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A differentiable quaternion implementation in tensorflow.

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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]( (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 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 >>>, 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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