{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Step 3: Fitting Peaks\n",
    "Notebook Code: [![License: MIT](https://img.shields.io/badge/License-GPLv3-blue.svg)](https://www.gnu.org/licenses/gpl-3.0) Notebook Prose: [![License: CC BY 4.0](https://img.shields.io/badge/License-CC_BY_4.0-lightgrey.svg)](https://creativecommons.org/licenses/by/4.0/)\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "vscode": {
     "languageId": "plaintext"
    }
   },
   "source": [
    "The meat of `hplc-py` is its ability to take in windowed regions of a chromatogram \n",
    "and fit a number of peaks such that the chromatogram in that region is well reconstructed. \n",
    "As is the theme in these notebooks, it's easier to look at a chromatogram and see \n",
    "what the reconstituted signals should like than to do it quantitatively. \n",
    "\n",
    "Ideally, one would have a physical model that would describe how an analyte interacts \n",
    "with the stationary phase of the chromatography column and a generative model that \n",
    "would capture the statistical distribution of the measurements as a function of time.\n",
    "However, having this in chromatography is exceedingly rare, so we are left with \n",
    "phenomenological descriptions of peak shape that we relate to chemical species and \n",
    "concentrations through calibration curves and control experiments. This is what \n",
    "`hplc-py` excels at–phenomenological quantitative description of signals in a chromatogram.\n",
    "It is important to note that `hplc-py` does **not** provide a model of the components \n",
    "of the chromatogram but rather fits the parameters of a minimal number of convolved \n",
    "signals that can capture the observed data in the chromatogram. In this notebook,\n",
    "we outline how this fitting procedure is executed and how the total chromatographic \n",
    "signal is reconstructed. \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "vscode": {
     "languageId": "plaintext"
    }
   },
   "source": [
    "## The Skew-Normal Distribution \n",
    "\n",
    "In `hplc-py`, we consider that each detected maximum in a chromatogram results from \n",
    "a single compound $i$ whose time-dependent signal intensity $S_i$ can be phenomenologically \n",
    "well described by an amplitude-weighted [skew normal](https://en.wikipedia.org/wiki/Skew_normal_distribution) distribution. Mathematically, this is defined as\n",
    "\n",
    "$$\n",
    "S_i(t) = \\frac{A}{\\sqrt{2\\pi\\sigma_i^2}} \\exp\\left[\\frac{(t - \\tau_i)^2}{2\\sigma_i^2}\\right]\\left[1 + \\text{erf}\\left(\\frac{\\alpha_i (t - \\tau_i)}{\\sqrt{2\\sigma^2}}\\right)\\right], \\tag{1}\n",
    "$$\n",
    "\n",
    "where $\\text{erf}$ is the [error function](https://en.wikipedia.org/wiki/Error_function), $A$ is the amplitude, $\\tau$ is the retention time, $\\sigma^2$ is \n",
    "the signal variance, and $\\alpha$ is the skew parameter. The skew normal distribution is \n",
    "used because the skew parameter $\\alpha$ can break symmetry, allowing for heavily \n",
    "tailed signals. When the distribution is unskewed, meaning $\\alpha = 0$, Eq. 1 simplifies to \n",
    "a Normal distribution symmetric about $\\tau$. To get a sense of how $\\alpha$ \n",
    "impacts the resulting signal, we can use `scipy.stats.skewnormal` to examine \n",
    "the amplitude-weighted output,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x16b72b940>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np \n",
    "import pandas as pd \n",
    "import scipy.stats\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "sns.set()\n",
    "\n",
    "# Set a range of skew parameters to demonstrate the signal as a function of time\n",
    "alpha_range = [-5, -1, 0, 1, 5]\n",
    "time = np.arange(0, 20, 0.01 )\n",
    "\n",
    "# Set constants for each signal\n",
    "A = 100\n",
    "tau = 10\n",
    "sigma = 3\n",
    "for alpha in alpha_range:\n",
    "    # Compute the skew normal distribution and plot the resulting signal.\n",
    "    signal = A * scipy.stats.skewnorm(alpha, loc=tau, scale=sigma).pdf(time)\n",
    "    plt.plot(time, signal, label=alpha, lw=2) \n",
    "\n",
    "# Add necessary labels\n",
    "plt.xlabel('time')\n",
    "plt.ylabel('$S$')\n",
    "plt.legend(title=r'$\\alpha$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When the skew parameter $\\alpha$ is large and negative, the signal is heavily\n",
    "skewed towards shorter retention times. Even though all signals in this plot\n",
    "have different heights and locations of the maxima, they all have identical\n",
    "values for $A$, $\\tau$, and $\\sigma$. The flexibility of $\\alpha$ in defining the \n",
    "signal trace allows for a broad array of peak shapes to be well described by \n",
    "this distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "vscode": {
     "languageId": "plaintext"
    }
   },
   "source": [
    "## Fitting Peak Windows\n",
    "As described in the notebook for Step 2, a chromatogram is broken down into\n",
    "multiple \"peak windows\" which likely contain overlapping analyte signals. Each \n",
    "window is fitted independently, which assumes that distant peaks have no influence \n",
    "on each other. As an example, let's look at a real peak window from a sample chromatogram.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Performing baseline correction: 100%|██████████| 299/299 [00:00<00:00, 2725.64it/s]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x16b8d2380>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from hplc.quant import Chromatogram\n",
    "import pandas as pd\n",
    "\n",
    "# Load an example chromatogram and correct the baseline\n",
    "df = pd.read_csv('data/sample_chromatogram.txt')\n",
    "chrom  = Chromatogram(df, cols={'time':'time_min', 'signal':'intensity_mV'},\n",
    "                      time_window=[10, 20])\n",
    "chrom.correct_baseline()\n",
    "\n",
    "# Assign the peak windows with a modified buffer and prominence filter\n",
    "windows = chrom._assign_windows(buffer=50, prominence=0.01)\n",
    "\n",
    "# Get the first peak window and plot\n",
    "first_peak = windows[(windows['window_type']=='peak') & (windows['window_id']==1)]\n",
    "plt.plot(first_peak['time_min'], first_peak['intensity_mV_corrected'], 'k-', label='window 1')\n",
    "plt.xlabel('time [min]')\n",
    "plt.ylabel('signal [mV]')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To determine the properties of this peak (including its area which is proportional\n",
    "to concentration), we will find the best-fit parameters using a non-linear least \n",
    "squares [trust region](https://en.wikipedia.org/wiki/Trust_region) fitting method\n",
    "as is implemented in `scipy.optimize.curve_fit` which is a robust estimation \n",
    "algorithm for bounded problems. \n",
    "\n",
    "To do so, we must provide i) initial guesses for the parameters $[A, \\tau, \\sigma, \\alpha]$\n",
    "and ii) reasonable bounds on their values. \n",
    "\n",
    "### Default settings for initial guesses of parameters\n",
    "In `hplc-py`, initial guesses are set given the properties of the observed \n",
    "chromatogram. These default parameter guesses are:\n",
    "\n",
    "* $A_0 \\rightarrow$ the observed value of the chromatogram at the location of the maxima\n",
    "* $\\tau_0 \\rightarrow$ the observed time-location of the maxima \n",
    "* $\\sigma_0 \\rightarrow$ one-half of the observed peak width at its half-maximal value\n",
    "* $\\alpha_0 \\rightarrow$ 0, which guesses that the peak is approximately Gaussian.\n",
    "\n",
    "These values are determined using peak measurements returned by `scipy.signal.find_peaks`\n",
    "and `scipy.signal.peak_widths`. These properties are accessible via the \n",
    "chromatogram attribute `.window_props` "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[65992.999952423, 10.98, 0.16630057317687066, 0]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Set the initial guesses from the window properties\n",
    "props = chrom.window_props[1]\n",
    "p0 = [props['amplitude'][0],\n",
    "     props['location'][0],\n",
    "     props['width'][0] / 2, \n",
    "     0]\n",
    "p0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Default bounds for parameters\n",
    "By default, `hplc-py` applies broad, permissive bounds on these parameters given \n",
    "information of the chromatogram. The default bounds given to each parameter are \n",
    "\n",
    "* $A \\in [0.01 \\times A_0, 100 \\times A_0]$ where $A_0$ is the initial guess for the amplitude.\n",
    "* $\\tau \\in [t_{min}, t_{max}]$ where $t_{min}$ and $t_{max}$ correspond to the minimum and maximum times in the peak window.\n",
    "* $\\sigma_{bounds} \\in [dt, \\frac{t_{max} - t_{min}}{2}]$ where $dt$ corresponds to the time sampling interval of the chromatogram.\n",
    "* $\\alpha \\in (-\\inf, +\\inf)$.\n",
    "\n",
    "These bounds can be overridden for all peak inferences by providing a dictionary \n",
    "of their values, as is specified in the documentation for `hplc.quant.Chromatogram.fit_peaks`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Give initial bounds for the parameters (lower, upper)\n",
    "bounds = [[], []]\n",
    "bounds[0] = [p0[0] * 0.1, first_peak['time_min'].min(), chrom._dt, -np.inf]\n",
    "bounds[1] = [p0[0] * 10, first_peak['time_min'].max(), 0.5 * (first_peak['time_min'].max() - first_peak['time_min'].min()), np.inf]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Optimization of parameters\n",
    "Given initial guesses and parameter bounds, the best-fit parameters are estimated \n",
    "by calling `scipy.optimize.curve_fit` on the observed data in the peak widow. The \n",
    "cost function is defined as a method `_fit_skewnorms` of a `Chromatogram`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimal parameters (amplitude, location, scale, skew) : [2.33773945e+04 1.09020036e+01 1.59217385e-01 7.03685471e-01]\n"
     ]
    }
   ],
   "source": [
    "import scipy.optimize\n",
    "\n",
    "# Perform the fit\n",
    "param_opt, _ = scipy.optimize.curve_fit(chrom._fit_skewnorms, first_peak['time_min'],\n",
    "                                        first_peak['intensity_mV_corrected'],\n",
    "                                        p0=p0, bounds=bounds)\n",
    "print(f'Optimal parameters (amplitude, location, scale, skew) : {param_opt}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the optimal parameters estimated, we can compare the inferred signal to \n",
    "the observed chromatogram "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1739eab90>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Compute the amplitude-weighted skewnorm with the inferred parameters\n",
    "fit = param_opt[0] * scipy.stats.skewnorm(param_opt[3], loc=param_opt[1], scale=param_opt[2]).pdf(first_peak['time_min'])\n",
    "\n",
    "# Plot the data and the observed peak\n",
    "plt.plot(first_peak['time_min'], first_peak['intensity_mV_corrected'], 'k-', label='window 1')\n",
    "plt.fill_between(first_peak['time_min'], fit, color='dodgerblue', label='inferred signal')\n",
    "plt.xlabel('time [min]')\n",
    "plt.ylabel('signal [mV]')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With an adequate reconstruction of the observed peak, the signal area is computed \n",
    "by integrating the signal over the entire time range of the peak window, and \n",
    "the procedure is repeated for the next peak window."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "<small> © Griffin Chure, 2024. This notebook and the code within are released under a \n",
    "[Creative-Commons CC-BY 4.0](https://creativecommons.org/licenses/by/4.0/) and \n",
    "[GPLv3](https://www.gnu.org/licenses/gpl-3.0) license, respectively.</small>\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": ".venv",
   "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": "3.10.9"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}