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POOptimize generator for multivariate polynomial exponents
 

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  1. POOptimize generator for multivariate polynomial exponents
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    <p>HI, I'm try to find a general expression to obtain exponents of a multivariate polynomial of order <code>order</code> and with <code>n_variables</code>, like the one presented in this <a href="http://www.siam.org/students/siuro/vol1issue1/S01002.pdf" rel="nofollow">reference</a> in equation (3).</p> <p>Here is my current code, which uses an <code>itertools.product</code> generator.</p> <pre><code>def generalized_taylor_expansion_exponents( order, n_variables ): """ Find the exponents of a multivariate polynomial expression of order `order` and `n_variable` number of variables. """ exps = (p for p in itertools.product(range(order+1), repeat=n_variables) if sum(p) &lt;= order) # discard the first element, which is all zeros.. exps.next() return exps </code></pre> <p>The desired out is this:</p> <pre><code>for i in generalized_taylor_expansion_exponents(order=3, n_variables=3): print i (0, 0, 1) (0, 0, 2) (0, 0, 3) (0, 1, 0) (0, 1, 1) (0, 1, 2) (0, 2, 0) (0, 2, 1) (0, 3, 0) (1, 0, 0) (1, 0, 1) (1, 0, 2) (1, 1, 0) (1, 1, 1) (1, 2, 0) (2, 0, 0) (2, 0, 1) (2, 1, 0) (3, 0, 0) </code></pre> <p>Actually this code executes fast, because the generator object is only created. If i want to fill a list with values from this generator execution really starts to be slow, mainly because of the high number of calls to <code>sum</code>. Tipical value for <code>order</code> and <code>n_variables</code> is 5 and 10, respectively.</p> <p>How can i significantly improve execution speed?</p> <p>Thanks for any help.</p> <p>Davide Lasagna</p>
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    1. COI don't really understand the details of what you're trying to do, but have you looked in numpy to see if there are any functions that can help you?
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