Source code for Stoner.analysis.fitting.models.generic

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
""":py:class:`lmfit.Model` model classes and functions for various generic models."""
# pylint: disable=invalid-name
__all__ = [
    "Linear",
    "Lorentzian_diff",
    "Model",
    "PowerLaw",
    "Quadratic",
    "StretchedExp",
    "linear",
    "lorentzian_diff",
    "powerLaw",
    "quadratic",
    "stretchedExp",
]

import numpy as np

from lmfit import Model
from lmfit.models import LinearModel as _Linear  # NOQA pylint: disable=unused-import
from lmfit.models import PowerLawModel as _PowerLaw  # NOQA pylint: disable=unused-import
from lmfit.models import QuadraticModel as _Quadratic  # NOQA pylint: disable=unused-import
from lmfit.models import update_param_vals


[docs]def linear(x, intercept, slope): """Calculate a linear function.""" return slope * x + intercept
[docs]def quadratic(x, a, b, c): r"""Calculate a simple quadratic fitting function. Args: x (aray): Input data a (float): Quadratic term co-efficient b (float): Linear term co-efficient c (float): Constant offset term Returns: Array of data. :math:`y=ax^2+bx+c` Example: .. plot:: samples/Fitting/Quadratic.py :include-source: :outname: quadratic """ return a * x ** 2 + b * x + c
[docs]def powerLaw(x, A, k): r"""Power Law Fitting Equation. Args: x (array): Input data A (float): Prefactor k (float): Pwoer Return: Power law. :math:`p=Ax^k` Example: .. plot:: samples/Fitting/Powerlaw.py :include-source: :outname: powerlaw """ return A * x ** k
[docs]def stretchedExp(x, A, beta, x_0): r"""Calculate a stretched exponential fuinction. Args: x (array): x data values A (float): Constant prefactor beta (float): Stretch factor x_0 (float): Scaling factor for x data Return: Data for a stretched exponentional function. The stretched exponential is defined as :math:`y=A\exp\left[\left(\frac{-x}{x_0}\right)^\beta\right]`. """ return A * np.exp(-((x / x_0) ** beta))
[docs]def lorentzian_diff(x, A, sigma, mu): r"""Implement a differential form of a Lorentzian peak. Args: x (array): x data A (flaot): Peak amplitude sigma (float): peak wideth mu (float): peak location in x Returns :math:`\frac{A \sigma \left(2 \mu - 2 x\right)}{\pi \left(\sigma^{2} + \left(- \mu + x\right)^{2}\right)^{2}}` Example: .. plot:: samples/Fitting/lorentzian.py :include-source: :outname: lorentzian_diff_func """ return A * sigma * (2 * mu - 2 * x) / (np.pi * (sigma ** 2 + (-mu + x) ** 2) ** 2)
[docs]class Linear(_Linear): """Simple linear fit class."""
[docs]class Quadratic(_Quadratic): r"""A Simple quadratic fitting function. Args: x (aray): Input data a (float): Quadratic term co-efficient b (float): Linear term co-efficient c (float): Constant offset term Returns: Array of data. :math:`y=ax^2+bx+c` Example: .. plot:: samples/Fitting/Quadratic.py :include-source: :outname: quadratic-class """
[docs]class PowerLaw(_PowerLaw): r"""Power Law Fitting Equation. Args: x (array): Input data A (float): Prefactor k (float): Pwoer Return: Power law. :math:`p=Ax^k` Example: .. plot:: samples/Fitting/Powerlaw.py :include-source: :outname: powerlaw-class """
[docs]class StretchedExp(Model): r"""A stretched exponential fuinction. Args: x (array): x data values A (float): Constant prefactor beta (float): Stretch factor x_0 (float): Scaling factor for x data Return: Data for a stretched exponentional function. The stretched exponential is defined as :math:`y=A\exp\left[\left(\frac{-x}{x_0}\right)^\beta\right]`. """ display_names = ["A", r"\beta", "x_0"] def __init__(self, *args, **kwargs): """Configure Initial fitting function.""" super().__init__(stretchedExp, *args, **kwargs)
[docs] def guess(self, data, x=None, **kwargs): """Guess parameters for the stretched exponential from data.""" A, beta, x0 = 1.0, 1.0, 1.0 if x is not None: A = data[np.argmin(np.abs(x))] x = np.log(x) y = np.log(-np.log(data / A)) d = np.column_stack((x, y)) d = d[~np.isnan(d).any(axis=1)] d = d[~np.isinf(d).any(axis=1)] d1, d2 = np.polyfit(d[:, 0], d[:, 1], 1) beta = d1 x0 = np.exp(d2 / beta) pars = self.make_params(A=A, beta=beta, x_0=x0) return update_param_vals(pars, self.prefix, **kwargs)
[docs]class Lorentzian_diff(Model): r"""Provides a lmfit Model rerprenting the differential form of a Lorentzian Peak. Args: x (array): x data A (flaot): Peak amplitude sigma (float): peak wideth mu (float): peak location in x Returns :math:`\frac{A \sigma \left(2 \mu - 2 x\right)}{\pi \left(\sigma^{2} + \left(- \mu + x\right)^{2}\right)^{2}}` Example: .. plot:: samples/Fitting/lorentzian.py :include-source: :outname: lorentzian_diff_class """ display_names = ["A", r"\sigma", r"\mu"] def __init__(self, *args, **kwargs): """Configure Initial fitting function.""" super().__init__(lorentzian_diff, *args, **kwargs)
[docs] def guess(self, data, x=None, **kwargs): """Guess parameters as gamma=2, H_k=0, M_s~(pi.f)^2/(mu_0^2.H)-H.""" if x is None: x = np.linspace(1, len(data), len(data) + 1) x1 = x[np.argmax(data)] x2 = x[np.argmin(data)] sigma = abs(x1 - x2) mu = (x1 + x2) / 2.0 y1 = np.max(data) y2 = np.min(data) dy = y1 - y2 A = dy * (4 * np.pi * sigma ** 2) / (3 * np.sqrt(3)) pars = self.make_params(A=A, sigma=sigma, mu=mu) pars["A"].min = 0 pars["sigma"].min = 0 pars["mu"].min = np.min(x) pars["mu"].max = np.max(x) return update_param_vals(pars, self.prefix, **kwargs)