init

README.md

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

binder/Dockerfile

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+FROM bnlxray/main:172e41f3bd7d

examples/example.ipynb

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

fitting_functions/__init__.py

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