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POCan I use my own Python class with numpy or some other matrix library?
 

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  1. POCan I use my own Python class with numpy or some other matrix library?
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    <p>I'd like to be able to do matrix operations using a Python class as the elements—in this case, a simple <a href="http://en.wikipedia.org/wiki/Galois_field" rel="nofollow">Galois field</a> implementation. It implements the necessary <code>__add__</code>, <code>__mul__</code>, <code>__sub__</code> etc.</p> <p>At first, I thought this should be possible with <a href="http://docs.scipy.org/doc/numpy/reference/arrays.ndarray.html" rel="nofollow">numpy arrays</a>, using the <code>dtype</code> parameter, but from <a href="http://docs.scipy.org/doc/numpy/reference/arrays.dtypes.html" rel="nofollow">the <code>dtype</code> documentation</a>, it seems that <code>dtype</code> can't be an arbitrary Python class. For example, I have a class <code>Galois</code> which does operations modulo 2:</p> <pre><code>&gt;&gt;&gt; from galois import Galois &gt;&gt;&gt; Galois(1) + Galois(0) Galois(1) &gt;&gt;&gt; Galois(1) + Galois(1) Galois(0) </code></pre> <p>I can try to use this in numpy:</p> <pre><code>&gt;&gt;&gt; import numpy as np &gt;&gt;&gt; a = np.identity(4, Galois) &gt;&gt;&gt; a array([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]], dtype=object) </code></pre> <p>But if I do operations on the matrices, the elements aren't following the methods of my class:</p> <pre><code>&gt;&gt;&gt; b = np.identity(4, Galois) &gt;&gt;&gt; a+b array([[2, 0, 0, 0], [0, 2, 0, 0], [0, 0, 2, 0], [0, 0, 0, 2]], dtype=object) </code></pre> <p>Is there any way to make this work with numpy?</p> <p>Is there any other Python matrix library that can do matrix operations (including inversion) on an arbitrary number-like class?</p> <h3>Update</h3> <p>Thanks for the answers so far. But I'm still not able to really use it as I hoped. Adds and multiplies seem good, but not matrix inversion. For example, let's try to get the <a href="http://en.wikipedia.org/wiki/Rijndael_S-box#Inverse_S-box" rel="nofollow">AES inverse S-box affine transform matrix</a> from the <a href="http://en.wikipedia.org/wiki/Rijndael_S-box#Forward_S-box" rel="nofollow">forward S-box affine transform matrix</a>.</p> <pre><code>class Galois(object): MODULO = 2 def __init__(self, val): self.val = int(val) % self.MODULO def __add__(self, val): return self.__class__((self.val + int(val)) % self.MODULO) def __sub__(self, val): return self.__class__((self.val - int(val)) % self.MODULO) def __mul__(self, val): return self.__class__((self.val * int(val)) % self.MODULO) def __int__(self): return self.val def __repr__(self): return "%s(%d)" % (self.__class__.__name__, self.val) def __float__(self): return float(self.val) if __name__ == "__main__": import numpy as np Gv = np.vectorize(Galois) a = Gv(np.identity(8)) + Gv(np.eye(8,8,-1)) + Gv(np.eye(8,8,-2)) + Gv(np.eye(8,8,-3)) + Gv(np.eye(8,8,-4)) + Gv(np.eye(8,8,4)) + Gv(np.eye(8,8,5)) + Gv(np.eye(8,8,6)) + Gv(np.eye(8,8,7)) print np.matrix(a) print np.matrix(a).I </code></pre> <p>The result:</p> <pre><code>[[Galois(1) Galois(0) Galois(0) Galois(0) Galois(1) Galois(1) Galois(1) Galois(1)] [Galois(1) Galois(1) Galois(0) Galois(0) Galois(0) Galois(1) Galois(1) Galois(1)] [Galois(1) Galois(1) Galois(1) Galois(0) Galois(0) Galois(0) Galois(1) Galois(1)] [Galois(1) Galois(1) Galois(1) Galois(1) Galois(0) Galois(0) Galois(0) Galois(1)] [Galois(1) Galois(1) Galois(1) Galois(1) Galois(1) Galois(0) Galois(0) Galois(0)] [Galois(0) Galois(1) Galois(1) Galois(1) Galois(1) Galois(1) Galois(0) Galois(0)] [Galois(0) Galois(0) Galois(1) Galois(1) Galois(1) Galois(1) Galois(1) Galois(0)] [Galois(0) Galois(0) Galois(0) Galois(1) Galois(1) Galois(1) Galois(1) Galois(1)]] [[ 0.4 0.4 -0.6 0.4 0.4 -0.6 0.4 -0.6] [-0.6 0.4 0.4 -0.6 0.4 0.4 -0.6 0.4] [ 0.4 -0.6 0.4 0.4 -0.6 0.4 0.4 -0.6] [-0.6 0.4 -0.6 0.4 0.4 -0.6 0.4 0.4] [ 0.4 -0.6 0.4 -0.6 0.4 0.4 -0.6 0.4] [ 0.4 0.4 -0.6 0.4 -0.6 0.4 0.4 -0.6] [-0.6 0.4 0.4 -0.6 0.4 -0.6 0.4 0.4] [ 0.4 -0.6 0.4 0.4 -0.6 0.4 -0.6 0.4]] </code></pre> <p>Not the result I hoped for. It seems that for the matrix inversion, numpy just converts the matrix to floats, then does the inversion with plain real numbers.</p>
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