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POFast tensor rotation with NumPy
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  1. POFast tensor rotation with NumPy
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    copied!<p>At the heart of an application (written in Python and using <a href="http://en.wikipedia.org/wiki/NumPy" rel="noreferrer">NumPy</a>) I need to rotate a 4th order tensor. Actually, I need to rotate a lot of tensors many times and this is my bottleneck. My naive implementation (below) involving eight nested loops seems to be quite slow, but I cannot see a way to leverage NumPy's matrix operations and, hopefully, speed things up. I've a feeling I should be using <code>np.tensordot</code>, but I don't see how.</p> <p>Mathematically, elements of the rotated tensor, T', are given by: T'<sub>ijkl</sub> = &Sigma; g<sub>ia</sub> g<sub>jb</sub> g<sub>kc</sub> g<sub>ld</sub> T<sub>abcd</sub> with the sum being over the repeated indices on the right hand side. T and Tprime are 3*3*3*3 NumPy arrays and the rotation matrix g is a 3*3 NumPy array. My slow implementation (taking ~0.04 seconds per call) is below.</p> <pre><code>#!/usr/bin/env python import numpy as np def rotT(T, g): Tprime = np.zeros((3,3,3,3)) for i in range(3): for j in range(3): for k in range(3): for l in range(3): for ii in range(3): for jj in range(3): for kk in range(3): for ll in range(3): gg = g[ii,i]*g[jj,j]*g[kk,k]*g[ll,l] Tprime[i,j,k,l] = Tprime[i,j,k,l] + \ gg*T[ii,jj,kk,ll] return Tprime if __name__ == "__main__": T = np.array([[[[ 4.66533067e+01, 5.84985000e-02, -5.37671310e-01], [ 5.84985000e-02, 1.56722231e+01, 2.32831900e-02], [ -5.37671310e-01, 2.32831900e-02, 1.33399259e+01]], [[ 4.60051700e-02, 1.54658176e+01, 2.19568200e-02], [ 1.54658176e+01, -5.18223500e-02, -1.52814920e-01], [ 2.19568200e-02, -1.52814920e-01, -2.43874100e-02]], [[ -5.35577630e-01, 1.95558600e-02, 1.31108757e+01], [ 1.95558600e-02, -1.51342210e-01, -6.67615000e-03], [ 1.31108757e+01, -6.67615000e-03, 6.90486240e-01]]], [[[ 4.60051700e-02, 1.54658176e+01, 2.19568200e-02], [ 1.54658176e+01, -5.18223500e-02, -1.52814920e-01], [ 2.19568200e-02, -1.52814920e-01, -2.43874100e-02]], [[ 1.57414726e+01, -3.86167500e-02, -1.55971950e-01], [ -3.86167500e-02, 4.65601977e+01, -3.57741000e-02], [ -1.55971950e-01, -3.57741000e-02, 1.34215636e+01]], [[ 2.58256300e-02, -1.49072770e-01, -7.38843000e-03], [ -1.49072770e-01, -3.63410500e-02, 1.32039847e+01], [ -7.38843000e-03, 1.32039847e+01, 1.38172700e-02]]], [[[ -5.35577630e-01, 1.95558600e-02, 1.31108757e+01], [ 1.95558600e-02, -1.51342210e-01, -6.67615000e-03], [ 1.31108757e+01, -6.67615000e-03, 6.90486240e-01]], [[ 2.58256300e-02, -1.49072770e-01, -7.38843000e-03], [ -1.49072770e-01, -3.63410500e-02, 1.32039847e+01], [ -7.38843000e-03, 1.32039847e+01, 1.38172700e-02]], [[ 1.33639532e+01, -1.26331100e-02, 6.84650400e-01], [ -1.26331100e-02, 1.34222177e+01, 1.67851800e-02], [ 6.84650400e-01, 1.67851800e-02, 4.89151396e+01]]]]) g = np.array([[ 0.79389393, 0.54184237, 0.27593346], [-0.59925749, 0.62028664, 0.50609776], [ 0.10306737, -0.56714313, 0.8171449 ]]) for i in range(100): Tprime = rotT(T,g) </code></pre> <p>Is there a way to make this go faster? Making the code generalise to other ranks of tensor would be useful, but is less important.</p>
 

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