![]() |
![]() |
Gwyddion Library Reference Manual | ![]() |
|
---|---|---|---|---|
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); 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); 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 derivation (as GwyNLFitDerFunc). For functions for whose analytic
derivation is not available or very impractical, gwy_math_nlfit_derive()
(computing the derivation 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_with_fixed()
when there are some
fixed 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_math_nlfit_fit_preset()
. Each one can be identified by a
unique name or a numeric id (the latter one may however change between
releases) the number of presets can be obtained with
gwy_math_nlfit_get_npresets()
. Preset properties can be obtained with
functions like gwy_math_nlfit_get_preset_nparams()
or
gwy_math_nlfit_get_preset_formula()
.
gdouble (*GwyNLFitFunc) (gdouble x, gint n_param, const gdouble *param, gpointer user_data, gboolean *fres);
Fitting function type.
x : |
The value to compute the function at. |
n_param : |
The number of parameters (size of param ).
|
param : |
Parameters. |
user_data : |
User data as passed to gwy_math_nlfit_fit() .
|
fres : |
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 derivation type.
x : |
x-data as passed to gwy_math_nlfit_fit() .
|
n_param : |
The number of parameters (size of param ).
|
param : |
Parameters. |
fixed_param : |
Which parameters should be treated as fixed (corresponding
entries are set to TRUE ).
|
fmarq : |
The fitting function. |
user_data : |
User data as passed to gwy_math_nlfit_fit() .
|
deriv : |
Array where the n_param partial derivations by each parameter are
to be stored.
|
dres : |
Set to TRUE if succeeds, FALSE on failure.
|
typedef struct { 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;
GwyNLFitter* gwy_math_nlfit_new (GwyNLFitFunc ff, GwyNLFitDerFunc df);
Creates a new Marquardt-Levenberg nonlinear fitter for function ff
.
ff : |
The fitted function. |
df : |
The derivation of fitted function. You can use gwy_math_nlfit_derive()
computing the derivation numerically, when you don't know the
derivation explicitely.
|
Returns : | The newly created fitter. |
void gwy_math_nlfit_free (GwyNLFitter *nlfit);
Completely frees a Marquardt-Levenberg nonlinear fitter.
nlfit : |
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.
nlfit : |
A Marquardt-Levenberg nonlinear fitter. |
n_dat : |
The number of data points in x , y .
|
x : |
Array of independent variable values. |
y : |
Array of dependent variable values. |
n_param : |
The nuber of parameters. |
param : |
Array of parameters (of size n_param ). Note the parameters must
be initialized to reasonably near values.
|
user_data : |
Any pointer that will be passed to the function and derivation
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.
nlfit : |
A Marquardt-Levenberg nonlinear fitter. |
n_dat : |
The number of data points in x , y , weight .
|
x : |
Array of independent variable values. |
y : |
Array of dependent variable values. |
weight : |
Array of weights associated to each data point. Can be NULL ,
weight of 1 is then used for all data.
|
n_param : |
The nuber of parameters. |
param : |
Array of parameters (of size n_param ). Note the parameters must
be initialized to reasonably near values.
|
fixed_param : |
Which parameters should be treated as fixed (set corresponding
element to TRUE for them). May be NULL if all parameters
are variable.
|
link_map : |
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.
|
user_data : |
Any pointer that will be passed to the function and derivation |
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
.
nlfit : |
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
.
nlfit : |
A Marquardt-Levenberg nonlinear fitter. |
maxiter : |
The maximum number of iterations. |
gdouble gwy_math_nlfit_get_dispersion (GwyNLFitter *nlfit);
Returns the residual sum divided by the number of degrees of freedom.
This function makes sense only after a successful fit.
nlfit : |
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 makes sense only after a successful fit.
nlfit : |
A Marquardt-Levenberg nonlinear fitter. |
par1 : |
First parameter index. |
par2 : |
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.
nlfit : |
A Marquardt-Levenberg nonlinear fitter. |
par : |
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 derivations of ff
x : |
The value to compute the derivation at. |
n_param : |
The nuber of parameters. |
param : |
Array of parameters (of size n_param ).
|
fixed_param : |
Which parameters should be treated as fixed (corresponding
entries are set to TRUE ).
|
ff : |
The fitted function. |
user_data : |
User data as passed to gwy_math_nlfit_fit() .
|
deriv : |
Array where the put the result to. |
dres : |
Set to TRUE if succeeds, FALSE on failure.
|