{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import openturns as ot\n",
    "import otmorris\n",
    "import time\n",
    "import numpy as np\n",
    "\n",
    "ot.RandomGenerator.SetSeed(1)\n",
    "b0 = ot.DistFunc.rNormal()\n",
    "alpha = ot.DistFunc.rNormal(10)\n",
    "beta = ot.DistFunc.rNormal(6*14)\n",
    "gamma = ot.DistFunc.rNormal(20*14)\n",
    "g = ot.Function(otmorris.MorrisFunction(alpha, beta, gamma, b0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.        , 0.05263158, 0.10526316, 0.15789474, 0.21052632,\n",
       "       0.26315789, 0.31578947, 0.36842105, 0.42105263, 0.47368421,\n",
       "       0.52631579, 0.57894737, 0.63157895, 0.68421053, 0.73684211,\n",
       "       0.78947368, 0.84210526, 0.89473684, 0.94736842, 1.        ])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.linspace(0.0, 1.0, 20)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p>[-47.1449]</p>"
      ],
      "text/plain": [
       "class=Point name=Unnamed dimension=1 values=[-47.1449]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "distributionList = [ot.Uniform(0,1)]*20\n",
    "myDistribution = ot.ComposedDistribution(distributionList)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_train = 1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Elapsed= 8.0120210647583\n"
     ]
    }
   ],
   "source": [
    "start = time.time()\n",
    "\n",
    "inputTrain = myDistribution.getSample(n_train)\n",
    "outputTrain = g(inputTrain)\n",
    "\n",
    "elapsed = (time.time() - start)\n",
    "print(\"Elapsed=\", elapsed)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Version rapide en Numpy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def w(x):\n",
    "    x=x.reshape(-1,1)\n",
    "    y= (2*x-1)*np.ones((20,1))\n",
    "    y[[2,4,6]]=2*(1.1*x[[2,4,6]]/(x[[2,4,6]]+0.1)-1/float(2))\n",
    "    return y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Morris_function(x, b0, alpha, beta):\n",
    "    delta=np.zeros((20,20,20))\n",
    "    delta[:5,:5,:5].fill(-10)\n",
    "    gamma=np.zeros((20,20,20,20))\n",
    "    gamma[:4,:4,:4,:4].fill(5)\n",
    "    W=np.sum(alpha.reshape(-1,1)*w(x))\n",
    "    W1=np.sum(beta*(w(x).reshape(1,-1)*w(x))*(np.arange(20).reshape(-1,1)<np.arange(20)))\n",
    "    W2=np.sum(delta*(w(x).reshape(-1,1,1)*w(x).reshape(1,-1,1)*w(x).reshape(1,1,-1))*(np.arange(20).reshape(-1,1,1)<np.arange(20).reshape(1,-1,1))*(np.arange(20).reshape(1,-1,1)<np.arange(20).reshape(1,1,-1)))\n",
    "    W3=np.sum(gamma*(w(x).reshape(-1,1,1,1)*w(x).reshape(1,-1,1,1)*w(x).reshape(1,1,-1,1)*w(x).reshape(1,1,1,-1))*(np.arange(20).reshape(-1,1,1,1)<np.arange(20).reshape(1,-1,1,1))*(np.arange(20).reshape(1,-1,1,1)<np.arange(20).reshape(1,1,-1,1))*(np.arange(20).reshape(1,1,-1,1)<np.arange(20).reshape(1,1,1,-1)))\n",
    "    y=W+W1+W2+W3+float(b0)\n",
    "    return y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.        , 0.05263158, 0.10526316, 0.15789474, 0.21052632,\n",
       "       0.26315789, 0.31578947, 0.36842105, 0.42105263, 0.47368421,\n",
       "       0.52631579, 0.57894737, 0.63157895, 0.68421053, 0.73684211,\n",
       "       0.78947368, 0.84210526, 0.89473684, 0.94736842, 1.        ])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.linspace(0.0, 1.0, 20)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha=np.append(20*np.ones(10),np.random.randn(10))\n",
    "beta=np.random.randn(20,20)\n",
    "beta[:6,:6].fill(-15)\n",
    "b0=np.random.randn(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(20,)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alpha.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(20, 20)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "beta.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-73.45407960721988"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Morris_function(x, b0,  alpha, beta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Version rapide OT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "class MorrisFunction(ot.OpenTURNSPythonFunction):\n",
    "    def __init__(self, alpha, beta, b0):\n",
    "        super(MorrisFunction, self).__init__(20, 1)\n",
    "        self.alpha = np.array(alpha)\n",
    "        # Create beta\n",
    "        self.beta = np.array(beta).reshape((20,20))\n",
    "        # Read b0\n",
    "        self.b0 = np.array(b0)\n",
    "        # Delta is deterministic\n",
    "        self.delta=np.zeros((20,20,20))\n",
    "        self.delta[:5,:5,:5].fill(-10)\n",
    "        # Gamma is deterministic\n",
    "        self.gamma=np.zeros((20,20,20,20))\n",
    "        self.gamma[:4,:4,:4,:4].fill(5)\n",
    "\n",
    "    def _exec(self, X):\n",
    "        x = np.array(X)\n",
    "        y = self.Morris_function(x)\n",
    "        Y = [y]\n",
    "        return Y\n",
    "    \n",
    "    def w(self, x):\n",
    "        x = x.reshape(-1,1)\n",
    "        y= (2*x-1)*np.ones((20,1))\n",
    "        y[[2,4,6]]=2*(1.1*x[[2,4,6]]/(x[[2,4,6]]+0.1)-1/float(2))\n",
    "        return y\n",
    "\n",
    "    def Morris_function(self, x):\n",
    "        W=np.sum(self.alpha.reshape(-1,1)*self.w(x))\n",
    "        W1=np.sum(self.beta*(self.w(x).reshape(1,-1)*self.w(x)) * \\\n",
    "                  (np.arange(20).reshape(-1,1)<np.arange(20)))\n",
    "        W2=np.sum(self.delta*(self.w(x).reshape(-1,1,1) * \\\n",
    "                              self.w(x).reshape(1,-1,1) * \\\n",
    "                              self.w(x).reshape(1,1,-1)) * \\\n",
    "                  (np.arange(20).reshape(-1,1,1) < np.arange(20).reshape(1,-1,1)) * \\\n",
    "                  (np.arange(20).reshape(1,-1,1) < np.arange(20).reshape(1,1,-1)))\n",
    "        W3=np.sum(self.gamma*(self.w(x).reshape(-1,1,1,1) * \\\n",
    "                              self.w(x).reshape(1,-1,1,1) * \\\n",
    "                              self.w(x).reshape(1,1,-1,1) * \\\n",
    "                              self.w(x).reshape(1,1,1,-1)) * \\\n",
    "                  (np.arange(20).reshape(-1,1,1,1) < np.arange(20).reshape(1,-1,1,1)) * \\\n",
    "                  (np.arange(20).reshape(1,-1,1,1) < np.arange(20).reshape(1,1,-1,1)) * \\\n",
    "                  (np.arange(20).reshape(1,1,-1,1) < np.arange(20).reshape(1,1,1,-1)))\n",
    "        y = W + W1 + W2 + W3 + float(b0)\n",
    "        return y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "ot.RandomGenerator.SetSeed(1)\n",
    "b0 = ot.DistFunc.rNormal()\n",
    "alpha = ot.DistFunc.rNormal(20)\n",
    "beta = ot.DistFunc.rNormal(20*20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "g = ot.Function(MorrisFunction(alpha, beta, b0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.        , 0.05263158, 0.10526316, 0.15789474, 0.21052632,\n",
       "       0.26315789, 0.31578947, 0.36842105, 0.42105263, 0.47368421,\n",
       "       0.52631579, 0.57894737, 0.63157895, 0.68421053, 0.73684211,\n",
       "       0.78947368, 0.84210526, 0.89473684, 0.94736842, 1.        ])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.linspace(0.0, 1.0, 20)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p>[-0.130249]</p>"
      ],
      "text/plain": [
       "class=Point name=Unnamed dimension=1 values=[-0.130249]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Elapsed= 2.741170883178711\n"
     ]
    }
   ],
   "source": [
    "start = time.time()\n",
    "\n",
    "inputTrain = myDistribution.getSample(n_train)\n",
    "outputTrain = g(inputTrain)\n",
    "\n",
    "elapsed = (time.time() - start)\n",
    "print(\"Elapsed=\", elapsed)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ce n'est pas beaucoup plus rapide en fait."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
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