{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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": 3,
   "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": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-8, 11, -10, 60]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1109a01d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#and generate some fake data\n",
    "Xf = np.linspace(-7, 10, 100)\n",
    "Yf = parabola(Xf, 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": 7,
   "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": 8,
   "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": 9,
   "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": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[Model]]\n",
      "    Model(parabola)\n",
      "[[Fit Statistics]]\n",
      "    # function evals   = 15\n",
      "    # data points      = 100\n",
      "    # variables        = 3\n",
      "    chi-square         = 1047.238\n",
      "    reduced chi-square = 10.796\n",
      "    Akaike info crit   = 240.874\n",
      "    Bayesian info crit = 248.690\n",
      "[[Variables]]\n",
      "    a0:   2.54746403 +/- 0.478801 (18.80%) (init= 0)\n",
      "    a1:  -0.01636483 +/- 0.080041 (489.11%) (init= 0)\n",
      "    a2:   0.51167689 +/- 0.014953 (2.92%) (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": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-8, 11, -10, 60]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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IDANWA4PisS+zk5uSzl0F9OmzhokT4dlnr6V9+5GsW9cS1ci53FA15FSfszTS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\nYr1VxAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117ce9410>"
      ]
     },
     "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": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x118369210>]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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AdO/eHYWFhUZtxzN368VwJ6pD1eiGLVu2xM2bN3WuxvwuXrwIb29vw2dPT0/D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\nB3uArAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110963910>"
      ]
     },
     "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": 13,
   "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": 14,
   "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": 15,
   "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": 16,
   "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": 17,
   "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   = 297\n",
      "    # data points      = 341\n",
      "    # variables        = 17\n",
      "    chi-square         = 0.169\n",
      "    reduced chi-square = 0.001\n",
      "    Akaike info crit   = -2560.961\n",
      "    Bayesian info crit = -2495.819\n",
      "[[Variables]]\n",
      "    cont_c:         1.03932300 +/- 0.003784 (0.36%) (init= 0.7928076)\n",
      "    Mg_amplitude:  -1.20464721 +/- 0.027784 (2.31%) (init= 10.18333)\n",
      "    Mg_sigma:       0.00066706 +/- 3.622285 (543020.52%) (init= 0.2)\n",
      "    Mg_center:      5183.61619 +/- 0.002489 (0.00%) (init= 5183.5)\n",
      "    Mg_gamma:       0.42473265 +/- 0.017813 (4.19%) (init= 0.2)\n",
      "    Mg_fwhm:        0.00240229 +/- 13.04497 (543020.52%)  == '3.6013100*Mg_sigma'\n",
      "    Mg_height:     -720.449419 +/- 3.91e+06 (543022.53%)  == '0.3989423*Mg_amplitude/max(1.e-15, Mg_sigma)'\n",
      "    g0_sigma:       0.08432131 +/- 0.005053 (5.99%) (init= 0.2)\n",
      "    g0_center:      5181.21352 +/- 0.004771 (0.00%) (init= 5181.2)\n",
      "    g0_amplitude:  -0.03739167 +/- 0.002145 (5.74%) (init=-1)\n",
      "    g0_fwhm:        0.19856152 +/- 0.011900 (5.99%)  == '2.3548200*g0_sigma'\n",
      "    g0_height:     -0.17690805 +/- 0.008844 (5.00%)  == '0.3989423*g0_amplitude/max(1.e-15, g0_sigma)'\n",
      "    g1_sigma:       0.08534003 +/- 0.005706 (6.69%) (init= 0.2)\n",
      "    g1_center:      5182.65022 +/- 0.005175 (0.00%) (init= 5182.7)\n",
      "    g1_amplitude:  -0.03475291 +/- 0.002326 (6.70%) (init=-1)\n",
      "    g1_fwhm:        0.20096042 +/- 0.013438 (6.69%)  == '2.3548200*g1_sigma'\n",
      "    g1_height:     -0.16246078 +/- 0.008907 (5.48%)  == '0.3989423*g1_amplitude/max(1.e-15, g1_sigma)'\n",
      "    g2_sigma:       0.07452672 +/- 0.004988 (6.69%) (init= 0.2)\n",
      "    g2_center:      5184.24999 +/- 0.004427 (0.00%) (init= 5184.2)\n",
      "    g2_amplitude:  -0.03397825 +/- 0.002432 (7.16%) (init=-1)\n",
      "    g2_fwhm:        0.17549701 +/- 0.011747 (6.69%)  == '2.3548200*g2_sigma'\n",
      "    g2_height:     -0.18188597 +/- 0.010123 (5.57%)  == '0.3989423*g2_amplitude/max(1.e-15, g2_sigma)'\n",
      "    g3_sigma:       0.06498473 +/- 0.004030 (6.20%) (init= 0.2)\n",
      "    g3_center:      5184.55809 +/- 0.003775 (0.00%) (init= 5184.6)\n",
      "    g3_amplitude:  -0.03240719 +/- 0.001961 (6.05%) (init=-1)\n",
      "    g3_fwhm:        0.15302735 +/- 0.009491 (6.20%)  == '2.3548200*g3_sigma'\n",
      "    g3_height:     -0.19894829 +/- 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_amplitude, Mg_sigma)    =  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)    =  0.469 \n",
      "    C(Mg_amplitude, g3_amplitude)  = -0.440 \n",
      "    C(Mg_sigma, g3_amplitude)    = -0.433 \n",
      "    C(Mg_sigma, g2_amplitude)    = -0.410 \n",
      "    C(cont_c, g2_amplitude)      =  0.401 \n",
      "    C(Mg_center, g2_amplitude)   =  0.395 \n",
      "    C(Mg_amplitude, g0_amplitude)  =  0.379 \n",
      "    C(Mg_gamma, g1_sigma)        = -0.336 \n",
      "    C(Mg_gamma, g0_amplitude)    = -0.319 \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)    =  0.306 \n",
      "    C(cont_c, g1_amplitude)      =  0.292 \n",
      "    C(Mg_sigma, g0_amplitude)    =  0.272 \n",
      "    C(cont_c, g3_amplitude)      =  0.272 \n",
      "    C(Mg_gamma, g2_sigma)        = -0.270 \n",
      "    C(Mg_center, g2_sigma)       = -0.263 \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_amplitude, Mg_center)   = -0.204 \n",
      "    C(g1_sigma, g3_amplitude)    = -0.203 \n",
      "    C(Mg_center, g3_amplitude)   =  0.202 \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)       =  0.186 \n",
      "    C(Mg_sigma, g0_sigma)        = -0.172 \n",
      "    C(g1_amplitude, g3_sigma)    = -0.168 \n",
      "    C(g1_amplitude, g2_sigma)    = -0.168 \n",
      "    C(cont_c, Mg_center)         =  0.146 \n",
      "    C(Mg_sigma, Mg_center)       = -0.142 \n",
      "    C(cont_c, g3_sigma)          = -0.136 \n",
      "    C(g0_amplitude, g2_amplitude)  = -0.135 \n",
      "    C(g2_sigma, g3_center)       =  0.124 \n",
      "    C(g2_center, g3_sigma)       = -0.122 \n",
      "    C(Mg_amplitude, g1_center)   =  0.121 \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)       = -0.110 \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": 18,
   "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": {
      "image/png": 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WW67dA5iYCGPGgDHP8dVXG+0VWV1BYSEsXCiIzOH2228mLi6OW24xgIUVKwKv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\nuWZf7z5v3kLc3AYzbJg7+gA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dHcBJdL9rn9q677Vmv7XPXSmlXJAeuSullAty+eJujDlg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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1181b28d0>"
      ]
     },
     "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))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "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": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}