ee_LARS.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import ee\n",
    "ee.Initialize()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "inputCSV = ee.FeatureCollection('users/ccrs2fy2020/transformedFeatures')\n",
    "inputCSV = inputCSV.toList(count=50000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def extractBands(feature):\n",
    "    feature = ee.Feature(feature)\n",
    "    return feature.toArray(properties=['B3', 'B4', 'B5', 'B6', 'B7', 'B8A', 'B11', 'B12',\n",
    "                          'RVI1', 'RVI2', 'RVI3', 'RVI4', 'GM1', 'GM2', 'GI', 'II', 'MSI',\n",
    "                          'PSSR', 'SGI', 'SR2', 'SR3', 'GVI', 'PSRI', 'NDVI3', 'SR5', 'SR6',\n",
    "                          'SR7', 'IPVI', 'ARI', 'ARI2', 'NDVI', 'GNDVI', 'NDWI', 'NDREVI', 'NDGI',\n",
    "                          'NDI1', 'NDI2', 'RENDVI', 'OSAVI', 'NMDI', 'HI', 'GVSP', 'MCARI',\n",
    "                          'TCARI', 'EVI', 'EVI2', 'RDVI', 'MSR', 'MSAVI', 'MSAVI2', 'MCARI2',\n",
    "                          'MTVI2', 'N', 'GEMI', 'MSR2', 'NLI', 'TDVI']).toList()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def extractVI(feature):\n",
    "    feature = ee.Feature(feature)\n",
    "    return feature.toArray(properties=['FCOVER']).toList()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "inputList = inputCSV.map(extractBands)\n",
    "outputList = inputCSV.map(extractVI)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = ee.Array(inputList)\n",
    "y = ee.Array(outputList)\n",
    "\n",
    "n = X.length().get([0])\n",
    "m = X.length().get([1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def centre(output):\n",
    "    output = ee.Array(output)\n",
    "    mean = output.reduce(ee.Reducer.mean(), [0]).get([0,0])\n",
    "    return output.subtract(mean)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def normalize(inputs):\n",
    "    inputs = ee.Array(inputs)\n",
    "\n",
    "    inputMeans = inputs.reduce(ee.Reducer.mean(), [0])\n",
    "    inputMeans = inputMeans.repeat(0, n)\n",
    "    inputs = inputs.subtract(inputMeans)\n",
    "    inputs = inputs.pow(2).reduce(ee.Reducer.sum(), [0]).pow(-0.5).repeat(0, n).multiply(inputs)\n",
    "\n",
    "    return inputs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def standardize(inputs):\n",
    "    inputs = ee.Array(inputs)\n",
    "\n",
    "    inputMeans = inputs.reduce(ee.Reducer.mean(), [0])\n",
    "    inputMeans = inputMeans.repeat(0, n)\n",
    "    inputs = inputs.subtract(inputMeans)\n",
    "\n",
    "    inputSTDevs = inputs.reduce(ee.Reducer.stdDev(), [0])\n",
    "    inputSTDevs = inputSTDevs.repeat(0, n)\n",
    "    inputs = inputs.divide(inputSTDevs)\n",
    "\n",
    "    return inputs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def setZero(num):\n",
    "    num = ee.Number(num);\n",
    "    return ee.Algorithms.If(num.abs().lt(0.00001), [0], [num])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = normalize(X)\n",
    "y = centre(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def LARSregression(iteration, inputs):\n",
    "    inputs = ee.Dictionary(inputs)\n",
    "    prediction = inputs.getArray('prediction')\n",
    "    coeff_arr = inputs.getArray('coeff_arr')\n",
    "\n",
    "    c = X.matrixTranspose().matrixMultiply(y.subtract(prediction))\n",
    "    c_abs = c.abs()\n",
    "    C_max = c_abs.get(c_abs.argmax())\n",
    "\n",
    "    maxLocs = c_abs.gte(C_max.subtract(0.00001))\n",
    "    signs = c.divide(c_abs)\n",
    "\n",
    "    signs_j = maxLocs.multiply(signs).matrixTranspose()\n",
    "    signs_jc = signs_j.abs().subtract(1).multiply(-1)\n",
    "\n",
    "    A = ee.List(ee.Array([ee.List.sequence(0, m.subtract(1))]).mask(signs_j).toList().get(0))\n",
    "    A_c = ee.List(ee.Array([ee.List.sequence(0, m.subtract(1))]).mask(signs_jc).toList().get(0))\n",
    "\n",
    "    signMatrix_j = signs_j.repeat(0, n)\n",
    "\n",
    "    X_A = X.multiply(signMatrix_j).mask(signs_j)\n",
    "    j = X_A.length().get([1])\n",
    "\n",
    "    G_A = X_A.matrixTranspose().matrixMultiply(X_A)\n",
    "\n",
    "    V1_A = ee.Array(ee.List.repeat([1], j))\n",
    "\n",
    "    G_Ai = G_A.matrixInverse()\n",
    "\n",
    "    A_A = V1_A.matrixTranspose().matrixMultiply(G_Ai).matrixMultiply(V1_A).get([0,0]).pow(-0.5)\n",
    "\n",
    "    w_A = G_Ai.matrixMultiply(V1_A).multiply(A_A)\n",
    "\n",
    "    u_A = X_A.matrixMultiply(w_A)\n",
    "\n",
    "    a = X.matrixTranspose().matrixMultiply(u_A)\n",
    "\n",
    "\n",
    "    def computeGammaRRay(index_j):\n",
    "        minus_j = C_max.subtract(c.get([index_j, 0])).divide(A_A.subtract(a.get([index_j, 0])))\n",
    "        plus_j = C_max.add(c.get([index_j, 0])).divide(A_A.add(a.get([index_j, 0])))\n",
    "\n",
    "        gammaRRay = ee.Array([minus_j, plus_j])\n",
    "        gammaRRay = gammaRRay.mask(gammaRRay.gte(0))\n",
    "        gammaRRay = gammaRRay.multiply(-1)\n",
    "\n",
    "        return gammaRRay.get(gammaRRay.argmax())\n",
    "\n",
    "\n",
    "    gammaRRay = ee.Array([A_c.map(computeGammaRRay)])\n",
    "    gamma = gammaRRay.get(gammaRRay.argmax()).multiply(-1)\n",
    "\n",
    "    prediction = prediction.add(u_A.multiply(gamma))\n",
    "    coefficients = X.matrixSolve(prediction)\n",
    "\n",
    "    coefficients = ee.Array(ee.List(coefficients.matrixTranspose().toList().get(0)).map(setZero))\n",
    "\n",
    "    coeff_arr = ee.Array.cat([coeff_arr, coefficients], 1)\n",
    "\n",
    "    return ee.Dictionary({'prediction':prediction, 'coeff_arr':coeff_arr})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "prediction = ee.Array(ee.List.repeat([0], n))\n",
    "coeff_arr = ee.Array(ee.List.repeat([0], m))\n",
    "initial = ee.Dictionary({'prediction':prediction, 'coeff_arr':coeff_arr})\n",
    "\n",
    "numIterations = ee.List.sequence(1, 10)\n",
    "finalOutput = ee.Dictionary(numIterations.iterate(LARSregression, initial))\n",
    "coeff_arr = finalOutput.getArray('coeff_arr')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "coeff_arr = coeff_arr.getInfo()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
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       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-1.049089</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.060490</td>\n",
       "      <td>2.910071</td>\n",
       "      <td>3.502416</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>6.004959</td>\n",
       "      <td>10.501651</td>\n",
       "      <td>12.242167</td>\n",
       "      <td>11.976399</td>\n",
       "      <td>11.313579</td>\n",
       "      <td>11.532077</td>\n",
       "      <td>11.766259</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.668025</td>\n",
       "      <td>2.071989</td>\n",
       "      <td>2.412328</td>\n",
       "      <td>2.771534</td>\n",
       "      <td>3.580097</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>0</td>\n",
       "      <td>3.248549</td>\n",
       "      <td>11.291032</td>\n",
       "      <td>13.977139</td>\n",
       "      <td>21.652785</td>\n",
       "      <td>22.597724</td>\n",
       "      <td>22.051865</td>\n",
       "      <td>20.888445</td>\n",
       "      <td>16.710684</td>\n",
       "      <td>11.646212</td>\n",
       "      <td>5.442043</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>4.979102</td>\n",
       "      <td>7.774777</td>\n",
       "      <td>9.641693</td>\n",
       "      <td>15.688312</td>\n",
       "      <td>16.780099</td>\n",
       "      <td>22.016667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50</th>\n",
       "      <td>0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>51</th>\n",
       "      <td>0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>8.042483</td>\n",
       "      <td>10.636971</td>\n",
       "      <td>7.845038</td>\n",
       "      <td>4.802174</td>\n",
       "      <td>4.852155</td>\n",
       "      <td>4.716000</td>\n",
       "      <td>3.407516</td>\n",
       "      <td>3.648006</td>\n",
       "      <td>1.129211</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>52</th>\n",
       "      <td>0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>53</th>\n",
       "      <td>0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>4.342963</td>\n",
       "      <td>6.787195</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>54</th>\n",
       "      <td>0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>55</th>\n",
       "      <td>0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>2.645382</td>\n",
       "      <td>2.676352</td>\n",
       "      <td>3.390192</td>\n",
       "      <td>2.066031</td>\n",
       "      <td>1.641574</td>\n",
       "      <td>0.736386</td>\n",
       "      <td>-1.671179</td>\n",
       "      <td>-2.485819</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>56</th>\n",
       "      <td>0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    0         1          2          3          4          5          6  \\\n",
       "0   0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "1   0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "2   0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "3   0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "4   0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "5   0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "6   0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "7   0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "8   0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "9   0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "10  0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "11  0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "12  0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "13  0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "14  0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "15  0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "16  0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "17  0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "18  0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "19  0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "20  0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "21  0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "22  0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "23  0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "24  0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "25  0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "26  0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "27  0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "28  0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "29  0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "30  0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "31  0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "32  0  0.000000   0.000000   0.000000   6.004959  10.501651  12.242167   \n",
       "33  0  0.000000   0.000000   0.000000   0.000000   0.000000   1.668025   \n",
       "34  0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "35  0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "36  0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "37  0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "38  0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "39  0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "40  0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "41  0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "42  0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "43  0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "44  0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "45  0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "46  0  3.248549  11.291032  13.977139  21.652785  22.597724  22.051865   \n",
       "47  0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "48  0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "49  0  0.000000   0.000000   0.000000   0.000000   4.979102   7.774777   \n",
       "50  0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "51  0  0.000000   8.042483  10.636971   7.845038   4.802174   4.852155   \n",
       "52  0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "53  0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "54  0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "55  0  0.000000   0.000000   2.645382   2.676352   3.390192   2.066031   \n",
       "56  0  0.000000   0.000000   0.000000   0.000000   0.000000   0.000000   \n",
       "\n",
       "            7          8          9         10  \n",
       "0    0.000000   0.000000   0.000000   0.000000  \n",
       "1    0.000000   0.000000   0.000000   0.000000  \n",
       "2    0.000000   0.000000   0.000000   0.000000  \n",
       "3    0.000000   0.000000   0.000000   0.000000  \n",
       "4    0.000000   0.000000   0.000000   0.000000  \n",
       "5    0.000000   0.000000   0.000000   0.000000  \n",
       "6    0.000000   0.000000   0.000000   0.000000  \n",
       "7    0.000000   0.000000   0.000000   0.000000  \n",
       "8    0.000000   0.000000   0.000000   0.000000  \n",
       "9    0.000000   0.000000   0.000000   0.000000  \n",
       "10   0.000000   0.000000   0.000000   0.000000  \n",
       "11   0.000000   0.000000   0.000000   0.000000  \n",
       "12   0.000000   0.000000   0.000000   0.000000  \n",
       "13   0.000000   0.000000   0.000000   0.000000  \n",
       "14   0.000000   0.000000   0.000000   0.000000  \n",
       "15   0.000000   0.000000   0.000000   0.000000  \n",
       "16  -0.784579  -2.437739  -2.516793  -2.468820  \n",
       "17   0.000000   0.000000   0.000000   0.000000  \n",
       "18   0.000000   0.000000   0.000000   0.000000  \n",
       "19   0.000000   0.000000   0.000000   0.000000  \n",
       "20   0.000000   0.000000   0.000000   0.000000  \n",
       "21   0.000000   0.000000   0.000000   0.000000  \n",
       "22   0.000000   0.000000   0.000000  -1.049089  \n",
       "23   0.000000   0.000000   0.000000   0.000000  \n",
       "24   0.000000   0.000000   0.000000   0.000000  \n",
       "25   0.000000   0.000000   0.000000   0.000000  \n",
       "26   0.000000   0.000000   0.000000   0.000000  \n",
       "27   0.000000   0.000000   0.000000   0.000000  \n",
       "28   0.000000   0.000000   0.000000   0.000000  \n",
       "29   0.000000   0.000000   0.000000   0.000000  \n",
       "30   0.000000   1.060490   2.910071   3.502416  \n",
       "31   0.000000   0.000000   0.000000   0.000000  \n",
       "32  11.976399  11.313579  11.532077  11.766259  \n",
       "33   2.071989   2.412328   2.771534   3.580097  \n",
       "34   0.000000   0.000000   0.000000   0.000000  \n",
       "35   0.000000   0.000000   0.000000   0.000000  \n",
       "36   0.000000   0.000000   0.000000   0.000000  \n",
       "37   0.000000   0.000000   0.000000   0.000000  \n",
       "38   0.000000   0.000000   0.000000   0.000000  \n",
       "39   0.000000   0.000000   0.000000   0.000000  \n",
       "40   0.000000   0.000000   0.000000   0.000000  \n",
       "41   0.000000   0.000000   0.000000   0.000000  \n",
       "42   0.000000   0.000000   0.000000   0.000000  \n",
       "43   0.000000   0.000000   0.000000   0.000000  \n",
       "44   0.000000   0.000000   0.000000   0.000000  \n",
       "45   0.000000   0.000000   0.000000   0.000000  \n",
       "46  20.888445  16.710684  11.646212   5.442043  \n",
       "47   0.000000   0.000000   0.000000   0.000000  \n",
       "48   0.000000   0.000000   0.000000   0.000000  \n",
       "49   9.641693  15.688312  16.780099  22.016667  \n",
       "50   0.000000   0.000000   0.000000   0.000000  \n",
       "51   4.716000   3.407516   3.648006   1.129211  \n",
       "52   0.000000   0.000000   0.000000   0.000000  \n",
       "53   0.000000   0.000000   4.342963   6.787195  \n",
       "54   0.000000   0.000000   0.000000   0.000000  \n",
       "55   1.641574   0.736386  -1.671179  -2.485819  \n",
       "56   0.000000   0.000000   0.000000   0.000000  "
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from pandas import DataFrame\n",
    "DataFrame(coeff_arr)"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [],
   "name": "GEE LARs Implementation.ipynb",
   "provenance": []
  },
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.6"
  },
  "pycharm": {
   "stem_cell": {
    "cell_type": "raw",
    "metadata": {
     "collapsed": false
    },
    "source": []
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}