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An implementation of quaternions for and written in tensorflow. Fully differentiable.

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# 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.Tensor`s
(or `tfq.Quaternion`s) 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](https://github.com/moble/quaternion/)
(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](https://github.com/moble/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)
```

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