Gaussian

Simples example

>>> from ffit.funcs.gaussian import Gaussian

# Call the fit method with x and y data.
>>> fit_result = Gaussian().fit(x, y)

# The result is a FitResult object that can be unpacked.
>>> res, res_func = fit_result

# One can combine multiple calls in one line.
>>> res = Gaussian().fit(x, y, guess=[1, 2, 3, 4]).plot(ax).res

Gaussian function.

\[ a \cdot \frac{A}{\sqrt{2\pi}\sigma} \cdot \exp\left(-\frac{(x - \mu)^2}{2\sigma^2}\right) + b \]

f(x) = (
    amplitude
    * np.exp(-((x - mu) ** 2) / (2 * sigma**2))
    / np.sqrt(2 * np.pi)
    / sigma
    + offset
)

Example

>>> import ffit as ff
>>> res = ff.Gaussian().fit(x, y).res

>>> res = ff.Gaussian().fit(x, y, guess=[1, 2, 3, 4]).plot(ax).res
>>> mu = res.mu

Final parameters

The final parameters are given by GaussianParam dataclass.

Source code in ffit/funcs/gaussian.py

class Gaussian(FitLogic[GaussianParam]):  # type: ignore
    r"""Gaussian function.
    ---------

    $$
    a \cdot \frac{A}{\sqrt{2\pi}\sigma} \cdot \exp\left(-\frac{(x - \mu)^2}{2\sigma^2}\right) + b
    $$

        f(x) = (
            amplitude
            * np.exp(-((x - mu) ** 2) / (2 * sigma**2))
            / np.sqrt(2 * np.pi)
            / sigma
            + offset
        )

    Example
    -------
        >>> import ffit as ff
        >>> res = ff.Gaussian().fit(x, y).res

        >>> res = ff.Gaussian().fit(x, y, guess=[1, 2, 3, 4]).plot(ax).res
        >>> mu = res.mu

    Final parameters
    -----------------
    The final parameters are given by [`GaussianParam`](../gaussian_param/) dataclass.
    """

    param: _t.Type[GaussianParam] = GaussianParam

    func = staticmethod(gaussian_func)
    _guess = staticmethod(gaussian_guess)
    normalize_res = staticmethod(normalize_res_list)

    _example_param = (0.2, 0.2, 0.2, 0.2)

fit

fit(x, data, mask=None, guess=None, method='leastsq', maxfev=10000, **kwargs)

Fit the data using the specified fitting function.

This function returns FitResult see the documentation for more information what is possible with it.

Parameters:

Name	Type	Description	Default
x	_ARRAY	The independent variable.	required
data	_ARRAY	The dependent variable.	required
mask	Optional[Union[_ARRAY, float]]	The mask array or threshold for data filtering (optional).	None
guess	Optional[Union[_T, tuple, list]]	The initial guess for fit parameters (optional).	None
method	Literal['least_squares', 'leastsq', 'curve_fit']	The fitting method to use. Valid options are "least_squares", "leastsq", and "curve_fit" (default: "leastsq").	'leastsq'
**kwargs		Additional keyword arguments.	{}

Returns:

Name	Type	Description
FitResult	FitWithErrorResult[_T]	The result of the fit, including the fitted parameters and the fitted function.

Raises:

Type	Description
ValueError	If an invalid fitting method is provided.

Source code in ffit/fit_logic.py

def fit(
    self,
    x: _ARRAY,
    data: _ARRAY,
    mask: _t.Optional[_t.Union[_ARRAY, float]] = None,
    guess: _t.Optional[_t.Union[_T, tuple, list]] = None,
    method: _t.Literal["least_squares", "leastsq", "curve_fit"] = "leastsq",
    maxfev: int = 10000,
    **kwargs,
) -> FitWithErrorResult[_T]:  # Tuple[_T, _t.Callable, _NDARRAY]:
    """
    Fit the data using the specified fitting function.

    This function returns [FitResult][ffit.fit_results.FitResult] see
    the documentation for more information what is possible with it.


    Args:
        x: The independent variable.
        data: The dependent variable.
        mask: The mask array or threshold for data filtering (optional).
        guess: The initial guess for fit parameters (optional).
        method: The fitting method to use. Valid options are "least_squares", "leastsq",
            and "curve_fit" (default: "leastsq").
        **kwargs: Additional keyword arguments.

    Returns:
        FitResult: The result of the fit, including the fitted parameters and the fitted function.

    Raises:
        ValueError: If an invalid fitting method is provided.

    """
    # Convert x and data to numpy arrays
    x, data = np.asarray(x), np.asarray(data)

    # Mask the data and check that length of masked data is greater than lens of params
    x_masked, data_masked = get_masked_data(x, data, mask, param_len(self.param))
    if len(x_masked) == 0 or len(data_masked) == 0:
        return FitWithErrorResult()

    # Get a guess if not provided
    if guess is None:
        guess = self._guess(x_masked, data_masked, **kwargs)

    guess = tuple(guess)  # type: ignore
    # Fit the data
    res, cov = self._fit(x_masked, data_masked, guess, method, maxfev=maxfev)

    # Normalize the result if necessary. Like some periodicity that should not be important
    if self.normalize_res is not None:  # type: ignore
        res = self.normalize_res(res)  # type: ignore

    # Convert the result to a parameter object (NamedTuple)
    # print(cov)
    if cov is not None:
        stds = np.diag(cov)
        if self.normalize_res is not None:  # type: ignore
            stds = self.normalize_res(stds)  # type: ignore
        param_std = self.param(*stds)
    else:
        param_std = None
    param = self.param(*res, std=param_std)

    full_func = getattr(self, "full_func", self.__class__().func)

    # print(res)
    return FitWithErrorResult(
        param,
        lambda x: full_func(x, *res),
        x=x,
        data=data,
        cov=cov,
        stderr=param_std,
        stdfunc=lambda x: self.get_func_std()(x, *res, *stds),
    )

async_fit async

async_fit(x, data, mask=None, guess=None, **kwargs)

Asynchronously fits the model to the provided data.

Parameters:

Name	Type	Description	Default
x	_ARRAY	The independent variable data.	required
data	_ARRAY	The dependent variable data to fit.	required
mask	Optional[Union[_ARRAY, float]]	An optional mask to apply to the data. Defaults to None.	None
guess	Optional[_T]	An optional initial guess for the fitting parameters. Defaults to None.	None
**kwargs		Additional keyword arguments to pass to the fitting function.	{}

Returns:

Type	Description
FitWithErrorResult[_T]	FitWithErrorResult[_T]: The result of the fitting process, including the fitted parameters and associated errors.

Source code in ffit/fit_logic.py

async def async_fit(
    self,
    x: _ARRAY,
    data: _ARRAY,
    mask: _t.Optional[_t.Union[_ARRAY, float]] = None,
    guess: _t.Optional[_T] = None,
    **kwargs,
) -> FitWithErrorResult[_T]:
    """
    Asynchronously fits the model to the provided data.

    Args:
        x (_ARRAY): The independent variable data.
        data (_ARRAY): The dependent variable data to fit.
        mask (Optional[Union[_ARRAY, float]], optional): An optional mask to apply to the data. Defaults to None.
        guess (Optional[_T], optional): An optional initial guess for the fitting parameters. Defaults to None.
        **kwargs: Additional keyword arguments to pass to the fitting function.

    Returns:
        FitWithErrorResult[_T]:
            The result of the fitting process, including the fitted parameters and associated errors.
    """
    return self.fit(x, data, mask, guess, **kwargs)

guess classmethod

guess(x, data, mask=None, guess=None, **kwargs)

Guess the initial fit parameters.

This function returns an object of the class FitResult. See its documentation for more information on what is possible with it.

Parameters:

Name	Type	Description	Default
x		The independent variable.	required
data		The dependent variable.	required
mask	Optional[Union[_ARRAY, float]]	The mask array or threshold for data filtering (optional).	None
guess	Optional[_T]	The initial guess for the fit parameters (optional).	None
**kwargs		Additional keyword arguments.	{}

Returns:

Name	Type	Description
FitResult	FitResult[_T]	The guess, including the guess parameters and the function based on the guess.

Examples:

>>> x = [1, 2, 3, 4, 5]
>>> data = [2, 4, 6, 8, 10]
>>> fit_guess = FitLogic.guess(x, data)
>>> fit_guess.plot()

Source code in ffit/fit_logic.py

@classmethod
def guess(
    cls,
    x,
    data,
    mask: _t.Optional[_t.Union[_ARRAY, float]] = None,
    guess: _t.Optional[_T] = None,
    **kwargs,
) -> FitResult[_T]:
    """Guess the initial fit parameters.

    This function returns an object of the class `FitResult`.
    See its documentation for more information on what is possible with it.

    Args:
        x: The independent variable.
        data: The dependent variable.
        mask: The mask array or threshold for data filtering (optional).
        guess: The initial guess for the fit parameters (optional).
        **kwargs: Additional keyword arguments.

    Returns:
        FitResult: The guess, including the guess parameters and the function based on the guess.


    Examples:
        >>> x = [1, 2, 3, 4, 5]
        >>> data = [2, 4, 6, 8, 10]
        >>> fit_guess = FitLogic.guess(x, data)
        >>> fit_guess.plot()
    """
    if guess is not None:
        return FitResult(
            cls.param(*guess), lambda x: cls.func(x, *guess), x=x, data=data
        )
    x_masked, data_masked = get_masked_data(x, data, mask, mask_min_len=1)
    guess_param = cls._guess(x_masked, data_masked, **kwargs)
    return FitResult(
        cls.param(*guess_param), lambda x: cls.func(x, *guess_param), x=x, data=data
    )

bootstrapping

bootstrapping(x, data, mask=None, guess=None, method='leastsq', sampling_len=None, sampling_portion=0.75, **kwargs)

Fit the data using the specified fitting function.

This function returns FitResult see the documentation for more information what is possible with it.

Parameters:

Name	Type	Description	Default
x	_ARRAY	The independent variable.	required
data	_ARRAY	The dependent variable.	required
mask	Optional[Union[_ARRAY, float]]	The mask array or threshold for data filtering (optional).	None
guess	Optional[Union[_T, tuple, list]]	The initial guess for fit parameters (optional).	None
method	Literal['least_squares', 'leastsq', 'curve_fit']	The fitting method to use. Valid options are "least_squares", "leastsq", and "curve_fit" (default: "leastsq").	'leastsq'
**kwargs		Additional keyword arguments.	{}

Returns:

Name	Type	Description
FitResult	FitWithErrorResult[_T]	The result of the fit, including the fitted parameters and the fitted function.

Raises:

Type	Description
ValueError	If an invalid fitting method is provided.

Source code in ffit/fit_logic.py

def bootstrapping(
    self,
    x: _ARRAY,
    data: _ARRAY,
    mask: _t.Optional[_t.Union[_ARRAY, float]] = None,
    guess: _t.Optional[_t.Union[_T, tuple, list]] = None,
    method: _t.Literal["least_squares", "leastsq", "curve_fit"] = "leastsq",
    sampling_len: _t.Optional[int] = None,
    sampling_portion: float = 0.75,
    **kwargs,
) -> FitWithErrorResult[_T]:  # Tuple[_T, _t.Callable, _NDARRAY]:
    """
    Fit the data using the specified fitting function.

    This function returns [FitResult][ffit.fit_results.FitResult] see
    the documentation for more information what is possible with it.


    Args:
        x: The independent variable.
        data: The dependent variable.
        mask: The mask array or threshold for data filtering (optional).
        guess: The initial guess for fit parameters (optional).
        method: The fitting method to use. Valid options are "least_squares", "leastsq",
            and "curve_fit" (default: "leastsq").
        **kwargs: Additional keyword arguments.

    Returns:
        FitResult: The result of the fit, including the fitted parameters and the fitted function.

    Raises:
        ValueError: If an invalid fitting method is provided.

    """
    # Convert x and data to numpy arrays
    x, data = np.asarray(x), np.asarray(data)

    mask = get_mask(mask, x)

    # Mask the data and check that length of masked data is greater than lens of params
    x_masked, data_masked = get_masked_data(x, data, mask, param_len(self.param))
    if len(x_masked) == 0 or len(data_masked) == 0:
        return FitWithErrorResult()

    # Get a guess if not provided
    if guess is None:
        guess = self._guess(x_masked, data_masked, **kwargs)

    # Fit ones to get the best initial guess
    guess, cov = self._fit(x_masked, data_masked, guess, method)

    # Set sampling length if not provided
    sampling_len = (
        int(min(max(len(x_masked) / 10, 1000), 10_000))
        if sampling_len is None
        else sampling_len
    )

    # Run fit on random subarrays
    all_res = []
    for xx, yy in get_random_subarrays(
        x_masked, data_masked, sampling_len, sampling_portion
    ):
        res, _ = self._fit(xx, yy, guess, method)
        if self.normalize_res is not None:  # type: ignore
            res = self.normalize_res(res)  # type: ignore
        all_res.append(res)

    res_means = np.mean(all_res, axis=0)
    bootstrap_std = np.std(all_res, axis=0)
    # print(cov)
    # total_std = np.sqrt(np.diag(cov) + bootstrap_std**2)
    total_std = bootstrap_std
    # print(res_means, total_std)

    # Convert the result to a parameter object (NamedTuple)
    param_std = self.param(*total_std)
    param = self.param(*res_means, std=param_std)

    full_func = getattr(self, "full_func", self.__class__().func)

    return FitWithErrorResult(
        param,
        lambda x: full_func(x, *res),
        x=x,
        data=data,
        cov=cov,
        stderr=param_std,
        stdfunc=lambda x: self.get_func_std()(x, *res_means, *total_std),
    )