diff --git a/.ipynb_checkpoints/tutorial1-checkpoint.ipynb b/.ipynb_checkpoints/tutorial1-checkpoint.ipynb
index 0bdf0e8..dc34657 100755
--- a/.ipynb_checkpoints/tutorial1-checkpoint.ipynb
+++ b/.ipynb_checkpoints/tutorial1-checkpoint.ipynb
@@ -1,5 +1,12 @@
 {
  "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "しろうず"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -685,7 +692,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 12,
    "metadata": {
     "ExecuteTime": {
      "end_time": "2016-04-13T22:41:18.151992",
@@ -799,12 +806,33 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 37,
    "metadata": {
-    "collapsed": true
+    "collapsed": false
    },
-   "outputs": [],
-   "source": []
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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r5qLELYl0rd81eMNNc+rRA2bPdhUaWy+Wn/f+TOrZVD8npQo7LQiqeDDG9h+47FCeu2Uu\n8fVDoLkoi4/DTzvU6qDDT9U5tCCo4mH9eoiIsJvWO5ThzWDe1nl0q98tAIm5FB4O3brZIudC9wbd\nmZ3i7g5DFV1aEFTxkDW6yM3qpruWUrdiXaqXc76zWkD50I/Qo2EPHX6qzqEFQRUPPvQfJGxJCK3m\noiw6/FT5mRYEVfSdPAk//ACxsa7C526eS1wDd30PAZU1/PSHHxyHZg0/nbvZXZOTKpq0IKiib9Ei\naNMGypd3HHrw5EE2HdpEh1odApCYH8TF2bsfN6H140jY4i5WFU1aEFTR58Ps5G+2fkNs3ViiwqP8\nnJSfxMe77liOrRfLT7t/4kTaCT8npQorLQiq6POh/yBkZiefz1VXwdatsH+/49CyUWVpX7M9C7ct\nDEBiqjDSgqCKtq1bITUVWrVyHOo1XhK3JBJXPwT7D7JERtq+kW++cRWuzUYqOy0IqmhLSLDj9V0M\nN/1l3y9UKFmBepXqBSAxP/Kh2Si+Qbx2LKvfaUFQRZuvq5uG4nDTnOLiIDHRbv7jUIuLW3Aq/RSb\nD5+zZbkqhrQgqKIrLQ2SkqBrV1fhc7eEeP9Bljp14KKLYOVKx6EiQlyDOBI2a7OR0oKgirLvv4cm\nTaBKFcehqWdTWbF3BZ3qdgpAYgHgS7NR/XjmbtFmI6UFQRVlPixmt2DbAjrU6kDpyNJ+TipAfJiP\n0OXSLny741vOZpz1c1KqsNGCoIouH/sPQnp0UU6dOtkmo2PHHIdeVPoimlZpypKdSwKQmCpMtCCo\nomnvXvj1V7tMtEPGmNCff5BTqVJwzTV2bSMXdLSRAi0IqqhKTITOne2S1w4lH0rGYzw0rdI0AIkF\nkC5joXykBUEVTQkJrvsPErYkEFc/DnExdyGosjqWXSxp3a5mO3Ye28me43sCkJgqLLQgqKLH67Uz\nd30sCIVOkya2GGza5Dg0IiyCLpd20eGnxZwWBFX0rFgBVatCrVqOQ89knOG7Hd/R5dIuAUgswER8\nnrWszUbFmxYEVfT4MLpo8a+LaX5xcyqVquTnpAqIDwUhrn4c32z9Bo/X4+ekVGGhBUEVPb70H2wu\npM1FWTp3hiVL4PRpx6E1y9ekRrkaLNuzLACJqcJAC4IqWo4dg1WroGNHV+EJWxJCc3e0/KpQAS6/\nHL791lV4fP147UcoxrQgqKJl/nzo0MGOy3dod+pudh/fTbsa7QKQWAGKi/Nt9VNdxqLY0oKgihYf\nmosStyTSuV5nwsPC/ZxUAYuPdz0f4dra17LuwDoOnz7s56RUYaAFQRUdxvi0O1rCloTCNTv5fFq3\nht9+szO1HSoRUYKOdToyb+u8ACSmQp0WBFV0JCeDxwNNnc8w9ng9zNs6j271uwUgsQIWFmaX/PZh\n1rIuY1E8aUFQRUfW6qYuZhgv37OcamWrcUn5SwKQWBD4YT6CcTHjWRVuWhBU0eGH5SqKjG7dYMEC\nSE93HNqgcgNKRpRk7YG1AUhMhTItCKpoOHMGvvsOuribYVzoh5vmFB0N9erB0qWOQ0VEm42KqXwV\nBBFpKiLPicgiEdkhIgdEZJ2IfCYig0WkRKATVeqCvvsOWrSASs5nGB85fYQ1+9fQsY67uQshS5ex\nUA5dsCCISGsRmQesBK4BvgdeA54EPgUM8AKwR0SG56cwiEi8iGwUkWQRGX6B49qJSLqI9HXw71HF\nlQ/NRfO3zeea2tdQMqKkn5MKMh/mI8TWjWXp7qWcSDvh56RUKMtrsfgpwCvAAGPMkfMdJCJXA48A\n/4ctEOc7Lgx4B+gM7AGWicg0Y8zGXI57CdC3KCp/EhJgzBh3oYV9uYrzufpq2LwZDhyAiy92FFqu\nRDna1mhL0vYkbmh0Q4ASVKEmryajhsaYdy9UDACMMT8YY24GXs3jfO2BFGPMDmNMOjARuDGX4x4E\nvgIO5HE+pWDXLti9G9o5n2FsjCl6HcpZoqIgNtYuBe6CLmNR/FywIBhj0rK+FpHz3k2ISKWcx59H\nTWBntse7Mr+X/Vw1gD7GmPeBQrZDiQqKxEQ77j7c+Qzjjb/Zm9MmVZr4O6vQ4Msuag3idBmLYsbJ\nKKMfRaRhzm+KSGdgtf9S4g0ge9+CFgV1YT70H2TtneyP3dHOnIFPP4WHH4bXX4dDh3w+pe+yCoLX\n6zi0VXQrTqSdYMvhLQFITIUiJxvOpgArReRvxpjRIhKJbed/AHg5n+fYDdTO9viSzO9l1xaYKPYv\ntArQXUTSjTHTc55sxIgRv38dExNDTExMPtNQRYbHA/PmwX/+4yo8YUsC97a+1+c0duyAG2+0+/L0\n6AErV8Jrr8GkSXatvaCpVw8qVrQrwLZu7Sg0a/hpwpYE/lz5zwFKUAVaUlISSUlJ+TvYGJPvD+B2\n4BgwHTvyaBtwrYP4cGAzUAeIAlYBTS9w/MdA3/P8zChlliwxpkULV6Enzp4wZf9d1hw9fdSnFA4f\nNqZxY2NeeskYr/d/358505iqVY1Zt86n0/vuoYeM+fe/XYVOWD3B9JrQy88JqWDKfO3M9TXX0cQ0\nY8w44APgBuAy4DZjzGIH8R7sHUUisA6YaIzZICLDRORPuYU4yU8VQ7NmQc+erkIXbFtA2xptqVCy\ngk8pDBtmuzCGD//jqhk9e8Irr0D//nD2rE+X8I0P8xG61u/Koh2LSPPk1T2oioJ8FwQRqSIi04F7\ngTuBz4BEEXnYyQWNMXONMY2NMQ2NMS9lfm+UMWZ0LsfebYz52sn5VTHjQ0GYlTKLng3dxWaZPh1+\n+cW+8OfmjjugcWN48UWfLuObTp3sPtOpqY5Dq5SuQpMqTVjy65IAJKZCjZM7hDVABeByY8w4Y8w9\nwK3AP0REx6apgrdrF+zcCVdd5TjUGONzQcjIgMcfh7feOv9+PCL252+/DXv3ur6Ub0qXtnMSFixw\nFa7LWBQfTgrCu0CsMeb3RdYz3723QkcCqWCYPduOoolwMjbCWnNgDZFhkT4NNx03DqpXt+vIXUit\nWnDnnfDCeadsFgAfd1HTZSyKh3wXBGPM88aYc8auGWN2G2OKwCLyqtDxpbko2d4duB1u6vXaZqJ/\n/jN/q20//jiMHw8HD7q6nO+ydlFzsaR1+5rt2XFsB3uO7wlAYiqU5LWWUb38nkisWr6npFQ+nDkD\nCxe63h1tVsosejZy31w0axaUKQP5HekcHW07l997z/UlfdOsmW3j2rTJcWhEWARdLu1C4pbEACSm\nQkledwg/iMjYzLWKciUilUTkfmA9uS9DoZT/LVpkVze96CLHoYdPH2b1/tXE1I1xffkPPoCHHnK2\nF8/DD8Po0XbqRIETge7dbTObC90bdGdWyiw/J6VCTV4FoQlwGJglIr+JSIKIfCwi74vIRBFZjV1v\n6Fbgr8aYdwKdsFKAfYveo4er0ITNCXSq28n16qZ79sD339t3/E40bw41arheWsh3vXvbYVEu9GzY\nk2+2fKPDT4u4vApCS+xS1zWBYcAGoCJQD8jALoF9hTHmGmOM9jqpgmFMUIebfvYZ9Otnm4ycuusu\n+Phj15f2TefOdvjp4cOOQ6PLRtO0alMWbV8UgMRUqBBzgU4mEfEA1YwxB0VkK9DOGBMKK7QgIuZC\nuasibNMm++K2c6fj/ZM9Xg/Rr0WzYtgKaleonXdADsZA06Ywdixcc43jcI4csatJbN0KlSs7j/fZ\njTfCzTfDkCGOQ1/87kX2HN/D2z3eDkBiqqCICMaYXP9w8rpDOAJcmvl13Xwcr1TgZTUXuRghtHT3\nUmqUq+GqGAD8+KMtCm7XJ6pUyfaDf/GFu3if9e4NM2a4Cu3VuBczkmegb8SKrrxe4CcDi0RkG3YZ\nieUisjW3j8CnqlQmPww3deuzz+zsY18WR73rLjuHISh69rTDT9Oc9wVcVvUywiSMNQfWBCAxFQry\nmtFzH3Yhu4bASOxic8cDnZRS55WaCj/9ZJuMXJiVMot3ergb++DxwJQpdvtmX1x/vW2x2bnTTlor\nUNWq2bU0vvvO8XMoIvRu3Jvpm6bTMrplgBJUwXTBgpDZSD8LQERaAf8xxmhBUMEzZw5cdx2ULes4\ndPvR7ew5voerLznvKOoL+uEHuxNlgwauwn8XGQm9etni8tBDvp3LlV697GgjF0W1V6NePLngSZ7u\n+HQAElPB5mSm8l1aDFTQTZsGffq4C904jV6NehEe5nxnNYCvv4a+fV2FnqNvX3u+oMgafuqiL6Bj\nnY4kH0pm7/FgLcykAkk7iVXhkZZm7xB693YVPm3TNG5s4m7upDH+LQhdu9o9aw4EY9fw5s3tP2jd\nOsehkeGRxNWP00lqRZQWBFV4JCXZMZ/VqjkOPXTqED/v/Zmul3Z1dekVK+ye9c2buwo/R8mSdrTR\ntGn+OZ8jIj5NUsvqR1BFjxYEVXhMneq6uWhWyiw61+tMqcjzrFOdh6y7Az9svfy7vn1h8mT/nc+R\nXr1cDz/t3qA7SduTOJV+ys9JqWDTgqAKB6/Xp/6DqRun0qeJu1iwSwD16uU6PFfx8bBkCZw86d/z\n5kunTrBhA+zf7zi0UqlKtKnRhvlb5wcgMRVMWhBU4bB8OVSoAI0aOQ49nX6a+dvmu55/sHcvbN8O\nV17pKvy8ypeHdu1c71vjm6gou0eCy7uE3o16M21TMNq7VCBpQVCFgw/NRfO2zqNN9TZcVNr5yqhg\n53F16eJqH5489ejhegFS3/Xr57rN6qamNzFt0zQyvBl+TkoFkxYEVTj4UBB8bS6aO9euHB0I3bvb\ngVNBWQ2iRw/bZnXkiOPQuhXrUrdiXb7d8W0AElPBogVBhb7kZDh2DNq2dRya4c1gRvIMbmzsbrip\nx2OXq46LcxWep2bNbDHYsCEw57+gsmXt5DSXzUb9m/bnq/Vf+TkpFUxaEFTomzTJNm+EOf91Tdqe\nRN2KdalTsY6rSy9bBjVr2o9AEAlys1H//vCVuxf1fs368fWGr/F4g7HjjwoELQgq9H35pV2y2U3o\nui+5+TJ3sWCbc1zu0plvQS0IN9xg53ekpjoObVC5AdXKVmPJziX+z0sFhRYEFdo2boTffnO13nSG\nN4MpG6cwoNkA15cPZP9Bluuvt3ciLl6TfVehAnTsaFeQdaF/M202Kkq0IKjQNmmSbdZw0Vy0cNtC\n6leq77q56LffbD1ysxGOE2XK2Ho3b15gr3NePjQb9W/Wn683fI3XeP2clAoGLQgqtAWxueibbyAm\nxg7ZD7Tu3YPYbNS7t61GJ044Dm1SpQkVS1Zk6a6lAUhMFTQtCCp0rV9vh0Re7Xy56nRPOlM2TqF/\ns/6uLz93buD7D7L06BHE4aeVK8NVV7muSP2b9WfS+kl+TkoFgxYEFbomTYIBA9w1F21fSMOLGrre\nKtPrLdiC0LAhlCgBa9cWzPXOMXCg6309b77sZr5c96WONioCtCCo0OVrc1Ez981Fq1bZ/Y/r1XN9\nCkdEbLPR3LkFc71z9O1r19BwMUmtWdVmVC1TVSepFQFaEFRoWrvWDrtxsYBQmieNqRunFprmoizx\n8UEsCBUq2E0aXHYuD2kxhPFrxvs5KVXQtCCo0PT55zB4sKvmotkps2l+cXNqVXC/YXEwCkJsrN0u\n+niw9iUcMgQmTHAVOqj5IKZsnMKZjDN+TkoVJC0IKvR4PDB+PNx2m6vwcb+M47aW7mIBjh6FlSvt\nCtEFqWxZaN8eFi4s2Ov+rkcPWL0adu1yHFqzfE1aRbdidkqwhkopf9CCoEJPUpLdzd7F9mSHTx9m\nwbYFPjUXzZ9v5x6UcreXjk+C2mxUooTtS3DZuazNRoWfFgQVesaNc3138N+1/yW+QTwVSlZwffmC\nmJ18PvHxQRx+CrbZaLy7F/V+zfoxb+s8jp456uekVEHRgqBCy8mTdme0QYNchX+2+jNub3W768sb\nE5z+gyzNm0NaGqSkBOf6dOxop2ivW+c4tGLJinS5tIsuZVGIaUFQoWXKFNteEx3tODTlUApbj2yl\nW/1uri+/fr3dCMfFxmx+IRLkZqOwMNuZP26cq/AhLYbw2erP/JyUKihaEFRoGTcObnf3Dv+z1Z8x\nqPkgIsLcb22WtbqpiOtT+CyoBQHg7rvtf4f0dMehNzS6gQ0HN5ByKFi3OMoXBV4QRCReRDaKSLKI\nDM/l54PR02lOAAAZzElEQVRF5JfMj8Ui0qKgc1RBsnu33Tu5d2/HoV7j5fPVn3NbK/ejiyC4/QdZ\nunaFxYvh9OkgJdCkCTRo4GoF1KjwKG5vdTtjV44NQGIq0Aq0IIhIGPAOEAdcBgwSkSY5DtsKdDTG\ntAKeB8YUZI4qiD75xK686WJ4z4JtCyhXohxXVLvC9eVPnIClS+18gGCqWBFatoTvvgtiEkOHwocf\nugq954p7+PSXT0n3OL/DUMFV0HcI7YEUY8wOY0w6MBH4w96GxpgfjTHHMh/+CARoryoVUjweGD0a\nhg1zFT7q51EMazMM8aGtJykJ2rWDcuVcn8JvskYbBU3//vD9967mJDSt2pQGlRswK8XdHgsqeAq6\nINQEdmZ7vIsLv+APBYL5Z6EKSkKCnXvQpo3j0H0n9jFv6zxubXmrTykEc3RRTkHvRyhTxq4j9ckn\nrsKHXjGUD1e4u8NQweO+9y3ARCQWuAu49nzHjBgx4vevY2JiiImJCXheKkA++ADuu89V6EcrP6J/\n0/6UL1He9eWNsU3m06e7PoVftW4Nhw7B9u1Qt26Qkhg61K42++STjpcQ6d+sP48kPMKu1F1cUv6S\nACWo8iMpKYmkpKR8HSumAGfAiMhVwAhjTHzm4ycAY4x5OcdxLYHJQLwxZst5zmUKMncVQDt3QqtW\n9nOZMo5CvcZL/bfqM2nAJNrWaOs6hfXrbWfy9u3BHWGU3a23wnXXuW5F850xcMUV8Npr0KWL4/D7\nZ95PzfI1ebrj0wFITrklIhhjcv0tL+gmo2VAAxGpIyJRwEDgD+/JRKQ2thjcdr5ioIqYDz+0Y98d\nFgOAxC2JXFTqIp+KAcDMmXa/+VApBhACzUYi8Kc/wXvvuQq/t829jFkxhgxvhp8TU4FSoAXBGOMB\nHgASgXXARGPMBhEZJiJ/yjzsH0Bl4D0RWSkiPxVkjqqAZWTA2LGu3wZ/sPwDhrXx/S30zJnQs6fP\np/Grbt3sQndpaUFM4vbbYdEi2LbNcWjr6q2pXaE2UzdODUBiKhAKtMnIn7TJqIiYMgVefdWOaHFo\n57GdtPqgFb8+8itlo8q6TuHwYdtOv39/cBa0u5B27WyLTUGvvPoH//d/tvnoP/9xHPrV+q9448c3\nWHz34gAkptwIpSYjpf7o9dfh4Yddhb7909vcefmdPhUDsAOcOnUKvWIAIdBsBPDAA3a0kYuNGvo0\n6cPO1J0s37Pc/3kpv9OCoIJn+XLYsQP69XMceiLtBGNXjuWhKx/yOY2s/oNQFPT5CGBvn2Jj4dNP\nHYdGhEXwYPsHeXPpm/7PS/mdFgQVPK+/Dg89ZFeTc+jjlR9zfb3rqVuxrk8pZGTYd+Ch1n+Q5cor\n7dywnTvzPjagHn4Y3noLvF7HofdccQ+zkmex5/ieACSm/EkLggqOnTvtW9+hQx2Herwe3lj6Bn+7\n6m8+p/Hjj1CrFlwSokPlIyJssZo2LciJXHutncLt4nalUqlKDG4xmPeXvR+AxJQ/aUFQwfH663Dn\nnXZzd4cmb5hMdJlorq51tc9phHJzUZY+fWBqsAfqiMAjj8Arr7gKf+jKhxj18yhOpJ3wc2LKn7Qg\nqIJ38KDtpHz0Ucehxhhe+O4FnrruKb+kMn166BeEbt3gp5/gyJEgJzJwoL2zW+x8xFCjixoRWy+W\nUctHBSAx5S9aEFTBe+MNu05OTefrFs5MnkmYhNGjYQ+f01i/HlJT7cb2oaxMGdun62I1av+KiIAn\nnoAXXnAV/tR1T/GfH/7D6fRgreut8qIFQRWso0ftukXDz9kKI0/GGJ7/7nmeuu4pn1Y1zTJ5sh3g\n5HCZnqAIiWYjgDvugLVr7Qgxh1pGt6RtjbZ8tPKjACSm/KEQ/CmoIuWNN6BXL6hXz3FowpYEjp89\nTt+mff2SSlZBKAx69YJ58+DUqSAnUqIEPPYYPPecq/CnOz7NS0te4kzGGT8npvxBC4IqOAcPwttv\nwz//6TjUa7w8Of9J/hX7L8LE91/blBTYt89u31wYVKlim7Zmzw52Jtj1jVatcjW7vH3N9lxR7Qod\ncRSitCCogvPii7Zj8tJLHYd+tf4rwiTMr3cHfftCeLhfTlcgBg6EL74IdhZAyZIwYoRdFtvF8jEv\nXP8CLy15ieNnnc98VoGlBUEVjJ077UzXp50vhZzhzeAfC//Bvzv/2y99BwCTJhWe5qIsN91km41S\nU4OdCXbRu/37ITHRcWiL6BZ0q9+NkT+MDEBiyhdaEFTBePppu6Jp9eqOQ0f/PJqa5WrS9dKufkll\n/XrbXFTY9lOqVMmuuRT0SWpgRxw9/zw8/rjd/tShZ2Oe5e2f3mbv8b0BSE65pQVBBd7Spfat7d//\n7jj08OnDPLvoWV6Pe91vdweffQZDhhSu5qIsIdNsBLbNrVIlu5+FQ5dWupR7rriHJxc8GYDElFu6\n/LUKLK8XOnSA+++3QxYdenjOw6R50nj/Bv90Qnq9UKeOXYGheXO/nLJAnThhl9lITrZbUAfdqlV2\nBb4NG2xxcCD1bCpN3mnC1IFTaV8zxCeDFCG6/LUKns8+s6/Ct93mOHTtgbVMWDuB52LdDXHMTVKS\nHbFTGIsBQNmyti9h3LhgZ5Lp8svtJIlnnnEcWr5EeV64/gUemvMQXuN80Tzlf1oQVOAcPGgnoL33\nnuPZXx6vh3tn3Mu/Yv9F1TJV/ZbSuHG2P7QwGzrUttKEzA3y88/Dl1/a9TUcuuPyOwgPC+eD5R8E\nIDHllBYEFTiPPGJ3im/rfL/j95e/T0RYBH9q86e8D86no0dth+zgwX47ZVB06GDXmluyJNiZZKpS\nBUaOtJUqPd1RaJiEMabXGJ5Jeoadx4K9xrfSgqACY84cO3Hp2Wcdh/567FeeXfQsY3qN8csktCyf\nfALdu0N0tN9OGRQi/7tLCBmDBtnODReroTar2owH2z/In2f/Ge0XDC7tVFb+99tv0KqV7T+4/npH\noR6vh87jOhPfIJ4nrn3Cbyl5vdCkCXz8ceGZnXwhBw9Cw4awbZvjvtzA+fVXezc4Zw60aeMoNM2T\nRvsx7Xmw/YPc0/qeACWoQDuVVUEyxr59HTLEcTEAePX7VzEYHuvwmF/T+uYbu2pohw5+PW3QVK0K\nN94Io0JpNenate2uakOGOF50KSo8ivF9x/PE/CdIPpQcoARVXvQOQfnXqFH244cf7EJoDvy0+ydu\nmHADy/+0nNoVavs1rV697Auoiw3aQtbq1XbE57Ztjp/qwLr9dru8xejRjkPf/eldPvnlExbftZgS\nEaH0jyo69A5BFYylS+Ef/7Azpxy+Qh04eYABkwYw6oZRfi8Ga9fCsmWFvzM5p5YtoUWLEJqoluWd\nd+Dbb237nEN/bvdnapWvxcNzHw5AYiovWhCUf+zfDwMG2J7Oxo0dhWZ4Mxj41UBubXErNzW9ye+p\nPf+83ZytdGm/nzroHn0UXnsthIagApQvD1Om2CHHDvdNEBE+7fMp3+74ljE/jwlQgup8tCAo350+\nbWdL3Xkn9O7tKNQYw4OzH6RERAm/TkDLsmEDLFxoJ0oXRV27QlSUXb01pDRtapsOb7rJdjY7UK5E\nOabcMoWnFjxF0vakwOSncqV9CMo3Ho9dNrRsWTvry+EEtBe+fYGvNnzFt3d+S7kS5fye3q23wmWX\nuVpGqdBITIQHHoB16yAyMtjZ5DByJIwda/dhdjgcasG2BQyaPIh5t82jRXSLACVY/GgfggoMrxfu\nu88usPPRR46LweifR/Phyg+ZPXh2QIrB8uUwfz785S9+P3VI6dbNrs80dmywM8nF3/4GcXG2V//E\nCUeh19e7njfj36THhB5sObwlQAmq7PQOQbmTVQzWr7fjzss5e0Ef/fNonv/2eRbcsYAGlRsEJL0O\nHeyK23fd5ffTh5yff7avuZs2Of5PEXher91lLTnZbvlWtqyj8FHLR/HCdy8E7HeluNE7BOVf6elw\nzz22gd5FMXhr6VsBLQZg9+IBVwusFkpt2tghqE+G4mrSYWF2CGrjxvZu4fBhR+HD2g7j6Y5PE/tp\nLOsOrAtQkgr0DkE5lZpqRxNFRsLEiY7e7XmNl8cSH2P25tnMGTKHuhXrBiTF/fvtIpwzZrhaRqnQ\nOnLEruI6cSJcd12ws8mF12s31Jk5076RqFfPUfjnqz/n0cRHmdhvIrH1YgOUZNGndwjKP5KT7boP\n9erB1KmOisGR00foM7EPy/YsY8ndSwJWDLxeOy/qnnuKVzEA22f77rtw991w8mSws8lFWJgdI/vA\nA7Y9b8ECR+G3tryVif0mcstXt/Desvd03aMA0IKg8ue//7XF4MEH4f337RaK+bR8z3LajmlL3Yp1\nmXf7PCqXqhywNP/zHzh+3O4BXxz16WP/M91zT4jNTcjugQfg88/tEhfPP+9oC87YerEsuXsJo34e\nxZCvh5B6NhQ2mC5CjDGF8sOmrgLu4EFjbrnFmEaNjFm+3FHo2Yyz5h8L/mEufvVi89+1/w1Qgv8z\ne7YxF19szLZtAb9USDt1yph27Yz597+DnUkedu0yJjbWmKuuMmbjRkehp9JOmWEzhpnar9c2iZsT\nA5Rg0ZT52pn76+r5fhDqH1oQAiwtzZi33rKvsH/7m32VySev12umbZxmGr3dyPSa0MvsSd0TwESt\n7783pkoV+1nZ19qaNY359NNgZ5IHj8eYd94x5qKLjHn8cWOOHnUUnrA5wdR+vba5ZdItZuvhrQFK\nsmjRgqDyz+MxZvJke0fQtasxq1c7Cl+6a6mJ/STWNHu3mZmTMidASf7RokW2bs2eXSCXKzTWr7dF\nYdSoYGeSD7t3G3P33cZERxvz9tvGnD6d79ATZ0+Y55KeMxe9fJF5LPExc/DkwQAmWvhpQVB5O3nS\nmPfft4WgTRv76ur15ivU4/WYqRummus+us7Ufr22eX/Z+ybdkx7ghK1PPzWmalVjErXVIFcpKcbU\nqWPME08Yk14w/0l8s2qVMT172sIwYoQxBw7kO3RP6h4zbMYwU+mlSua+GfeZjQedNUMVFxcqCDrs\ntDjzeuG772D8ePj6a9sb+be/QceOdluuPKw7sI7xa8YzYc0EqpapyqNXP0r/Zv2JCMt/h7NbBw/C\nX/9qt/GdNg2aNQv4JQutAwfgttvsyKOPP7Yb64S89evh9ddh0iTo0sV2QPfoka9VdPef2M97y97j\ng58/oFnVZgxuPph+zfoFdDBDYXKhYacFXhBEJB54AzvCaawx5uVcjnkL6A6cBO40xqzK5RgtCG4c\nOmTXc0hIgLlz7U4rgwfDwIF2g5MLOJ1+mm93fEvClgQStiSQejaVQc0HMaTFEFpGt0TyUUR8dfw4\nfPCBHU10663w3HNFcxVTf/N67evriy/aYbnDhxeSrUSPHLEr940fD7/8Ap0728lt3brl+ft6JuMM\nczfPZcKaCSRsSeDKmlfSrX43utXvRouLWxTI72soCpmCICJhQDLQGdgDLAMGGmM2ZjumO/CAMaan\niFwJvGmMuSqXc2lBuBBj7FvDTZvsugbLltnFffbuhU6d7B9VXBw0apRr+LEzx0g+lMzKfStZvmc5\ny/YsY9Nvm2hdvTVx9eOIaxBH2xpt/brn8fl4PHarhQkT7OjXzp3tjNyWLQN+6SJn/35bRCdMsDOb\nb73VbmxXqlSwM8uHvXvtSn6JiXYLvKgoO9kk66NZM7uvcy5raqWeTWXhtoUkbEkgcUsih08fpk2N\nNrSt3pa2NdrSIroFdSvWJSo8Kgj/sIIVSgXhKuAZY0z3zMdPYNuzXs52zAfAQmPMfzMfbwBijDH7\nc5yr+BUEY+DsWfs2OTUVjh61f+H798O+ffbz7t2wZQts3mz/YBo1gtatoW1b0ttczvF6NUnNOEnq\n2VT2n9jP/pP72Xdi3+8fW45sYfPhzZzJOEODyg1oFd2KdjXa0bZGW1pGt6RUZOBeOYyx/7SdO22L\nwYYNsGKF3WulRg17EzNkiOMJrioXR4/axWknT4aVK+3raevW9qNxY6hVy948huybaGNg+3b7Jifr\nY9Mmewdcr55tF7vkEqhWzd4KRUfbrytXhnLl2B9+mp+PrGf53p9ZtmcZ6w+uZ1fqLmqWq0mDyg2o\nW7Eu0WWiqVa2GtFl7ecqpatQLqoc5UuUp0xUmQJ5MxQIoVQQ+gFxxpg/ZT6+FWhvjHko2zEzgBeN\nMd9nPp4HPG6MWZHjXK4Kwr6d+3jkqRsxGAQwZJ3DZP5/9sfm9+/+/jNjQMjxOPPn5n9xAPYpt8eY\n7DEYfr8MXsR4ETyI8YLxIHgRrxfwEGa8YDKI8KYj3nQAPOGReMIiSQ+P4lRUFKciozgTGcGZiAjO\nRoRxOjKcsxFhZIR58HCWNDlOethxvKQTZcoT6S1HpClPaW80pTzRlPJUo5S3GqU80ZT3XEq59AaU\n8kYjmf/QnE+zr4/T02179qlT9vPJk3DsmK1nYWFQs6Z9s9esmb0L6NgRqlfP+V9S+cuRI7YvZsUK\nezO5ebMtyidP2qJQvjxUqGA/ly5tVy2JiDj3c3j4HwuI06+dHHc+kWknqXxsK1UOp1D+xB7KndxH\n2ZP77edT+yl15gglzqZSIu044Z400qLKcTaqHGmRpTkdGcGvFWFLRQ+7ynk4UMbDwdIZ/FYqg4Ol\nznK0ZBonIzI4FZHOmQgPJTPCKZMRRUlPBFGecCJMOBHecCK99utIbxgR3ggiTRjhJhwxYQggCGIk\n8zNkfTfM2L+47D+THD/LMvTGZ+nSt3v+npQcLlQQAt/7F0Ajsk1HjYmJISYmJs+YiIgIykdmdS5J\ntg+ytSmGZf5UMn8kv784CmG/f+9/x8h5HmedN9v5Mh+bzMdGwiA8Eq+EY8Ij8YaFQ1gkJiwCb1iE\n/RweiTeqNBkRJTERUUQAUQilECpLCSKIIkKiCJcoIrCfI39/XIKSYeUoFVaeSEr+/m+80B9ioB9H\nRNgN70uXtp/LlLEvNtHRjhfCVH5QqdL/WhCzO3UKfvvN3oymptqifeoUZGTYop7zc/YJx9nfBOTn\nayfHXVgZzl7cgt20YHceR4Z50ok6e5wSZ1OJSD9NuCeNsIw0wj1pXOpJo6HHfh1+No2wk2mEe9PB\nGASD12RwVs5wOuwUZ8LOkEE6HjLIkDQyyCBDMvBIOulkkCHpeMSDwYs38w2hVwxZ/8t6DODN+q5k\nfmR+7eWPT0JJB218SUlJJCUl5evYYDQZjTDGxGc+zk+T0UagkzYZKaWU70JpcbtlQAMRqSMiUcBA\nYHqOY6YDt8PvBeRozmKglFLK/wq0ycgY4xGRB4BE/jfsdIOIDLM/NqONMbNFpIeIbMYOOy0G25so\npVTw6cQ0pZQqRkKpyUgppVSI0oKglFIK0IKglFIqkxYEpZRSgBYEpZRSmbQgKKWUArQgKKWUyqQF\nQSmlFKAFQSmlVCYtCEoppQAtCEoppTJpQVBKKQVoQVBKKZVJC4JSSimgmBaE/G4np/5HnzNn9Ply\nRp8vZwL1fGlBUPmiz5kz+nw5o8+XM1oQlFJKBZQWBKWUUkAh30Iz2DkopVRhdL4tNAttQVBKKeVf\n2mSklFIK0IKglFIqU7EqCCLSX0TWiohHRFrn+NnfRSRFRDaISLdg5RiqROQZEdklIisyP+KDnVMo\nEpF4EdkoIskiMjzY+YQ6EdkuIr+IyEoR+SnY+YQiERkrIvtFZHW271USkUQR2SQiCSJSwR/XKlYF\nAVgD3AQsyv5NEWkK3Aw0BboD74lIrp0uxdxIY0zrzI+5wU4m1IhIGPAOEAdcBgwSkSbBzSrkeYEY\nY8wVxpj2wU4mRH2M/Z3K7glgnjGmMbAA+Ls/LlSsCoIxZpMxJgXI+WJ/IzDRGJNhjNkOpAD6y3ku\nLZIX1h5IMcbsMMakAxOxv1vq/IRi9jrklDFmMXAkx7dvBD7N/PpToI8/rqX/IayawM5sj3dnfk/9\n0QMiskpEPvTXLWoRk/P3aBf6e5QXA3wjIstE5N5gJ1OIXGyM2Q9gjNkHXOyPk0b44yShRES+AaKz\nfwv7S/eUMWZGcLIqHC703AHvAc8ZY4yIPA+MBO4p+CxVEXONMWaviFTFFoYNme+IlTN+mT9Q5AqC\nMaari7DdQK1sjy/J/F6x4uC5GwNocT3XbqB2tsfF8vfICWPM3szPB0VkCrbZTQtC3vaLSLQxZr+I\nVAMO+OOkxbnJKHt7+HRgoIhEiUg9oAGgIx6yyfyly9IXWBusXELYMqCBiNQRkShgIPZ3S+VCREqL\nSNnMr8sA3dDfq/MRzn3NujPz6zuAaf64SJG7Q7gQEekDvA1UAWaKyCpjTHdjzHoR+RJYD6QDfzY6\nhTunV0TkcuyokO3AsOCmE3qMMR4ReQBIxL7ZGmuM2RDktEJZNDAlcxmaCGC8MSYxyDmFHBGZAMQA\nF4nIr8AzwEvAJBG5G9iBHSXp+7X0dU8ppRQU7yYjpZRS2WhBUEopBWhBUEoplUkLglJKKUALglJK\nqUxaEJRSSgFaEJRSSmXSgqCUUgrQgqCUUiqTFgSl/EBEqojIHhH5Z7bvtRSR0yLSL5i5KZVfunSF\nUn6SufXqDKAj8AuwHPjRGDM0qIkplU9aEJTyIxEZid3NahFwLXC5MeZUcLNSKn+0ICjlR5nLXv+C\nXUL9amPM8iCnpFS+aR+CUv5VD7vZkgHqBzkXpRzROwSl/EREIoAfgY3YDZZGAC2NMbuCmZdS+aUF\nQSk/EZGXsLuktTDGHBeROUBJY0xskFNTKl+0yUgpPxCRjsAjwG3GmOOZ374TaCoiw4OWmFIO6B2C\nUkopQO8QlFJKZdKCoJRSCtCCoJRSKpMWBKWUUoAWBKWUUpm0ICillAK0ICillMqkBUEppRSgBUEp\npVSm/we7nl+NBVu1EAAAAABJRU5ErkJggg==\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f0a76b274d0>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "x = np.linspace(-10, 10, 300)\n",
+    "sigmax0c = [[1.0,0.0,\"blue\"],[2.0,0.0,\"red\"],[2.0,1.0,\"green\"]]\n",
+    "for sigma,x0,c in sigmax0c:\n",
+    "    y = sigma/np.sqrt(2*np.pi)*np.exp(-(x-x0)**2/2/sigma**2)\n",
+    "    plt.plot(x, y ,color= c)\n",
+    "    plt.xlabel(\"x\",fontsize=14)\n",
+    "    plt.ylabel('f(x)',fontsize=14)\n",
+    "    plt.xlim(x.min() * 1.1, x.max() * 1.1)\n",
+    "    plt.ylim(-0.1, y.max() * 1.1)"
+   ]
   },
   {
    "cell_type": "markdown",
@@ -829,7 +857,10 @@
     "collapsed": true
    },
    "outputs": [],
-   "source": []
+   "source": [
+    "Gitではファイルの状態を好きなときに更新履歴として保存しておくことができる。\n",
+    "これにより、一度編集したファイルを過去の状態に戻したり、編集箇所の差分を表示できたりする。"
+   ]
   },
   {
    "cell_type": "markdown",
@@ -845,7 +876,9 @@
     "collapsed": true
    },
    "outputs": [],
-   "source": []
+   "source": [
+    "開発の本流から分岐し、本流の開発を邪魔することなく作業を続ける"
+   ]
   },
   {
    "cell_type": "markdown",
@@ -861,7 +894,11 @@
     "collapsed": true
    },
    "outputs": [],
-   "source": []
+   "source": [
+    "ファイルやディレクトリの追加・変更をリポジトリに記録する操作のこと。\n",
+    "コミットを実行するとリポジトリの中では前回コミットした時の状態から現在の状態までの差分を記録した\n",
+    "コミットと呼ばれるものが作成される。"
+   ]
   },
   {
    "cell_type": "markdown",
@@ -877,7 +914,10 @@
     "collapsed": true
    },
    "outputs": [],
-   "source": []
+   "source": [
+    "最後にpullをしてから次のpushをするまでの間に、他の人がpushをしてリモートリポジトリを更新して\n",
+    "しまった場合、マージを行って他の履歴での変更を取り込むまで自分のpushは拒否される。"
+   ]
   },
   {
    "cell_type": "markdown",
@@ -893,7 +933,10 @@
     "collapsed": true
    },
    "outputs": [],
-   "source": []
+   "source": [
+    "リモートリポジトリで自分の手元のローカルリポジトリの変更履歴を共有するには、\n",
+    "ローカルリポジトリ内の変更履歴をアップロードする必要があり、そのために行われる操作。"
+   ]
   },
   {
    "cell_type": "markdown",
@@ -909,7 +952,9 @@
     "collapsed": true
    },
    "outputs": [],
-   "source": []
+   "source": [
+    "リモートリポジトリからローカルリポジトリを更新するために行う操作。"
+   ]
   },
   {
    "cell_type": "markdown",
diff --git a/.ipynb_checkpoints/tutorial2-checkpoint.ipynb b/.ipynb_checkpoints/tutorial2-checkpoint.ipynb
index 1daf2a3..cc7dd9d 100755
--- a/.ipynb_checkpoints/tutorial2-checkpoint.ipynb
+++ b/.ipynb_checkpoints/tutorial2-checkpoint.ipynb
@@ -11,9 +11,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Numpy.array, 線形代数\n",
+    "1.　Numpy.array\n",
     "\n",
-    "関数・クラス"
+    "2.　線形代数"
    ]
   },
   {
@@ -75,7 +75,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 2,
    "metadata": {
     "ExecuteTime": {
      "end_time": "2016-04-14T17:25:01.955260",
@@ -96,7 +96,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 3,
    "metadata": {
     "ExecuteTime": {
      "end_time": "2016-04-14T17:26:03.246088",
@@ -109,7 +109,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      " 1.0 2.0\n"
+      "1.0 2.0\n"
      ]
     }
    ],
@@ -126,7 +126,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 4,
    "metadata": {
     "ExecuteTime": {
      "end_time": "2016-04-14T17:26:44.397700",
@@ -160,7 +160,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 5,
    "metadata": {
     "ExecuteTime": {
      "end_time": "2016-04-14T17:30:35.733918",
@@ -192,7 +192,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 6,
    "metadata": {
     "ExecuteTime": {
      "end_time": "2016-04-14T17:31:03.276585",
@@ -216,7 +216,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 7,
    "metadata": {
     "ExecuteTime": {
      "end_time": "2016-04-14T17:31:32.249121",
@@ -240,7 +240,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 8,
    "metadata": {
     "ExecuteTime": {
      "end_time": "2016-04-14T17:33:25.325194",
@@ -254,13 +254,13 @@
      "output_type": "stream",
      "text": [
       "mat_c = \n",
-      "[[-0.46069112 -0.66713647 -0.36786955]\n",
-      " [-1.29150856 -1.00761822  0.87512984]\n",
-      " [-0.07997831  1.43295736 -0.95610688]]\n",
+      "[[ 0.7098218  -0.12500305 -0.21118774]\n",
+      " [-0.78079864  0.47330276 -2.1775981 ]\n",
+      " [-0.67046144  1.09486459  0.50351885]]\n",
       "inv_c = \n",
-      "[[-0.16948184 -0.67936369 -0.55661584]\n",
-      " [-0.76089729  0.23970171  0.51216143]\n",
-      " [-1.12621142  0.41607973 -0.23174953]]\n"
+      "[[ 1.50426168 -0.09652577  0.21347225]\n",
+      " [ 1.06296269  0.12379175  0.98120134]\n",
+      " [-0.3083316  -0.39770508  0.13672241]]\n"
      ]
     }
    ],
@@ -277,7 +277,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 24,
+   "execution_count": 9,
    "metadata": {
     "ExecuteTime": {
      "end_time": "2016-04-14T17:34:32.268191",
@@ -291,7 +291,7 @@
      "output_type": "stream",
      "text": [
       "solution :\n",
-      "[ 1.13177768 -0.24116484  0.07646277]\n"
+      "[-2.1288032  -2.60355377 -0.1804809 ]\n"
      ]
     }
    ],
@@ -315,8 +315,13 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## 多項式フィッティング\n",
-    "\n",
+    "## 多項式フィッティング"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
     "以下のデータ［$x_i, y_i$］を、N次多項式で近似せよ。\n",
     "\n",
     "$N=1,3, 10$の結果と、データ点を重ねて描画せよ"
@@ -324,15 +329,53 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 25,
+   "execution_count": 15,
    "metadata": {
-    "ExecuteTime": {
-     "end_time": "2016-04-14T17:44:10.734183",
-     "start_time": "2016-04-14T17:44:10.732362"
-    },
-    "collapsed": true
+    "collapsed": false
    },
    "outputs": [],
+   "source": [
+    "%matplotlib inline\n",
+    "import matplotlib.pyplot as plt"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[<matplotlib.lines.Line2D at 0x7fd16c388510>]"
+      ]
+     },
+     "execution_count": 20,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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PY1GPSiGQmY9m5gkgVikaVfdVIn/J53kczvNYnOexqEerTswJjEfEAxHxgRbtU5K0iktW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\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7fd16c5b6910>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "x = np.linspace(0, 1.0, 20)\n",
+    "y = np.sin(x*5.0) + np.random.randn(len(x))*0.1\n",
+    "plt.plot(x, y, 'ro')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
    "source": [
     "# データの読み込み、描画"
    ]
@@ -381,7 +424,9 @@
     "collapsed": true
    },
    "outputs": [],
-   "source": []
+   "source": [
+    "aaaaaaあああああああああ"
+   ]
   }
  ],
  "metadata": {
diff --git a/tutorial1.ipynb b/tutorial1.ipynb
index 0bdf0e8..dc34657 100755
--- a/tutorial1.ipynb
+++ b/tutorial1.ipynb
@@ -1,5 +1,12 @@
 {
  "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "しろうず"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -685,7 +692,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 12,
    "metadata": {
     "ExecuteTime": {
      "end_time": "2016-04-13T22:41:18.151992",
@@ -799,12 +806,33 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 37,
    "metadata": {
-    "collapsed": true
+    "collapsed": false
    },
-   "outputs": [],
-   "source": []
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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NbDHYsCEw57+gsmXt5DSXzUb9m/bnq/Vf+TkpFUxaEFTomzTJNm+EOf91Tdqe\nRN2KdalTsY6rSy9bBjVr2o9AEAlys1H//vCVuxf1fs368fWGr/F4g7HjjwoELQgq9H35pV2y2U3o\nui+5+TJ3sWCbc1zu0plvQS0IN9xg53ekpjoObVC5AdXKVmPJziX+z0sFhRYEFdo2boTffnO13nSG\nN4MpG6cwoNkA15cPZP9Bluuvt3ciLl6TfVehAnTsaFeQdaF/M202Kkq0IKjQNmmSbdZw0Vy0cNtC\n6leq77q56LffbD1ysxGOE2XK2Ho3b15gr3NePjQb9W/Wn683fI3XeP2clAoGLQgqtAWxueibbyAm\nxg7ZD7Tu3YPYbNS7t61GJ044Dm1SpQkVS1Zk6a6lAUhMFTQtCCp0rV9vh0Re7Xy56nRPOlM2TqF/\ns/6uLz93buD7D7L06BHE4aeVK8NVV7muSP2b9WfS+kl+TkoFgxYEFbomTYIBA9w1F21fSMOLGrre\nKtPrLdiC0LAhlCgBa9cWzPXOMXCg6309b77sZr5c96WONioCtCCo0OVrc1Ez981Fq1bZ/Y/r1XN9\nCkdEbLPR3LkFc71z9O1r19BwMUmtWdVmVC1TVSepFQFaEFRoWrvWDrtxsYBQmieNqRunFprmoizx\n8UEsCBUq2E0aXHYuD2kxhPFrxvs5KVXQtCCo0PT55zB4sKvmotkps2l+cXNqVXC/YXEwCkJsrN0u\n+niw9iUcMgQmTHAVOqj5IKZsnMKZjDN+TkoVJC0IKvR4PDB+PNx2m6vwcb+M47aW7mIBjh6FlSvt\nCtEFqWxZaN8eFi4s2Ov+rkcPWL0adu1yHFqzfE1aRbdidkqwhkopf9CCoEJPUpLdzd7F9mSHTx9m\nwbYFPjUXzZ9v5x6UcreXjk+C2mxUooTtS3DZuazNRoWfFgQVesaNc3138N+1/yW+QTwVSlZwffmC\nmJ18PvHxQRx+CrbZaLy7F/V+zfoxb+s8jp456uekVEHRgqBCy8mTdme0QYNchX+2+jNub3W768sb\nE5z+gyzNm0NaGqSkBOf6dOxop2ivW+c4tGLJinS5tIsuZVGIaUFQoWXKFNteEx3tODTlUApbj2yl\nW/1uri+/fr3dCMfFxmx+IRLkZqOwMNuZP26cq/AhLYbw2erP/JyUKihaEFRoGTcObnf3Dv+z1Z8x\nqPkgIsLcb22WtbqpiOtT+CyoBQHg7rvtf4f0dMehNzS6gQ0HN5ByKFi3OMoXBV4QRCReRDaKSLKI\nDM/l54PR02lOAAAZzElEQVRF5JfMj8Ui0qKgc1RBsnu33Tu5d2/HoV7j5fPVn3NbK/ejiyC4/QdZ\nunaFxYvh9OkgJdCkCTRo4GoF1KjwKG5vdTtjV44NQGIq0Aq0IIhIGPAOEAdcBgwSkSY5DtsKdDTG\ntAKeB8YUZI4qiD75xK686WJ4z4JtCyhXohxXVLvC9eVPnIClS+18gGCqWBFatoTvvgtiEkOHwocf\nugq954p7+PSXT0n3OL/DUMFV0HcI7YEUY8wOY0w6MBH4w96GxpgfjTHHMh/+CARoryoVUjweGD0a\nhg1zFT7q51EMazMM8aGtJykJ2rWDcuVcn8JvskYbBU3//vD9967mJDSt2pQGlRswK8XdHgsqeAq6\nINQEdmZ7vIsLv+APBYL5Z6EKSkKCnXvQpo3j0H0n9jFv6zxubXmrTykEc3RRTkHvRyhTxq4j9ckn\nrsKHXjGUD1e4u8NQweO+9y3ARCQWuAu49nzHjBgx4vevY2JiiImJCXheKkA++ADuu89V6EcrP6J/\n0/6UL1He9eWNsU3m06e7PoVftW4Nhw7B9u1Qt26Qkhg61K42++STjpcQ6d+sP48kPMKu1F1cUv6S\nACWo8iMpKYmkpKR8HSumAGfAiMhVwAhjTHzm4ycAY4x5OcdxLYHJQLwxZst5zmUKMncVQDt3QqtW\n9nOZMo5CvcZL/bfqM2nAJNrWaOs6hfXrbWfy9u3BHWGU3a23wnXXuW5F850xcMUV8Npr0KWL4/D7\nZ95PzfI1ebrj0wFITrklIhhjcv0tL+gmo2VAAxGpIyJRwEDgD+/JRKQ2thjcdr5ioIqYDz+0Y98d\nFgOAxC2JXFTqIp+KAcDMmXa/+VApBhACzUYi8Kc/wXvvuQq/t829jFkxhgxvhp8TU4FSoAXBGOMB\nHgASgXXARGPMBhEZJiJ/yjzsH0Bl4D0RWSkiPxVkjqqAZWTA2LGu3wZ/sPwDhrXx/S30zJnQs6fP\np/Grbt3sQndpaUFM4vbbYdEi2LbNcWjr6q2pXaE2UzdODUBiKhAKtMnIn7TJqIiYMgVefdWOaHFo\n57GdtPqgFb8+8itlo8q6TuHwYdtOv39/cBa0u5B27WyLTUGvvPoH//d/tvnoP/9xHPrV+q9448c3\nWHz34gAkptwIpSYjpf7o9dfh4Yddhb7909vcefmdPhUDsAOcOnUKvWIAIdBsBPDAA3a0kYuNGvo0\n6cPO1J0s37Pc/3kpv9OCoIJn+XLYsQP69XMceiLtBGNXjuWhKx/yOY2s/oNQFPT5CGBvn2Jj4dNP\nHYdGhEXwYPsHeXPpm/7PS/mdFgQVPK+/Dg89ZFeTc+jjlR9zfb3rqVuxrk8pZGTYd+Ch1n+Q5cor\n7dywnTvzPjagHn4Y3noLvF7HofdccQ+zkmex5/ieACSm/EkLggqOnTvtW9+hQx2Herwe3lj6Bn+7\n6m8+p/Hjj1CrFlwSokPlIyJssZo2LciJXHutncLt4nalUqlKDG4xmPeXvR+AxJQ/aUFQwfH663Dn\nnXZzd4cmb5hMdJlorq51tc9phHJzUZY+fWBqsAfqiMAjj8Arr7gKf+jKhxj18yhOpJ3wc2LKn7Qg\nqIJ38KDtpHz0Ucehxhhe+O4FnrruKb+kMn166BeEbt3gp5/gyJEgJzJwoL2zW+x8xFCjixoRWy+W\nUctHBSAx5S9aEFTBe+MNu05OTefrFs5MnkmYhNGjYQ+f01i/HlJT7cb2oaxMGdun62I1av+KiIAn\nnoAXXnAV/tR1T/GfH/7D6fRgreut8qIFQRWso0ftukXDz9kKI0/GGJ7/7nmeuu4pn1Y1zTJ5sh3g\n5HCZnqAIiWYjgDvugLVr7Qgxh1pGt6RtjbZ8tPKjACSm/KEQ/CmoIuWNN6BXL6hXz3FowpYEjp89\nTt+mff2SSlZBKAx69YJ58+DUqSAnUqIEPPYYPPecq/CnOz7NS0te4kzGGT8npvxBC4IqOAcPwttv\nwz//6TjUa7w8Of9J/hX7L8LE91/blBTYt89u31wYVKlim7Zmzw52Jtj1jVatcjW7vH3N9lxR7Qod\ncRSitCCogvPii7Zj8tJLHYd+tf4rwiTMr3cHfftCeLhfTlcgBg6EL74IdhZAyZIwYoRdFtvF8jEv\nXP8CLy15ieNnnc98VoGlBUEVjJ077UzXp50vhZzhzeAfC//Bvzv/2y99BwCTJhWe5qIsN91km41S\nU4OdCXbRu/37ITHRcWiL6BZ0q9+NkT+MDEBiyhdaEFTBePppu6Jp9eqOQ0f/PJqa5WrS9dKufkll\n/XrbXFTY9lOqVMmuuRT0SWpgRxw9/zw8/rjd/tShZ2Oe5e2f3mbv8b0BSE65pQVBBd7Spfat7d//\n7jj08OnDPLvoWV6Pe91vdweffQZDhhSu5qIsIdNsBLbNrVIlu5+FQ5dWupR7rriHJxc8GYDElFu6\n/LUKLK8XOnSA+++3QxYdenjOw6R50nj/Bv90Qnq9UKeOXYGheXO/nLJAnThhl9lITrZbUAfdqlV2\nBb4NG2xxcCD1bCpN3mnC1IFTaV8zxCeDFCG6/LUKns8+s6/Ct93mOHTtgbVMWDuB52LdDXHMTVKS\nHbFTGIsBQNmyti9h3LhgZ5Lp8svtJIlnnnEcWr5EeV64/gUemvMQXuN80Tzlf1oQVOAcPGgnoL33\nnuPZXx6vh3tn3Mu/Yv9F1TJV/ZbSuHG2P7QwGzrUttKEzA3y88/Dl1/a9TUcuuPyOwgPC+eD5R8E\nIDHllBYEFTiPPGJ3im/rfL/j95e/T0RYBH9q86e8D86no0dth+zgwX47ZVB06GDXmluyJNiZZKpS\nBUaOtJUqPd1RaJiEMabXGJ5Jeoadx4K9xrfSgqACY84cO3Hp2Wcdh/567FeeXfQsY3qN8csktCyf\nfALdu0N0tN9OGRQi/7tLCBmDBtnODReroTar2owH2z/In2f/Ge0XDC7tVFb+99tv0KqV7T+4/npH\noR6vh87jOhPfIJ4nrn3Cbyl5vdCkCXz8ceGZnXwhBw9Cw4awbZvjvtzA+fVXezc4Zw60aeMoNM2T\nRvsx7Xmw/YPc0/qeACWoQDuVVUEyxr59HTLEcTEAePX7VzEYHuvwmF/T+uYbu2pohw5+PW3QVK0K\nN94Io0JpNenate2uakOGOF50KSo8ivF9x/PE/CdIPpQcoARVXvQOQfnXqFH244cf7EJoDvy0+ydu\nmHADy/+0nNoVavs1rV697Auoiw3aQtbq1XbE57Ztjp/qwLr9dru8xejRjkPf/eldPvnlExbftZgS\nEaH0jyo69A5BFYylS+Ef/7Azpxy+Qh04eYABkwYw6oZRfi8Ga9fCsmWFvzM5p5YtoUWLEJqoluWd\nd+Dbb237nEN/bvdnapWvxcNzHw5AYiovWhCUf+zfDwMG2J7Oxo0dhWZ4Mxj41UBubXErNzW9ye+p\nPf+83ZytdGm/nzroHn0UXnsthIagApQvD1Om2CHHDvdNEBE+7fMp3+74ljE/jwlQgup8tCAo350+\nbWdL3Xkn9O7tKNQYw4OzH6RERAm/TkDLsmEDLFxoJ0oXRV27QlSUXb01pDRtapsOb7rJdjY7UK5E\nOabcMoWnFjxF0vakwOSncqV9CMo3Ho9dNrRsWTvry+EEtBe+fYGvNnzFt3d+S7kS5fye3q23wmWX\nuVpGqdBITIQHHoB16yAyMtjZ5DByJIwda/dhdjgcasG2BQyaPIh5t82jRXSLACVY/GgfggoMrxfu\nu88usPPRR46LweifR/Phyg+ZPXh2QIrB8uUwfz785S9+P3VI6dbNrs80dmywM8nF3/4GcXG2V//E\nCUeh19e7njfj36THhB5sObwlQAmq7PQOQbmTVQzWr7fjzss5e0Ef/fNonv/2eRbcsYAGlRsEJL0O\nHeyK23fd5ffTh5yff7avuZs2Of5PEXher91lLTnZbvlWtqyj8FHLR/HCdy8E7HeluNE7BOVf6elw\nzz22gd5FMXhr6VsBLQZg9+IBVwusFkpt2tghqE+G4mrSYWF2CGrjxvZu4fBhR+HD2g7j6Y5PE/tp\nLOsOrAtQkgr0DkE5lZpqRxNFRsLEiY7e7XmNl8cSH2P25tnMGTKHuhXrBiTF/fvtIpwzZrhaRqnQ\nOnLEruI6cSJcd12ws8mF12s31Jk5076RqFfPUfjnqz/n0cRHmdhvIrH1YgOUZNGndwjKP5KT7boP\n9erB1KmOisGR00foM7EPy/YsY8ndSwJWDLxeOy/qnnuKVzEA22f77rtw991w8mSws8lFWJgdI/vA\nA7Y9b8ECR+G3tryVif0mcstXt/Desvd03aMA0IKg8ue//7XF4MEH4f337RaK+bR8z3LajmlL3Yp1\nmXf7PCqXqhywNP/zHzh+3O4BXxz16WP/M91zT4jNTcjugQfg88/tEhfPP+9oC87YerEsuXsJo34e\nxZCvh5B6NhQ2mC5CjDGF8sOmrgLu4EFjbrnFmEaNjFm+3FHo2Yyz5h8L/mEufvVi89+1/w1Qgv8z\ne7YxF19szLZtAb9USDt1yph27Yz597+DnUkedu0yJjbWmKuuMmbjRkehp9JOmWEzhpnar9c2iZsT\nA5Rg0ZT52pn76+r5fhDqH1oQAiwtzZi33rKvsH/7m32VySev12umbZxmGr3dyPSa0MvsSd0TwESt\n7783pkoV+1nZ19qaNY359NNgZ5IHj8eYd94x5qKLjHn8cWOOHnUUnrA5wdR+vba5ZdItZuvhrQFK\nsmjRgqDyz+MxZvJke0fQtasxq1c7Cl+6a6mJ/STWNHu3mZmTMidASf7RokW2bs2eXSCXKzTWr7dF\nYdSoYGeSD7t3G3P33cZERxvz9tvGnD6d79ATZ0+Y55KeMxe9fJF5LPExc/DkwQAmWvhpQVB5O3nS\nmPfft4WgTRv76ur15ivU4/WYqRummus+us7Ufr22eX/Z+ybdkx7ghK1PPzWmalVjErXVIFcpKcbU\nqWPME08Yk14w/0l8s2qVMT172sIwYoQxBw7kO3RP6h4zbMYwU+mlSua+GfeZjQedNUMVFxcqCDrs\ntDjzeuG772D8ePj6a9sb+be/QceOdluuPKw7sI7xa8YzYc0EqpapyqNXP0r/Zv2JCMt/h7NbBw/C\nX/9qt/GdNg2aNQv4JQutAwfgttvsyKOPP7Yb64S89evh9ddh0iTo0sV2QPfoka9VdPef2M97y97j\ng58/oFnVZgxuPph+zfoFdDBDYXKhYacFXhBEJB54AzvCaawx5uVcjnkL6A6cBO40xqzK5RgtCG4c\nOmTXc0hIgLlz7U4rgwfDwIF2g5MLOJ1+mm93fEvClgQStiSQejaVQc0HMaTFEFpGt0TyUUR8dfw4\nfPCBHU10663w3HNFcxVTf/N67evriy/aYbnDhxeSrUSPHLEr940fD7/8Ap0728lt3brl+ft6JuMM\nczfPZcKaCSRsSeDKmlfSrX43utXvRouLWxTI72soCpmCICJhQDLQGdgDLAMGGmM2ZjumO/CAMaan\niFwJvGmMuSqXc2lBuBBj7FvDTZvsugbLltnFffbuhU6d7B9VXBw0apRr+LEzx0g+lMzKfStZvmc5\ny/YsY9Nvm2hdvTVx9eOIaxBH2xpt/brn8fl4PHarhQkT7OjXzp3tjNyWLQN+6SJn/35bRCdMsDOb\nb73VbmxXqlSwM8uHvXvtSn6JiXYLvKgoO9kk66NZM7uvcy5raqWeTWXhtoUkbEkgcUsih08fpk2N\nNrSt3pa2NdrSIroFdSvWJSo8Kgj/sIIVSgXhKuAZY0z3zMdPYNuzXs52zAfAQmPMfzMfbwBijDH7\nc5yr+BUEY+DsWfs2OTUVjh61f+H798O+ffbz7t2wZQts3mz/YBo1gtatoW1b0ttczvF6NUnNOEnq\n2VT2n9jP/pP72Xdi3+8fW45sYfPhzZzJOEODyg1oFd2KdjXa0bZGW1pGt6RUZOBeOYyx/7SdO22L\nwYYNsGKF3WulRg17EzNkiOMJrioXR4/axWknT4aVK+3raevW9qNxY6hVy948huybaGNg+3b7Jifr\nY9Mmewdcr55tF7vkEqhWzd4KRUfbrytXhnLl2B9+mp+PrGf53p9ZtmcZ6w+uZ1fqLmqWq0mDyg2o\nW7Eu0WWiqVa2GtFl7ecqpatQLqoc5UuUp0xUmQJ5MxQIoVQQ+gFxxpg/ZT6+FWhvjHko2zEzgBeN\nMd9nPp4HPG6MWZHjXK4Kwr6d+3jkqRsxGAQwZJ3DZP5/9sfm9+/+/jNjQMjxOPPn5n9xAPYpt8eY\n7DEYfr8MXsR4ETyI8YLxIHgRrxfwEGa8YDKI8KYj3nQAPOGReMIiSQ+P4lRUFKciozgTGcGZiAjO\nRoRxOjKcsxFhZIR58HCWNDlOethxvKQTZcoT6S1HpClPaW80pTzRlPJUo5S3GqU80ZT3XEq59AaU\n8kYjmf/QnE+zr4/T02179qlT9vPJk3DsmK1nYWFQs6Z9s9esmb0L6NgRqlfP+V9S+cuRI7YvZsUK\nezO5ebMtyidP2qJQvjxUqGA/ly5tVy2JiDj3c3j4HwuI06+dHHc+kWknqXxsK1UOp1D+xB7KndxH\n2ZP77edT+yl15gglzqZSIu044Z400qLKcTaqHGmRpTkdGcGvFWFLRQ+7ynk4UMbDwdIZ/FYqg4Ol\nznK0ZBonIzI4FZHOmQgPJTPCKZMRRUlPBFGecCJMOBHecCK99utIbxgR3ggiTRjhJhwxYQggCGIk\n8zNkfTfM2L+47D+THD/LMvTGZ+nSt3v+npQcLlQQAt/7F0Ajsk1HjYmJISYmJs+YiIgIykdmdS5J\ntg+ytSmGZf5UMn8kv784CmG/f+9/x8h5HmedN9v5Mh+bzMdGwiA8Eq+EY8Ij8YaFQ1gkJiwCb1iE\n/RweiTeqNBkRJTERUUQAUQilECpLCSKIIkKiCJcoIrCfI39/XIKSYeUoFVaeSEr+/m+80B9ioB9H\nRNgN70uXtp/LlLEvNtHRjhfCVH5QqdL/WhCzO3UKfvvN3oymptqifeoUZGTYop7zc/YJx9nfBOTn\nayfHXVgZzl7cgt20YHceR4Z50ok6e5wSZ1OJSD9NuCeNsIw0wj1pXOpJo6HHfh1+No2wk2mEe9PB\nGASD12RwVs5wOuwUZ8LOkEE6HjLIkDQyyCBDMvBIOulkkCHpeMSDwYs38w2hVwxZ/8t6DODN+q5k\nfmR+7eWPT0JJB218SUlJJCUl5evYYDQZjTDGxGc+zk+T0UagkzYZKaWU70JpcbtlQAMRqSMiUcBA\nYHqOY6YDt8PvBeRozmKglFLK/wq0ycgY4xGRB4BE/jfsdIOIDLM/NqONMbNFpIeIbMYOOy0G25so\npVTw6cQ0pZQqRkKpyUgppVSI0oKglFIK0IKglFIqkxYEpZRSgBYEpZRSmbQgKKWUArQgKKWUyqQF\nQSmlFKAFQSmlVCYtCEoppQAtCEoppTJpQVBKKQVoQVBKKZVJC4JSSimgmBaE/G4np/5HnzNn9Ply\nRp8vZwL1fGlBUPmiz5kz+nw5o8+XM1oQlFJKBZQWBKWUUkAh30Iz2DkopVRhdL4tNAttQVBKKeVf\n2mSklFIK0IKglFIqU7EqCCLSX0TWiohHRFrn+NnfRSRFRDaISLdg5RiqROQZEdklIisyP+KDnVMo\nEpF4EdkoIskiMjzY+YQ6EdkuIr+IyEoR+SnY+YQiERkrIvtFZHW271USkUQR2SQiCSJSwR/XKlYF\nAVgD3AQsyv5NEWkK3Aw0BboD74lIrp0uxdxIY0zrzI+5wU4m1IhIGPAOEAdcBgwSkSbBzSrkeYEY\nY8wVxpj2wU4mRH2M/Z3K7glgnjGmMbAA+Ls/LlSsCoIxZpMxJgXI+WJ/IzDRGJNhjNkOpAD6y3ku\nLZIX1h5IMcbsMMakAxOxv1vq/IRi9jrklDFmMXAkx7dvBD7N/PpToI8/rqX/IayawM5sj3dnfk/9\n0QMiskpEPvTXLWoRk/P3aBf6e5QXA3wjIstE5N5gJ1OIXGyM2Q9gjNkHXOyPk0b44yShRES+AaKz\nfwv7S/eUMWZGcLIqHC703AHvAc8ZY4yIPA+MBO4p+CxVEXONMWaviFTFFoYNme+IlTN+mT9Q5AqC\nMaari7DdQK1sjy/J/F6x4uC5GwNocT3XbqB2tsfF8vfICWPM3szPB0VkCrbZTQtC3vaLSLQxZr+I\nVAMO+OOkxbnJKHt7+HRgoIhEiUg9oAGgIx6yyfyly9IXWBusXELYMqCBiNQRkShgIPZ3S+VCREqL\nSNnMr8sA3dDfq/MRzn3NujPz6zuAaf64SJG7Q7gQEekDvA1UAWaKyCpjTHdjzHoR+RJYD6QDfzY6\nhTunV0TkcuyokO3AsOCmE3qMMR4ReQBIxL7ZGmuM2RDktEJZNDAlcxmaCGC8MSYxyDmFHBGZAMQA\nF4nIr8AzwEvAJBG5G9iBHSXp+7X0dU8ppRQU7yYjpZRS2WhBUEopBWhBUEoplUkLglJKKUALglJK\nqUxaEJRSSgFaEJRSSmXSgqCUUgrQgqCUUiqTFgSl/EBEqojIHhH5Z7bvtRSR0yLSL5i5KZVfunSF\nUn6SufXqDKAj8AuwHPjRGDM0qIkplU9aEJTyIxEZid3NahFwLXC5MeZUcLNSKn+0ICjlR5nLXv+C\nXUL9amPM8iCnpFS+aR+CUv5VD7vZkgHqBzkXpRzROwSl/EREIoAfgY3YDZZGAC2NMbuCmZdS+aUF\nQSk/EZGXsLuktTDGHBeROUBJY0xskFNTKl+0yUgpPxCRjsAjwG3GmOOZ374TaCoiw4OWmFIO6B2C\nUkopQO8QlFJKZdKCoJRSCtCCoJRSKpMWBKWUUoAWBKWUUpm0ICillAK0ICillMqkBUEppRSgBUEp\npVSm/we7nl+NBVu1EAAAAABJRU5ErkJggg==\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f0a76b274d0>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "x = np.linspace(-10, 10, 300)\n",
+    "sigmax0c = [[1.0,0.0,\"blue\"],[2.0,0.0,\"red\"],[2.0,1.0,\"green\"]]\n",
+    "for sigma,x0,c in sigmax0c:\n",
+    "    y = sigma/np.sqrt(2*np.pi)*np.exp(-(x-x0)**2/2/sigma**2)\n",
+    "    plt.plot(x, y ,color= c)\n",
+    "    plt.xlabel(\"x\",fontsize=14)\n",
+    "    plt.ylabel('f(x)',fontsize=14)\n",
+    "    plt.xlim(x.min() * 1.1, x.max() * 1.1)\n",
+    "    plt.ylim(-0.1, y.max() * 1.1)"
+   ]
   },
   {
    "cell_type": "markdown",
@@ -829,7 +857,10 @@
     "collapsed": true
    },
    "outputs": [],
-   "source": []
+   "source": [
+    "Gitではファイルの状態を好きなときに更新履歴として保存しておくことができる。\n",
+    "これにより、一度編集したファイルを過去の状態に戻したり、編集箇所の差分を表示できたりする。"
+   ]
   },
   {
    "cell_type": "markdown",
@@ -845,7 +876,9 @@
     "collapsed": true
    },
    "outputs": [],
-   "source": []
+   "source": [
+    "開発の本流から分岐し、本流の開発を邪魔することなく作業を続ける"
+   ]
   },
   {
    "cell_type": "markdown",
@@ -861,7 +894,11 @@
     "collapsed": true
    },
    "outputs": [],
-   "source": []
+   "source": [
+    "ファイルやディレクトリの追加・変更をリポジトリに記録する操作のこと。\n",
+    "コミットを実行するとリポジトリの中では前回コミットした時の状態から現在の状態までの差分を記録した\n",
+    "コミットと呼ばれるものが作成される。"
+   ]
   },
   {
    "cell_type": "markdown",
@@ -877,7 +914,10 @@
     "collapsed": true
    },
    "outputs": [],
-   "source": []
+   "source": [
+    "最後にpullをしてから次のpushをするまでの間に、他の人がpushをしてリモートリポジトリを更新して\n",
+    "しまった場合、マージを行って他の履歴での変更を取り込むまで自分のpushは拒否される。"
+   ]
   },
   {
    "cell_type": "markdown",
@@ -893,7 +933,10 @@
     "collapsed": true
    },
    "outputs": [],
-   "source": []
+   "source": [
+    "リモートリポジトリで自分の手元のローカルリポジトリの変更履歴を共有するには、\n",
+    "ローカルリポジトリ内の変更履歴をアップロードする必要があり、そのために行われる操作。"
+   ]
   },
   {
    "cell_type": "markdown",
@@ -909,7 +952,9 @@
     "collapsed": true
    },
    "outputs": [],
-   "source": []
+   "source": [
+    "リモートリポジトリからローカルリポジトリを更新するために行う操作。"
+   ]
   },
   {
    "cell_type": "markdown",
diff --git a/tutorial2.ipynb b/tutorial2.ipynb
index e6bc8ae..691bddf 100755
--- a/tutorial2.ipynb
+++ b/tutorial2.ipynb
@@ -75,7 +75,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 2,
    "metadata": {
     "ExecuteTime": {
      "end_time": "2016-04-14T17:25:01.955260",
@@ -96,7 +96,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 3,
    "metadata": {
     "ExecuteTime": {
      "end_time": "2016-04-14T17:26:03.246088",
@@ -109,7 +109,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      " 1.0 2.0\n"
+      "1.0 2.0\n"
      ]
     }
    ],
@@ -126,7 +126,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 4,
    "metadata": {
     "ExecuteTime": {
      "end_time": "2016-04-14T17:26:44.397700",
@@ -160,7 +160,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 5,
    "metadata": {
     "ExecuteTime": {
      "end_time": "2016-04-14T17:30:35.733918",
@@ -192,7 +192,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 6,
    "metadata": {
     "ExecuteTime": {
      "end_time": "2016-04-14T17:31:03.276585",
@@ -216,7 +216,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 7,
    "metadata": {
     "ExecuteTime": {
      "end_time": "2016-04-14T17:31:32.249121",
@@ -240,7 +240,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 8,
    "metadata": {
     "ExecuteTime": {
      "end_time": "2016-04-14T17:33:25.325194",
@@ -254,13 +254,13 @@
      "output_type": "stream",
      "text": [
       "mat_c = \n",
-      "[[-0.46069112 -0.66713647 -0.36786955]\n",
-      " [-1.29150856 -1.00761822  0.87512984]\n",
-      " [-0.07997831  1.43295736 -0.95610688]]\n",
+      "[[ 0.7098218  -0.12500305 -0.21118774]\n",
+      " [-0.78079864  0.47330276 -2.1775981 ]\n",
+      " [-0.67046144  1.09486459  0.50351885]]\n",
       "inv_c = \n",
-      "[[-0.16948184 -0.67936369 -0.55661584]\n",
-      " [-0.76089729  0.23970171  0.51216143]\n",
-      " [-1.12621142  0.41607973 -0.23174953]]\n"
+      "[[ 1.50426168 -0.09652577  0.21347225]\n",
+      " [ 1.06296269  0.12379175  0.98120134]\n",
+      " [-0.3083316  -0.39770508  0.13672241]]\n"
      ]
     }
    ],
@@ -277,7 +277,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 24,
+   "execution_count": 9,
    "metadata": {
     "ExecuteTime": {
      "end_time": "2016-04-14T17:34:32.268191",
@@ -291,7 +291,7 @@
      "output_type": "stream",
      "text": [
       "solution :\n",
-      "[ 1.13177768 -0.24116484  0.07646277]\n"
+      "[-2.1288032  -2.60355377 -0.1804809 ]\n"
      ]
     }
    ],
@@ -315,8 +315,13 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## 多項式フィッティング\n",
-    "\n",
+    "## 多項式フィッティング"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
     "以下のデータ［$x_i, y_i$］を、N次多項式で近似せよ。\n",
     "\n",
     "$N=1,3, 10$の結果と、データ点を重ねて描画せよ"
@@ -324,15 +329,53 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 25,
+   "execution_count": 15,
    "metadata": {
-    "ExecuteTime": {
-     "end_time": "2016-04-14T17:44:10.734183",
-     "start_time": "2016-04-14T17:44:10.732362"
-    },
-    "collapsed": true
+    "collapsed": false
    },
    "outputs": [],
+   "source": [
+    "%matplotlib inline\n",
+    "import matplotlib.pyplot as plt"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[<matplotlib.lines.Line2D at 0x7fd16c388510>]"
+      ]
+     },
+     "execution_count": 20,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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PY1GPSiGQmY9m5gkgVikaVfdVIn/J53kczvNYnOexqEerTswJjEfEAxHxgRbtU5K0iktW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\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7fd16c5b6910>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "x = np.linspace(0, 1.0, 20)\n",
+    "y = np.sin(x*5.0) + np.random.randn(len(x))*0.1\n",
+    "plt.plot(x, y, 'ro')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
    "source": [
     "# データの読み込み、描画"
    ]
@@ -374,6 +417,42 @@
     "が求まる"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 52,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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2wuSECXYui78/+PnBoym5b3rDBoJeakG7ZyP4ss1k2v63rbsrUsmMBooDrggU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\nSimlnEIDRSmllFNooCillHKK/wPGQSHeOLZhSQAAAABJRU5ErkJggg==\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7fd15ea6a7d0>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "import warnings\n",
+    "warnings.simplefilter('ignore', np.RankWarning)\n",
+    "x = np.linspace(0, 1.0, 20)\n",
+    "y = np.sin(x*5.0) + np.random.randn(len(x))*0.1\n",
+    "N = [[1,\"blue\",\"N=1\"],[3,\"red\",\"N=3\"],[10,\"green\",\"N=10\"]]\n",
+    "plt.plot(x, y, \"ro\")\n",
+    "for n,c,l in N:\n",
+    "    z = np.polyfit(x, y, n)\n",
+    "    p = np.poly1d(z)\n",
+    "    plt.plot(x, p(x),color= c,label= l)\n",
+    "    plt.ylim(-1.5,1.5)\n",
+    "    plt.xlim(0, 1)\n",
+    "    plt.xlabel(\"x\",fontsize=14)\n",
+    "    plt.ylabel('y',fontsize=14)\n",
+    "    plt.legend(loc='upper right')"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
diff --git a/tutorial3.ipynb b/tutorial3.ipynb
index b0661fb..5175055 100755
--- a/tutorial3.ipynb
+++ b/tutorial3.ipynb
@@ -31,7 +31,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 1,
    "metadata": {
     "ExecuteTime": {
      "end_time": "2016-04-14T18:06:11.631499",
@@ -51,7 +51,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 2,
    "metadata": {
     "ExecuteTime": {
      "end_time": "2016-04-14T18:07:35.308000",
@@ -63,10 +63,10 @@
     {
      "data": {
       "text/plain": [
-       "[<matplotlib.lines.Line2D at 0x7fcbb2688650>]"
+       "[<matplotlib.lines.Line2D at 0x7f97af8b4c10>]"
       ]
      },
-     "execution_count": 3,
+     "execution_count": 2,
      "metadata": {},
      "output_type": "execute_result"
     },
@@ -74,7 +74,7 @@
      "data": {
       "image/png": 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LiqBrV51laJKhoEBHfiR9F6N9++Cdd2wzliSpVw969cru8MVEJ/QpU2wxrqQ5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\nEJbQjTEmISyhG2NMQvx/u7BLb8aDDPkAAAAASUVORK5CYII=\n",
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7fcbb4b78d90>"
+       "<matplotlib.figure.Figure at 0x7f97b6606690>"
       ]
      },
      "metadata": {},
@@ -108,12 +108,45 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 3,
    "metadata": {
-    "collapsed": true
+    "collapsed": false
    },
-   "outputs": [],
-   "source": []
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[<matplotlib.lines.Line2D at 0x7f97af32c890>]"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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9hDCynnOVTKdoU1RWVlJRURE7jLzR+ytdaX5vkP73l21Cz2bJmeHA4hDCihDC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\npIQSuohISvx/gIrqsFAGNDkAAAAASUVORK5CYII=\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f97d83a0d10>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "def Lorentz_res(x):\n",
+    "    A = 1\n",
+    "    x0 = 1\n",
+    "    gamma = 1\n",
+    "    y0 = 1\n",
+    "    \n",
+    "    return  A * gamma / (1.0 + ((x-x0)/gamma)**2.0)\n",
+    "x = np.arange(-6, 6, 0.1)\n",
+    "y = Lorentz_res(x)\n",
+    "\n",
+    "plt.plot(x, y)"
+   ]
   },
   {
    "cell_type": "markdown",
@@ -165,7 +198,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 5,
    "metadata": {
     "collapsed": false
    },
@@ -178,7 +211,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 6,
    "metadata": {
     "ExecuteTime": {
      "end_time": "2016-04-14T18:14:24.076595",
@@ -190,10 +223,10 @@
     {
      "data": {
       "text/plain": [
-       "[<matplotlib.lines.Line2D at 0x7fcbac9a0d90>]"
+       "[<matplotlib.lines.Line2D at 0x7f97a9880b10>]"
       ]
      },
-     "execution_count": 7,
+     "execution_count": 6,
      "metadata": {},
      "output_type": "execute_result"
     },
@@ -201,7 +234,7 @@
      "data": {
       "image/png": 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dT5nZbYC7e9CAtUwys18HTgH/A9ju7j9MuEg9MbMlwNPAe4GjwMPAle5+INGC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\ngg==\n",
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7fcbaca495d0>"
+       "<matplotlib.figure.Figure at 0x7f97a9f25d10>"
       ]
      },
      "metadata": {},
@@ -230,7 +263,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 26,
    "metadata": {
     "collapsed": false
    },
@@ -255,7 +288,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 27,
    "metadata": {
     "collapsed": true
    },
@@ -273,7 +306,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 28,
    "metadata": {
     "collapsed": true
    },
@@ -284,7 +317,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 29,
    "metadata": {
     "collapsed": false
    },
@@ -295,7 +328,7 @@
        "(array([ 2.18669214, -0.00855874,  0.44299388,  0.01660112]), 1)"
       ]
      },
-     "execution_count": 13,
+     "execution_count": 29,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -306,9 +339,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 32,
    "metadata": {
-    "collapsed": true
+    "collapsed": false
    },
    "outputs": [],
    "source": [
@@ -317,12 +350,12 @@
     "gamma = result[0][2]\n",
     "y0 = result[0][3]\n",
     "\n",
-    "y_fit = (np.ones(len(x_lorentz)) * y0 + A * gamma / (1.0 + ((x_lorentz-np.ones(len(x_lorentz))*x0)/gamma)**2.0))"
+    "y_fit = (y0 + A * gamma / (1.0 + ((x_lorentz-x0)/gamma)**2.0))"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": 33,
    "metadata": {
     "collapsed": false
    },
@@ -330,10 +363,10 @@
     {
      "data": {
       "text/plain": [
-       "<matplotlib.legend.Legend at 0x7fcbac473150>"
+       "<matplotlib.legend.Legend at 0x7f97a9336950>"
       ]
      },
-     "execution_count": 21,
+     "execution_count": 33,
      "metadata": {},
      "output_type": "execute_result"
     },
@@ -341,7 +374,7 @@
      "data": {
       "image/png": 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3zCNidST2NAonCeNFfsHM9N+1n/q4rg6efx5qapr2/fznMGxY9xXYC5KSknr9DFN/kZiY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\nACEBXwghAoQEfCGECBD/H11uHSDg9tp/AAAAAElFTkSuQmCC\n",
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7fcbac546ad0>"
+       "<matplotlib.figure.Figure at 0x7f97a93d43d0>"
       ]
      },
      "metadata": {},
@@ -390,6 +423,257 @@
     "を記載する。"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[<matplotlib.lines.Line2D at 0x7f97a95fcc50>]"
+      ]
+     },
+     "execution_count": 14,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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/GsArO27NbKH8X+BVFLeqK9z9zoDXUw5fAI0M7ZXy5/z448+xb98Rlpd3oRx+tvSy0/YY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\nf+4Yl1r/8O7uAAAAAElFTkSuQmCC\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f97a95a14d0>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "x_gauss = np.loadtxt(\"tutorial3_files/x_gauss.txt\")\n",
+    "y_gauss = np.loadtxt(\"tutorial3_files/y_gauss.txt\")\n",
+    "plt.plot(x_gauss, y_gauss, 'o')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 34,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def gauss(x, A, x0, sigma, y0):\n",
+    "    return y0 + A * np.exp(-(x-x0)**2/2/sigma**2)/np.sqrt(2*np.pi*sigma**2)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 35,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def gauss_res(parameters, x, y):\n",
+    "    A = parameters[0]\n",
+    "    x0 = parameters[1]\n",
+    "    sigma = parameters[2]\n",
+    "    y0 = parameters[3]    \n",
+    "    return np.sum(np.square(y -gauss(x, A, x0, sigma, y0)))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 36,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "param_init = [1.0, 0.1, 0.4, 0.1,0.1]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 37,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "1.9202835055048979"
+      ]
+     },
+     "execution_count": 37,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "gauss_res(param_init, x_gauss, y_gauss)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 38,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "      fun: 0.32082664256511895\n",
+       " hess_inv: array([[  1.54225572e-01,   3.55703983e-04,   4.01148196e-02,\n",
+       "         -2.59155448e-02,   0.00000000e+00],\n",
+       "       [  3.55703983e-04,   1.65085929e-02,   2.29696339e-04,\n",
+       "          9.07708431e-05,   0.00000000e+00],\n",
+       "       [  4.01148196e-02,   2.29696339e-04,   2.11639765e-02,\n",
+       "         -6.75867172e-03,   0.00000000e+00],\n",
+       "       [ -2.59155448e-02,   9.07708431e-05,  -6.75867172e-03,\n",
+       "          8.51471202e-03,   0.00000000e+00],\n",
+       "       [  0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
+       "          0.00000000e+00,   1.00000000e+00]])\n",
+       "      jac: array([  5.36441803e-07,  -1.52736902e-07,  -2.23517418e-07,\n",
+       "         4.91738319e-07,   0.00000000e+00])\n",
+       "  message: 'Optimization terminated successfully.'\n",
+       "     nfev: 98\n",
+       "      nit: 10\n",
+       "     njev: 14\n",
+       "   status: 0\n",
+       "  success: True\n",
+       "        x: array([  1.49461571e+00,   2.00574061e-01,   5.93345626e-01,\n",
+       "         7.29379155e-04,   1.00000000e-01])"
+      ]
+     },
+     "execution_count": 38,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "result = scipy.optimize.minimize(gauss_res,param_init,args=(x_gauss,y_gauss))\n",
+    "result"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 41,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([  1.49461571e+00,   2.00574061e-01,   5.93345626e-01,\n",
+       "         7.29379155e-04,   1.00000000e-01])"
+      ]
+     },
+     "execution_count": 41,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "result['x']"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 42,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<matplotlib.legend.Legend at 0x7f97a921e410>"
+      ]
+     },
+     "execution_count": 42,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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LHhzG10s/oaxMExKiGPvkfUS08YBmGYS1k8HEkw7EARVcHf0tMd2M1AuW3k0F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\nhBBthAR8IYRoIyTgCyFEG/H/QpVLBXT+vTgAAAAASUVORK5CYII=\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f97a9300590>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "y_fit = gauss(x_gauss, result['x'][0], result['x'][1], result['x'][2], result['x'][3])\n",
+    "plt.plot(x_gauss, y_gauss, 'o', label=\"observed\")\n",
+    "plt.plot(x_gauss, y_fit, 'r', alpha=0.5, linewidth=4.0, label=\"fitted\")\n",
+    "plt.legend()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "ename": "ValueError",
+     "evalue": "setting an array element with a sequence.",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
+      "\u001b[1;32m<ipython-input-13-199c97d30bb4>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m     10\u001b[0m     \u001b[1;32mreturn\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0my_gauss\u001b[0m \u001b[1;33m-\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mones\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx_gauss\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m*\u001b[0m \u001b[0my0\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0mA\u001b[0m \u001b[1;33m*\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mexp\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx_gauss\u001b[0m\u001b[1;33m-\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mones\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx_gauss\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0mx0\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m/\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m/\u001b[0m\u001b[0msigma\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m/\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msqrt\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpi\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0msigma\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     11\u001b[0m \u001b[0mparam_init\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;36m1.0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0.4\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m1.0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 12\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mminimize\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mgauss_res\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mparam_init\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx_gauss\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0my_gauss\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mmethod\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m\"nelder-mead\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     13\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     14\u001b[0m \u001b[0mA\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
+      "\u001b[1;32m/home/shirouzu/anaconda2/lib/python2.7/site-packages/scipy/optimize/_minimize.pyc\u001b[0m in \u001b[0;36mminimize\u001b[1;34m(fun, x0, args, method, jac, hess, hessp, bounds, constraints, tol, callback, options)\u001b[0m\n\u001b[0;32m    433\u001b[0m                       callback=callback, **options)\n\u001b[0;32m    434\u001b[0m     \u001b[1;32melif\u001b[0m \u001b[0mmeth\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;34m'nelder-mead'\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 435\u001b[1;33m         \u001b[1;32mreturn\u001b[0m \u001b[0m_minimize_neldermead\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfun\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mx0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mcallback\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0moptions\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    436\u001b[0m     \u001b[1;32melif\u001b[0m \u001b[0mmeth\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;34m'powell'\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    437\u001b[0m         \u001b[1;32mreturn\u001b[0m \u001b[0m_minimize_powell\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfun\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mx0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mcallback\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0moptions\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
+      "\u001b[1;32m/home/shirouzu/anaconda2/lib/python2.7/site-packages/scipy/optimize/optimize.pyc\u001b[0m in \u001b[0;36m_minimize_neldermead\u001b[1;34m(func, x0, args, callback, xtol, ftol, maxiter, maxfev, disp, return_all, **unknown_options)\u001b[0m\n\u001b[0;32m    437\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0mretall\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    438\u001b[0m         \u001b[0mallvecs\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[0msim\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 439\u001b[1;33m     \u001b[0mfsim\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mfunc\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx0\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    440\u001b[0m     \u001b[0mnonzdelt\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m0.05\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    441\u001b[0m     \u001b[0mzdelt\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m0.00025\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
+      "\u001b[1;31mValueError\u001b[0m: setting an array element with a sequence."
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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/GsArO27NbKH8X+BVFLeqK9z9zoDXUw5fAI0M7ZXy5/z448+xb98Rlpd3oRx+tvSy0/YY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\nf+4Yl1r/8O7uAAAAAElFTkSuQmCC\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f97a98c2310>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "from scipy.optimize import minimize,leastsq\n",
+    "x_gauss = np.loadtxt(\"tutorial3_files/x_gauss.txt\")\n",
+    "y_gauss = np.loadtxt(\"tutorial3_files/y_gauss.txt\")\n",
+    "plt.plot(x_gauss, y_gauss, 'o')\n",
+    "def gauss_res(parameters, x, y):\n",
+    "    A = parameters[0]\n",
+    "    x0 = parameters[1]\n",
+    "    sigma = parameters[2]\n",
+    "    y0 = parameters[3]    \n",
+    "    return (y_gauss -(np.ones(len(x_gauss)) * y0 + A * np.exp(-(x_gauss-np.ones(len(x_gauss))*x0)**2/2/sigma**2)/np.sqrt(2*np.pi*sigma**2)))**2\n",
+    "param_init = [1.0, 0, 0.4, 1.0]\n",
+    "result = minimize(gauss_res,param_init,args=(x_gauss,y_gauss),method=\"nelder-mead\")\n",
+    "result\n",
+    "A = result[0][0]\n",
+    "x0 = result[0][1]\n",
+    "sigma = result[0][2]\n",
+    "y0 = result[0][3]\n",
+    "y_fit = np.ones(len(x_gauss)) * y0 + A * np.exp(-(x_gauss-np.ones(len(x_gauss))*x0)**2/2/sigma**2)/np.sqrt(2*np.pi*sigma**2)\n",
+    "plt.plot(x_gauss, y_gauss, 'o', label=\"observed\")\n",
+    "plt.plot(x_gauss, y_fit, 'r', alpha=0.5, linewidth=4.0, label=\"fitted\")\n",
+    "plt.legend()"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,