{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "97e0342c",
   "metadata": {},
   "source": [
    "# Fitting of sequential 1D cuts\n",
    "\n",
    "After a spectrum has been measured, it is sensible to extract some of the physical quantities of excitations. In this tutorial, one possible method of doing so by the use of QELine as well as LMFIT is presented. The data is the MnF2 data set where only as subset of the data is used. Specifically from 4.8 meV to 6.9 meV and the parameters wanted are the positions and widths of the magnon along two cuts in $Q$. More specifically, there will be performed a cut from (-1,0,-67) RLU to (-1,0,1) RLU to (0,0,1) RLU. For each of the two segments, the data is split into horizontal (energy) slices of same energy width and Gaussians are used to model the spin wave line shapes. Below is the data as seen before the fitting routine has been performed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "acf18505",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-05-01T08:22:33.984159Z",
     "iopub.status.busy": "2023-05-01T08:22:33.984159Z",
     "iopub.status.idle": "2023-05-01T08:22:43.606597Z",
     "shell.execute_reply": "2023-05-01T08:22:43.606136Z"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "from MJOLNIR.Data import DataSet\n",
    "from MJOLNIR import _tools # Usefull tools useful across MJOLNIR\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from lmfit.models import GaussianModel\n",
    "\n",
    "plt.rcParams['figure.figsize'] = [18, 16]\n",
    "plt.rcParams['figure.dpi'] = 200\n",
    "\n",
    "\n",
    "numbers = '483-490,492-500'\n",
    "files = _tools.fileListGenerator(numbers,r'C:\\Users\\lass_j\\Documents\\CAMEA2018',year=2018)\n",
    "ds = DataSet.DataSet(files)\n",
    "ds.convertDataFile(binning=8)\n",
    "\n",
    "\n",
    "# utility function to return points in array before a given value\n",
    "def index_of(arrval, value):\n",
    "    \"\"\"Return index of array *at or below* value.\"\"\"\n",
    "    if value < min(arrval):\n",
    "        return 0\n",
    "    if np.sum(np.diff(arrval))>0: # Positive change\n",
    "        return max(np.where(arrval <= value)[0])\n",
    "    else:\n",
    "        return max(np.where(arrval >= value)[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "59981520",
   "metadata": {},
   "source": [
    "Define the two cuts to be performed; between (-1,0,-1.2) and (-1,0,1) further on to (0,0,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "5c1a0766",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-05-01T08:22:43.609628Z",
     "iopub.status.busy": "2023-05-01T08:22:43.609628Z",
     "iopub.status.idle": "2023-05-01T08:22:46.620660Z",
     "shell.execute_reply": "2023-05-01T08:22:46.619651Z"
    }
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 3600x1147 with 1 Axes>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Define qut in Q space\n",
    "q1 = [-1,0,-1.2]\n",
    "q2 = [-1,0,1.0]\n",
    "q3 = [0,0,1.0]\n",
    "\n",
    "# Create two different energy ranges for the cut from q1 to q2 and q2 to q3\n",
    "EBins = np.array([np.linspace(ds.energy.min(),ds.energy.max(),31),np.linspace(ds.energy.min(),ds.energy.max(),25)],dtype=object)\n",
    "\n",
    "# Perform the cut and plot it. Returns a cutObject\n",
    "ax,Data,Bin = ds.plotCutQELine(QPoints=[q1,q2,q3],width=0.05,minPixel=0.01,EnergyBins=EBins,plotSeperator=True) #\n",
    "\n",
    "ax.set_clim(0,5e-6)\n",
    "ax.get_figure()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "13010157",
   "metadata": {},
   "source": [
    "The following code is rahter complex but in a larger picture, first the cut between $q_1$ and $q_2$ is dealt with followed by $q_2$ and $q_3$. For each of the cuts, the returned data (in the form of Pandas Dataframes) are grouped together in energy slices, i.e. same energy transfers are grouped togehter. \n",
    "\n",
    "For the first cut, a fitting function is created consisting 3 Gaussians while for the second two Gaussians are used. For both cuts, energies below 1.6 meV are ignored while only for the second cut energies above 6.1 meV. \n",
    "\n",
    "For each energy cut the suitable model is fitted and the parameters are extracted and saved in the <code>center3D</code> and <code>center3DErr</code>. Lastly, the points are plotted on top of the figure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "5e086995",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-05-01T08:22:46.623660Z",
     "iopub.status.busy": "2023-05-01T08:22:46.622691Z",
     "iopub.status.idle": "2023-05-01T08:22:48.376079Z",
     "shell.execute_reply": "2023-05-01T08:22:48.375461Z"
    }
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 3600x1147 with 1 Axes>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Define plotting parameters for error bar plot to be created\n",
    "ErrorBarKwargs = {'markersize':4, 'capsize':2,'elinewidth':1,'markeredgewidth':2,'mfc':'white','fmt':'o'}\n",
    "\n",
    "out = [] # Holder for fitting results\n",
    "\n",
    "# Loop through the different cuts\n",
    "for ID,_cutdata in enumerate(Data):\n",
    "# ID: which segment, either 0: q1->q2, or 1: q2->q3\n",
    "# _data: pandas frame containing data for this cut\n",
    "\n",
    "    for _,_data in _cutdata.groupby('Energy'):\n",
    "        # Transpose as to easier perform fit\n",
    "        x = _data[['H','K','L','Energy']]\n",
    "\n",
    "        # Calculate intensity and remove points that has not been measured\n",
    "\n",
    "        y = _data['Int'].values\n",
    "        NoNNans = (_data['Monitor']>0).values\n",
    "\n",
    "        y = y[NoNNans]\n",
    "        x = x[NoNNans]\n",
    "\n",
    "\n",
    "        # Fit depends on which cut is in question\n",
    "        if ID==0:\n",
    "            # Fit consists of three 1D Gaussians\n",
    "            gauss1 = GaussianModel(prefix='g1_')\n",
    "            gauss2 = GaussianModel(prefix='g2_') # Give the Gaussians different prefixes\n",
    "            gauss3 = GaussianModel(prefix='g3_')\n",
    "\n",
    "            # Model is simply the sum of these\n",
    "            mod = gauss1 + gauss2 + gauss3\n",
    "\n",
    "            # Direction along which to fit\n",
    "            fittingX = x['L']\n",
    "\n",
    "            E = x['Energy'].values[0]\n",
    "            if E<1.6:\n",
    "                continue\n",
    "\n",
    "            # Cut out portions to make use of the automatic parameter estimation\n",
    "            ix1 = fittingX< -0.1 # All points before -0.1 is for first Gaussian\n",
    "            ix2 = np.logical_and(fittingX> -0.1,fittingX<0.5) # Between ix1 and ix2 is second Gaussian\n",
    "            ix3 = fittingX>0.5 # values bigger than 0.5\n",
    "            # Third Gaussian is from 0.5 and the rest.\n",
    "\n",
    "            # Use lmfit's parameter starting guess\n",
    "            pars = gauss1.guess(y[ix1],x=fittingX[ix1].values)\n",
    "            pars.update(gauss2.guess(y[ix2],x=fittingX[ix2].values))\n",
    "            pars.update(gauss3.guess(y[ix3],x=fittingX[ix3].values))\n",
    "\n",
    "        elif ID == 1:\n",
    "\n",
    "            # Repeat procedure from above for second segment with only 2 Gaussians or 1 depending on energy\n",
    "            fittingX = x['H'].values\n",
    "            gauss1 = GaussianModel(prefix='g1_')\n",
    "            E = x['Energy'].values[0]\n",
    "            if E<1.6:\n",
    "                continue\n",
    "            if E<6.1:\n",
    "\n",
    "                gauss2 = GaussianModel(prefix='g2_')\n",
    "\n",
    "                mod = gauss1 + gauss2\n",
    "\n",
    "                ix1 = fittingX<-0.5\n",
    "                ix2 = np.logical_not(ix1)\n",
    "\n",
    "                pars = gauss1.guess(y[ix1],x=fittingX[ix1])\n",
    "                pars.update(gauss2.guess(y[ix2],x=fittingX[ix2]))\n",
    "            elif E<6.45:\n",
    "                mod = gauss1\n",
    "                pars = gauss1.guess(y,x=fittingX)\n",
    "            else:\n",
    "                continue\n",
    "\n",
    "        # Perform fit and save results in the 'out' array\n",
    "        result = mod.fit(y, pars, x=fittingX)\n",
    "        out.append(result)\n",
    "\n",
    "        # For plotting Centres and widths are needed (Their errors are extracted as well, but unused)\n",
    "        centres = []\n",
    "        centres_err = []\n",
    "        widths = []\n",
    "        widths_err = []\n",
    "        for parname, par in result.params.items():\n",
    "            if 'center' in parname:\n",
    "                centres.append(par.value)\n",
    "                centres_err.append(par.stderr)\n",
    "            if 'sigma' in parname:\n",
    "                widths.append(par.value)\n",
    "                widths_err.append(par.stderr)\n",
    "\n",
    "        # Depending on segment, the centres of the Gaussians are either [-1,0,c] or [c,0,-1]\n",
    "        # 'Errors' refers to the errorbars and are in this case plotted as the widths\n",
    "        if ID == 0:\n",
    "            Center3D    = np.array([[-1.0,0,c] for c in centres])\n",
    "            Center3DErr = np.array([[-1.0,0,c+err] for c,err in zip(centres,widths)])\n",
    "\n",
    "        elif ID == 1:\n",
    "            Center3D    = np.array([[c,0,1] for c in centres])\n",
    "            Center3DErr = np.array([[c+err,0,1] for c,err in zip(centres,widths)])\n",
    "\n",
    "        # Calculate the position along the plot for the HKL points.\n",
    "        XPosition = np.concatenate([ax.calculatePositionInv(c.reshape(1,-1)) for c in Center3D])\n",
    "        XPositionErr = np.concatenate([ax.calculatePositionInv(CE.reshape(1,-1)) for CE in Center3DErr])-XPosition\n",
    "        # The above is needed as an axis only has one x-axis and plotting multiple segments require some trickery,\n",
    "        # resulting in rescaling and offsets. It is all taken care of in the converterFunction of the axis.\n",
    "\n",
    "\n",
    "        ax.errorbar(XPosition,[x.values[0][-1]]*len(XPosition),xerr=XPositionErr,c = 'b', **ErrorBarKwargs)\n",
    "        # plot the errorbar on top of intensity data\n",
    "        \n",
    "ax.get_figure()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "860caa2b",
   "metadata": {},
   "source": [
    "If one does not like to work with pandas DataFrames, one can convert them into a set of numpy arrays. However, this then requires the user to deal with all of the indices themself. Further, if LMFIT is not your cup of tea, many other fitting routines exist for Python, e.g. the <code>scipy.optimize.curve_fit</code>."
   ]
  }
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