numpy installing, and rotational matrix generator

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http://askubuntu.com/questions/359254/how-to-install-numpy-and-scipy-for-python

Ok, lets follow the installation guide:

  1. It says you need python 2.7 (which you already have): 
    $ python --version
Python 2.7.4
  2. Then it says that you need the numpy package too, version >= 1.4.1: 
    apt-cache policy python-numpy
python-numpy:
Installed: (none)
Candidate: 1:1.7.1-1ubuntu1
Version table:
 1:1.7.1-1ubuntu1 0
    500 http://archive.ubuntu.com/ubuntu/ raring/main amd64 Packages

    As you can see, I have available numpy version 1.7.1, so lets proceed to install it:

    sudo apt-get install python-numpy
  3. Now it says that we need cython, lets check if that package is availabe: 
    apt-cache policy cython
cython:
Installed: (none)
Candidate: 0.17.4-0ubuntu1
Version table:
 0.17.4-0ubuntu1 0
    500 http://archive.ubuntu.com/ubuntu/ raring/main amd64 Packages

    We have it, we install it:

    sudo apt-get install cython

    Please, do notice that there are other packages that are dependency that are being installed too.

  4. Oddly enough, we also need the scipy module too: 
    sudo apt-get install python-scipy
  5. Testing. Open python in a terminal and type the following: 
    $ python
Python 2.7.4 (default, Sep 26 2013, 03:20:26) 
[GCC 4.7.3] on linux2
Type "help", "copyright", "credits" or "license" for more information.
>>> import numpy
>>> import scipy
>>> import cython
>>> exit()

    The above, has to be without errors. If something went wrong, go up and read the guide again, you forgot/skiped a step.

original from http://stackoverflow.com/questions/6802577/python-rotation-of-3d-vector
and modified little bit.

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 <math.h>"
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):
ax = axis
mat = np.eye(3,3)
axis[0] = axis[0]/sqrt(np.dot(ax, ax))
axis[1] = axis[1]/sqrt(np.dot(ax, ax))
axis[2] = axis[2]/sqrt(np.dot(ax, ax))
a = cos(theta/2.)
b = -1*axis[0]*sin(theta/2.)
c = -1*axis[1]*sin(theta/2.)
d = -1*axis[2]*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]])

ax = [1.0,-1.0,0.0]
th = np.pi/4
print(rotation_matrix_numpy(ax,th))

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