_multifit_fdfsolver * s)
{
    printf ("iter: %3u x = % 15.8f % 15.8f % 15.8f "
          "|f(x)| = %g\n",
          iter,
          gsl_vector_get (s->x, 0),
          gsl_vector_get (s->x, 1),
          gsl_vector_get (s->x, 2),
          gsl_blas_dnrm2 (s->f));
}

理想情况下，它应该简单地生成一个简短的数据集，该数据集遵循衰减指数，顶部有一些白噪声，然后对其进行拟合。

为了让它在 Windows 中的 Code::Blocks 中运行，我按照此处概述的过程进行操作:installing GSL on Windows XP 32bit for use with codeblocks

即使使用 -Wall 和 -Wextra 标志，它也可以在没有警告的情况下进行编译。但是，它在以下行上失败:gsl_multifit_fdfsolver_set (s, &f, &x.vector);，并出现错误:multifit\fdfsolver.c:132:错误: vector 长度与求解器不匹配。调用默认 GSL 错误处理程序。

我有点惊讶地发现这个应该是原始示例代码，但我们在这里。所以我希望有比我更有知识的人能告诉我这个简单的例子做错了什么。

Answer 1

发现了:他们错误地分配了初始 vector 。固定代码在这里:

#include <stdlib.h>
#include <stdio.h>
#include <stdlib.h>
#include <stdio.h>
#include <gsl/gsl_rng.h>
#include <gsl/gsl_randist.h>
#include <gsl/gsl_vector.h>
#include <gsl/gsl_blas.h>
#include <gsl/gsl_multifit_nlin.h>
#define N 40
#define FIT(i) gsl_vector_get(s->x, i)
#define ERR(i) sqrt(gsl_matrix_get(covar,i,i))

struct data {
    size_t n;
    double * y;
    double * sigma;
};

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 *sigma = ((struct data *) data)->sigma;

    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])/sigma[i]);
    }

    return GSL_SUCCESS;
}

int expb_df (const gsl_vector * x, void *data, gsl_matrix * J)
{
    size_t n = ((struct data *)data)->n;
    double *sigma = ((struct data *) data)->sigma;

    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 s = sigma[i];
        double e = exp(-lambda * t);
        gsl_matrix_set (J, i, 0, e/s);
        gsl_matrix_set (J, i, 1, -t * A * e/s);
        gsl_matrix_set (J, i, 2, 1/s);
    }
    return GSL_SUCCESS;
}

int expb_fdf (const gsl_vector * x, void *data, gsl_vector * f, gsl_matrix * J)
{
    expb_f (x, data, f);
    expb_df (x, data, J);

    return GSL_SUCCESS;
}


void print_state (size_t iter, gsl_multifit_fdfsolver * s);

int main (void)
{
    const gsl_multifit_fdfsolver_type *T;
    gsl_multifit_fdfsolver *s;
    int status;
    unsigned int i, iter = 0;
    const size_t n = N;
    const size_t p = 3;

    gsl_matrix *covar = gsl_matrix_alloc (p, p);
    double y[N], sigma[N];
    struct data d = { n, y, sigma};
    gsl_multifit_function_fdf f;
    gsl_vector *x = gsl_vector_alloc(p);
    for (i=0; i<p; i++)
    {
        gsl_vector_set(x,i,i==0 ? 1 : 0);
    }
    const gsl_rng_type * type;
    gsl_rng * r;

    gsl_rng_env_setup();

    type = gsl_rng_default;
    r = gsl_rng_alloc (type);

    f.f = &expb_f;
    f.df = &expb_df;
    f.fdf = &expb_fdf;
    f.n = n;
    f.p = p;
    f.params = &d;

  /* This is the data to be fitted */

    for (i = 0; i < n; i++)
    {
        double t = i;
        y[i] = 1.0 + 5 * exp (-0.1 * t) + gsl_ran_gaussian (r, 0.1);
        sigma[i] = 0.1;
        printf ("data: %u %g %g\n", i, y[i], sigma[i]);
    };
    T = gsl_multifit_fdfsolver_lmsder;
    s = gsl_multifit_fdfsolver_alloc (T, n, p);
    gsl_multifit_fdfsolver_set (s, &f, x);

    print_state (iter, s);

    do
    {
        iter++;
        status = gsl_multifit_fdfsolver_iterate (s);

        printf ("status = %s\n", gsl_strerror (status));

        print_state (iter, s);

        if (status)
        break;

        status = gsl_multifit_test_delta (s->dx, s->x,
                                        1e-4, 1e-4);
    }
    while (status == GSL_CONTINUE && iter < 500);
    gsl_multifit_covar (s->J, 0.0, covar);
    {
        double chi = gsl_blas_dnrm2(s->f);
        double dof = n - p;
        double c = GSL_MAX_DBL(1, chi / sqrt(dof));

        printf("chisq/dof = %g\n",  pow(chi, 2.0) / dof);

        printf ("A      = %.5f +/- %.5f\n", FIT(0), c*ERR(0));
        printf ("lambda = %.5f +/- %.5f\n", FIT(1), c*ERR(1));
        printf ("b      = %.5f +/- %.5f\n", FIT(2), c*ERR(2));
    }

    printf ("status = %s\n", gsl_strerror (status));

    gsl_multifit_fdfsolver_free (s);
    gsl_matrix_free (covar);
    gsl_rng_free (r);
    gsl_vector_free(x);
    return 0;
}

void print_state (size_t iter, gsl_multifit_fdfsolver * s)
{
    printf ("iter: %3u x = % 15.8f % 15.8f % 15.8f "
          "|f(x)| = %g\n",
          iter,
          gsl_vector_get (s->x, 0),
          gsl_vector_get (s->x, 1),
          gsl_vector_get (s->x, 2),
          gsl_blas_dnrm2 (s->f));
}