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‎doc/pub/week41/html/week41-bs.html

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‎doc/pub/week41/ipynb/ipynb-week41-src.tar.gz

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‎doc/pub/week41/ipynb/week41.ipynb

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‎doc/src/week41/_minted-week41/8F742E4CFCF99BA69821AA2655DBFD5ABBBAD84E10F49A5F4278A7252110B6CA.pygtex

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\begin{Verbatim}[commandchars=\\\{\},codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8\relax}]
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\PYG{l+s+sd}{\PYGZdq{}\PYGZdq{}\PYGZdq{}}
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\PYG{l+s+sd}{Simple code that tests XOR and OR gates with linear regression}
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\PYG{l+s+sd}{and logistic regression}
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\PYG{l+s+sd}{\PYGZdq{}\PYGZdq{}\PYGZdq{}}
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\PYG{k+kn}{import} \PYG{n+nn}{matplotlib.pyplot} \PYG{k}{as} \PYG{n+nn}{plt}
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\PYG{k+kn}{from} \PYG{n+nn}{sklearn.linear\PYGZus{}model} \PYG{k+kn}{import} \PYG{n}{LogisticRegression}
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\PYG{k+kn}{import} \PYG{n+nn}{numpy} \PYG{k}{as} \PYG{n+nn}{np}
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\PYG{c+c1}{\PYGZsh{} Design matrix}
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\PYG{n}{X} \PYG{o}{=} \PYG{n}{np}\PYG{o}{.}\PYG{n}{array}\PYG{p}{([} \PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{,} \PYG{l+m+mi}{0}\PYG{p}{,} \PYG{l+m+mi}{0}\PYG{p}{],} \PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{,} \PYG{l+m+mi}{0}\PYG{p}{,} \PYG{l+m+mi}{1}\PYG{p}{],} \PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{,} \PYG{l+m+mi}{1}\PYG{p}{,} \PYG{l+m+mi}{0}\PYG{p}{],[}\PYG{l+m+mi}{1}\PYG{p}{,} \PYG{l+m+mi}{1}\PYG{p}{,} \PYG{l+m+mi}{1}\PYG{p}{]],}\PYG{n}{dtype}\PYG{o}{=}\PYG{n}{np}\PYG{o}{.}\PYG{n}{float64}\PYG{p}{)}
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\PYG{n+nb}{print}\PYG{p}{(}\PYG{l+s+sa}{f}\PYG{l+s+s2}{\PYGZdq{}The X.TX matrix:}\PYG{l+s+si}{\PYGZob{}}\PYG{n}{X}\PYG{o}{.}\PYG{n}{T}\PYG{+w}{ }\PYG{o}{@}\PYG{+w}{ }\PYG{n}{X}\PYG{l+s+si}{\PYGZcb{}}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{)}
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\PYG{n}{Xinv} \PYG{o}{=} \PYG{n}{np}\PYG{o}{.}\PYG{n}{linalg}\PYG{o}{.}\PYG{n}{pinv}\PYG{p}{(}\PYG{n}{X}\PYG{o}{.}\PYG{n}{T} \PYG{o}{@} \PYG{n}{X}\PYG{p}{)}
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\PYG{n+nb}{print}\PYG{p}{(}\PYG{l+s+sa}{f}\PYG{l+s+s2}{\PYGZdq{}The invers of X.TX matrix:}\PYG{l+s+si}{\PYGZob{}}\PYG{n}{Xinv}\PYG{l+s+si}{\PYGZcb{}}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{)}
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\PYG{c+c1}{\PYGZsh{} The XOR gate}
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\PYG{n}{yXOR} \PYG{o}{=} \PYG{n}{np}\PYG{o}{.}\PYG{n}{array}\PYG{p}{(} \PYG{p}{[} \PYG{l+m+mi}{0}\PYG{p}{,} \PYG{l+m+mi}{1} \PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{,} \PYG{l+m+mi}{0}\PYG{p}{])}
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\PYG{n}{ThetaXOR} \PYG{o}{=} \PYG{n}{Xinv} \PYG{o}{@} \PYG{n}{X}\PYG{o}{.}\PYG{n}{T} \PYG{o}{@} \PYG{n}{yXOR}
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\PYG{n+nb}{print}\PYG{p}{(}\PYG{l+s+sa}{f}\PYG{l+s+s2}{\PYGZdq{}The values of theta for the XOR gate:}\PYG{l+s+si}{\PYGZob{}}\PYG{n}{ThetaXOR}\PYG{l+s+si}{\PYGZcb{}}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{)}
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\PYG{n+nb}{print}\PYG{p}{(}\PYG{l+s+sa}{f}\PYG{l+s+s2}{\PYGZdq{}The linear regression prediction for the XOR gate:}\PYG{l+s+si}{\PYGZob{}}\PYG{n}{X}\PYG{+w}{ }\PYG{o}{@}\PYG{+w}{ }\PYG{n}{ThetaXOR}\PYG{l+s+si}{\PYGZcb{}}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{)}
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\PYG{c+c1}{\PYGZsh{} The OR gate}
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\PYG{n}{yOR} \PYG{o}{=} \PYG{n}{np}\PYG{o}{.}\PYG{n}{array}\PYG{p}{(} \PYG{p}{[} \PYG{l+m+mi}{0}\PYG{p}{,} \PYG{l+m+mi}{1} \PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{,} \PYG{l+m+mi}{1}\PYG{p}{])}
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\PYG{n}{ThetaOR} \PYG{o}{=} \PYG{n}{Xinv} \PYG{o}{@} \PYG{n}{X}\PYG{o}{.}\PYG{n}{T} \PYG{o}{@} \PYG{n}{yOR}
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\PYG{n+nb}{print}\PYG{p}{(}\PYG{l+s+sa}{f}\PYG{l+s+s2}{\PYGZdq{}The values of theta for the OR gate:}\PYG{l+s+si}{\PYGZob{}}\PYG{n}{ThetaOR}\PYG{l+s+si}{\PYGZcb{}}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{)}
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\PYG{n+nb}{print}\PYG{p}{(}\PYG{l+s+sa}{f}\PYG{l+s+s2}{\PYGZdq{}The linear regression prediction for the OR gate:}\PYG{l+s+si}{\PYGZob{}}\PYG{n}{X}\PYG{+w}{ }\PYG{o}{@}\PYG{+w}{ }\PYG{n}{ThetaOR}\PYG{l+s+si}{\PYGZcb{}}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{)}
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\PYG{c+c1}{\PYGZsh{} The OR gate}
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\PYG{n}{yAND} \PYG{o}{=} \PYG{n}{np}\PYG{o}{.}\PYG{n}{array}\PYG{p}{(} \PYG{p}{[} \PYG{l+m+mi}{0}\PYG{p}{,} \PYG{l+m+mi}{0} \PYG{p}{,}\PYG{l+m+mi}{0}\PYG{p}{,} \PYG{l+m+mi}{1}\PYG{p}{])}
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\PYG{n}{ThetaAND} \PYG{o}{=} \PYG{n}{Xinv} \PYG{o}{@} \PYG{n}{X}\PYG{o}{.}\PYG{n}{T} \PYG{o}{@} \PYG{n}{yAND}
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\PYG{n+nb}{print}\PYG{p}{(}\PYG{l+s+sa}{f}\PYG{l+s+s2}{\PYGZdq{}The values of theta for the AND gate:}\PYG{l+s+si}{\PYGZob{}}\PYG{n}{ThetaAND}\PYG{l+s+si}{\PYGZcb{}}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{)}
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\PYG{n+nb}{print}\PYG{p}{(}\PYG{l+s+sa}{f}\PYG{l+s+s2}{\PYGZdq{}The linear regression prediction for the AND gate:}\PYG{l+s+si}{\PYGZob{}}\PYG{n}{X}\PYG{+w}{ }\PYG{o}{@}\PYG{+w}{ }\PYG{n}{ThetaAND}\PYG{l+s+si}{\PYGZcb{}}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{)}
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\PYG{c+c1}{\PYGZsh{} Now we change to logistic regression}
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\PYG{c+c1}{\PYGZsh{} Logistic Regression}
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\PYG{n}{logreg} \PYG{o}{=} \PYG{n}{LogisticRegression}\PYG{p}{()}
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\PYG{n}{logreg}\PYG{o}{.}\PYG{n}{fit}\PYG{p}{(}\PYG{n}{X}\PYG{p}{,} \PYG{n}{yOR}\PYG{p}{)}
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\PYG{n+nb}{print}\PYG{p}{(}\PYG{l+s+s2}{\PYGZdq{}Test set accuracy with Logistic Regression for OR gate: }\PYG{l+s+si}{\PYGZob{}:.2f\PYGZcb{}}\PYG{l+s+s2}{\PYGZdq{}}\PYG{o}{.}\PYG{n}{format}\PYG{p}{(}\PYG{n}{logreg}\PYG{o}{.}\PYG{n}{score}\PYG{p}{(}\PYG{n}{X}\PYG{p}{,}\PYG{n}{yOR}\PYG{p}{)))}
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\PYG{n}{logreg}\PYG{o}{.}\PYG{n}{fit}\PYG{p}{(}\PYG{n}{X}\PYG{p}{,} \PYG{n}{yXOR}\PYG{p}{)}
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\PYG{n+nb}{print}\PYG{p}{(}\PYG{l+s+s2}{\PYGZdq{}Test set accuracy with Logistic Regression for XOR gate: }\PYG{l+s+si}{\PYGZob{}:.2f\PYGZcb{}}\PYG{l+s+s2}{\PYGZdq{}}\PYG{o}{.}\PYG{n}{format}\PYG{p}{(}\PYG{n}{logreg}\PYG{o}{.}\PYG{n}{score}\PYG{p}{(}\PYG{n}{X}\PYG{p}{,}\PYG{n}{yXOR}\PYG{p}{)))}
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\PYG{n}{logreg}\PYG{o}{.}\PYG{n}{fit}\PYG{p}{(}\PYG{n}{X}\PYG{p}{,} \PYG{n}{yAND}\PYG{p}{)}
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\PYG{n+nb}{print}\PYG{p}{(}\PYG{l+s+s2}{\PYGZdq{}Test set accuracy with Logistic Regression for AND gate: }\PYG{l+s+si}{\PYGZob{}:.2f\PYGZcb{}}\PYG{l+s+s2}{\PYGZdq{}}\PYG{o}{.}\PYG{n}{format}\PYG{p}{(}\PYG{n}{logreg}\PYG{o}{.}\PYG{n}{score}\PYG{p}{(}\PYG{n}{X}\PYG{p}{,}\PYG{n}{yAND}\PYG{p}{)))}
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\end{Verbatim}

‎doc/src/week41/_minted-week41/8FDA801D9EBD40558C744590672A037CBBBAD84E10F49A5F4278A7252110B6CA.pygtex

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\begin{Verbatim}[commandchars=\\\{\},codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8\relax}]
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\PYG{k+kn}{from} \PYG{n+nn}{\PYGZus{}\PYGZus{}future\PYGZus{}\PYGZus{}} \PYG{k+kn}{import} \PYG{n}{division}
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\PYG{k+kn}{from} \PYG{n+nn}{sympy} \PYG{k+kn}{import} \PYG{o}{*}
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\PYG{n}{x} \PYG{o}{=} \PYG{n}{symbols}\PYG{p}{(}\PYG{l+s+s1}{\PYGZsq{}x\PYGZsq{}}\PYG{p}{)}
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\PYG{n}{expr} \PYG{o}{=} \PYG{n}{sqrt}\PYG{p}{(}\PYG{n}{x}\PYG{o}{*}\PYG{n}{x}\PYG{o}{+}\PYG{n}{exp}\PYG{p}{(}\PYG{n}{x}\PYG{o}{*}\PYG{n}{x}\PYG{p}{))}
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\PYG{n}{simplify}\PYG{p}{(}\PYG{n}{expr}\PYG{p}{)}
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\PYG{n}{derivative} \PYG{o}{=} \PYG{n}{diff}\PYG{p}{(}\PYG{n}{expr}\PYG{p}{,}\PYG{n}{x}\PYG{p}{)}
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\PYG{n+nb}{print}\PYG{p}{(}\PYG{n}{python}\PYG{p}{(}\PYG{n}{expr}\PYG{p}{))}
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\PYG{n+nb}{print}\PYG{p}{(}\PYG{n}{python}\PYG{p}{(}\PYG{n}{derivative}\PYG{p}{))}
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\end{Verbatim}

‎doc/src/week41/_minted-week41/91DA298044DB0DCD8186DE2877A3BBC1BBBAD84E10F49A5F4278A7252110B6CA.pygtex

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\begin{Verbatim}[commandchars=\\\{\},codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8\relax}]
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\PYG{l+s+sd}{\PYGZdq{}\PYGZdq{}\PYGZdq{}The sigmoid function (or the logistic curve) is a}
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\PYG{l+s+sd}{function that takes any real number, z, and outputs a number (0,1).}
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\PYG{l+s+sd}{It is useful in neural networks for assigning weights on a relative scale.}
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\PYG{l+s+sd}{The value z is the weighted sum of parameters involved in the learning algorithm.\PYGZdq{}\PYGZdq{}\PYGZdq{}}
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\PYG{k+kn}{import} \PYG{n+nn}{numpy}
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\PYG{k+kn}{import} \PYG{n+nn}{matplotlib.pyplot} \PYG{k}{as} \PYG{n+nn}{plt}
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\PYG{k+kn}{import} \PYG{n+nn}{math} \PYG{k}{as} \PYG{n+nn}{mt}
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\PYG{n}{z} \PYG{o}{=} \PYG{n}{numpy}\PYG{o}{.}\PYG{n}{arange}\PYG{p}{(}\PYG{o}{\PYGZhy{}}\PYG{l+m+mi}{5}\PYG{p}{,} \PYG{l+m+mi}{5}\PYG{p}{,} \PYG{l+m+mf}{.1}\PYG{p}{)}
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\PYG{n}{sigma\PYGZus{}fn} \PYG{o}{=} \PYG{n}{numpy}\PYG{o}{.}\PYG{n}{vectorize}\PYG{p}{(}\PYG{k}{lambda} \PYG{n}{z}\PYG{p}{:} \PYG{l+m+mi}{1}\PYG{o}{/}\PYG{p}{(}\PYG{l+m+mi}{1}\PYG{o}{+}\PYG{n}{numpy}\PYG{o}{.}\PYG{n}{exp}\PYG{p}{(}\PYG{o}{\PYGZhy{}}\PYG{n}{z}\PYG{p}{)))}
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\PYG{n}{sigma} \PYG{o}{=} \PYG{n}{sigma\PYGZus{}fn}\PYG{p}{(}\PYG{n}{z}\PYG{p}{)}
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\PYG{n}{fig} \PYG{o}{=} \PYG{n}{plt}\PYG{o}{.}\PYG{n}{figure}\PYG{p}{()}
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\PYG{n}{ax} \PYG{o}{=} \PYG{n}{fig}\PYG{o}{.}\PYG{n}{add\PYGZus{}subplot}\PYG{p}{(}\PYG{l+m+mi}{111}\PYG{p}{)}
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\PYG{n}{ax}\PYG{o}{.}\PYG{n}{plot}\PYG{p}{(}\PYG{n}{z}\PYG{p}{,} \PYG{n}{sigma}\PYG{p}{)}
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\PYG{n}{ax}\PYG{o}{.}\PYG{n}{set\PYGZus{}ylim}\PYG{p}{([}\PYG{o}{\PYGZhy{}}\PYG{l+m+mf}{0.1}\PYG{p}{,} \PYG{l+m+mf}{1.1}\PYG{p}{])}
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\PYG{n}{ax}\PYG{o}{.}\PYG{n}{set\PYGZus{}xlim}\PYG{p}{([}\PYG{o}{\PYGZhy{}}\PYG{l+m+mi}{5}\PYG{p}{,}\PYG{l+m+mi}{5}\PYG{p}{])}
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\PYG{n}{ax}\PYG{o}{.}\PYG{n}{grid}\PYG{p}{(}\PYG{k+kc}{True}\PYG{p}{)}
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\PYG{n}{ax}\PYG{o}{.}\PYG{n}{set\PYGZus{}xlabel}\PYG{p}{(}\PYG{l+s+s1}{\PYGZsq{}z\PYGZsq{}}\PYG{p}{)}
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\PYG{n}{ax}\PYG{o}{.}\PYG{n}{set\PYGZus{}title}\PYG{p}{(}\PYG{l+s+s1}{\PYGZsq{}sigmoid function\PYGZsq{}}\PYG{p}{)}
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\PYG{n}{plt}\PYG{o}{.}\PYG{n}{show}\PYG{p}{()}
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\PYG{l+s+sd}{\PYGZdq{}\PYGZdq{}\PYGZdq{}Step Function\PYGZdq{}\PYGZdq{}\PYGZdq{}}
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\PYG{n}{z} \PYG{o}{=} \PYG{n}{numpy}\PYG{o}{.}\PYG{n}{arange}\PYG{p}{(}\PYG{o}{\PYGZhy{}}\PYG{l+m+mi}{5}\PYG{p}{,} \PYG{l+m+mi}{5}\PYG{p}{,} \PYG{l+m+mf}{.02}\PYG{p}{)}
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\PYG{n}{step\PYGZus{}fn} \PYG{o}{=} \PYG{n}{numpy}\PYG{o}{.}\PYG{n}{vectorize}\PYG{p}{(}\PYG{k}{lambda} \PYG{n}{z}\PYG{p}{:} \PYG{l+m+mf}{1.0} \PYG{k}{if} \PYG{n}{z} \PYG{o}{\PYGZgt{}=} \PYG{l+m+mf}{0.0} \PYG{k}{else} \PYG{l+m+mf}{0.0}\PYG{p}{)}
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\PYG{n}{step} \PYG{o}{=} \PYG{n}{step\PYGZus{}fn}\PYG{p}{(}\PYG{n}{z}\PYG{p}{)}
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\PYG{n}{fig} \PYG{o}{=} \PYG{n}{plt}\PYG{o}{.}\PYG{n}{figure}\PYG{p}{()}
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\PYG{n}{ax} \PYG{o}{=} \PYG{n}{fig}\PYG{o}{.}\PYG{n}{add\PYGZus{}subplot}\PYG{p}{(}\PYG{l+m+mi}{111}\PYG{p}{)}
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\PYG{n}{ax}\PYG{o}{.}\PYG{n}{plot}\PYG{p}{(}\PYG{n}{z}\PYG{p}{,} \PYG{n}{step}\PYG{p}{)}
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\PYG{n}{ax}\PYG{o}{.}\PYG{n}{set\PYGZus{}ylim}\PYG{p}{([}\PYG{o}{\PYGZhy{}}\PYG{l+m+mf}{0.5}\PYG{p}{,} \PYG{l+m+mf}{1.5}\PYG{p}{])}
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\PYG{n}{ax}\PYG{o}{.}\PYG{n}{set\PYGZus{}xlim}\PYG{p}{([}\PYG{o}{\PYGZhy{}}\PYG{l+m+mi}{5}\PYG{p}{,}\PYG{l+m+mi}{5}\PYG{p}{])}
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\PYG{n}{ax}\PYG{o}{.}\PYG{n}{grid}\PYG{p}{(}\PYG{k+kc}{True}\PYG{p}{)}
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\PYG{n}{ax}\PYG{o}{.}\PYG{n}{set\PYGZus{}xlabel}\PYG{p}{(}\PYG{l+s+s1}{\PYGZsq{}z\PYGZsq{}}\PYG{p}{)}
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\PYG{n}{ax}\PYG{o}{.}\PYG{n}{set\PYGZus{}title}\PYG{p}{(}\PYG{l+s+s1}{\PYGZsq{}step function\PYGZsq{}}\PYG{p}{)}
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\PYG{n}{plt}\PYG{o}{.}\PYG{n}{show}\PYG{p}{()}
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\PYG{l+s+sd}{\PYGZdq{}\PYGZdq{}\PYGZdq{}Sine Function\PYGZdq{}\PYGZdq{}\PYGZdq{}}
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\PYG{n}{z} \PYG{o}{=} \PYG{n}{numpy}\PYG{o}{.}\PYG{n}{arange}\PYG{p}{(}\PYG{o}{\PYGZhy{}}\PYG{l+m+mi}{2}\PYG{o}{*}\PYG{n}{mt}\PYG{o}{.}\PYG{n}{pi}\PYG{p}{,} \PYG{l+m+mi}{2}\PYG{o}{*}\PYG{n}{mt}\PYG{o}{.}\PYG{n}{pi}\PYG{p}{,} \PYG{l+m+mf}{0.1}\PYG{p}{)}
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\PYG{n}{t} \PYG{o}{=} \PYG{n}{numpy}\PYG{o}{.}\PYG{n}{sin}\PYG{p}{(}\PYG{n}{z}\PYG{p}{)}
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\PYG{n}{fig} \PYG{o}{=} \PYG{n}{plt}\PYG{o}{.}\PYG{n}{figure}\PYG{p}{()}
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\PYG{n}{ax} \PYG{o}{=} \PYG{n}{fig}\PYG{o}{.}\PYG{n}{add\PYGZus{}subplot}\PYG{p}{(}\PYG{l+m+mi}{111}\PYG{p}{)}
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\PYG{n}{ax}\PYG{o}{.}\PYG{n}{plot}\PYG{p}{(}\PYG{n}{z}\PYG{p}{,} \PYG{n}{t}\PYG{p}{)}
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\PYG{n}{ax}\PYG{o}{.}\PYG{n}{set\PYGZus{}ylim}\PYG{p}{([}\PYG{o}{\PYGZhy{}}\PYG{l+m+mf}{1.0}\PYG{p}{,} \PYG{l+m+mf}{1.0}\PYG{p}{])}
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\PYG{n}{ax}\PYG{o}{.}\PYG{n}{set\PYGZus{}xlim}\PYG{p}{([}\PYG{o}{\PYGZhy{}}\PYG{l+m+mi}{2}\PYG{o}{*}\PYG{n}{mt}\PYG{o}{.}\PYG{n}{pi}\PYG{p}{,}\PYG{l+m+mi}{2}\PYG{o}{*}\PYG{n}{mt}\PYG{o}{.}\PYG{n}{pi}\PYG{p}{])}
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\PYG{n}{ax}\PYG{o}{.}\PYG{n}{grid}\PYG{p}{(}\PYG{k+kc}{True}\PYG{p}{)}
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\PYG{n}{ax}\PYG{o}{.}\PYG{n}{set\PYGZus{}xlabel}\PYG{p}{(}\PYG{l+s+s1}{\PYGZsq{}z\PYGZsq{}}\PYG{p}{)}
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\PYG{n}{ax}\PYG{o}{.}\PYG{n}{set\PYGZus{}title}\PYG{p}{(}\PYG{l+s+s1}{\PYGZsq{}sine function\PYGZsq{}}\PYG{p}{)}
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\PYG{n}{plt}\PYG{o}{.}\PYG{n}{show}\PYG{p}{()}
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\PYG{l+s+sd}{\PYGZdq{}\PYGZdq{}\PYGZdq{}Plots a graph of the squashing function used by a rectified linear}
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\PYG{l+s+sd}{unit\PYGZdq{}\PYGZdq{}\PYGZdq{}}
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\PYG{n}{z} \PYG{o}{=} \PYG{n}{numpy}\PYG{o}{.}\PYG{n}{arange}\PYG{p}{(}\PYG{o}{\PYGZhy{}}\PYG{l+m+mi}{2}\PYG{p}{,} \PYG{l+m+mi}{2}\PYG{p}{,} \PYG{l+m+mf}{.1}\PYG{p}{)}
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\PYG{n}{zero} \PYG{o}{=} \PYG{n}{numpy}\PYG{o}{.}\PYG{n}{zeros}\PYG{p}{(}\PYG{n+nb}{len}\PYG{p}{(}\PYG{n}{z}\PYG{p}{))}
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\PYG{n}{y} \PYG{o}{=} \PYG{n}{numpy}\PYG{o}{.}\PYG{n}{max}\PYG{p}{([}\PYG{n}{zero}\PYG{p}{,} \PYG{n}{z}\PYG{p}{],} \PYG{n}{axis}\PYG{o}{=}\PYG{l+m+mi}{0}\PYG{p}{)}
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\PYG{n}{fig} \PYG{o}{=} \PYG{n}{plt}\PYG{o}{.}\PYG{n}{figure}\PYG{p}{()}
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\PYG{n}{ax} \PYG{o}{=} \PYG{n}{fig}\PYG{o}{.}\PYG{n}{add\PYGZus{}subplot}\PYG{p}{(}\PYG{l+m+mi}{111}\PYG{p}{)}
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\PYG{n}{ax}\PYG{o}{.}\PYG{n}{plot}\PYG{p}{(}\PYG{n}{z}\PYG{p}{,} \PYG{n}{y}\PYG{p}{)}
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\PYG{n}{ax}\PYG{o}{.}\PYG{n}{set\PYGZus{}ylim}\PYG{p}{([}\PYG{o}{\PYGZhy{}}\PYG{l+m+mf}{2.0}\PYG{p}{,} \PYG{l+m+mf}{2.0}\PYG{p}{])}
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\PYG{n}{ax}\PYG{o}{.}\PYG{n}{set\PYGZus{}xlim}\PYG{p}{([}\PYG{o}{\PYGZhy{}}\PYG{l+m+mf}{2.0}\PYG{p}{,} \PYG{l+m+mf}{2.0}\PYG{p}{])}
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\PYG{n}{ax}\PYG{o}{.}\PYG{n}{grid}\PYG{p}{(}\PYG{k+kc}{True}\PYG{p}{)}
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\PYG{n}{ax}\PYG{o}{.}\PYG{n}{set\PYGZus{}xlabel}\PYG{p}{(}\PYG{l+s+s1}{\PYGZsq{}z\PYGZsq{}}\PYG{p}{)}
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\PYG{n}{ax}\PYG{o}{.}\PYG{n}{set\PYGZus{}title}\PYG{p}{(}\PYG{l+s+s1}{\PYGZsq{}Rectified linear unit\PYGZsq{}}\PYG{p}{)}
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\PYG{n}{plt}\PYG{o}{.}\PYG{n}{show}\PYG{p}{()}
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\end{Verbatim}

‎doc/src/week41/_minted-week41/A94A396A1D27720ED5CDB1E3A9707FD7BBBAD84E10F49A5F4278A7252110B6CA.pygtex

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\begin{Verbatim}[commandchars=\\\{\},codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8\relax}]
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\PYG{l+s+sd}{\PYGZdq{}\PYGZdq{}\PYGZdq{}}
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\PYG{l+s+sd}{Simple code that tests XOR, OR and AND gates with linear regression}
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\PYG{l+s+sd}{\PYGZdq{}\PYGZdq{}\PYGZdq{}}
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\PYG{k+kn}{import} \PYG{n+nn}{numpy} \PYG{k}{as} \PYG{n+nn}{np}
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\PYG{c+c1}{\PYGZsh{} Design matrix}
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\PYG{n}{X} \PYG{o}{=} \PYG{n}{np}\PYG{o}{.}\PYG{n}{array}\PYG{p}{([} \PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{,} \PYG{l+m+mi}{0}\PYG{p}{,} \PYG{l+m+mi}{0}\PYG{p}{],} \PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{,} \PYG{l+m+mi}{0}\PYG{p}{,} \PYG{l+m+mi}{1}\PYG{p}{],} \PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{,} \PYG{l+m+mi}{1}\PYG{p}{,} \PYG{l+m+mi}{0}\PYG{p}{],[}\PYG{l+m+mi}{1}\PYG{p}{,} \PYG{l+m+mi}{1}\PYG{p}{,} \PYG{l+m+mi}{1}\PYG{p}{]],}\PYG{n}{dtype}\PYG{o}{=}\PYG{n}{np}\PYG{o}{.}\PYG{n}{float64}\PYG{p}{)}
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\PYG{n+nb}{print}\PYG{p}{(}\PYG{l+s+sa}{f}\PYG{l+s+s2}{\PYGZdq{}The X.TX matrix:}\PYG{l+s+si}{\PYGZob{}}\PYG{n}{X}\PYG{o}{.}\PYG{n}{T}\PYG{+w}{ }\PYG{o}{@}\PYG{+w}{ }\PYG{n}{X}\PYG{l+s+si}{\PYGZcb{}}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{)}
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\PYG{n}{Xinv} \PYG{o}{=} \PYG{n}{np}\PYG{o}{.}\PYG{n}{linalg}\PYG{o}{.}\PYG{n}{pinv}\PYG{p}{(}\PYG{n}{X}\PYG{o}{.}\PYG{n}{T} \PYG{o}{@} \PYG{n}{X}\PYG{p}{)}
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\PYG{n+nb}{print}\PYG{p}{(}\PYG{l+s+sa}{f}\PYG{l+s+s2}{\PYGZdq{}The invers of X.TX matrix:}\PYG{l+s+si}{\PYGZob{}}\PYG{n}{Xinv}\PYG{l+s+si}{\PYGZcb{}}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{)}
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\PYG{c+c1}{\PYGZsh{} The XOR gate}
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\PYG{n}{yXOR} \PYG{o}{=} \PYG{n}{np}\PYG{o}{.}\PYG{n}{array}\PYG{p}{(} \PYG{p}{[} \PYG{l+m+mi}{0}\PYG{p}{,} \PYG{l+m+mi}{1} \PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{,} \PYG{l+m+mi}{0}\PYG{p}{])}
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\PYG{n}{ThetaXOR} \PYG{o}{=} \PYG{n}{Xinv} \PYG{o}{@} \PYG{n}{X}\PYG{o}{.}\PYG{n}{T} \PYG{o}{@} \PYG{n}{yXOR}
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\PYG{n+nb}{print}\PYG{p}{(}\PYG{l+s+sa}{f}\PYG{l+s+s2}{\PYGZdq{}The values of theta for the XOR gate:}\PYG{l+s+si}{\PYGZob{}}\PYG{n}{ThetaXOR}\PYG{l+s+si}{\PYGZcb{}}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{)}
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\PYG{n+nb}{print}\PYG{p}{(}\PYG{l+s+sa}{f}\PYG{l+s+s2}{\PYGZdq{}The linear regression prediction for the XOR gate:}\PYG{l+s+si}{\PYGZob{}}\PYG{n}{X}\PYG{+w}{ }\PYG{o}{@}\PYG{+w}{ }\PYG{n}{ThetaXOR}\PYG{l+s+si}{\PYGZcb{}}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{)}
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\PYG{c+c1}{\PYGZsh{} The OR gate}
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\PYG{n}{yOR} \PYG{o}{=} \PYG{n}{np}\PYG{o}{.}\PYG{n}{array}\PYG{p}{(} \PYG{p}{[} \PYG{l+m+mi}{0}\PYG{p}{,} \PYG{l+m+mi}{1} \PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{,} \PYG{l+m+mi}{1}\PYG{p}{])}
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\PYG{n}{ThetaOR} \PYG{o}{=} \PYG{n}{Xinv} \PYG{o}{@} \PYG{n}{X}\PYG{o}{.}\PYG{n}{T} \PYG{o}{@} \PYG{n}{yOR}
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\PYG{n+nb}{print}\PYG{p}{(}\PYG{l+s+sa}{f}\PYG{l+s+s2}{\PYGZdq{}The values of theta for the OR gate:}\PYG{l+s+si}{\PYGZob{}}\PYG{n}{ThetaOR}\PYG{l+s+si}{\PYGZcb{}}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{)}
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\PYG{n+nb}{print}\PYG{p}{(}\PYG{l+s+sa}{f}\PYG{l+s+s2}{\PYGZdq{}The linear regression prediction for the OR gate:}\PYG{l+s+si}{\PYGZob{}}\PYG{n}{X}\PYG{+w}{ }\PYG{o}{@}\PYG{+w}{ }\PYG{n}{ThetaOR}\PYG{l+s+si}{\PYGZcb{}}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{)}
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\PYG{c+c1}{\PYGZsh{} The OR gate}
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\PYG{n}{yAND} \PYG{o}{=} \PYG{n}{np}\PYG{o}{.}\PYG{n}{array}\PYG{p}{(} \PYG{p}{[} \PYG{l+m+mi}{0}\PYG{p}{,} \PYG{l+m+mi}{0} \PYG{p}{,}\PYG{l+m+mi}{0}\PYG{p}{,} \PYG{l+m+mi}{1}\PYG{p}{])}
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\PYG{n}{ThetaAND} \PYG{o}{=} \PYG{n}{Xinv} \PYG{o}{@} \PYG{n}{X}\PYG{o}{.}\PYG{n}{T} \PYG{o}{@} \PYG{n}{yAND}
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\PYG{n+nb}{print}\PYG{p}{(}\PYG{l+s+sa}{f}\PYG{l+s+s2}{\PYGZdq{}The values of theta for the AND gate:}\PYG{l+s+si}{\PYGZob{}}\PYG{n}{ThetaAND}\PYG{l+s+si}{\PYGZcb{}}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{)}
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\PYG{n+nb}{print}\PYG{p}{(}\PYG{l+s+sa}{f}\PYG{l+s+s2}{\PYGZdq{}The linear regression prediction for the AND gate:}\PYG{l+s+si}{\PYGZob{}}\PYG{n}{X}\PYG{+w}{ }\PYG{o}{@}\PYG{+w}{ }\PYG{n}{ThetaAND}\PYG{l+s+si}{\PYGZcb{}}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{)}
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\end{Verbatim}

‎doc/src/week41/_minted-week41/FAB7E87618A8A8AABAD77C666F19DDCDBBBAD84E10F49A5F4278A7252110B6CA.pygtex

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\begin{Verbatim}[commandchars=\\\{\},codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8\relax}]
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\PYG{c+c1}{\PYGZsh{} and now neural networks with Scikit\PYGZhy{}Learn and the XOR}
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\PYG{k+kn}{from} \PYG{n+nn}{sklearn.neural\PYGZus{}network} \PYG{k+kn}{import} \PYG{n}{MLPClassifier}
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\PYG{k+kn}{from} \PYG{n+nn}{sklearn.datasets} \PYG{k+kn}{import} \PYG{n}{make\PYGZus{}classification}
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\PYG{n}{X}\PYG{p}{,} \PYG{n}{yXOR} \PYG{o}{=} \PYG{n}{make\PYGZus{}classification}\PYG{p}{(}\PYG{n}{n\PYGZus{}samples}\PYG{o}{=}\PYG{l+m+mi}{100}\PYG{p}{,} \PYG{n}{random\PYGZus{}state}\PYG{o}{=}\PYG{l+m+mi}{1}\PYG{p}{)}
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\PYG{n}{FFNN} \PYG{o}{=} \PYG{n}{MLPClassifier}\PYG{p}{(}\PYG{n}{random\PYGZus{}state}\PYG{o}{=}\PYG{l+m+mi}{1}\PYG{p}{,} \PYG{n}{max\PYGZus{}iter}\PYG{o}{=}\PYG{l+m+mi}{300}\PYG{p}{)}\PYG{o}{.}\PYG{n}{fit}\PYG{p}{(}\PYG{n}{X}\PYG{p}{,} \PYG{n}{yXOR}\PYG{p}{)}
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\PYG{n}{FFNN}\PYG{o}{.}\PYG{n}{predict\PYGZus{}proba}\PYG{p}{(}\PYG{n}{X}\PYG{p}{)}
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\PYG{n+nb}{print}\PYG{p}{(}\PYG{l+s+sa}{f}\PYG{l+s+s2}{\PYGZdq{}Test set accuracy with Feed Forward Neural Network for XOR gate:}\PYG{l+s+si}{\PYGZob{}}\PYG{n}{FFNN}\PYG{o}{.}\PYG{n}{score}\PYG{p}{(}\PYG{n}{X}\PYG{p}{,}\PYG{+w}{ }\PYG{n}{yXOR}\PYG{p}{)}\PYG{l+s+si}{\PYGZcb{}}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{)}
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\end{Verbatim}

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