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‎README.md

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# fitting.git
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Some example fits
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Work with this by installing [docker](https://www.docker.com/) and pip and then running
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~~~
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pip install jupyter-repo2docker
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jupyter-repo2docker --editable .
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~~~
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Change `tree` to `lab` in the URL for JupyterLab.

‎binder/Dockerfile

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FROM bnlxray/main:172e41f3bd7d

‎examples/LSCO_30_LH_grazout.txt

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‎examples/example.ipynb

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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [],
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"source": [
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"import lmfit\n",
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"import numpy as np\n",
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"import copy\n",
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"import matplotlib.pyplot as plt\n",
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"from fitting_functions import paramagnon\n",
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"from matplotlib.ticker import AutoMinorLocator\n",
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"\n",
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"%matplotlib widget"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [],
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"source": [
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"E_, I_ = np.loadtxt('LSCO_30_LH_grazout.txt', unpack=True, skiprows=1)\n",
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"E_ *= -1\n",
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"choose = np.logical_and(E_>-.5, E_<2.5)\n",
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"E = E_[choose]\n",
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"I = I_[choose]\n",
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"dd_onset = 1."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [],
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"source": [
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"model = (lmfit.models.GaussianModel(prefix='el_') + lmfit.Model(paramagnon, prefix='mag_')\n",
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" + lmfit.models.PseudoVoigtModel(prefix='dd0_')\n",
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" + lmfit.models.PseudoVoigtModel(prefix='dd1_')\n",
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" + lmfit.models.PseudoVoigtModel(prefix='dd2_')\n",
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" + lmfit.models.ConstantModel())\n",
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"params = model.make_params()\n",
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"\n",
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"fwhm = 2*np.sqrt(2*np.log(2))\n",
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"res = 0.13/fwhm\n",
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" \n",
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"params['el_center'].set(value=0, vary=False)\n",
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"params['el_amplitude'].set(value=100, min=0)\n",
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"params['el_sigma'].set(value=res, vary=False)\n",
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"\n",
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"params['mag_center'].set(value=.35)\n",
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"params['mag_sigma'].set(value=.05, min=0)\n",
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"params['mag_amplitude'].set(value=20, min=0)\n",
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"\n",
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"params['mag_res'].set(value=res, vary=False)\n",
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"params['mag_kBT'].set(value=8.617e-5*25, vary=False)\n",
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"\n",
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"params['dd0_center'].set(value=1.6, min=1, max=3)\n",
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"params['dd0_sigma'].set(value=0.1, min=0)\n",
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"params['dd0_amplitude'].set(value=300)\n",
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"\n",
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"params['dd1_center'].set(value=1.8, min=1, max=3)\n",
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"params['dd1_sigma'].set(value=0.1, min=0)\n",
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"params['dd1_amplitude'].set(value=300)\n",
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"\n",
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"params['dd2_center'].set(value=2, min=1, max=3)\n",
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"params['dd2_sigma'].set(value=0.1, min=0)\n",
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"params['dd2_amplitude'].set(value=300)\n",
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"\n",
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"params_dd = copy.deepcopy(params)\n",
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"\n",
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"for key in params_dd.keys():\n",
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" if key[:2] in ['el', 'ma']:\n",
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" params_dd[key].set(vary=False)\n",
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" else:\n",
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" params_dd[key].set(vary=True)\n",
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"\n",
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"# Fit dds and force leading edge accuracy by artificial weighting\n",
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"dd_region = np.logical_or(E<-.3, E>dd_onset)\n",
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"weights = .1 + np.exp(-1*((E-1.1)/.3)**2)\n",
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"params_dd['c'].set(value=I.min(), vary=False) \n",
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"result_dds = model.fit(I[dd_region], x=E[dd_region], params=params_dd,\n",
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" weights=weights[dd_region])\n",
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"\n",
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"#fig, ax = plt.subplots()\n",
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"#result_dds.plot_fit(ax=ax, show_init=True)\n",
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"\n",
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"# assign and fix values for dds \n",
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"for key in params.keys():\n",
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" if key[:2] == 'dd':\n",
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" params[key].set(value=result_dds.params[key].value, vary=False)\n",
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"\n",
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"params['c'].set(value=I.min(), vary=False) \n",
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"result = model.fit(I, x=E, params=params)\n",
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"\n",
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"# fig, ax = plt.subplots()\n",
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"# result.plot_fit(ax=ax, show_init=True)\n",
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"# \n",
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"# print(result.fit_report())"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"application/vnd.jupyter.widget-view+json": {
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"model_id": "6f43ec06c63d4193aa1ccdeaf15bd7a1",
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"version_major": 2,
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"version_minor": 0
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},
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"text/plain": [
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"Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"[[Model]]\n",
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" (((((Model(gaussian, prefix='el_') + Model(paramagnon, prefix='mag_')) + Model(pvoigt, prefix='dd0_')) + Model(pvoigt, prefix='dd1_')) + Model(pvoigt, prefix='dd2_')) + Model(constant))\n",
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"[[Fit Statistics]]\n",
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" # fitting method = leastsq\n",
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" # function evals = 63\n",
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" # data points = 98\n",
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" # variables = 4\n",
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" chi-square = 10179.8497\n",
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" reduced chi-square = 108.296273\n",
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" Akaike info crit = 463.033409\n",
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" Bayesian info crit = 473.373278\n",
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"[[Variables]]\n",
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" el_amplitude: 8.72381742 +/- 0.86393752 (9.90%) (init = 100)\n",
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" el_center: 0 (fixed)\n",
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" el_sigma: 0.05520592 (fixed)\n",
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" mag_amplitude: 33.4456677 +/- 0.94889600 (2.84%) (init = 20)\n",
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" mag_center: 0.26702044 +/- 0.00309973 (1.16%) (init = 0.35)\n",
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" mag_sigma: 0.22941715 +/- 0.01224635 (5.34%) (init = 0.05)\n",
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" mag_res: 0.05520592 (fixed)\n",
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" mag_kBT: 0.00215425 (fixed)\n",
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" dd0_amplitude: 682.9913 (fixed)\n",
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" dd0_center: 1.80157 (fixed)\n",
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" dd0_sigma: 0.2914458 (fixed)\n",
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" dd0_fraction: 1.772421e-11 (fixed)\n",
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" dd1_amplitude: 227.6857 (fixed)\n",
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" dd1_center: 1.717436 (fixed)\n",
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" dd1_sigma: 0.1024631 (fixed)\n",
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" dd1_fraction: 3.824163e-13 (fixed)\n",
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" dd2_amplitude: 568.9392 (fixed)\n",
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" dd2_center: 2.099117 (fixed)\n",
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" dd2_sigma: 0.2531614 (fixed)\n",
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" dd2_fraction: 0.9321681 (fixed)\n",
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" c: 7.519076 (fixed)\n",
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" el_fwhm: 0.13000000 +/- 0.00000000 (0.00%) == '2.3548200*el_sigma'\n",
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" el_height: 63.0421515 +/- 6.24319350 (9.90%) == '0.3989423*el_amplitude/max(2.220446049250313e-16, el_sigma)'\n",
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" dd0_fwhm: 0.2 (fixed)\n",
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" dd0_height: 1182.043 (fixed)\n",
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" dd1_fwhm: 0.2 (fixed)\n",
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" dd1_height: 1182.043 (fixed)\n",
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" dd2_fwhm: 0.2 (fixed)\n",
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" dd2_height: 1182.043 (fixed)\n",
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"[[Correlations]] (unreported correlations are < 0.100)\n",
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" C(mag_amplitude, mag_sigma) = 0.830\n",
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" C(mag_center, mag_sigma) = 0.443\n",
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" C(mag_amplitude, mag_center) = 0.343\n",
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" C(el_amplitude, mag_amplitude) = -0.289\n",
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" C(el_amplitude, mag_sigma) = -0.272\n"
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]
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},
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{
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"data": {
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"text/plain": [
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"16336"
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]
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},
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"execution_count": 4,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"result = model.fit(I, x=E, params=params)\n",
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"\n",
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"fig, ax = plt.subplots()\n",
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"\n",
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"x_fit = np.linspace(E.min(), E.max(), 1000)\n",
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"\n",
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"components = result.eval_components(x=x_fit)\n",
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"constant = components.pop('constant')\n",
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"dd0 = components.pop('dd0_')\n",
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"dd1 = components.pop('dd1_')\n",
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"dd2 = components.pop('dd2_')\n",
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"\n",
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"BG = constant + dd0 + dd1 + dd2\n",
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"\n",
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"ax.plot(x_fit, BG, 'k:', label='BG')\n",
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"for model_name, model_value in components.items():\n",
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" ax.plot(x_fit, model_value + BG, '-', label=model_name.strip('_'))\n",
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"\n",
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"y_fit = result.eval(**result.best_values, x=x_fit)\n",
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"ax.plot(x_fit, y_fit, color=[0.5]*3, label='fit', lw=3, alpha=0.5)\n",
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"ax.plot(E, I, 'k.', label='data')\n",
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"\n",
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"ax.set_xlabel('Energy loss (eV)')\n",
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"ax.set_ylabel('I')\n",
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"ax.legend()\n",
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"ax.axis([-.4, dd_onset, 0, 400])\n",
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"\n",
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"ax.xaxis.set_minor_locator(AutoMinorLocator(2))\n",
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"ax.yaxis.set_minor_locator(AutoMinorLocator(2))\n",
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"\n",
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"print(result.fit_report())\n",
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"\n",
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"result.dump(open('fit_info.json','w'))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {},
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"outputs": [],
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"source": [
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"ci = result.ci_report()\n",
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"with open('ci_info.text','w') as f:\n",
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" f.write(ci)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.8.3"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 4
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}

‎fitting_functions/__init__.py

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from .lineshapes import (paramagnon, magnon, bose, make_gaussian_kernal,
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convolve, zero2Linear, zero2Quad, antisymlorz,
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plane2D, plane3D, plane3Dcentered, lorentzianSq2D,
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lorentzianSq2DRot, lorentzianSq3D, error)

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