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cs224/minepy-TICe-value-does-not-match-original-implementation.ipynb

Created May 18, 2018 07:27
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Jupyter Notebook to demonstrate differences between the TICe values delivered by minepy and by MINEv2.jar
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minepy-TICe-value-does-not-match-original-implementation.ipynb
{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Christian Schuhegger \n",
"last updated: 2018-05-18 \n",
"\n",
"CPython 3.6.3\n",
"IPython 6.2.1\n",
"\n",
"numpy 1.14.2\n",
"pandas 0.22.0\n",
"matplotlib 2.2.2\n",
"sklearn 0.19.1\n",
"minepy b'1.2.2'\n"
]
}
],
"source": [
"%load_ext watermark\n",
"%watermark -a 'Christian Schuhegger' -u -d -v -p numpy,pandas,matplotlib,sklearn,minepy"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import numpy as np, scipy, scipy.stats as stats, pandas as pd, matplotlib.pyplot as plt, seaborn as sns\n",
"import minepy, sklearn.metrics, sklearn.feature_selection.mutual_info_\n",
"\n",
"pd.set_option('display.max_columns', 500)\n",
"pd.set_option('display.width', 1000)\n",
"# pd.set_option('display.float_format', lambda x: '%.2f' % x)\n",
"np.set_printoptions(edgeitems=10)\n",
"np.set_printoptions(suppress=True)\n",
"np.core.arrayprint._line_width = 180\n",
"\n",
"sns.set()"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
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"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x = np.linspace(0, 1, 1000)\n",
"y = np.sin(10 * np.pi * x) + x\n",
"plt.plot(x,y);"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
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" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
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"\n",
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" vertical-align: top;\n",
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" <td>0.064855</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
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" <tr>\n",
" <th>4</th>\n",
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" <td>0.129462</td>\n",
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"</table>\n",
"</div>"
],
"text/plain": [
" x y\n",
"0 0.000000 0.000000\n",
"1 0.001001 0.032443\n",
"2 0.002002 0.064855\n",
"3 0.003003 0.097205\n",
"4 0.004004 0.129462"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df = pd.DataFrame(np.array([x,y]).T, columns=['x','y'])\n",
"df.head()"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
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" <th>121</th>\n",
" <th>122</th>\n",
" <th>123</th>\n",
" <th>124</th>\n",
" <th>125</th>\n",
" <th>126</th>\n",
" <th>127</th>\n",
" <th>128</th>\n",
" <th>129</th>\n",
" <th>130</th>\n",
" <th>131</th>\n",
" <th>132</th>\n",
" <th>133</th>\n",
" <th>134</th>\n",
" <th>135</th>\n",
" <th>136</th>\n",
" <th>137</th>\n",
" <th>138</th>\n",
" <th>139</th>\n",
" <th>140</th>\n",
" <th>141</th>\n",
" <th>142</th>\n",
" <th>143</th>\n",
" <th>144</th>\n",
" <th>145</th>\n",
" <th>146</th>\n",
" <th>147</th>\n",
" <th>148</th>\n",
" <th>149</th>\n",
" <th>150</th>\n",
" <th>151</th>\n",
" <th>152</th>\n",
" <th>153</th>\n",
" <th>154</th>\n",
" <th>155</th>\n",
" <th>156</th>\n",
" <th>157</th>\n",
" <th>158</th>\n",
" <th>159</th>\n",
" <th>160</th>\n",
" <th>161</th>\n",
" <th>162</th>\n",
" <th>163</th>\n",
" <th>164</th>\n",
" <th>165</th>\n",
" <th>166</th>\n",
" <th>167</th>\n",
" <th>168</th>\n",
" <th>169</th>\n",
" <th>170</th>\n",
" <th>171</th>\n",
" <th>172</th>\n",
" <th>173</th>\n",
" <th>174</th>\n",
" <th>175</th>\n",
" <th>176</th>\n",
" <th>177</th>\n",
" <th>178</th>\n",
" <th>179</th>\n",
" <th>180</th>\n",
" <th>181</th>\n",
" <th>182</th>\n",
" <th>183</th>\n",
" <th>184</th>\n",
" <th>185</th>\n",
" <th>186</th>\n",
" <th>187</th>\n",
" <th>188</th>\n",
" <th>189</th>\n",
" <th>190</th>\n",
" <th>191</th>\n",
" <th>192</th>\n",
" <th>193</th>\n",
" <th>194</th>\n",
" <th>195</th>\n",
" <th>196</th>\n",
" <th>197</th>\n",
" <th>198</th>\n",
" <th>199</th>\n",
" <th>200</th>\n",
" <th>201</th>\n",
" <th>202</th>\n",
" <th>203</th>\n",
" <th>204</th>\n",
" <th>205</th>\n",
" <th>206</th>\n",
" <th>207</th>\n",
" <th>208</th>\n",
" <th>209</th>\n",
" <th>210</th>\n",
" <th>211</th>\n",
" <th>212</th>\n",
" <th>213</th>\n",
" <th>214</th>\n",
" <th>215</th>\n",
" <th>216</th>\n",
" <th>217</th>\n",
" <th>218</th>\n",
" <th>219</th>\n",
" <th>220</th>\n",
" <th>221</th>\n",
" <th>222</th>\n",
" <th>223</th>\n",
" <th>224</th>\n",
" <th>225</th>\n",
" <th>226</th>\n",
" <th>227</th>\n",
" <th>228</th>\n",
" <th>229</th>\n",
" <th>230</th>\n",
" <th>231</th>\n",
" <th>232</th>\n",
" <th>233</th>\n",
" <th>234</th>\n",
" <th>235</th>\n",
" <th>236</th>\n",
" <th>237</th>\n",
" <th>238</th>\n",
" <th>239</th>\n",
" <th>240</th>\n",
" <th>241</th>\n",
" <th>242</th>\n",
" <th>243</th>\n",
" <th>244</th>\n",
" <th>245</th>\n",
" <th>246</th>\n",
" <th>247</th>\n",
" <th>248</th>\n",
" <th>249</th>\n",
" <th>...</th>\n",
" <th>750</th>\n",
" <th>751</th>\n",
" <th>752</th>\n",
" <th>753</th>\n",
" <th>754</th>\n",
" <th>755</th>\n",
" <th>756</th>\n",
" <th>757</th>\n",
" <th>758</th>\n",
" <th>759</th>\n",
" <th>760</th>\n",
" <th>761</th>\n",
" <th>762</th>\n",
" <th>763</th>\n",
" <th>764</th>\n",
" <th>765</th>\n",
" <th>766</th>\n",
" <th>767</th>\n",
" <th>768</th>\n",
" <th>769</th>\n",
" <th>770</th>\n",
" <th>771</th>\n",
" <th>772</th>\n",
" <th>773</th>\n",
" <th>774</th>\n",
" <th>775</th>\n",
" <th>776</th>\n",
" <th>777</th>\n",
" <th>778</th>\n",
" <th>779</th>\n",
" <th>780</th>\n",
" <th>781</th>\n",
" <th>782</th>\n",
" <th>783</th>\n",
" <th>784</th>\n",
" <th>785</th>\n",
" <th>786</th>\n",
" <th>787</th>\n",
" <th>788</th>\n",
" <th>789</th>\n",
" <th>790</th>\n",
" <th>791</th>\n",
" <th>792</th>\n",
" <th>793</th>\n",
" <th>794</th>\n",
" <th>795</th>\n",
" <th>796</th>\n",
" <th>797</th>\n",
" <th>798</th>\n",
" <th>799</th>\n",
" <th>800</th>\n",
" <th>801</th>\n",
" <th>802</th>\n",
" <th>803</th>\n",
" <th>804</th>\n",
" <th>805</th>\n",
" <th>806</th>\n",
" <th>807</th>\n",
" <th>808</th>\n",
" <th>809</th>\n",
" <th>810</th>\n",
" <th>811</th>\n",
" <th>812</th>\n",
" <th>813</th>\n",
" <th>814</th>\n",
" <th>815</th>\n",
" <th>816</th>\n",
" <th>817</th>\n",
" <th>818</th>\n",
" <th>819</th>\n",
" <th>820</th>\n",
" <th>821</th>\n",
" <th>822</th>\n",
" <th>823</th>\n",
" <th>824</th>\n",
" <th>825</th>\n",
" <th>826</th>\n",
" <th>827</th>\n",
" <th>828</th>\n",
" <th>829</th>\n",
" <th>830</th>\n",
" <th>831</th>\n",
" <th>832</th>\n",
" <th>833</th>\n",
" <th>834</th>\n",
" <th>835</th>\n",
" <th>836</th>\n",
" <th>837</th>\n",
" <th>838</th>\n",
" <th>839</th>\n",
" <th>840</th>\n",
" <th>841</th>\n",
" <th>842</th>\n",
" <th>843</th>\n",
" <th>844</th>\n",
" <th>845</th>\n",
" <th>846</th>\n",
" <th>847</th>\n",
" <th>848</th>\n",
" <th>849</th>\n",
" <th>850</th>\n",
" <th>851</th>\n",
" <th>852</th>\n",
" <th>853</th>\n",
" <th>854</th>\n",
" <th>855</th>\n",
" <th>856</th>\n",
" <th>857</th>\n",
" <th>858</th>\n",
" <th>859</th>\n",
" <th>860</th>\n",
" <th>861</th>\n",
" <th>862</th>\n",
" <th>863</th>\n",
" <th>864</th>\n",
" <th>865</th>\n",
" <th>866</th>\n",
" <th>867</th>\n",
" <th>868</th>\n",
" <th>869</th>\n",
" <th>870</th>\n",
" <th>871</th>\n",
" <th>872</th>\n",
" <th>873</th>\n",
" <th>874</th>\n",
" <th>875</th>\n",
" <th>876</th>\n",
" <th>877</th>\n",
" <th>878</th>\n",
" <th>879</th>\n",
" <th>880</th>\n",
" <th>881</th>\n",
" <th>882</th>\n",
" <th>883</th>\n",
" <th>884</th>\n",
" <th>885</th>\n",
" <th>886</th>\n",
" <th>887</th>\n",
" <th>888</th>\n",
" <th>889</th>\n",
" <th>890</th>\n",
" <th>891</th>\n",
" <th>892</th>\n",
" <th>893</th>\n",
" <th>894</th>\n",
" <th>895</th>\n",
" <th>896</th>\n",
" <th>897</th>\n",
" <th>898</th>\n",
" <th>899</th>\n",
" <th>900</th>\n",
" <th>901</th>\n",
" <th>902</th>\n",
" <th>903</th>\n",
" <th>904</th>\n",
" <th>905</th>\n",
" <th>906</th>\n",
" <th>907</th>\n",
" <th>908</th>\n",
" <th>909</th>\n",
" <th>910</th>\n",
" <th>911</th>\n",
" <th>912</th>\n",
" <th>913</th>\n",
" <th>914</th>\n",
" <th>915</th>\n",
" <th>916</th>\n",
" <th>917</th>\n",
" <th>918</th>\n",
" <th>919</th>\n",
" <th>920</th>\n",
" <th>921</th>\n",
" <th>922</th>\n",
" <th>923</th>\n",
" <th>924</th>\n",
" <th>925</th>\n",
" <th>926</th>\n",
" <th>927</th>\n",
" <th>928</th>\n",
" <th>929</th>\n",
" <th>930</th>\n",
" <th>931</th>\n",
" <th>932</th>\n",
" <th>933</th>\n",
" <th>934</th>\n",
" <th>935</th>\n",
" <th>936</th>\n",
" <th>937</th>\n",
" <th>938</th>\n",
" <th>939</th>\n",
" <th>940</th>\n",
" <th>941</th>\n",
" <th>942</th>\n",
" <th>943</th>\n",
" <th>944</th>\n",
" <th>945</th>\n",
" <th>946</th>\n",
" <th>947</th>\n",
" <th>948</th>\n",
" <th>949</th>\n",
" <th>950</th>\n",
" <th>951</th>\n",
" <th>952</th>\n",
" <th>953</th>\n",
" <th>954</th>\n",
" <th>955</th>\n",
" <th>956</th>\n",
" <th>957</th>\n",
" <th>958</th>\n",
" <th>959</th>\n",
" <th>960</th>\n",
" <th>961</th>\n",
" <th>962</th>\n",
" <th>963</th>\n",
" <th>964</th>\n",
" <th>965</th>\n",
" <th>966</th>\n",
" <th>967</th>\n",
" <th>968</th>\n",
" <th>969</th>\n",
" <th>970</th>\n",
" <th>971</th>\n",
" <th>972</th>\n",
" <th>973</th>\n",
" <th>974</th>\n",
" <th>975</th>\n",
" <th>976</th>\n",
" <th>977</th>\n",
" <th>978</th>\n",
" <th>979</th>\n",
" <th>980</th>\n",
" <th>981</th>\n",
" <th>982</th>\n",
" <th>983</th>\n",
" <th>984</th>\n",
" <th>985</th>\n",
" <th>986</th>\n",
" <th>987</th>\n",
" <th>988</th>\n",
" <th>989</th>\n",
" <th>990</th>\n",
" <th>991</th>\n",
" <th>992</th>\n",
" <th>993</th>\n",
" <th>994</th>\n",
" <th>995</th>\n",
" <th>996</th>\n",
" <th>997</th>\n",
" <th>998</th>\n",
" <th>999</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>x</th>\n",
" <td>0.0</td>\n",
" <td>0.001001</td>\n",
" <td>0.002002</td>\n",
" <td>0.003003</td>\n",
" <td>0.004004</td>\n",
" <td>0.005005</td>\n",
" <td>0.006006</td>\n",
" <td>0.007007</td>\n",
" <td>0.008008</td>\n",
" <td>0.009009</td>\n",
" <td>0.010010</td>\n",
" <td>0.011011</td>\n",
" <td>0.012012</td>\n",
" <td>0.013013</td>\n",
" <td>0.014014</td>\n",
" <td>0.015015</td>\n",
" <td>0.016016</td>\n",
" <td>0.017017</td>\n",
" <td>0.018018</td>\n",
" <td>0.019019</td>\n",
" <td>0.020020</td>\n",
" <td>0.021021</td>\n",
" <td>0.022022</td>\n",
" <td>0.023023</td>\n",
" <td>0.024024</td>\n",
" <td>0.025025</td>\n",
" <td>0.026026</td>\n",
" <td>0.027027</td>\n",
" <td>0.028028</td>\n",
" <td>0.029029</td>\n",
" <td>0.030030</td>\n",
" <td>0.031031</td>\n",
" <td>0.032032</td>\n",
" <td>0.033033</td>\n",
" <td>0.034034</td>\n",
" <td>0.035035</td>\n",
" <td>0.036036</td>\n",
" <td>0.037037</td>\n",
" <td>0.038038</td>\n",
" <td>0.039039</td>\n",
" <td>0.040040</td>\n",
" <td>0.041041</td>\n",
" <td>0.042042</td>\n",
" <td>0.043043</td>\n",
" <td>0.044044</td>\n",
" <td>0.045045</td>\n",
" <td>0.046046</td>\n",
" <td>0.047047</td>\n",
" <td>0.048048</td>\n",
" <td>0.049049</td>\n",
" <td>0.050050</td>\n",
" <td>0.051051</td>\n",
" <td>0.052052</td>\n",
" <td>0.053053</td>\n",
" <td>0.054054</td>\n",
" <td>0.055055</td>\n",
" <td>0.056056</td>\n",
" <td>0.057057</td>\n",
" <td>0.058058</td>\n",
" <td>0.059059</td>\n",
" <td>0.060060</td>\n",
" <td>0.061061</td>\n",
" <td>0.062062</td>\n",
" <td>0.063063</td>\n",
" <td>0.064064</td>\n",
" <td>0.065065</td>\n",
" <td>0.066066</td>\n",
" <td>0.067067</td>\n",
" <td>0.068068</td>\n",
" <td>0.069069</td>\n",
" <td>0.070070</td>\n",
" <td>0.071071</td>\n",
" <td>0.072072</td>\n",
" <td>0.073073</td>\n",
" <td>0.074074</td>\n",
" <td>0.075075</td>\n",
" <td>0.076076</td>\n",
" <td>0.077077</td>\n",
" <td>0.078078</td>\n",
" <td>0.079079</td>\n",
" <td>0.080080</td>\n",
" <td>0.081081</td>\n",
" <td>0.082082</td>\n",
" <td>0.083083</td>\n",
" <td>0.084084</td>\n",
" <td>0.085085</td>\n",
" <td>0.086086</td>\n",
" <td>0.087087</td>\n",
" <td>0.088088</td>\n",
" <td>0.089089</td>\n",
" <td>0.090090</td>\n",
" <td>0.091091</td>\n",
" <td>0.092092</td>\n",
" <td>0.093093</td>\n",
" <td>0.094094</td>\n",
" <td>0.095095</td>\n",
" <td>0.096096</td>\n",
" <td>0.097097</td>\n",
" <td>0.098098</td>\n",
" <td>0.099099</td>\n",
" <td>0.100100</td>\n",
" <td>0.101101</td>\n",
" <td>0.102102</td>\n",
" <td>0.103103</td>\n",
" <td>0.104104</td>\n",
" <td>0.105105</td>\n",
" <td>0.106106</td>\n",
" <td>0.107107</td>\n",
" <td>0.108108</td>\n",
" <td>0.109109</td>\n",
" <td>0.110110</td>\n",
" <td>0.111111</td>\n",
" <td>0.112112</td>\n",
" <td>0.113113</td>\n",
" <td>0.114114</td>\n",
" <td>0.115115</td>\n",
" <td>0.116116</td>\n",
" <td>0.117117</td>\n",
" <td>0.118118</td>\n",
" <td>0.119119</td>\n",
" <td>0.120120</td>\n",
" <td>0.121121</td>\n",
" <td>0.122122</td>\n",
" <td>0.123123</td>\n",
" <td>0.124124</td>\n",
" <td>0.125125</td>\n",
" <td>0.126126</td>\n",
" <td>0.127127</td>\n",
" <td>0.128128</td>\n",
" <td>0.129129</td>\n",
" <td>0.130130</td>\n",
" <td>0.131131</td>\n",
" <td>0.132132</td>\n",
" <td>0.133133</td>\n",
" <td>0.134134</td>\n",
" <td>0.135135</td>\n",
" <td>0.136136</td>\n",
" <td>0.137137</td>\n",
" <td>0.138138</td>\n",
" <td>0.139139</td>\n",
" <td>0.140140</td>\n",
" <td>0.141141</td>\n",
" <td>0.142142</td>\n",
" <td>0.143143</td>\n",
" <td>0.144144</td>\n",
" <td>0.145145</td>\n",
" <td>0.146146</td>\n",
" <td>0.147147</td>\n",
" <td>0.148148</td>\n",
" <td>0.149149</td>\n",
" <td>0.150150</td>\n",
" <td>0.151151</td>\n",
" <td>0.152152</td>\n",
" <td>0.153153</td>\n",
" <td>0.154154</td>\n",
" <td>0.155155</td>\n",
" <td>0.156156</td>\n",
" <td>0.157157</td>\n",
" <td>0.158158</td>\n",
" <td>0.159159</td>\n",
" <td>0.160160</td>\n",
" <td>0.161161</td>\n",
" <td>0.162162</td>\n",
" <td>0.163163</td>\n",
" <td>0.164164</td>\n",
" <td>0.165165</td>\n",
" <td>0.166166</td>\n",
" <td>0.167167</td>\n",
" <td>0.168168</td>\n",
" <td>0.169169</td>\n",
" <td>0.170170</td>\n",
" <td>0.171171</td>\n",
" <td>0.172172</td>\n",
" <td>0.173173</td>\n",
" <td>0.174174</td>\n",
" <td>0.175175</td>\n",
" <td>0.176176</td>\n",
" <td>0.177177</td>\n",
" <td>0.178178</td>\n",
" <td>0.179179</td>\n",
" <td>0.180180</td>\n",
" <td>0.181181</td>\n",
" <td>0.182182</td>\n",
" <td>0.183183</td>\n",
" <td>0.184184</td>\n",
" <td>0.185185</td>\n",
" <td>0.186186</td>\n",
" <td>0.187187</td>\n",
" <td>0.188188</td>\n",
" <td>0.189189</td>\n",
" <td>0.190190</td>\n",
" <td>0.191191</td>\n",
" <td>0.192192</td>\n",
" <td>0.193193</td>\n",
" <td>0.194194</td>\n",
" <td>0.195195</td>\n",
" <td>0.196196</td>\n",
" <td>0.197197</td>\n",
" <td>0.198198</td>\n",
" <td>0.199199</td>\n",
" <td>0.20020</td>\n",
" <td>0.201201</td>\n",
" <td>0.202202</td>\n",
" <td>0.203203</td>\n",
" <td>0.204204</td>\n",
" <td>0.205205</td>\n",
" <td>0.206206</td>\n",
" <td>0.207207</td>\n",
" <td>0.208208</td>\n",
" <td>0.209209</td>\n",
" <td>0.210210</td>\n",
" <td>0.211211</td>\n",
" <td>0.212212</td>\n",
" <td>0.213213</td>\n",
" <td>0.214214</td>\n",
" <td>0.215215</td>\n",
" <td>0.216216</td>\n",
" <td>0.217217</td>\n",
" <td>0.218218</td>\n",
" <td>0.219219</td>\n",
" <td>0.220220</td>\n",
" <td>0.221221</td>\n",
" <td>0.222222</td>\n",
" <td>0.223223</td>\n",
" <td>0.224224</td>\n",
" <td>0.225225</td>\n",
" <td>0.226226</td>\n",
" <td>0.227227</td>\n",
" <td>0.228228</td>\n",
" <td>0.229229</td>\n",
" <td>0.230230</td>\n",
" <td>0.231231</td>\n",
" <td>0.232232</td>\n",
" <td>0.233233</td>\n",
" <td>0.234234</td>\n",
" <td>0.235235</td>\n",
" <td>0.236236</td>\n",
" <td>0.237237</td>\n",
" <td>0.238238</td>\n",
" <td>0.239239</td>\n",
" <td>0.240240</td>\n",
" <td>0.241241</td>\n",
" <td>0.242242</td>\n",
" <td>0.243243</td>\n",
" <td>0.244244</td>\n",
" <td>0.245245</td>\n",
" <td>0.246246</td>\n",
" <td>0.247247</td>\n",
" <td>0.248248</td>\n",
" <td>0.249249</td>\n",
" <td>...</td>\n",
" <td>0.750751</td>\n",
" <td>0.751752</td>\n",
" <td>0.752753</td>\n",
" <td>0.753754</td>\n",
" <td>0.754755</td>\n",
" <td>0.755756</td>\n",
" <td>0.756757</td>\n",
" <td>0.757758</td>\n",
" <td>0.758759</td>\n",
" <td>0.759760</td>\n",
" <td>0.760761</td>\n",
" <td>0.761762</td>\n",
" <td>0.762763</td>\n",
" <td>0.763764</td>\n",
" <td>0.764765</td>\n",
" <td>0.765766</td>\n",
" <td>0.766767</td>\n",
" <td>0.767768</td>\n",
" <td>0.768769</td>\n",
" <td>0.769770</td>\n",
" <td>0.770771</td>\n",
" <td>0.771772</td>\n",
" <td>0.772773</td>\n",
" <td>0.773774</td>\n",
" <td>0.774775</td>\n",
" <td>0.775776</td>\n",
" <td>0.776777</td>\n",
" <td>0.777778</td>\n",
" <td>0.778779</td>\n",
" <td>0.779780</td>\n",
" <td>0.780781</td>\n",
" <td>0.781782</td>\n",
" <td>0.782783</td>\n",
" <td>0.783784</td>\n",
" <td>0.784785</td>\n",
" <td>0.785786</td>\n",
" <td>0.786787</td>\n",
" <td>0.787788</td>\n",
" <td>0.788789</td>\n",
" <td>0.789790</td>\n",
" <td>0.790791</td>\n",
" <td>0.791792</td>\n",
" <td>0.792793</td>\n",
" <td>0.793794</td>\n",
" <td>0.794795</td>\n",
" <td>0.795796</td>\n",
" <td>0.796797</td>\n",
" <td>0.797798</td>\n",
" <td>0.798799</td>\n",
" <td>0.79980</td>\n",
" <td>0.800801</td>\n",
" <td>0.801802</td>\n",
" <td>0.802803</td>\n",
" <td>0.803804</td>\n",
" <td>0.804805</td>\n",
" <td>0.805806</td>\n",
" <td>0.806807</td>\n",
" <td>0.807808</td>\n",
" <td>0.808809</td>\n",
" <td>0.809810</td>\n",
" <td>0.810811</td>\n",
" <td>0.811812</td>\n",
" <td>0.812813</td>\n",
" <td>0.813814</td>\n",
" <td>0.814815</td>\n",
" <td>0.815816</td>\n",
" <td>0.816817</td>\n",
" <td>0.817818</td>\n",
" <td>0.818819</td>\n",
" <td>0.819820</td>\n",
" <td>0.820821</td>\n",
" <td>0.821822</td>\n",
" <td>0.822823</td>\n",
" <td>0.823824</td>\n",
" <td>0.824825</td>\n",
" <td>0.825826</td>\n",
" <td>0.826827</td>\n",
" <td>0.827828</td>\n",
" <td>0.828829</td>\n",
" <td>0.829830</td>\n",
" <td>0.830831</td>\n",
" <td>0.831832</td>\n",
" <td>0.832833</td>\n",
" <td>0.833834</td>\n",
" <td>0.834835</td>\n",
" <td>0.835836</td>\n",
" <td>0.836837</td>\n",
" <td>0.837838</td>\n",
" <td>0.838839</td>\n",
" <td>0.839840</td>\n",
" <td>0.840841</td>\n",
" <td>0.841842</td>\n",
" <td>0.842843</td>\n",
" <td>0.843844</td>\n",
" <td>0.844845</td>\n",
" <td>0.845846</td>\n",
" <td>0.846847</td>\n",
" <td>0.847848</td>\n",
" <td>0.848849</td>\n",
" <td>0.849850</td>\n",
" <td>0.850851</td>\n",
" <td>0.851852</td>\n",
" <td>0.852853</td>\n",
" <td>0.853854</td>\n",
" <td>0.854855</td>\n",
" <td>0.855856</td>\n",
" <td>0.856857</td>\n",
" <td>0.857858</td>\n",
" <td>0.858859</td>\n",
" <td>0.859860</td>\n",
" <td>0.860861</td>\n",
" <td>0.861862</td>\n",
" <td>0.862863</td>\n",
" <td>0.863864</td>\n",
" <td>0.864865</td>\n",
" <td>0.865866</td>\n",
" <td>0.866867</td>\n",
" <td>0.867868</td>\n",
" <td>0.868869</td>\n",
" <td>0.869870</td>\n",
" <td>0.870871</td>\n",
" <td>0.871872</td>\n",
" <td>0.872873</td>\n",
" <td>0.873874</td>\n",
" <td>0.874875</td>\n",
" <td>0.875876</td>\n",
" <td>0.876877</td>\n",
" <td>0.877878</td>\n",
" <td>0.878879</td>\n",
" <td>0.879880</td>\n",
" <td>0.880881</td>\n",
" <td>0.881882</td>\n",
" <td>0.882883</td>\n",
" <td>0.883884</td>\n",
" <td>0.884885</td>\n",
" <td>0.885886</td>\n",
" <td>0.886887</td>\n",
" <td>0.887888</td>\n",
" <td>0.888889</td>\n",
" <td>0.889890</td>\n",
" <td>0.890891</td>\n",
" <td>0.891892</td>\n",
" <td>0.892893</td>\n",
" <td>0.893894</td>\n",
" <td>0.894895</td>\n",
" <td>0.895896</td>\n",
" <td>0.896897</td>\n",
" <td>0.897898</td>\n",
" <td>0.898899</td>\n",
" <td>0.899900</td>\n",
" <td>0.900901</td>\n",
" <td>0.901902</td>\n",
" <td>0.902903</td>\n",
" <td>0.903904</td>\n",
" <td>0.904905</td>\n",
" <td>0.905906</td>\n",
" <td>0.906907</td>\n",
" <td>0.907908</td>\n",
" <td>0.908909</td>\n",
" <td>0.909910</td>\n",
" <td>0.910911</td>\n",
" <td>0.911912</td>\n",
" <td>0.912913</td>\n",
" <td>0.913914</td>\n",
" <td>0.914915</td>\n",
" <td>0.915916</td>\n",
" <td>0.916917</td>\n",
" <td>0.917918</td>\n",
" <td>0.918919</td>\n",
" <td>0.919920</td>\n",
" <td>0.920921</td>\n",
" <td>0.921922</td>\n",
" <td>0.922923</td>\n",
" <td>0.923924</td>\n",
" <td>0.924925</td>\n",
" <td>0.925926</td>\n",
" <td>0.926927</td>\n",
" <td>0.927928</td>\n",
" <td>0.928929</td>\n",
" <td>0.929930</td>\n",
" <td>0.930931</td>\n",
" <td>0.931932</td>\n",
" <td>0.932933</td>\n",
" <td>0.933934</td>\n",
" <td>0.934935</td>\n",
" <td>0.935936</td>\n",
" <td>0.936937</td>\n",
" <td>0.937938</td>\n",
" <td>0.938939</td>\n",
" <td>0.939940</td>\n",
" <td>0.940941</td>\n",
" <td>0.941942</td>\n",
" <td>0.942943</td>\n",
" <td>0.943944</td>\n",
" <td>0.944945</td>\n",
" <td>0.945946</td>\n",
" <td>0.946947</td>\n",
" <td>0.947948</td>\n",
" <td>0.948949</td>\n",
" <td>0.949950</td>\n",
" <td>0.950951</td>\n",
" <td>0.951952</td>\n",
" <td>0.952953</td>\n",
" <td>0.953954</td>\n",
" <td>0.954955</td>\n",
" <td>0.955956</td>\n",
" <td>0.956957</td>\n",
" <td>0.957958</td>\n",
" <td>0.958959</td>\n",
" <td>0.959960</td>\n",
" <td>0.960961</td>\n",
" <td>0.961962</td>\n",
" <td>0.962963</td>\n",
" <td>0.963964</td>\n",
" <td>0.964965</td>\n",
" <td>0.965966</td>\n",
" <td>0.966967</td>\n",
" <td>0.967968</td>\n",
" <td>0.968969</td>\n",
" <td>0.969970</td>\n",
" <td>0.970971</td>\n",
" <td>0.971972</td>\n",
" <td>0.972973</td>\n",
" <td>0.973974</td>\n",
" <td>0.974975</td>\n",
" <td>0.975976</td>\n",
" <td>0.976977</td>\n",
" <td>0.977978</td>\n",
" <td>0.978979</td>\n",
" <td>0.979980</td>\n",
" <td>0.980981</td>\n",
" <td>0.981982</td>\n",
" <td>0.982983</td>\n",
" <td>0.983984</td>\n",
" <td>0.984985</td>\n",
" <td>0.985986</td>\n",
" <td>0.986987</td>\n",
" <td>0.987988</td>\n",
" <td>0.988989</td>\n",
" <td>0.989990</td>\n",
" <td>0.990991</td>\n",
" <td>0.991992</td>\n",
" <td>0.992993</td>\n",
" <td>0.993994</td>\n",
" <td>0.994995</td>\n",
" <td>0.995996</td>\n",
" <td>0.996997</td>\n",
" <td>0.997998</td>\n",
" <td>0.998999</td>\n",
" <td>1.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>y</th>\n",
" <td>0.0</td>\n",
" <td>0.032443</td>\n",
" <td>0.064855</td>\n",
" <td>0.097205</td>\n",
" <td>0.129462</td>\n",
" <td>0.161595</td>\n",
" <td>0.193573</td>\n",
" <td>0.225365</td>\n",
" <td>0.256942</td>\n",
" <td>0.288272</td>\n",
" <td>0.319326</td>\n",
" <td>0.350074</td>\n",
" <td>0.380487</td>\n",
" <td>0.410536</td>\n",
" <td>0.440192</td>\n",
" <td>0.469426</td>\n",
" <td>0.498211</td>\n",
" <td>0.526519</td>\n",
" <td>0.554323</td>\n",
" <td>0.581596</td>\n",
" <td>0.608314</td>\n",
" <td>0.634450</td>\n",
" <td>0.659979</td>\n",
" <td>0.684877</td>\n",
" <td>0.709121</td>\n",
" <td>0.732688</td>\n",
" <td>0.755554</td>\n",
" <td>0.777699</td>\n",
" <td>0.799102</td>\n",
" <td>0.819743</td>\n",
" <td>0.839601</td>\n",
" <td>0.858659</td>\n",
" <td>0.876899</td>\n",
" <td>0.894303</td>\n",
" <td>0.910855</td>\n",
" <td>0.926541</td>\n",
" <td>0.941345</td>\n",
" <td>0.955253</td>\n",
" <td>0.968254</td>\n",
" <td>0.980335</td>\n",
" <td>0.991485</td>\n",
" <td>1.001694</td>\n",
" <td>1.010953</td>\n",
" <td>1.019254</td>\n",
" <td>1.026590</td>\n",
" <td>1.032954</td>\n",
" <td>1.038341</td>\n",
" <td>1.042747</td>\n",
" <td>1.046168</td>\n",
" <td>1.048603</td>\n",
" <td>1.050049</td>\n",
" <td>1.050506</td>\n",
" <td>1.049975</td>\n",
" <td>1.048457</td>\n",
" <td>1.045954</td>\n",
" <td>1.042471</td>\n",
" <td>1.038012</td>\n",
" <td>1.032581</td>\n",
" <td>1.026186</td>\n",
" <td>1.018833</td>\n",
" <td>1.010532</td>\n",
" <td>1.001290</td>\n",
" <td>0.991119</td>\n",
" <td>0.980029</td>\n",
" <td>0.968032</td>\n",
" <td>0.955142</td>\n",
" <td>0.941371</td>\n",
" <td>0.926735</td>\n",
" <td>0.911248</td>\n",
" <td>0.894928</td>\n",
" <td>0.877791</td>\n",
" <td>0.859856</td>\n",
" <td>0.841140</td>\n",
" <td>0.821664</td>\n",
" <td>0.801448</td>\n",
" <td>0.780512</td>\n",
" <td>0.758879</td>\n",
" <td>0.736571</td>\n",
" <td>0.713610</td>\n",
" <td>0.690021</td>\n",
" <td>0.665828</td>\n",
" <td>0.641056</td>\n",
" <td>0.615730</td>\n",
" <td>0.589876</td>\n",
" <td>0.563521</td>\n",
" <td>0.536692</td>\n",
" <td>0.509417</td>\n",
" <td>0.481723</td>\n",
" <td>0.453638</td>\n",
" <td>0.425192</td>\n",
" <td>0.396414</td>\n",
" <td>0.367333</td>\n",
" <td>0.337979</td>\n",
" <td>0.308381</td>\n",
" <td>0.278571</td>\n",
" <td>0.248578</td>\n",
" <td>0.218434</td>\n",
" <td>0.188168</td>\n",
" <td>0.157813</td>\n",
" <td>0.127398</td>\n",
" <td>0.096955</td>\n",
" <td>0.066516</td>\n",
" <td>0.036111</td>\n",
" <td>0.005771</td>\n",
" <td>-0.024473</td>\n",
" <td>-0.054590</td>\n",
" <td>-0.084549</td>\n",
" <td>-0.114319</td>\n",
" <td>-0.143870</td>\n",
" <td>-0.173172</td>\n",
" <td>-0.202195</td>\n",
" <td>-0.230909</td>\n",
" <td>-0.259285</td>\n",
" <td>-0.287294</td>\n",
" <td>-0.314906</td>\n",
" <td>-0.342095</td>\n",
" <td>-0.368831</td>\n",
" <td>-0.395088</td>\n",
" <td>-0.420838</td>\n",
" <td>-0.446055</td>\n",
" <td>-0.470714</td>\n",
" <td>-0.494788</td>\n",
" <td>-0.518253</td>\n",
" <td>-0.541085</td>\n",
" <td>-0.563260</td>\n",
" <td>-0.584756</td>\n",
" <td>-0.605549</td>\n",
" <td>-0.625619</td>\n",
" <td>-0.644945</td>\n",
" <td>-0.663506</td>\n",
" <td>-0.681283</td>\n",
" <td>-0.698258</td>\n",
" <td>-0.714413</td>\n",
" <td>-0.729730</td>\n",
" <td>-0.744195</td>\n",
" <td>-0.757791</td>\n",
" <td>-0.770504</td>\n",
" <td>-0.782320</td>\n",
" <td>-0.793227</td>\n",
" <td>-0.803213</td>\n",
" <td>-0.812268</td>\n",
" <td>-0.820380</td>\n",
" <td>-0.827542</td>\n",
" <td>-0.833745</td>\n",
" <td>-0.838982</td>\n",
" <td>-0.843246</td>\n",
" <td>-0.846534</td>\n",
" <td>-0.848839</td>\n",
" <td>-0.850160</td>\n",
" <td>-0.850494</td>\n",
" <td>-0.849839</td>\n",
" <td>-0.848195</td>\n",
" <td>-0.845563</td>\n",
" <td>-0.841944</td>\n",
" <td>-0.837342</td>\n",
" <td>-0.831759</td>\n",
" <td>-0.825200</td>\n",
" <td>-0.817671</td>\n",
" <td>-0.809177</td>\n",
" <td>-0.799728</td>\n",
" <td>-0.789329</td>\n",
" <td>-0.777993</td>\n",
" <td>-0.765727</td>\n",
" <td>-0.752544</td>\n",
" <td>-0.738455</td>\n",
" <td>-0.723474</td>\n",
" <td>-0.707614</td>\n",
" <td>-0.690890</td>\n",
" <td>-0.673317</td>\n",
" <td>-0.654912</td>\n",
" <td>-0.635693</td>\n",
" <td>-0.615677</td>\n",
" <td>-0.594882</td>\n",
" <td>-0.573329</td>\n",
" <td>-0.551038</td>\n",
" <td>-0.528030</td>\n",
" <td>-0.504326</td>\n",
" <td>-0.479949</td>\n",
" <td>-0.454923</td>\n",
" <td>-0.429270</td>\n",
" <td>-0.403016</td>\n",
" <td>-0.376185</td>\n",
" <td>-0.348803</td>\n",
" <td>-0.320896</td>\n",
" <td>-0.292491</td>\n",
" <td>-0.263614</td>\n",
" <td>-0.234293</td>\n",
" <td>-0.204557</td>\n",
" <td>-0.174433</td>\n",
" <td>-0.143951</td>\n",
" <td>-0.113139</td>\n",
" <td>-0.082027</td>\n",
" <td>-0.050645</td>\n",
" <td>-0.019023</td>\n",
" <td>0.012809</td>\n",
" <td>0.044820</td>\n",
" <td>0.076980</td>\n",
" <td>0.109258</td>\n",
" <td>0.141623</td>\n",
" <td>0.174044</td>\n",
" <td>0.20649</td>\n",
" <td>0.238929</td>\n",
" <td>0.271331</td>\n",
" <td>0.303665</td>\n",
" <td>0.335899</td>\n",
" <td>0.368004</td>\n",
" <td>0.399947</td>\n",
" <td>0.431699</td>\n",
" <td>0.463228</td>\n",
" <td>0.494506</td>\n",
" <td>0.525501</td>\n",
" <td>0.556185</td>\n",
" <td>0.586527</td>\n",
" <td>0.616500</td>\n",
" <td>0.646073</td>\n",
" <td>0.675220</td>\n",
" <td>0.703911</td>\n",
" <td>0.732121</td>\n",
" <td>0.759821</td>\n",
" <td>0.786985</td>\n",
" <td>0.813588</td>\n",
" <td>0.839605</td>\n",
" <td>0.865010</td>\n",
" <td>0.889779</td>\n",
" <td>0.913889</td>\n",
" <td>0.937318</td>\n",
" <td>0.960042</td>\n",
" <td>0.982040</td>\n",
" <td>1.003292</td>\n",
" <td>1.023778</td>\n",
" <td>1.043477</td>\n",
" <td>1.062373</td>\n",
" <td>1.080447</td>\n",
" <td>1.097682</td>\n",
" <td>1.114062</td>\n",
" <td>1.129572</td>\n",
" <td>1.144198</td>\n",
" <td>1.157926</td>\n",
" <td>1.170744</td>\n",
" <td>1.182639</td>\n",
" <td>1.193602</td>\n",
" <td>1.203622</td>\n",
" <td>1.212690</td>\n",
" <td>1.220798</td>\n",
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" <td>1.0</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>2 rows × 1000 columns</p>\n",
"</div>"
],
"text/plain": [
" 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 \\\n",
"x 0.0 0.001001 0.002002 0.003003 0.004004 0.005005 0.006006 0.007007 0.008008 0.009009 0.010010 0.011011 0.012012 0.013013 0.014014 0.015015 0.016016 0.017017 0.018018 0.019019 0.020020 0.021021 0.022022 0.023023 0.024024 0.025025 0.026026 0.027027 0.028028 0.029029 0.030030 0.031031 0.032032 0.033033 0.034034 0.035035 0.036036 0.037037 0.038038 0.039039 0.040040 0.041041 0.042042 0.043043 0.044044 0.045045 0.046046 0.047047 0.048048 0.049049 0.050050 0.051051 0.052052 0.053053 0.054054 0.055055 0.056056 0.057057 0.058058 0.059059 0.060060 0.061061 0.062062 0.063063 0.064064 0.065065 0.066066 0.067067 0.068068 0.069069 0.070070 0.071071 0.072072 0.073073 0.074074 0.075075 0.076076 0.077077 0.078078 0.079079 0.080080 0.081081 0.082082 0.083083 0.084084 0.085085 0.086086 0.087087 0.088088 0.089089 0.090090 0.091091 0.092092 0.093093 0.094094 0.095095 0.096096 0.097097 0.098098 0.099099 \n",
"y 0.0 0.032443 0.064855 0.097205 0.129462 0.161595 0.193573 0.225365 0.256942 0.288272 0.319326 0.350074 0.380487 0.410536 0.440192 0.469426 0.498211 0.526519 0.554323 0.581596 0.608314 0.634450 0.659979 0.684877 0.709121 0.732688 0.755554 0.777699 0.799102 0.819743 0.839601 0.858659 0.876899 0.894303 0.910855 0.926541 0.941345 0.955253 0.968254 0.980335 0.991485 1.001694 1.010953 1.019254 1.026590 1.032954 1.038341 1.042747 1.046168 1.048603 1.050049 1.050506 1.049975 1.048457 1.045954 1.042471 1.038012 1.032581 1.026186 1.018833 1.010532 1.001290 0.991119 0.980029 0.968032 0.955142 0.941371 0.926735 0.911248 0.894928 0.877791 0.859856 0.841140 0.821664 0.801448 0.780512 0.758879 0.736571 0.713610 0.690021 0.665828 0.641056 0.615730 0.589876 0.563521 0.536692 0.509417 0.481723 0.453638 0.425192 0.396414 0.367333 0.337979 0.308381 0.278571 0.248578 0.218434 0.188168 0.157813 0.127398 \n",
"\n",
" 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 \\\n",
"x 0.100100 0.101101 0.102102 0.103103 0.104104 0.105105 0.106106 0.107107 0.108108 0.109109 0.110110 0.111111 0.112112 0.113113 0.114114 0.115115 0.116116 0.117117 0.118118 0.119119 0.120120 0.121121 0.122122 0.123123 0.124124 0.125125 0.126126 0.127127 0.128128 0.129129 0.130130 0.131131 0.132132 0.133133 0.134134 0.135135 0.136136 0.137137 0.138138 0.139139 0.140140 0.141141 0.142142 0.143143 0.144144 0.145145 0.146146 0.147147 0.148148 0.149149 0.150150 0.151151 0.152152 0.153153 0.154154 0.155155 0.156156 0.157157 0.158158 0.159159 0.160160 0.161161 0.162162 0.163163 0.164164 0.165165 0.166166 0.167167 0.168168 0.169169 0.170170 0.171171 0.172172 0.173173 0.174174 0.175175 0.176176 0.177177 0.178178 0.179179 0.180180 0.181181 0.182182 0.183183 0.184184 0.185185 0.186186 0.187187 0.188188 0.189189 0.190190 0.191191 0.192192 0.193193 0.194194 0.195195 0.196196 0.197197 0.198198 \n",
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"\n",
" 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 ... 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 \\\n",
"x 0.199199 0.20020 0.201201 0.202202 0.203203 0.204204 0.205205 0.206206 0.207207 0.208208 0.209209 0.210210 0.211211 0.212212 0.213213 0.214214 0.215215 0.216216 0.217217 0.218218 0.219219 0.220220 0.221221 0.222222 0.223223 0.224224 0.225225 0.226226 0.227227 0.228228 0.229229 0.230230 0.231231 0.232232 0.233233 0.234234 0.235235 0.236236 0.237237 0.238238 0.239239 0.240240 0.241241 0.242242 0.243243 0.244244 0.245245 0.246246 0.247247 0.248248 0.249249 ... 0.750751 0.751752 0.752753 0.753754 0.754755 0.755756 0.756757 0.757758 0.758759 0.759760 0.760761 0.761762 0.762763 0.763764 0.764765 0.765766 0.766767 0.767768 0.768769 0.769770 0.770771 0.771772 0.772773 0.773774 0.774775 0.775776 0.776777 0.777778 0.778779 0.779780 0.780781 0.781782 0.782783 0.783784 0.784785 0.785786 0.786787 0.787788 0.788789 0.789790 0.790791 0.791792 0.792793 0.793794 0.794795 0.795796 0.796797 0.797798 \n",
"y 0.174044 0.20649 0.238929 0.271331 0.303665 0.335899 0.368004 0.399947 0.431699 0.463228 0.494506 0.525501 0.556185 0.586527 0.616500 0.646073 0.675220 0.703911 0.732121 0.759821 0.786985 0.813588 0.839605 0.865010 0.889779 0.913889 0.937318 0.960042 0.982040 1.003292 1.023778 1.043477 1.062373 1.080447 1.097682 1.114062 1.129572 1.144198 1.157926 1.170744 1.182639 1.193602 1.203622 1.212690 1.220798 1.227940 1.234110 1.239301 1.243510 1.246734 1.248971 ... -0.248971 -0.246734 -0.243510 -0.239301 -0.234110 -0.227940 -0.220798 -0.212690 -0.203622 -0.193602 -0.182639 -0.170744 -0.157926 -0.144198 -0.129572 -0.114062 -0.097682 -0.080447 -0.062373 -0.043477 -0.023778 -0.003292 0.017960 0.039958 0.062682 0.086111 0.110221 0.134990 0.160395 0.186412 0.213015 0.240179 0.267879 0.296089 0.324780 0.353927 0.383500 0.413473 0.443815 0.474499 0.505494 0.536772 0.568301 0.600053 0.631996 0.664101 0.696335 0.728669 \n",
"\n",
" 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 \\\n",
"x 0.798799 0.79980 0.800801 0.801802 0.802803 0.803804 0.804805 0.805806 0.806807 0.807808 0.808809 0.809810 0.810811 0.811812 0.812813 0.813814 0.814815 0.815816 0.816817 0.817818 0.818819 0.819820 0.820821 0.821822 0.822823 0.823824 0.824825 0.825826 0.826827 0.827828 0.828829 0.829830 0.830831 0.831832 0.832833 0.833834 0.834835 0.835836 0.836837 0.837838 0.838839 0.839840 0.840841 0.841842 0.842843 0.843844 0.844845 0.845846 0.846847 0.847848 0.848849 0.849850 0.850851 0.851852 0.852853 0.853854 0.854855 0.855856 0.856857 0.857858 0.858859 0.859860 0.860861 0.861862 0.862863 0.863864 0.864865 0.865866 0.866867 0.867868 0.868869 0.869870 0.870871 0.871872 0.872873 0.873874 0.874875 0.875876 0.876877 0.877878 0.878879 0.879880 0.880881 0.881882 0.882883 0.883884 0.884885 0.885886 0.886887 0.887888 0.888889 0.889890 0.890891 0.891892 0.892893 0.893894 0.894895 0.895896 0.896897 \n",
"y 0.761071 0.79351 0.825956 0.858377 0.890742 0.923020 0.955180 0.987191 1.019023 1.050645 1.082027 1.113139 1.143951 1.174433 1.204557 1.234293 1.263614 1.292491 1.320896 1.348803 1.376185 1.403016 1.429270 1.454923 1.479949 1.504326 1.528030 1.551038 1.573329 1.594882 1.615677 1.635693 1.654912 1.673317 1.690890 1.707614 1.723474 1.738455 1.752544 1.765727 1.777993 1.789329 1.799728 1.809177 1.817671 1.825200 1.831759 1.837342 1.841944 1.845563 1.848195 1.849839 1.850494 1.850160 1.848839 1.846534 1.843246 1.838982 1.833745 1.827542 1.820380 1.812268 1.803213 1.793227 1.782320 1.770504 1.757791 1.744195 1.729730 1.714413 1.698258 1.681283 1.663506 1.644945 1.625619 1.605549 1.584756 1.563260 1.541085 1.518253 1.494788 1.470714 1.446055 1.420838 1.395088 1.368831 1.342095 1.314906 1.287294 1.259285 1.230909 1.202195 1.173172 1.143870 1.114319 1.084549 1.054590 1.024473 0.994229 \n",
"\n",
" 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 \\\n",
"x 0.897898 0.898899 0.899900 0.900901 0.901902 0.902903 0.903904 0.904905 0.905906 0.906907 0.907908 0.908909 0.909910 0.910911 0.911912 0.912913 0.913914 0.914915 0.915916 0.916917 0.917918 0.918919 0.919920 0.920921 0.921922 0.922923 0.923924 0.924925 0.925926 0.926927 0.927928 0.928929 0.929930 0.930931 0.931932 0.932933 0.933934 0.934935 0.935936 0.936937 0.937938 0.938939 0.939940 0.940941 0.941942 0.942943 0.943944 0.944945 0.945946 0.946947 0.947948 0.948949 0.949950 0.950951 0.951952 0.952953 0.953954 0.954955 0.955956 0.956957 0.957958 0.958959 0.959960 0.960961 0.961962 0.962963 0.963964 0.964965 0.965966 0.966967 0.967968 0.968969 0.969970 0.970971 0.971972 0.972973 0.973974 0.974975 0.975976 0.976977 0.977978 0.978979 0.979980 0.980981 0.981982 0.982983 0.983984 0.984985 0.985986 0.986987 0.987988 0.988989 0.989990 0.990991 0.991992 0.992993 0.993994 0.994995 0.995996 \n",
"y 0.963889 0.933484 0.903045 0.872602 0.842187 0.811832 0.781566 0.751422 0.721429 0.691619 0.662021 0.632667 0.603586 0.574808 0.546362 0.518277 0.490583 0.463308 0.436479 0.410124 0.384270 0.358944 0.334172 0.309979 0.286390 0.263429 0.241121 0.219488 0.198552 0.178336 0.158860 0.140144 0.122209 0.105072 0.088752 0.073265 0.058629 0.044858 0.031968 0.019971 0.008881 -0.001290 -0.010532 -0.018833 -0.026186 -0.032581 -0.038012 -0.042471 -0.045954 -0.048457 -0.049975 -0.050506 -0.050049 -0.048603 -0.046168 -0.042747 -0.038341 -0.032954 -0.026590 -0.019254 -0.010953 -0.001694 0.008515 0.019665 0.031746 0.044747 0.058655 0.073459 0.089145 0.105697 0.123101 0.141341 0.160399 0.180257 0.200898 0.222301 0.244446 0.267312 0.290879 0.315123 0.340021 0.365550 0.391686 0.418404 0.445677 0.473481 0.501789 0.530574 0.559808 0.589464 0.619513 0.649926 0.680674 0.711728 0.743058 0.774635 0.806427 0.838405 0.870538 \n",
"\n",
" 996 997 998 999 \n",
"x 0.996997 0.997998 0.998999 1.0 \n",
"y 0.902795 0.935145 0.967557 1.0 \n",
"\n",
"[2 rows x 1000 columns]"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"dft = df.T\n",
"dft.head()"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"df.to_csv('minepy_example_1.csv', index=False)\n",
"dft.to_csv('minepy_example_1_t.csv', sep='\\t')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" java -jar MINEv2.jar ./minepy_example_1.csv 0 cv=0.1 -equitability id=fewBoxes\n",
" Analysis Parameters...\n",
" MIC estimator = MICe\n",
" alpha = 0.75\n",
" numClumpsFactor = 5\n",
" alphaTICe = 0,334\n",
" debug level = 0\n",
" required common values fraction = 0.1\n",
"\n",
" less minepy_example_1.csv,fewBoxes,Results.csv"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
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"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>X var</th>\n",
" <th>Y var</th>\n",
" <th>n</th>\n",
" <th>MICe (strength)</th>\n",
" <th>TICe (presence of relationship)</th>\n",
" <th>MICe-p^2 (nonlinearity)</th>\n",
" <th>MASe (non-monotonicity)</th>\n",
" <th>MEVe (functionality)</th>\n",
" <th>MCNe (complexity)</th>\n",
" <th>Linear regression (p)</th>\n",
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" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>x</td>\n",
" <td>y</td>\n",
" <td>1000</td>\n",
" <td>0.91567</td>\n",
" <td>0.87916</td>\n",
" <td>0.854032</td>\n",
" <td>0.62961</td>\n",
" <td>0.91567</td>\n",
" <td>7.189825</td>\n",
" <td>0.24827</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" X var Y var n MICe (strength) TICe (presence of relationship) MICe-p^2 (nonlinearity) MASe (non-monotonicity) MEVe (functionality) MCNe (complexity) Linear regression (p)\n",
"0 x y 1000 0.91567 0.87916 0.854032 0.62961 0.91567 7.189825 0.24827"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df_result = pd.read_csv('minepy_example_1.csv,fewBoxes,Results.csv', sep=',', header=0, index_col=None)\n",
"df_result"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1.0000000000000002"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"mine = minepy.MINE(alpha=0.75, c=5, est=\"mic_approx\")\n",
"mine.compute_score(x, y)\n",
"mine.mic()"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.9134642841131009"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"mine_e = minepy.MINE(alpha=0.75, c=5, est=\"mic_e\")\n",
"mine_e.compute_score(x, y)\n",
"mine_e.mic()"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"258.6551399514505"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"mine_e.tic()"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"0.4354463635546305"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"mine_e.tic(norm=True)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"177.82794100389228"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.power(len(df), 0.75)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" mictools null -c 5 minepy_example_1_t.csv null_dist.txt # -b 178 or -b 0.75\n",
" mictools pval -c 5 minepy_example_1_t.csv null_dist.txt . # -b 178 or -b 0.75\n",
" The minimum p-value with a total of 200000 permutations is 5.000000e-06\n",
" mictools adjust pval.txt .\n",
" mictools strength -c 5 -a 0.75 minepy_example_1_t.csv pval_adj.txt strength.txt"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
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"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Var1</th>\n",
" <th>Var2</th>\n",
" <th>None</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>x</td>\n",
" <td>y</td>\n",
" <td>0.000005</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Var1 Var2 None\n",
"0 x y 0.000005"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pd.read_csv('pval.txt', sep='\\t', header=0, index_col=None)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
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" <thead>\n",
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" <th></th>\n",
" <th>Var1</th>\n",
" <th>Var2</th>\n",
" <th>None</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>x</td>\n",
" <td>y</td>\n",
" <td>0.0</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Var1 Var2 None\n",
"0 x y 0.0"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pd.read_csv('pval_adj.txt', sep='\\t', header=0, index_col=None)"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
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"\n",
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"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Class</th>\n",
" <th>Var1</th>\n",
" <th>Var2</th>\n",
" <th>TICePVal</th>\n",
" <th>PearsonR</th>\n",
" <th>SpearmanRho</th>\n",
" <th>MICe</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>None</td>\n",
" <td>x</td>\n",
" <td>y</td>\n",
" <td>0.0</td>\n",
" <td>0.24827</td>\n",
" <td>0.235509</td>\n",
" <td>0.913464</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Class Var1 Var2 TICePVal PearsonR SpearmanRho MICe\n",
"0 None x y 0.0 0.24827 0.235509 0.913464"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pd.read_csv('strength.txt', sep='\\t', header=0, index_col=None)"
]
}
],
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"kernelspec": {
"display_name": "Python 3",
"language": "python",
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@cs224
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cs224 commented May 18, 2018

This notebook is associated with the following issue report on github: minepy/minepy#15

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