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#include <libgwyddion/gwyddion.h> gdouble (*GwyNLFitFunc) (gdouble x,gint n_param,const gdouble *param,gpointer user_data,gboolean *fres); void (*GwyNLFitDerFunc) (gdouble x,gint n_param,const gdouble *param,const gboolean *fixed_param,GwyNLFitFunc fmarq,gpointer user_data,gdouble *deriv,gboolean *dres); struct GwyNLFitter; GwyNLFitter * gwy_math_nlfit_new (GwyNLFitFunc ff,GwyNLFitDerFunc df); void gwy_math_nlfit_free (GwyNLFitter *nlfit); gdouble gwy_math_nlfit_fit (GwyNLFitter *nlfit,gint n_dat,const gdouble *x,const gdouble *y,gint n_param,gdouble *param,gpointer user_data); gdouble gwy_math_nlfit_fit_full (GwyNLFitter *nlfit,gint n_dat,const gdouble *x,const gdouble *y,const gdouble *weight,gint n_param,gdouble *param,const gboolean *fixed_param,const gint *link_map,gpointer user_data); gint gwy_math_nlfit_get_max_iterations (GwyNLFitter *nlfit); void gwy_math_nlfit_set_max_iterations (GwyNLFitter *nlfit,gint maxiter); gboolean gwy_math_nlfit_succeeded (GwyNLFitter *nlfit); gdouble gwy_math_nlfit_get_dispersion (GwyNLFitter *nlfit); gdouble gwy_math_nlfit_get_correlations (GwyNLFitter *nlfit,gint par1,gint par2); gdouble gwy_math_nlfit_get_sigma (GwyNLFitter *nlfit,gint par); void gwy_math_nlfit_derive (gdouble x,gint n_param,const gdouble *param,const gboolean *fixed_param,GwyNLFitFunc ff,gpointer user_data,gdouble *deriv,gboolean *dres);
A new Marquardt-Levenberg nonlinear least square fitter can be created with
gwy_math_nlfit_new(), specifying the function to fit (as GwyNLFitFunc) and
its derivative (as GwyNLFitDerFunc). For functions for whose analytic
derivative is not available or very impractical, gwy_math_nlfit_derive()
(computing the derivative numerically) can be used instead.
A fitter can be then repeatedly used on different data either in
gwy_math_nlfit_fit(), or gwy_math_nlfit_fit_full() when there are some
fixed or linked parameters. Arbitrary additional (non-fitting) parameters
can be passed to the fited function in user_data.
After a successfull fit additional fit information can be obtained with
gwy_math_nlfit_get_dispersion(), gwy_math_nlfit_get_correlations(),
gwy_math_nlfit_get_sigma(). Note these functions may be used only after a
successfull fit. When a fitter is no longer needed, it should be freed with
gwy_math_nlfit_free().
Several common functions are also available as fitting presets that can be
fitted with gwy_nlfit_preset_fit(). See GwyNLFitPreset for details.
gdouble (*GwyNLFitFunc) (gdouble x,gint n_param,const gdouble *param,gpointer user_data,gboolean *fres);
Fitting function type.
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The value to compute the function at. |
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The number of parameters (size of param). |
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Parameters. |
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User data as passed to gwy_math_nlfit_fit(). |
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Set to TRUE if succeeds, FALSE on failure. |
Returns : |
The value at x. |
void (*GwyNLFitDerFunc) (gdouble x,gint n_param,const gdouble *param,const gboolean *fixed_param,GwyNLFitFunc fmarq,gpointer user_data,gdouble *deriv,gboolean *dres);
Fitting function partial derivative type.
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x-data as passed to gwy_math_nlfit_fit(). |
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The number of parameters (size of param). |
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Parameters. |
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Which parameters should be treated as fixed (corresponding
entries are set to TRUE). |
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The fitting function. |
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User data as passed to gwy_math_nlfit_fit(). |
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Array where the n_param partial derivatives by each parameter are
to be stored. |
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Set to TRUE if succeeds, FALSE on failure. |
struct GwyNLFitter {
GwyNLFitFunc fmarq; /* fitting function */
GwyNLFitDerFunc dmarq; /* fitting function derivations */
gint maxiter; /* max number of iterations */
gboolean eval; /* success? */
gdouble *covar; /* covariance matrix */
gdouble dispersion; /* dispersion */
gdouble mfi; /* fitting parameters --
fi, snizeni, zvyseni lambda, minimalni lambda */
gdouble mdec;
gdouble minc;
gdouble mtol;
};
GwyNLFitter * gwy_math_nlfit_new (GwyNLFitFunc ff,GwyNLFitDerFunc df);
Creates a new Marquardt-Levenberg nonlinear fitter for function ff.
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The fitted function. |
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The derivative of fitted function. You can use gwy_math_nlfit_derive()
computing the derivative numerically, when you don't know the
derivative explicitely. |
Returns : |
The newly created fitter. |
void gwy_math_nlfit_free (GwyNLFitter *nlfit);
Completely frees a Marquardt-Levenberg nonlinear fitter.
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A Marquardt-Levenberg nonlinear fitter. |
gdouble gwy_math_nlfit_fit (GwyNLFitter *nlfit,gint n_dat,const gdouble *x,const gdouble *y,gint n_param,gdouble *param,gpointer user_data);
Performs a nonlinear fit of nlfit function on (x,y) data.
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A Marquardt-Levenberg nonlinear fitter. |
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The number of data points in x, y. |
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Array of independent variable values. |
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Array of dependent variable values. |
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The nuber of parameters. |
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Array of parameters (of size n_param). Note the parameters must
be initialized to reasonably near values. |
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Any pointer that will be passed to the function and derivative
as user_data. |
Returns : |
The final residual sum, a negative number in the case of failure. |
gdouble gwy_math_nlfit_fit_full (GwyNLFitter *nlfit,gint n_dat,const gdouble *x,const gdouble *y,const gdouble *weight,gint n_param,gdouble *param,const gboolean *fixed_param,const gint *link_map,gpointer user_data);
Performs a nonlinear fit of nlfit function on (x,y) data, allowing
some fixed parameters.
Initial values of linked (dependent) parameters are overwritten by master
values, their fixed_param property is ignored and master's property
controls whether all are fixed or all variable.
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A Marquardt-Levenberg nonlinear fitter. |
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The number of data points in x, y, weight. |
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Array of independent variable values. |
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Array of dependent variable values. |
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Array of weights associated to each data point. Can be NULL,
weight of 1 is then used for all data. |
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The nuber of parameters. |
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Array of parameters (of size n_param). Note the parameters must
be initialized to reasonably near values. |
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Which parameters should be treated as fixed (set corresponding
element to TRUE for them). May be NULL if all parameters
are variable. |
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Map of linked parameters. One of linked parameters is master,
Values in this array are indices of corresponding master
parameter for each parameter (for independent parameters set
link_map[i] == i). May be NULL if all parameter are
independent. |
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Any pointer that will be passed to the function and derivative |
Returns : |
The final residual sum, a negative number in the case of failure. |
gint gwy_math_nlfit_get_max_iterations (GwyNLFitter *nlfit);
Returns the maximum number of iterations of nonlinear fitter nlfit.
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A Marquardt-Levenberg nonlinear fitter. |
Returns : |
The maximum number of iterations. |
void gwy_math_nlfit_set_max_iterations (GwyNLFitter *nlfit,gint maxiter);
Sets the maximum number of iterations for nonlinear fitter nlfit.
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A Marquardt-Levenberg nonlinear fitter. |
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The maximum number of iterations. |
gboolean gwy_math_nlfit_succeeded (GwyNLFitter *nlfit);
Obtains the status of the last fitting.
Fitting failure can be (and usually should be) also determined by checking
for negative return value of gwy_math_nlfit_fit() or
gwy_math_nlfit_fit_full(). This function allows to test it later.
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A Marquardt-Levenberg nonlinear fitter. |
Returns : |
TRUE if the last fitting suceeded, FALSE if it failed. |
Since 2.7
gdouble gwy_math_nlfit_get_dispersion (GwyNLFitter *nlfit);
Returns the residual sum divided by the number of degrees of freedom.
This function can be used only after a successful fit.
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A Marquardt-Levenberg nonlinear fitter. |
Returns : |
The dispersion. |
gdouble gwy_math_nlfit_get_correlations (GwyNLFitter *nlfit,gint par1,gint par2);
Returns the correlation coefficient between par1-th and par2-th parameter.
This function can be used only after a successful fit.
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A Marquardt-Levenberg nonlinear fitter. |
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First parameter index. |
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Second parameter index. |
Returns : |
The correlation coefficient. |
gdouble gwy_math_nlfit_get_sigma (GwyNLFitter *nlfit,gint par);
Returns the standard deviation of parameter number par.
This function makes sense only after a successful fit.
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A Marquardt-Levenberg nonlinear fitter. |
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Parameter index. |
Returns : |
The SD of par-th parameter. |
void gwy_math_nlfit_derive (gdouble x,gint n_param,const gdouble *param,const gboolean *fixed_param,GwyNLFitFunc ff,gpointer user_data,gdouble *deriv,gboolean *dres);
Numerically computes the partial derivative of a fitting function.
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The value to compute the derivative at. |
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The nuber of parameters. |
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Array of parameters (of size n_param). |
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Which parameters should be treated as fixed (corresponding
entries are set to TRUE). |
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The fitted function. |
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User data as passed to gwy_math_nlfit_fit(). |
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Array where the put the result to. |
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Set to TRUE if succeeds, FALSE on failure. |