Classes
=======

quaternion()
------------

.. py:class:: quaternion(attitude[,matrix = np.identity(3)])

The Quaternion class. 

`attitude` can be:

* a number (of any type, complex are included);

 >>> import qmath
 >>> qmath.quaternion(1)
 (1.0)
 >>> qmath.quaternion(1+1j)
 (1.0+1.0i)

* a list or a numpy array of the components with respect to `1, i, j` and `k`; 

 >>> qmath.quaternion([1,2,3,4])
 (1.0+2.0i+3.0j+4.0k)
 >>> qmath.quaternion(np.array([1,2,3,4]))
 (1.0+2.0i+3.0j+4.0k)

* a string of the form `'a+bi+cj+dk'`;

 >>> qmath.quaternion('1+1i+3j-2k')
 (1.0+1.0i+3.0j-2.0k)

* a rotation about an axis using pairs (rotation angle, axis of rotation);

 >>> qmath.quaternion(0.5 * math.pi, [0,0,1])
 (0.968912421711+0.247403959255k)

* a list whose components are Euler angles;

 >>> import math
 >>> qmath.quaternion([0.0,math.pi / 6,math.pi / 3])
 (0.836516303738+0.482962913145i+0.224143868042j-0.129409522551k)

* a 3X3 rotation matrix. The matrix must be given as a numpy array.

 >>> import numpy as np
 >>> qmath.quaternion(np.array([[0  ,-0.8 ,-0.6],
 ...                            [0.8,-0.36, 0.48],
 ...                            [0.6,0.48 ,-0.64]]))
 (0.707106781187i+0.565685424949j+0.424264068712k)

`matrix` is a 3X3 symmetric matrix defining the product in the quaternion algebra. The identity matrix is by default: this choiche yields to classical Hamilton quaternions. Different choiches of this matrix lead to generalized quaternion algebras. For example, if 

 `matrix = np.array([[-1,0,0],[0,1,0],[0,0,-1]])`
 
one gets the algebra of square matrices of order two.

hurwitz()
---------

.. py:class:: hurwitz(attitude[,matrix = np.identity(3)])

The class of Hurwitz quaternions, i.e. quaternions whose components are integers. 

`attitude` can be the same as for quaternion class, if the components as a quaternion are integers.