{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sampling"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We show how to construct correlated sample with Gaussian copula."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import chaospy as cp\n",
    "import numpy as np\n",
    "\n",
    "from econsa.correlation import gc_correlation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First we specify the marginal distributions and correlation matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "corr = [[1.0, 0.6, 0.2], [0.6, 1.0, 0.0], [0.2, 0.0, 1.0]]\n",
    "marginals = (\n",
    "    cp.Normal(mu=1230),\n",
    "    cp.Normal(mu=0.0135),\n",
    "    cp.Uniform(lower=1.15, upper=3.15),\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We then transform the correlation matrix using equation (4.5) in Kucherenko et al. (2012)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "corr_transformed = gc_correlation(marginals, corr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we are ready to use transformed correlation matrix to sample from a Gaussian copula."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.    ,  0.6018,  0.2013],\n",
       "       [ 0.6018,  1.    , -0.0018],\n",
       "       [ 0.2013, -0.0018,  1.    ]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "copula = cp.Nataf(cp.J(*marginals), corr_transformed)\n",
    "corr_copula = np.corrcoef(copula.sample(100000))\n",
    "\n",
    "np.round(corr_copula, decimals=4)"
   ]
  }
 ],
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