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    <p>I just wanted to mention that if speed is required, wrapping unutbu's code in scipy's weave.inline and passing an already existing matrix as a parameter yields a 20-fold decrease in the running time.</p> <p>The code (in rotation_matrix_test.py):</p> <pre><code>import numpy as np import timeit from math import cos, sin, sqrt import numpy.random as nr from scipy import weave def rotation_matrix_weave(axis, theta, mat = None): if mat == None: mat = np.eye(3,3) support = "#include &lt;math.h&gt;" code = """ double x = sqrt(axis[0] * axis[0] + axis[1] * axis[1] + axis[2] * axis[2]); double a = cos(theta / 2.0); double b = -(axis[0] / x) * sin(theta / 2.0); double c = -(axis[1] / x) * sin(theta / 2.0); double d = -(axis[2] / x) * sin(theta / 2.0); mat[0] = a*a + b*b - c*c - d*d; mat[1] = 2 * (b*c - a*d); mat[2] = 2 * (b*d + a*c); mat[3*1 + 0] = 2*(b*c+a*d); mat[3*1 + 1] = a*a+c*c-b*b-d*d; mat[3*1 + 2] = 2*(c*d-a*b); mat[3*2 + 0] = 2*(b*d-a*c); mat[3*2 + 1] = 2*(c*d+a*b); mat[3*2 + 2] = a*a+d*d-b*b-c*c; """ weave.inline(code, ['axis', 'theta', 'mat'], support_code = support, libraries = ['m']) return mat def rotation_matrix_numpy(axis, theta): mat = np.eye(3,3) axis = axis/sqrt(np.dot(axis, axis)) a = cos(theta/2.) b, c, d = -axis*sin(theta/2.) return np.array([[a*a+b*b-c*c-d*d, 2*(b*c-a*d), 2*(b*d+a*c)], [2*(b*c+a*d), a*a+c*c-b*b-d*d, 2*(c*d-a*b)], [2*(b*d-a*c), 2*(c*d+a*b), a*a+d*d-b*b-c*c]]) </code></pre> <p>The timing:</p> <pre><code>&gt;&gt;&gt; import timeit &gt;&gt;&gt; &gt;&gt;&gt; setup = """ ... import numpy as np ... import numpy.random as nr ... ... from rotation_matrix_test import rotation_matrix_weave ... from rotation_matrix_test import rotation_matrix_numpy ... ... mat1 = np.eye(3,3) ... theta = nr.random() ... axis = nr.random(3) ... """ &gt;&gt;&gt; &gt;&gt;&gt; timeit.repeat("rotation_matrix_weave(axis, theta, mat1)", setup=setup, number=100000) [0.36641597747802734, 0.34883809089660645, 0.3459300994873047] &gt;&gt;&gt; timeit.repeat("rotation_matrix_numpy(axis, theta)", setup=setup, number=100000) [7.180983066558838, 7.172032117843628, 7.180462837219238] </code></pre>
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