Tensorflow Quaternion

An implementation of quaternions for tensorflow. Fully differentiable.

The tfquaternion module provides an implementation of quaternions as a tensorflow graph. tfquaternion offers module functions for the basic quaternion arithmetic operations as well as a Quaternion class which supports the relevant magic methods. This is similar to the tensorflow API, e.g. tfq.quaternion_multiply vs. tf.multiply and tfq.Quaternion vs tf.Tensor. Note that all functions starting with tf.quaternion_... assume that it's arguments are tf.Tensors (or tfq.Quaternions) that can be casted to tfq.Quaternion, i.e. the shape must be (..., 4).

This implementation is mostly compatible with a small subset of moble's quaternion implementation (ensured by using slightly adapted versions of his tests). HOwever, there are at least two major differences: First, tfquaternion is type specific as is tensorflow, i.e. two quaternions of different dtypes can not be multiplied. Second, tfquaternion supports operations on arrays of quaternions.

Installation

You can either use pypi

pip install tfquaternion

or install the latest version from git as development package:

git clone https://github.com/PhilJd/tf-quaternion.git
cd tf-quaternion
pip install -e .

The -e option only links the working copy to the python site-packages, so to upgrade, you only need to run git pull.

Usage

Before getting started, an important note on the division: This library resembles the division behaviour of moble's quaternion. While in general the division operator is not defined (from the notation q1/q2 one can not conclude if q1/q2 = q1 * q2^-1 or q1/q2 = q2^-1 * q1), we follow moble's implementation, i.e. tfq.quaternion_divide and Quaternion.__truediv__ compute q1/q2 = q1 * 1/q2.

Example

A simple rotation by a quaternion can look like this:

>>> import tfquaternion as tfq
>>> import tensorflow as tf
>>> s = tf.Session()
>>> points = tf.constant([[1, 0, 0], [0, 1, 0], [0, 0, 1]], dtype=tf.float32)
>>> quat = tfq.Quaternion([0, 1, 0, 0])  rotate by 180 degrees around x axis
>>> s.run(tf.matmul(quat.as_rotation_matrix(), points))
array([[ 1.,  0.,  0.], [ 0., -1.,  0.], [ 0.,  0., -1.]], dtype=float32)

API

class Quaternion

The usage of the *-Operator depends on the multiplier. If the multiplier is a Quaternion, quaternion multiplication is performed while multiplication with a tf.Tensor uses tf.multiply. The behaviour of division is similar, except if the dividend is a scalar, then the inverse of the quaternion is computed.

tfq.Quaternion([1, 0, 0, 0]) * tfq.Quaternion([0, 4, 0, 0])
>>> tfq.Quaternion([0, 4, 0, 0)
tfq.Quaternion([1, 0, 0, 0]) * tf.Tensor([0, 4, 0, 0])
>>> tf.Quaternion([0, 0, 0, 0)