{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "ename": "RuntimeError",
     "evalue": "module compiled against API version 0xa but this version of numpy is 0x9",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mRuntimeError\u001b[0m                              Traceback (most recent call last)",
      "\u001b[0;31mRuntimeError\u001b[0m: module compiled against API version 0xa but this version of numpy is 0x9"
     ]
    },
    {
     "ename": "ImportError",
     "evalue": "numpy.core.multiarray failed to import",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mImportError\u001b[0m                               Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-1-63ea9c24d0f9>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mnumpy\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0;32mimport\u001b[0m \u001b[0mmatplotlib\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpyplot\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      3\u001b[0m \u001b[0mget_ipython\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmagic\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34mu'matplotlib inline'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/opt/anaconda2/lib/python2.7/site-packages/matplotlib/pyplot.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     27\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mcycler\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mcycler\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     28\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mmatplotlib\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 29\u001b[0;31m \u001b[0;32mimport\u001b[0m \u001b[0mmatplotlib\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcolorbar\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     30\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mmatplotlib\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mstyle\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     31\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mmatplotlib\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0m_pylab_helpers\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minteractive\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/opt/anaconda2/lib/python2.7/site-packages/matplotlib/colorbar.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     30\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     31\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mmatplotlib\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mmpl\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 32\u001b[0;31m \u001b[0;32mimport\u001b[0m \u001b[0mmatplotlib\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0martist\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mmartist\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     33\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mmatplotlib\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcbook\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mcbook\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     34\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mmatplotlib\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcollections\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mcollections\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/opt/anaconda2/lib/python2.7/site-packages/matplotlib/artist.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     12\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mmatplotlib\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcbook\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mmplDeprecation\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     13\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mmatplotlib\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mdocstring\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrcParams\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 14\u001b[0;31m from .transforms import (Bbox, IdentityTransform, TransformedBbox,\n\u001b[0m\u001b[1;32m     15\u001b[0m                          TransformedPath, Transform)\n\u001b[1;32m     16\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0;34m.\u001b[0m\u001b[0mpath\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mPath\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/opt/anaconda2/lib/python2.7/site-packages/matplotlib/transforms.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     37\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mnumpy\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     38\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mnumpy\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mma\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 39\u001b[0;31m from matplotlib._path import (affine_transform, count_bboxes_overlapping_bbox,\n\u001b[0m\u001b[1;32m     40\u001b[0m     update_path_extents)\n\u001b[1;32m     41\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mnumpy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlinalg\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0minv\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mImportError\u001b[0m: numpy.core.multiarray failed to import"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Lmfit provides a high-level interface to non-linear optimization and curve fitting problems for Python.\n",
    "#It builds on and extends many of the optimization methods of scipy.optimize.\n",
    "#The advantage is the ease on parameter settings, change of fitting algorithms,\n",
    "#estimation of confidence intervals, and multiple model combination and a set of ready-to-use fitting models.\n",
    "#I'll show some examples like line deblending and continuum estimation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#let's start with a simple one\n",
    "def parabola(x, a0, a1, a2):\n",
    "    return a2*x**2 + a1*x + a0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-8, 11, -10, 60]"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Sy8q9uCyrsu60/WPg+p55twEHIuIq4EAybRMg792/vlv4fOk7Vjdu3Fjp3au+O9ayKqWG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\nDyWpdDd5AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fbf3567c0b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#and generate some fake data\n",
    "Xf = np.linspace(-7, 10, 100)\n",
    "Yf = parabola(X, 3, 0.1, 0.5)+np.random.randn(100)*3\n",
    "plt.plot(Xf, Yf, 'k.')\n",
    "plt.axis([-8, 11, -10, 60])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['a0', 'a1', 'a2']\n",
      "['x']\n"
     ]
    }
   ],
   "source": [
    "#Lmfit works with Model objects that is the law of the fitting function\n",
    "from lmfit import Model\n",
    "\n",
    "#first, let's create a model from scratch using our parabola function\n",
    "pmodel = Model(parabola)\n",
    "\n",
    "#LmFit automatically recognizes what is a parameter and an independent variable\n",
    "#note: the Model object params are not the ones that will be minimized, they are model properties\n",
    "print(pmodel.param_names)\n",
    "print(pmodel.independent_vars)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<Parameter 'a0', -inf, bounds=[-inf:inf]>\n"
     ]
    }
   ],
   "source": [
    "#the central part of LmFit is the Parameters object. it behaves like a dict and contains the parameters\n",
    "#and values that are going to be adjusted. we create them like this:\n",
    "params = pmodel.make_params()\n",
    "print(params['a0'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameters([('a0', <Parameter 'a0', 1, bounds=[-5:5]>), ('a1', <Parameter 'a1', -inf, bounds=[-inf:inf]>), ('a2', <Parameter 'a2', -inf, bounds=[-inf:inf]>)])\n"
     ]
    }
   ],
   "source": [
    "#we can set each parameter value separately, and their range\n",
    "params['a0'].set(value=1, min=-5, max=5)\n",
    "print(params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[Model]]\n",
      "    Model(parabola)\n",
      "[[Fit Statistics]]\n",
      "    # function evals   = 14\n",
      "    # data points      = 100\n",
      "    # variables        = 3\n",
      "    chi-square         = 926.644\n",
      "    reduced chi-square = 9.553\n",
      "    Akaike info crit   = 228.640\n",
      "    Bayesian info crit = 236.455\n",
      "[[Variables]]\n",
      "    a0:   3.13800548 +/- 0.450390 (14.35%) (init= 0)\n",
      "    a1:   0.05806008 +/- 0.075292 (129.68%) (init= 0)\n",
      "    a2:   0.49203068 +/- 0.014066 (2.86%) (init= 0)\n",
      "[[Correlations]] (unreported correlations are <  0.100)\n",
      "    C(a0, a2)                    = -0.697 \n",
      "    C(a1, a2)                    = -0.560 \n",
      "    C(a0, a1)                    =  0.219 \n",
      "\n"
     ]
    }
   ],
   "source": [
    "#so, let's perform the fit giving initial values for every parameter (the fit will fail otherwise)\n",
    "result = pmodel.fit(Yf, x=Xf, a0=0, a1=0, a2=0)\n",
    "#the Results object has several attributes, including a pretty report\n",
    "print(result.fit_report())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-8, 11, -10, 60]"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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2y/n++zYMGLCa++9vT7duyZVfBDSWTs6KJzhHC0Lbbgv77PMYBQV3U1v7e2pq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\n8oQCvohInlDAFxHJE/8fHtlQpU9/LakAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fbf359283c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#let's see how it is\n",
    "plt.plot(Xf, Yf, 'k.')\n",
    "plt.plot(Xf, result.init_fit, 'r--')\n",
    "plt.plot(Xf, result.best_fit, 'b-')\n",
    "plt.axis([-8, 11, -10, 60])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fbf35087a90>]"
      ]
     },
     "execution_count": 150,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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zm/HeCwoKlNPcBQUFqX3OxcXFfOVuoDjcGeuCjY0NAPN4qamhoQGWlpbK2ZD6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\nM0Ec7owxZoI43BljzARxuDPGmAn6fwprrnnDRdMEAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fbf35754390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#ok, now let's turn adventure mode on\n",
    "#we're going to perform a high-resolution spectrum deblending. let's have a look at it:\n",
    "spec = np.genfromtxt('mg.dat', unpack=True)\n",
    "plt.plot(spec[0], spec[1], 'k-', lw=0.7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#for that, we'll use a constant model for the continuum, a voigt for the Mg line and gaussian for additional lines\n",
    "from lmfit.models import VoigtModel, GaussianModel, ConstantModel\n",
    "\n",
    "#on LmFit we can combine several models to fit data, so to make things easier, let's separate them\n",
    "#calling a the model to make the continuum:\n",
    "cont = ConstantModel(prefix='cont_')\n",
    "#on built-in models we can guess the parameters instead of setting each one\n",
    "pars = cont.guess(spec[1], x=spec[0])\n",
    "#this will create the Parameters object that will store every parameter of each model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#now the Voigt model for the main Mg line\n",
    "mg = VoigtModel(prefix='Mg_')\n",
    "#we can update the parameters using the guess\n",
    "pars.update(mg.guess(spec[1], x=spec[0]))\n",
    "#but if we take it like that it's going to be a mess, so we set some constraints\n",
    "pars['Mg_center'].set(5183.5)\n",
    "pars['Mg_sigma'].set(0.2)\n",
    "pars['Mg_gamma'].set(0.2, vary=True)\n",
    "#now, we have 4 lines to fit a gaussian, and will be easier to create a function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def call_gauss(cen, no, pars):\n",
    "    \n",
    "    #since we can have a lot of parameters, it is good to identify each one\n",
    "    label='g'+str(no)+'_'\n",
    "    gauss = GaussianModel(prefix=label)\n",
    "    #so they would be called g1_sigma for example.\n",
    "    \n",
    "    #now we're going to include this model parameters inside the existing Parameters object\n",
    "    #I'll do it separately, because using guess would use the entire data\n",
    "    pars.update(gauss.make_params())\n",
    "    #and give them initial values\n",
    "    pars[label+'center'].set(cen, min=cen-0.05, max=cen+0.05)\n",
    "    pars[label+'amplitude'].set(-1, max=-0.001)\n",
    "    pars[label+'sigma'].set(0.2, max=0.3)\n",
    "    #now we return this Model object, since we already modified the Parameters object\n",
    "    return gauss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 194,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<lmfit.Model: (((((Model(constant, prefix='cont_') + Model(voigt, prefix='Mg_')) + Model(gaussian, prefix='g0_')) + Model(gaussian, prefix='g1_')) + Model(gaussian, prefix='g2_')) + Model(gaussian, prefix='g3_'))>\n"
     ]
    }
   ],
   "source": [
    "#here we have the approximate lambdas\n",
    "lbd = [5181.2, 5182.7, 5184.2, 5184.6]\n",
    "#so let's sum the models\n",
    "finmod = cont + mg\n",
    "for n, l in enumerate(lbd):\n",
    "    finmod = finmod + call_gauss(l, n, pars)\n",
    "print(finmod)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[Model]]\n",
      "    (((((Model(constant, prefix='cont_') + Model(voigt, prefix='Mg_')) + Model(gaussian, prefix='g0_')) + Model(gaussian, prefix='g1_')) + Model(gaussian, prefix='g2_')) + Model(gaussian, prefix='g3_'))\n",
      "[[Fit Statistics]]\n",
      "    # function evals   = 317\n",
      "    # data points      = 341\n",
      "    # variables        = 17\n",
      "    chi-square         = 0.169\n",
      "    reduced chi-square = 0.001\n",
      "    Akaike info crit   = -2560.957\n",
      "    Bayesian info crit = -2495.815\n",
      "[[Variables]]\n",
      "    cont_c:         1.03933539 +/- 0.003784 (0.36%) (init= 0.7928076)\n",
      "    Mg_sigma:       0.00066759 +/- 3.618121 (541971.16%) (init= 0.2)\n",
      "    Mg_center:      5183.61619 +/- 0.002490 (0.00%) (init= 5183.5)\n",
      "    Mg_amplitude:  -1.20474720 +/- 0.027774 (2.31%) (init= 10.18333)\n",
      "    Mg_gamma:       0.42477708 +/- 0.017812 (4.19%) (init= 0.2)\n",
      "    Mg_fwhm:        0.00240418 +/- 13.02997 (541971.16%)  == '3.6013100*Mg_sigma'\n",
      "    Mg_height:     -719.944618 +/- 3.90e+06 (541973.17%)  == '0.3989423*Mg_amplitude/max(1.e-15, Mg_sigma)'\n",
      "    g0_sigma:       0.08432610 +/- 0.005053 (5.99%) (init= 0.2)\n",
      "    g0_center:      5181.21351 +/- 0.004769 (0.00%) (init= 5181.2)\n",
      "    g0_amplitude:  -0.03739501 +/- 0.002145 (5.74%) (init=-1)\n",
      "    g0_fwhm:        0.19857280 +/- 0.011900 (5.99%)  == '2.3548200*g0_sigma'\n",
      "    g0_height:     -0.17691380 +/- 0.008843 (5.00%)  == '0.3989423*g0_amplitude/max(1.e-15, g0_sigma)'\n",
      "    g1_sigma:       0.08533138 +/- 0.005706 (6.69%) (init= 0.2)\n",
      "    g1_center:      5182.65002 +/- 0.008950 (0.00%) (init= 5182.7)\n",
      "    g1_amplitude:  -0.03474847 +/- 0.002327 (6.70%) (init=-1)\n",
      "    g1_fwhm:        0.20094004 +/- 0.013438 (6.69%)  == '2.3548200*g1_sigma'\n",
      "    g1_height:     -0.16245647 +/- 0.008909 (5.48%)  == '0.3989423*g1_amplitude/max(1.e-15, g1_sigma)'\n",
      "    g2_sigma:       0.07450954 +/- 0.004988 (6.70%) (init= 0.2)\n",
      "    g2_center:      5184.24999 +/- 0.002743 (0.00%) (init= 5184.2)\n",
      "    g2_amplitude:  -0.03396740 +/- 0.002434 (7.17%) (init=-1)\n",
      "    g2_fwhm:        0.17545657 +/- 0.011747 (6.70%)  == '2.3548200*g2_sigma'\n",
      "    g2_height:     -0.18186978 +/- 0.010126 (5.57%)  == '0.3989423*g2_amplitude/max(1.e-15, g2_sigma)'\n",
      "    g3_sigma:       0.06498671 +/- 0.004031 (6.20%) (init= 0.2)\n",
      "    g3_center:      5184.55809 +/- 0.003774 (0.00%) (init= 5184.6)\n",
      "    g3_amplitude:  -0.03240532 +/- 0.001961 (6.05%) (init=-1)\n",
      "    g3_fwhm:        0.15303201 +/- 0.009493 (6.20%)  == '2.3548200*g3_sigma'\n",
      "    g3_height:     -0.19893073 +/- 0.010362 (5.21%)  == '0.3989423*g3_amplitude/max(1.e-15, g3_sigma)'\n",
      "[[Correlations]] (unreported correlations are <  0.100)\n",
      "    C(Mg_amplitude, Mg_gamma)    = -0.961 \n",
      "    C(Mg_sigma, Mg_gamma)        = -0.956 \n",
      "    C(cont_c, Mg_amplitude)      = -0.905 \n",
      "    C(Mg_sigma, Mg_amplitude)    =  0.872 \n",
      "    C(cont_c, Mg_gamma)          =  0.834 \n",
      "    C(cont_c, Mg_sigma)          = -0.747 \n",
      "    C(g2_sigma, g2_amplitude)    = -0.679 \n",
      "    C(g1_sigma, g1_amplitude)    = -0.664 \n",
      "    C(g3_sigma, g3_amplitude)    = -0.639 \n",
      "    C(g0_sigma, g0_amplitude)    = -0.638 \n",
      "    C(Mg_amplitude, g2_amplitude)  = -0.557 \n",
      "    C(Mg_gamma, g2_amplitude)    =  0.519 \n",
      "    C(Mg_gamma, g1_amplitude)    =  0.514 \n",
      "    C(cont_c, g0_amplitude)      = -0.493 \n",
      "    C(Mg_amplitude, g1_amplitude)  = -0.481 \n",
      "    C(Mg_sigma, g1_amplitude)    = -0.475 \n",
      "    C(Mg_gamma, g3_amplitude)    =  0.468 \n",
      "    C(Mg_amplitude, g3_amplitude)  = -0.439 \n",
      "    C(Mg_sigma, g3_amplitude)    = -0.432 \n",
      "    C(Mg_sigma, g2_amplitude)    = -0.411 \n",
      "    C(cont_c, g2_amplitude)      =  0.402 \n",
      "    C(Mg_center, g2_amplitude)   =  0.395 \n",
      "    C(Mg_amplitude, g0_amplitude)  =  0.380 \n",
      "    C(Mg_gamma, g1_sigma)        = -0.335 \n",
      "    C(Mg_gamma, g0_amplitude)    = -0.320 \n",
      "    C(g1_amplitude, g2_amplitude)  =  0.318 \n",
      "    C(Mg_amplitude, g1_sigma)    =  0.316 \n",
      "    C(cont_c, g0_sigma)          =  0.313 \n",
      "    C(g1_amplitude, g3_amplitude)  =  0.311 \n",
      "    C(Mg_sigma, g1_sigma)        =  0.307 \n",
      "    C(Mg_amplitude, g2_sigma)    =  0.307 \n",
      "    C(cont_c, g1_amplitude)      =  0.292 \n",
      "    C(Mg_sigma, g0_amplitude)    =  0.273 \n",
      "    C(cont_c, g3_amplitude)      =  0.272 \n",
      "    C(Mg_gamma, g2_sigma)        = -0.271 \n",
      "    C(Mg_center, g2_sigma)       = -0.264 \n",
      "    C(g2_amplitude, g3_amplitude)  =  0.255 \n",
      "    C(Mg_gamma, g3_sigma)        = -0.249 \n",
      "    C(Mg_amplitude, g0_sigma)    = -0.240 \n",
      "    C(Mg_sigma, g3_sigma)        =  0.234 \n",
      "    C(Mg_amplitude, g3_sigma)    =  0.228 \n",
      "    C(cont_c, g2_sigma)          = -0.218 \n",
      "    C(g1_sigma, g2_amplitude)    = -0.209 \n",
      "    C(Mg_center, Mg_amplitude)   = -0.206 \n",
      "    C(g1_sigma, g3_amplitude)    = -0.203 \n",
      "    C(Mg_center, g3_amplitude)   =  0.203 \n",
      "    C(Mg_gamma, g0_sigma)        =  0.202 \n",
      "    C(Mg_sigma, g2_sigma)        =  0.197 \n",
      "    C(cont_c, g1_sigma)          = -0.191 \n",
      "    C(Mg_center, Mg_gamma)       =  0.188 \n",
      "    C(Mg_sigma, g0_sigma)        = -0.172 \n",
      "    C(g1_amplitude, g2_sigma)    = -0.168 \n",
      "    C(g1_amplitude, g3_sigma)    = -0.168 \n",
      "    C(cont_c, Mg_center)         =  0.147 \n",
      "    C(Mg_sigma, Mg_center)       = -0.143 \n",
      "    C(g0_amplitude, g2_amplitude)  = -0.136 \n",
      "    C(cont_c, g3_sigma)          = -0.136 \n",
      "    C(g2_sigma, g3_center)       =  0.124 \n",
      "    C(g2_center, g3_sigma)       = -0.122 \n",
      "    C(Mg_amplitude, g1_center)   = -0.120 \n",
      "    C(cont_c, g1_center)         =  0.112 \n",
      "    C(g1_sigma, g2_sigma)        =  0.111 \n",
      "    C(g1_sigma, g3_sigma)        =  0.110 \n",
      "    C(Mg_gamma, g1_center)       =  0.109 \n",
      "    C(g2_sigma, g3_sigma)        = -0.101 \n",
      "\n"
     ]
    }
   ],
   "source": [
    "#now we perform the fit\n",
    "result = finmod.fit(spec[1], pars, x=spec[0])\n",
    "print(result.fit_report())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mg 5183.62\n",
      "g0 5181.21\n",
      "g1 5182.65\n",
      "g2 5184.25\n",
      "g3 5184.56\n"
     ]
    },
    {
     "data": {
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VR7du3QQC5PXX98mNN4pYLIVF3S1H5LrrUgU6y/XXD5apU6dWqe9dDfcKmjz5TYFjEh+/\nsczrWq1WqV27tjRo8Kt07mz/OjQ0VB544AF57rnnBJDs7GwXVF3S+afuli1bJkOHDr3kff4zZswo\nDvdXX31VbDZb8fgaDRs2lOzsbImPj5dGjRpJnz59BJBJk6bIf/8r0rPnWQH73UDx8Sfliy/0Yqzy\nvCVLDgtMETghINKwYYHAS1KzZs/i7/X+/ftXqVA/T8O9gqxWq4SH/yxwWHJzyzbGu31Mm9pijFWK\n7laUfv36SadOneSOO+6Q5s2bu6DiSzt58uRF/e+AbNiw4aI2Dz74oISGhkqLFi1k5MiRxff8jho1\nSgDp16+fADJ9+nSxWq3Sr18/adOmjYhI0TCnTQQmSs2aJwVEmjYVef55fYBKuVdhocjcuSIDB0pR\nl0uutGy5XGCg3H33ODHGSHp6unTu3FkASU1N9XTJ5eJouFe5afbcxWKxcOONIUBDvvxyc5nWtc/J\nOhARC4MH25f16tWLDRs2sGbNGqKiopxe7+XUqlWLmJgYAG6//XYCAgL44IMPLmqzYcMGYmNj6dmz\nJ6tWrSqeBPjJJ59k+PDhJCUlkZCQwOjRo4v+X25k586dZGRksHHjRgICjtO1609ER9/AN99AdDQ8\n+SS0agX/939QWOi2w1XVUH4+TJsGkZHC0KGQni40a/YOMTHXs2BBXWARH3wwjX79+hEVFcXKlSvZ\nvn07nTt39nTpruXIbwBXfFT2M3cRkVWrjguIDB/+fZnWmzhxohjzkdSpY5Pzk7Ccn5QDuOipU3f4\n4Ycf5IYbbpDs7Gy57bbbpHbt2sWTe1itVgkJCZGHHnpIJk+eLIAMGTJEwsLCpLCwUPbu3St33HGH\n7Ny5s3h769atK74oPGDAAOncubM89dRT4uPjI6eLTtdXrxa59lopemDqhPz5z1NKfYBMqbLIzRWZ\nOtU+nwOIREaeEBgp8fEJwgXDeIwePVo6depUoQkyKhO0W6bibDYRX98j0rjxkjKtd+ONw8TXN1Nu\nu+23ZVlZWcXhnpKS4uRKHXd+ZMzHHntMhg0bJu+//74A8sEHH0hKSkpxjVca9riwsFDCwsLknnvu\nkXr16snYsWNl8eLFAsjcuXOL29lsIk8+uU7gsMAZefjhby+7TaUcZbOJzJljf8raPpKryPffi4wf\n/3fx8/OTsLAwAWTXrl2eLtUlNNydpEWLlWKxHC7TLX/Nmg0VsE8OcqFJkybJ119/7dwCy8hqtUp8\nfPxFffDGGNmyZYvk5eUVL5s1a9YVt3PjjTdK3bp1BeyTi+fk5EhgYGCJv0oGDhwoDRvGi7//ZjEm\nXxYvduXRKW939qzIHXdI8bMXCxf+djtuYmKi9OzZU/bv3y8//fSTZwt1IQ13Jxky5FsBkbQ0x+Yo\nzcnJEWMeFbA/xlwZ5eTkyMaNGyU9PV2GDx9+0fj2wcHBAlxy3JsLnZ8LEpAdRY+wXnPNNRdNbpCc\nnFz85/GECS8KbJJataxyieE7lLqsnJwcGT9+vMyevVzi4kSMsQ+Tcd99D8sf//hHsVqtkpubKwEB\nARfNd+qtNNyd5OWX7eH+7LMZDrXfuHGjwNfSqFGWiytzjT179lzUv345qampAvbpw86bMmWKAPLO\nO+/IN998I/Hx8dKgQQM5c+aMrFmzRqCNBATkyzXX6MNPynGTJk0SqCGwTozJlujox+SDDz4oPrl4\n/fXXZfXq1QKUeHLbG2m4O0lKymqBw9Knj2OnmzNnfipwTG666biLK/OswsJCiY6Olrfeeqt4WV5e\nXvH98YCEhoYWz/xeUFAgoaGhcvXVnwqIzJjhnvv8VdWWk5MjwcHB0qLFVwIi3bv/q7g7sHnz5tK1\na1fp0qWLTJs27aK/Ir2Zo+HujJmYvFpERFtgMWlp1zjUfunSY0Bdrr++wKV1eZqPjw+bN198i6i/\nvz/z588nJSWFJk2a0L59e0JCQgDw9fUlMTGR3bsnUaNGN8aOtXLTTU0JDg7yRPmqiti4cSNnz7bg\n3Lnh3H8/vPXW02zbNoqkpCRGjBjB1KlTmTRpEsuXLyc0NJRWrVp5uuRKQ+9zL0Xt2rWpUWM9J0+G\ncfBg6e1TUgIAGDDAz8WVVU5NmzZlxIgRdO/evTjYz7v22mvZtm0z5849QUFBWx58cL6HqlRVRWpq\nKjCRoCDhuefsy9q1a8d9991HgwYN6N27NzabjY8//piOHTtisWiknaf/Ew5o2/YIACtWlN52166m\nBAYeQ08gSnr44YeZPHkyEya0JSDgMF9+Ge7pklQlt3TpNuB2xo0z1K1b8vXu3bvj62vvgOjYsaN7\ni6vkNNwd0KNHIHCO5cvliu3y8wvIyoqldesDGOOe2qoSX19f/vKXv/Dii5Po1m0T2dnd2LYt19Nl\nqUps6dJGgC/33nvpH6jg4GBmzpxJmzZtGDp0qHuLq+Q03B3QuXNHIIXFi/Ov2G7OnE1AU3r2tLql\nrqps9GgbAK+9dtTDlajKKj8/n8OH+9OgwSGioy/fbtSoUezYsYNBgwa5r7gqQMPdAXFxccAK0tP9\nyM6+fLuZM+2d8nffrX0ypRkyJAZYyrx5ekFVXdqaNbuBBHr10hOA8tBwd0D79u0xZiU2m4XVqy/f\nbtWqQHx9M+nWrbb7iquimjZtSmjoTxw8WJ9duzxdjaqMvvrqJGDhxhsDPF1KlaTh7oCgoCBGjWoG\n2Ph//+9HCi8xzOHZs+c4ejSGiIj92t/uoIQE+186c+Z4uBBVKS1dGgCc5qabmnm6lCpJw91BM2a8\nSb16+1i+3JdPPvmkxOuzZm0AGnHttf7uL66K6tu3BZDO99979zMBqny2bWtEUNBqwsKCPV1KlaTh\n7iA/Pz/uuqsF0IMff1xZ4vXPPrP3C959d2s3V1Z1de3aFVjMsmWGAs13dYGTJ+HMmcY0bZrh6VKq\nLA33MhgwwAABJCWVvGsmNTWUgIAjtG9fw/2FVVFdunQBFpOb68uaNc7d9tGjR8nI0GCoqlautP+M\ndemid56Vl4Z7GfTuDb6+hRw8GMfRo79dwc/JKeTkyXjattX+9rKoW7cuTZrsAGwsXuy87X766ac0\nbNiQhIQEbDab8zas3Oa77+wPDg4e3NDDlVRdGu5lEBwMCQlZwDBWrkwuXj5r1iGgDgMGZHmstqqq\nY8emBAX96rRwLygoYOLEiQAcOnSoxPg3qmqwn7lvo2/fOE+XUmVpuJfR6NGhQCu+/np38bJZswqA\ns4waVctjdVVV7du3Jz//e1auFHJyKr69mTNnsm/fPqZOnQrAzz//XPGNKrfbvTuEgIBthIfrEBXl\npeFeRrfe6ocxeSxc2BKArCz4+ecmwDfEx1/l0dqqopiYGKzWReTlGZKTS29/JVarlRdeeIG4uDju\nv/9+WrRowZIlS5xSp3Kfs2fhzJn6tGp1FqP9nOWm4V5GdetCTMxGjhy5lo0bM3n3XcjLCyQ8/Atq\n1NCLqWUVExMD2Edkc2RgtsvJzs5m+PDh/Prrrzz55JMYY+jZs2fRqIKqKlm06ABgoVevME+XUqVp\nuJfDhAkGEOLjj/PEE1Z8fX+gTx8N9vKIiooCTtOgQWaFztz/9re/MW/ePF5//XVGjhwJ2H9x7N27\nl+wrjRmhKp1vvtkBwIgRkR6upGrTcC+HMWO68sYbxwkOroHV+iOFhaO44447PF1WlRQSEkLjxo2p\nVSud5GQoz80tBw4c4P333+evf/0rf/vb34r/lLf/VQDp6enOLFm52Jo1OUAOAwe28XQpVZqGezk9\n9FBzMjMbAIOA0wwcONDTJVVZbdu2RWQlp07Btm1lX3/9+vUAjBgx4qLl58Nd75ipWjIyggkJOYiv\nr/a3V4SGewUEBgZy4MABtmzZgp9f9Zx5yRnatm3LyZP2WZlWlnz4t1Tnwz02Nvai5a1btyYwMFDD\nvQqx2WxkZTWiUaMzni6lytNwr6AmTZpw1VV6l0xFREREcOzYCmrXlnL1u2/YsIE2bdoxbVooCQnQ\nty/MmAEWiw/t27cnJSXF6TUr19ixYy8iLYmIuPLEOKp0DoW7MWaQMWabMWaHMWbiJV5vboxJMsas\nN8akGWMGO79U5a3atm0LCDExWeUK9/XrN5KX9yHjx4OPD2Rmwh/+AGPGwKBBN7JixQqOHDni9LqV\n8y1ZsgfwIz4+pLSmqhSlhrsxxgeYClwPRAO3G2N+Py/KP4DPRSQeuA14y9mFKu8VEREBQNOm+0hP\ntw8a5ajTp0+ze/cNZGT05MUXITkZNm2CSZPgf/+DtLSHEBG++eYbF1WvLqWwECZMgLvugu3bHV9v\n1arjAPTu3chFlVUfjpy5JwA7RGSXiOQDs4Bhv2sjQM2iz8OAg84rUXm7du3aYbFY8PdfC0BZelGS\nktKBf9O161Eef9y+zBh46il45hmYO7cOTZs+zQsvvMDZs2edX7y6pKeegpdfhtmzYcSIAgoKHOtm\n2brVfrtUp06hriyvWnAk3JsC+y/4OqNo2YWeBcYYYzKA+cDDTqlOVQtBQUG0bt2arKwfsVjKdlF1\nypQAIID//IcSg7Y98wz07w/Hjv0/9uwJ5LXXXnNq3erSjh+HyZNh+PDTREZOYtMmP4YPn+3Quvv3\nB+Ljk0W9ei4ushpw1gXV24HpIhIODAZmGGNKbNsYM84Yk2qMSc3MzHTSrpU3iImJYdu2tXTsiMP9\n7mfPwrJlUQQEfE3PnvVLvO7jA598AqGhPtSq9RVTp75NXl6ekytXv/fxx5CXBwsXXsuePa8RFHSQ\n+fPDSHbgjT1+vA5hYZk6uqoTOBLuB4AL57kKL1p2obuBzwFEJBkIBEr87hWRaSLSRUS61K9f8odR\nVV/t27dn+/btJCRYWbUKrA4M4/3VV1BYGETHjqsuOwZJ48bw6qtw6lQUR48OYo7O6edyn34KQUGb\naNDgCJs2/cIDD9QBBjB79pUHcSssLCQnJ5wmTfQ2SGdwJNzXABHGmFbGGH/sF0zn/q7NPmAAgDEm\nCnu466m5clj79u2xWq00arST7Gy40q3p+/bt4+DBg7zxRhawk9tuu/LIgXfeCYmJgjGv8OWXSc4t\nXF3kxAlITRVycr7g3nvvJTw8nDvuCAR8mTv3yn817diRATSndWsdg98ZSg13ESkEHgIWAluw3xWz\n2RjzL2PM0KJmjwH3GmM2Ap8CfxQRvVFVOWzQoEHUrl2b118fBVy+a+bpp5+mRYsWNG3anTVrQvD3\n/5S77x57xW1bLDB1qgHq8O23HXUCDxdavBhEDLCIHj16ABAbC4GBOezaFU5W1uXnPFi+/BBgoWPH\nQPcU6+Uc6nMXkfkiEikibUTk30XLnhGRuUWfp4tIoojEikiciPzgyqKV96lVqxYTJ04kO3sjcIR5\n806UaJOcnMykSZO49dZbueaajwELzz0XSVhY6aMHxsbC1VfvITd3LPPm/eL8A1AA/PQT+PvnYkwq\nCQkJgP3aR2zsGUR6Fz9NfCmpqfbg79atjltq9Xb6hKqqNMaPH09KSgoWy2p+/rnkjNlfffUV/v7+\nvPfe++zd25e+feHxx0c5vP1XXqkBGJ5/3td5RauLpKRAaGg6HTtGERLy24NIAwf6AxGsWLH7sutu\n2mTvtklMbODqMqsFDXdVaVgsFhISEuja9SxZWQ3Zvfviq6qLFy+mR48e/PJLCNu32x+QKYuuXRtS\no8Z/SUmJKtcAZerKcnIgLQ0KClbSvn37i167/nr7X1fLlpWcXP683bv98PU9Tu3aGkvOoP+LqtIZ\nPtx+xvfxx789C3fixAnWr19P//79mT4datSAm28u23aNMfTosRTI5+WXnVevslu/3n6XU1bWohLj\nLcXHG4wpJD096LLrHztWhzp1jrm6zGpDw11VOqNGxQCH+O673OJlycnJiAjdu/fjs89g5EgILcdD\njD17tkXkfWbMEPbvL729ctzq1cWfFU3C8pugIKhT5yCHDl36zqasrCzy85vTrJk+h+AsGu6q0mnV\nqiVBQT+zcWMTzj9ztG7dOowxZGR0ISur7F0y53Xt2hV4BZtN0AdWnWvjRggLywEOX3Kk1MjILAoK\nYjlwoOToJKmpvwKNiYrS6yHOouGuKh1jDPHxOykoCGbRIvsdtevXryciIoLp04No3do+rG95JCYm\nYsx+OnTzMc9mAAAcUUlEQVT4hffeg2PaC+A0v/wCdesewMfHp2ikz4vZp6KswzffbCrx2tKl9sDv\n1q22q8usNjTcVaV02231gJO88459/tN169bRsuVwli2DBx6w37teHnXq1KFDhw4EBU0hJwemTHFe\nzdWZ1Wp/8MzHZwutW7cmICCgRJubbrJ3ySxYUPI36tq19vc5MVGfXHcWDXdVKQ0a1B/4gAULgklN\nPcnevXvZu3ccYWEw9srPLJWqd+/ebNw4iyFD8nnzTftdHqpiduyA3Fw4dy7lspPXxMf7Y0we69f7\nlHht61YfoJDoaO2WcRYNd1UptW3blqZNPwMKuOuufGAC27a14R//gNoV/Mv9j3/8I/n5+ezZ8xgn\nT8KsWc6ouHr7pei5sCNHfixxMfU8Pz9o1OggBw+Gc+7cuYteO3iwFqGhR7jECb8qJw13VSkZYxgz\nZgAi40hPrw+8yNChwiOPVHzbnTt35t1332XfvhlYLFt4800bOlhGxWzZYv+3sDDtitNOduvmg0gc\nixb9NsZPTk4O5861oGnTyw9NoMpOw11VWuPGjUPkY6AD1133PF9+aXDWPORjx45l5sxPsNneYN06\nywW38any2LoVGjQ4B+RcMdyHDWsCBPPJJ6nFyzZt2g60JTpaf8M6k4a7qrRat27NG2+8wZgxnXjp\npSH4Ork7duDAgYSEzMHPL4c333TutqubrVuhVq3DAFcM9x497G9iUtJvs2ItXXoE8KVLlxourbG6\n0XBXldpDDz3EjBkziI2Ndfq2AwICGDiwO8HBX/D553D0qNN3US2IwLZtYLWm06pVK2pf4aJIRAQE\nBORx/HgrTpywDw6XnGwfZmLQIJ1+yZk03FW1Fh8fz6lTL5CfDx9+6OlqqqYDB+yzYh0+/DN9+vS5\nYluLBaKisoEENmzYAMCmTcEYc4K4uJArrqvKRsNdVWtxcXHAFmJjs/jvf9ELq+Wwdav937NnU+nd\nu3ep7a+7LhCIZ9ky+4oZGeGEhW3VqfWcTMNdVWv2cIcOHdby66/2IWtV2ZwPd9ha6pk7wMiRwYCF\nhQvtk2mfPduC5s0Pu7LEaknDXVVr4eHh1KlTh8zMt7FYcvn3vzM8XVKVs20b+Phk0759fVq3bl1q\n+06dICDgJJs2teHjjwsACz176gUPZ9NwV9WaMYY//OEPLFw4G5vtCxYsqElubunrqd9s3JiL1ZrO\nrbc6NnGKxQKdO2/mzJnrePRRP2Ad/fvXdW2R1ZCGu6r2nn32Wdq1awd8hNVak5kzz3i6pCpl82Yr\nsJWhQ4eW2va8hx46DRzAxycP+GfRaJ3KmTTcVbUXFhZGeno6ycnPAxm8+aaGu6Oys+HEiWB8fXcQ\nHR3t8Hq9enUEYrFa61O37gpatGjhuiKrKQ13pbBP8RcX1wGYwcaNjTh0yNMVVQ2//mr/t2XLfHzL\n8JRZeHg49eoZ4AwdO3bE6K0yTqfhrlSRwMBAGjf+CRELX3zh6WqqhvR0+72jnTpdfvq8SzHGMHXq\nVPz8/MrUnaMcp+Gu1AViYgyBgbs03B2UkpIFFHL11Y3LvO6oUaPIy8vjEWeMBqdK0HBX6gIRERGI\nfM6yZaJdMw7YsCEX2EnHjpcfT+ZKjDHaJeMiGu5KXSAyMpK8vBmIGL780kZWVvUZhnb+/Pm88847\nWK1Wh9fZudMP2OLQ/e3KvTTclbqAfUTDdJo1O8MTT6wjKiqK/Px8T5flctOnT2fIkCHcf//93Hzz\nzQ4FfGEhHDlSE4vlV5o0aeKGKlVZaLgrdYHevXsTEhLC/v2vk53diYMHrXz33XeeLsvl5s6dS6tW\nrXj11Vf55ptveOGFF0pdZ9cusNl8adDgBJbyTmqrXEbfEaUuUKNGjaLBr2YDFsLCxjJ9+nQPV+V6\nKSkp9OzZk8cee4x+/frx+eefl7rO+dmXWrbUSWgrIw13pX7n2WefpW/fBkREFFKjxl2sWLEC8eLh\nIg8cOMDBgwdJSEgAoE+fPmzatKnU6w3nw719e53UujLScFfqd7p27UpS0mJGjfLl8OEITpwQDh48\n6OmyXGZ10RyD58O9R48eiAgppQyRuXFjHnCAdu3Kfhukcj0Nd6Uu48YbQcQCDCItLc3T5bjM6tWr\n8fPzKx7+uFu3bhhjSE5OvuJ6GzfmA1uIiopyQ5WqrDTclbqMrl2hXj0bcINXh3tKSgqxsbHMmRNI\nmzaQkBBGy5YPsmTJksuuIwK7dwcAW4mJiXFbrcpxGu5KXYbFAjfcYMGYIWzYsMnT5biE1WolNTWV\nxo3/wJgxUKcO+PvD/v2vs2xZNufOnbvkert3Q26uP/7+W2jevLmbq1aOcCjcjTGDjDHbjDE7jDET\nL9NmlDEm3Riz2RjzP+eWqZRn3HADiISRkuLj6VJcYtu2bZw5k8vq1XcREQFJSfDTT1CzppXCwiks\nXPjDJddbt87+b5s2Z/Q2yEqq1HfFGOMDTAWuB6KB240x0b9rEwE8ASSKSAzwVxfUqpTbDRwIFksh\ne/a0Jy8vz9PlON38+fOBP3LkSE1efRVCQqBBA/jXvwzQnREjPmDYsGGcOHHiovXWrhWggM6dAzxR\ntnKAI79yE4AdIrJLRPKBWcCw37W5F5gqIicBRETnzFJeoWZNiIk5hshgtpy/989LiAjTp39EUNAE\n4uNh8ODfXhs3LoDwcCstW05h3rx5PPnkkxetu3TpGWAziYmd3Vu0cpgj4d4U2H/B1xlFyy4UCUQa\nY1YYY1YZYwY5q0ClPO2GGwCiWbRol6dLcaoNGzaweXNtcnLa8PDDcOH4XX5+8Je/+LBnTytuvfXf\nTJs2jZ07dwJgs8G6dT4Ys56RI0d6qHpVGmd1lvkCEUBf4HbgPWNMrd83MsaMM8akGmNSMzMznbRr\npVzrrrvqATBvnneNXvjxxx9jsdxFcLBw660lX7/7bggKApEHEBFmz54NwNq1BeTmBhMbe5J69eq5\nuWrlKEfC/QDQ7IKvw4uWXSgDmCsiBSKyG/gVe9hfRESmiUgXEelSv3798taslFu1a+dLUNA+1q/3\nnu/ZwsJCZs78Ah+fW7npJkONGiXb1KkDY8bAnDmhxMdfUxzuU6bYbwt99NF4d5asysiRcF8DRBhj\nWhlj/IHbgLm/azMH+1k7xph62LtpvOtvWFWtdehwhKyseA4cOObpUpxi1apVZGa2p6AghNtvv3y7\nhx+GnBxo3PgfrFu3jl27djFvXj5+frsZPbqP+wpWZVZquItIIfAQsBDYAnwuIpuNMf8yxpyfH2sh\ncNwYkw4kAX8XkeOuKlopd7v55ppAMO+95x33uy9atAgYSnCw0L//5dt16AB9+8KGDYmAD//85/uc\nPNmVHj0O6y2QlZzx1IBIXbp0kdTUVI/sW6myOn68kHr1IC5uIevXD/F0ORXWo0dP1q37iiFDGvHV\nV1du+9139qEYwsPfJCMjG5hIUtI++vbVh5c8wRizVkS6lNZOf/Uq5YC6dX2pXXsHW7b8/kaxqufU\nqVOkpOSSn9+o6E6gKxsyBG6+GTIyHgImEh6+RIO9CtBwV8pB3bufIS+vA+vX7/F0KRWSlJSEyGCM\nEYY48EeIMTB9Ojz/PDz+OOzc2dfVJSon0HBXykFjxjQEfHj33V89XUqFLFq0CItlGF27Cg0bOrZO\nSAg88QS89JJ97BlV+Wm4K+WgkSObYUw2ixZ5upKKWbBgDTZbZ264QX/8vZm+u0o5yN/fEB6+gz17\n2jg0gXRltHv3bvbsaQlYGDjQ09UoV9JwV6oM+va1YrO1Yd68zZ4upVzst0AOICTESpdS77dQVZmG\nu1JlcPfdLQD4+OP9pbSsnBYtWoSPzyD697fgq1OfejV9e5Uqg9696+Hjc4KVK6vmj86yZfuxWlsy\nYICnK1GupmfuSpWBMdCqVQaHDrUjJyfH0+WUyZEjRzhyxD4lnoa799NwV6qM+vQxQEu+/z7d06WU\nyfr164EB1KmTR3R0qc1VFafhrlQZ3XhjTQC+//7S84tWVqmpa4G+9O9vLhq7XXmnqtlxqJQHXXdd\nE+Akq1cHerqUMvn55/1AE+2SqSb0zF2pMgoM9CM4eD07dlSdcWZsNlvxReCrr/ZwMcotNNyVKofm\nzfeQnd2EQ4c8XYlj0tLSOHeuEyEhuURFeboa5Q4a7kqVQ3x8FgBLltg8XIljkpKSgKvp2VPQYdir\nB32blSqHXr2CgTPMn5/t6VIcMnv2ciCCa68N8nQpyk003JUqh9jYGGAFP/9c+W87OXjwIMnJ9v72\n3r09XIxyGw13pcqhffv2wFL27w/lxAlPV3Nlc+bMAa6mRg0b8TqndbWh4a5UOdSsWZOGDe1zwK9a\n5eFiSrF27Vp8ffvRs6eOJ1OdaLgrVU5xcQVAIStXerqSK1u/fg+FhVHaJVPNaLgrVU7durUHNrB4\nca6nS7ksq9XK5s21AIve317NaLgrVU5jx47FmFWkphoKCz1dzaXt3LmT/Pwu+PjYSEjwdDXKnTTc\nlSqnFi1a0L27UFAQwMqVZzxdziX98ssvQHfatcuhRg1PV6PcScNdqQp46ql+APznPykeruTSdu7c\nA3QlMVGvpFY3+o4rVQGDB7fH3z+TpKQ8T5dySRs2FAAh9Onj6UqUu+mZu1IVYAxERh7j9Olojh07\n5ulySkhPtw9P3L27hwtRbqfhrlQF9e8fBLTim29We7qUEvbvb4K//2lat/Z0JcrdNNyVqqBbbgkH\n4MsvD3q4kpJOnYqiceN9OjlHNaThrlQFde3qizH5bNhQuW5HycjIxmZrR2TkSU+XojxAw12pCgoI\ngEaNMjhypDVWq9XT5RRbsOA4AF26VNKb8JVLabgr5QRxcWex2eJJT9/p6VKK/fxzLmCjX78QT5ei\nPEDDXSknGDgwBAhgzpx9ni6l2Nq1vkA6XbtGeroU5QEa7ko5wciR9vlUk5LyPVyJnQjs3t2QGjXS\nqFWrlqfLUR6g4a6UEzRr5o+f3362bg3zdCkA7NgBeXkhNG9+2NOlKA9xKNyNMYOMMduMMTuMMROv\n0O5mY4wYY7o4r0SlqobGjfdw9GgbT5cBQHKyABAfXzmfnFWuV2q4G2N8gKnA9UA0cLsxJvoS7UKB\nR4DKOciGUi4WHX0Gq7URv/6a4+lSWLToDHCGXr3qeLoU5SGOnLknADtEZJeI5AOzgGGXaPcc8BJQ\neQe3VsqFevf2B2DOHM93hSxfng+sJjFRxx2orhwJ96bA/gu+zihaVswY0wloJiLzrrQhY8w4Y0yq\nMSY1MzOzzMUqVZldf30TIIclSzx7fnPuHOzdW4saNdLo0KGDR2tRnlPhC6rGGAvwOvBYaW1FZJqI\ndBGRLvXr16/orpWqVKKj2wLrSEvz7JOqa9cKIr506lSAxaL3TFRXjrzzB4BmF3wdXrTsvFCgPbDE\nGLMH6A7M1Yuqqrrx9/enTp1fOXSoMXkevI65YMEJAG68sYHnilAe50i4rwEijDGtjDH+wG3A3PMv\nishpEaknIi1FpCWwChgqIqkuqVipSiwy8hg2mz8bN3quhsWLc4BdDBigXTLVWanhLiKFwEPAQmAL\n8LmIbDbG/MsYM9TVBSpVlXTvbh9+cdmyAo/VsHlzKBbLatq3b++xGpTnOTQTk4jMB+b/btkzl2nb\nt+JlKVU1de/eDNjPjz+G8Nhjtd2+/4wMyM4Oo1mzDAICAty+f1V56NUWpZwoOjoaWMXatX4e2X9y\nsg3QkSCVhrtSTtW2bVtgFZmZIRz2wO3uCxeeBnK57rqG7t+5qlQ03JVyoqCgIBo23A1Aigee1V6+\nvABYR/fundy/c1WpaLgr5WTR0XkYU0Bysnv3W1AAO3bUxscntah7SFVnGu5KOVlUVEssljRWrRK3\n7jctDaxWP1q1Ooqfn2f6/FXloeGulJNFRkZitS5n9WoodON1zZUr7VP8JSb6uG+nqtLScFfKySIj\nI4FV5OQYfvnFfftduPAUcIjrroty305VpaXhrpSTxcXFYX9QG1atct9+V6/2AVbRs2cP9+1UVVoa\n7ko5WePGjWnYMJfAwNNuC/fjxyEzsxahoek0b97cPTtVlZqGu1Iu0LlzJ/z917ot3M/fdtm+fTbG\nGPfsVFVqGu5KuUCnTp04c+ZHfv3VflbtaitWWAEriYmBrt+ZqhI03JVygUGDBiGyEnDPw0xJSTnA\nL3TqFOn6nakqQcNdKRdITExk7NiOgJVnn13g0n1ZrbBhQwCQTExMjEv3paoODXelXOSdd16jbt2D\nrFnjy9q1a122n/R0yMnxw5hVtGvXzmX7UVWLhrtSLuLn58ewYQ2Abrz00qsu28/5YQ5atz6iw/yq\nYhruSrlQnz4BQE2+/XY7ubmumTg7ORkslhPEx9d0yfZV1aThrpQLde9u/zc3N5bly5e7ZB8rVtiw\n2ZbToYPOvKR+o+GulAtFREDt2oLFksiCBc6/sHr8OGzfbgGSdVo9dRENd6VcyBj7vKqBgf1YtmyZ\n07f/20NSGu7qYhruSrlYjx5w7lwLNmzYTX5+vlO3nZwMxlgJDNxE69atnbptVbVpuCvlYvZ+dwsF\nBXH84uRhIpOTwd9/C/37d8PX16H57lU1oeGulIslJIAxAnQnNTXVadu1WiElxUZe3hKuu+46p21X\neQcNd6VcLCwMoqLAz+9qpz7MtGkTnD1rv5iq4a5+T8NdKTfo0cMg0o3Nm9Odts3zd1bWr7+jaIIQ\npX6j4a6UG3TvDoWFYWzalIeIc+ZWXbpU8PE5SL9+rXSYX1WChrtSbnD+YaasrCiOHj1a4e2JQFKS\nFat1Mb17X13h7Snvo+GulBtER0ONGoVAT9LTK941s2MHZGb6Akvp2bNnhbenvI+Gu1JuYLFA9+6F\nQF+nhPvSpec/W0ZUlE6IrUrScFfKTQYNCgCuYs2aAxXe1tKlEBBwmlat8gkM1NmXVEka7kq5yYAB\n9oueq1cHV3hbS5dCYOBqoqP1rF1dmj7SppSbxMaCv/9Zdu9uWaHt7Nlj//DxWcBVV13ljNKUF9Iz\nd6XcxMcHIiIOkpvbneMVmDV70SL7v1brAu1vV5el4a6UG/XqlQ+0ISlpV7m38cMPULfuOWCrjgSp\nLsuhcDfGDDLGbDPG7DDGTLzE648aY9KNMWnGmJ+MMS2cX6pSVd9NN9UC4Ntvz5VrfasVfvwRmjTZ\nhL+/P3Fxcc4sT3mRUsPdGOMDTAWuB6KB240x0b9rth7oIiIdgS+Al51dqFLe4JprGmPMAVaurFWu\n9desgVOnoLBwAXFxcTpnqrosR87cE4AdIrJLRPKBWcCwCxuISJKInD8VWQWEO7dMpbyDj4+FunVT\n2L27LeUZ2v2HH+wjTO7d+yHdunVzfoHKazgS7k2B/Rd8nVG07HLuBpw/n5hSXqJ9+z1YrcGUZ2Km\nH36Atm2zOHduH71793Z+ccprOPWCqjFmDNAFeOUyr48zxqQaY1IzMzOduWulqoy+fW1ALu+9d5Ax\nY8bw9ttvO7TekSP2yTlgPg0bNmTo0KGuLFNVcY6E+wGg2QVfhxctu4gx5hrgKWCoiORdakMiMk1E\nuohIl/r165enXqWqvLi4CGAxn32Ww8yZM3nggQdw5GTn66/BZoPt21/gnnvuwd/f3/XFqirLkXBf\nA0QYY1oZY/yB24C5FzYwxsQD72IP9ooPeaeUF+vVqxd+fouANvTr9yAAP//8c6nrzZ4NDRqcAH7h\nzjvvdG2RqsorNdxFpBB4CFgIbAE+F5HNxph/GWPO/134ChACzDbGbDDGzL3M5pSq9urWrctPPz2I\nMTbi4l4hJCSEpKSkK66TmQlLloDF8jWdO3emXbt27ilWVVkODT8gIvOB+b9b9swFn1/j5LqU8mpX\nX92WQYNg9uwgevXqU2q4z5lj75I5fPgN/v73P7ipSlWV6ROqSnnIXXdBRgY0azaGLVu2cPjw4cu2\n/d//oE6d40Aat912m/uKVFWWhrtSHjJsmH3y7IwM+x++l+t337bN3iVjzHT69+9HkyZN3Filqqo0\n3JXykMBAuPVWWLKkLiEhLVm8ePEl2731Fvj42Dh+/BVGjx7t5ipVVaXhrpQHPfII5OQYmjd/hZkz\nZ7Jjx46LXj96FN57DyIjU/H3P8mIESM8VKmqajTclfKg6Gi46SbYv38EPj5NGTJkCPv27St+/d//\nhtxcYffuPzNq1Chq1SrfmDSq+tFwV8rDXnwRcnMtdOmygsOHj5CYmMjMmTO5995pTJliReRt8vPT\nePrppz1dqqpCNNyV8rDISHj2WVi8uB4jR27DZjOMGfMC778/hMDA44wff4r58+cTGRnp6VJVFaLT\n7ClVCTzxBOzcCR9+2JDatfdisUCdOjYWL/ahQ4cnPV2eqoI03JWqBIyB99+HIUNg/nxDeDg88IAP\nDRp4ujJVVWm4K1VJGAMjRtg/lKoo7XNXSikvpOGulFJeSMNdKaW8kIa7Ukp5IQ13pZTyQhruSinl\nhTTclVLKC2m4K6WUFzIi4pkdG5MJ7PXIzi+tHnDM00V4SHU99up63FB9j90bjruFiNQvrZHHwr2y\nMcakikgXT9fhCdX12KvrcUP1PfbqdNzaLaOUUl5Iw10ppbyQhvtvpnm6AA+qrsdeXY8bqu+xV5vj\n1j53pZTyQnrmrpRSXsjrw90Ys8cY84sxZoMxJrVo2S3GmM3GGJsxpssFbf2MMR8Vtd9ijHnigtc+\nNMYcNcZs8sRxlJUzjtsY08wYk2SMSS9a7xFPHY+jnHTcgcaY1caYjUXr/dNTx1MWzvpeL3rdxxiz\n3hjznbuPo6yc+DNeYjtVmoh49QewB6j3u2VRQDtgCdDlguV3ALOKPq9RtG7Loq97A52ATZ4+Jncd\nN9AY6FS0PBT4FYj29LG54bgNEFK03A9IAbp7+tjccewXvP4o8D/gO08fl7uO+1Lbqcof1XImJhHZ\nAmCMKfESEGyM8QWCgHwgq2idpcaYlu6r0vnKetwicgI4VLTuGWPMFqApkO62op2gHMctQHZRG7+i\njyp5cao83+vGmHBgCPBv7CFf5ZTnuL2N13fLYH8zfzDGrDXGjCul7RfAWeyBtg94tSjgqiKnHnfR\nL7Z47GexlZlTjruoW2IDcBRYJCKV/bjBee/5/wGPAzaXVepczjrusmyn0qsOZ+69ROSAMaYBsMgY\ns1VEll6mbQJgBZoAtYFlxpgfRWSXu4p1IqcdtzEmBPgS+KuIVPazHKcct4hYgThjTC3ga2NMexGp\n7NdbKnzsQDRwVETWGmP6uqXqinPW93pZtlPpef2Zu4gcKPr3KPA19jf3cu4AvheRgqL2K4Aq+aiy\ns47bGOOHPdhnishXrq264pz9fovIKSAJGOSaip3HSceeCAw1xuwBZgH9jTGfuLTwCnLWe17G7VR6\nXh3uxphgY0zo+c+Ba4ErnX3tA/pf0L47sNXVdTqbs47b2DssPwC2iMjrrq264px43PWLztgxxgQB\nA6nk3wfOOnYReUJEwkWkJXAbsFhExri0+Apw4nte1u1Ufp6+ouvKD6A1sLHoYzPwVNHym4AMIA84\nAiwsWh4CzC5qmw78/YJtfYq9n66gaN27PX18rj5uoBf2fsg0YEPRx2BPH58bjrsjsL7ouDcBz3j6\n2Nz5vX7BNvtSye+WceJ7fsntVOUPfUJVKaW8kFd3yyilVHWl4a6UUl5Iw10ppbyQhrtSSnkhDXel\nlPJCGu5KKeWFNNyVUsoLabgrpZQX+v8n6tTsUrvytgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fbf34bd8278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#let's check the resulting fit\n",
    "plt.plot(spec[0], spec[1], 'k-')\n",
    "plt.plot(spec[0], result.best_fit, 'b-')\n",
    "\n",
    "#and extract the fitted lambdas\n",
    "for p in result.params:\n",
    "    if 'center' in p:\n",
    "        print('%s %.2f'%(p.split('_')[0], result.params[p].value))"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}