# 9. Trajectory transformations (“on-the-fly” transformations)

In MDAnalysis, a transformation is a function/function-like class that modifies the data for the current `Timestep` and returns the `Timestep`. For instance, coordinate transformations, such as PBC corrections and molecule fitting are often required for some analyses and visualization. Transformation functions (`transformation_1` and `transformation_2` in the following example) can be called by the user for any given `Timestep` of the trajectory,

    u = MDAnalysis.Universe(topology, trajectory)

    for ts in u.trajectory:
       ts = transformation_2(transformation_1(ts))

where they change the coordinates of the timestep `ts` in place. There is nothing special about these transformations except that they have to be written in such a way that they change the `Timestep` in place.

As described under Workflows, multiple transformations can be grouped together and associated with a trajectory so that the trajectory is transformed on-the-fly, i.e., the data read from the trajectory file will be changed before it is made available in, say, the `AtomGroup.positions` attribute.

The submodule `MDAnalysis.transformations` contains a collection of transformations (see Transformations in MDAnalysis) that can be immediately used but one can always write custom transformations (see Creating transformations).

## 9.1. Workflows

Instead of manually applying transformations, it is much more convenient to associate a whole workflow of transformations with a trajectory and have the transformations be called automatically.

A workflow is a sequence (tuple or list) of transformation functions that will be applied in this order. For example,

    workflow = [transformation_1, transformation_2]

would effectively result in

    ts = transformation_2(transformation_1(ts))

for every time step in the trajectory.

One can add a workflow using the `Universe.trajectory.add_transformations` method of a trajectory (where the list `workflow` is taken from the example above),

    u.trajectory.add_transformations(*workflow)

or upon `Universe` creation using the keyword argument transformations:

    u = MDAnalysis.Universe(topology, trajectory, transformations=workflow)

Note that in these two cases, the workflow cannot be changed after having being added.

## 9.2. Creating transformations

A simple transformation can also be a function that takes a `Timestep` as input, modifies it, and returns it. If it takes no other arguments but a `Timestep` can be defined as the following example:

    def up_by_2(ts):
        """
        Translate all coordinates by 2 angstroms up along the Z dimension.
        """
        ts.positions = ts.positions + np.array([0, 0, 2], dtype=np.float32)
        return ts

If the transformation requires other arguments besides the `Timestep`, the following two methods can be used to create such transformation:

### 9.2.1. Creating complex transformation classes

It is implemented by inheriting from `MDAnalysis.transformations.base.TransformationBase`, which defines `__call__()` for the transformation class and can be applied directly to a `Timestep`. `_transform()` has to be defined and include the operations on the `MDAnalysis.coordinates.base.Timestep`.

So, a transformation class can be roughly defined as follows:

    from MDAnalysis.transformations import TransformationBase

    class up_by_x_class(TransformationBase):
        def __init__(self, distance):
            self.distance = distance

        def _transform(self, ts):
            ts.positions = ts.positions + np.array([0, 0, self.distance], dtype=np.float32)
            return ts

It is the default construction method in `MDAnalysis.transformations` from release 2.0.0 onwards because it can be reliably serialized. See `MDAnalysis.transformations.translate` for a simple example.

### 9.2.2. Creating complex transformation closure functions

Transformation can also be a wrapped function takes the `Timestep` object as argument. So in this case, a transformation function (closure) can be roughly defined as follows:

    def up_by_x_func(distance):
        """
        Creates a transformation that will translate all coordinates by a given amount along the Z dimension.
        """
        def wrapped(ts):
            ts.positions = ts.positions + np.array([0, 0, distance], dtype=np.float32)
            return ts
        return wrapped

An alternative to using a wrapped function is using partials from `functools`. The above function can be written as:

    import functools

    def up_by_x(ts, distance):
        ts.positions = ts.positions + np.array([0, 0, distance], dtype=np.float32)
        return ts

    up_by_2 = functools.partial(up_by_x, distance=2)

Although functions (closures) work as transformations, they are not used in in MDAnalysis from release 2.0.0 onwards because they cannot be reliably serialized and thus a `Universe` with such transformations cannot be used with common parallelization schemes (e.g., ones based on `multiprocessing`). For detailed descriptions about how to write a closure-style transformation, please refer to MDAnalysis 1.x documentation.

## 9.3. Transformations in MDAnalysis

The module `MDAnalysis.transformations` contains transformations that can be immediately used in your own workflows. In order to use any of these transformations, the module must first be imported:

    import MDAnalysis.transformations

A workflow can then be added to a trajectory as described above. Notably, the parameter max_threads can be defined when creating a transformation instance to limit the maximum threads. (See `MDAnalysis.transformations.base.TransformationBase` for more details) Whether a specific transformation can be used along with parallel analysis can be assessed by checking its `parallelizable` attribute.

See Currently implemented transformations for more on the existing transformations in `MDAnalysis.transformations`.

## 9.4. How to transformations

Translating the coordinates of a single frame (although one would normally add the transformation to a workflow, as shown in the subsequent examples):

    u = MDAnalysis.Universe(topology, trajectory)
    new_ts = MDAnalysis.transformations.translate([1,1,1])(u.trajectory.ts)

Create a workflow and add it to the trajectory:

    u = MDAnalysis.Universe(topology, trajectory)
    workflow = [MDAnalysis.transformations.translate([1,1,1]),
                MDAnalysis.transformations.translate([1,2,3])]
    u.trajectory.add_transformations(*workflow)

Giving a workflow as a keyword argument when defining the universe:

    workflow = [MDAnalysis.transformations.translate([1,1,1]),
                MDAnalysis.transformations.translate([1,2,3])]
    u = MDAnalysis.Universe(topology, trajectory, transformations=workflow)

## 9.5. Building blocks for Transformation Classes

Transformations normally ultilize the power of NumPy to get better performance on array operations. However, when it comes to parallelism, NumPy will sometimes oversubscribe the threads, either by hyper threading (when it uses OpenBlas backend), or by working with other parallel engines (e.g. Dask).

In MDAnalysis, we use threadpoolctl inside `TransformationBase` to control the maximum threads for transformations.

It is also possible to apply a global thread limit by setting the external environmental varibale, e.g. `OMP_NUM_THREADS=1 MKL_NUM_THREADS=1 OPENBLAS_NUM_THREADS=1 BLIS_NUM_THREADS=1 python script.py`. Read more about parallelism and resource management in scikit-learn documentations.

Users are advised to benchmark code because interaction between different libraries can lead to sub-optimal performance with defaults.

- 9.5.1. Transformations Base Class — `MDAnalysis.transformations.base`

## 9.6. Currently implemented transformations

- 9.6.1. Trajectory translation — `MDAnalysis.transformations.translate`
- 9.6.2. Trajectory rotation — `MDAnalysis.transformations.rotate`
- 9.6.3. Trajectory Coordinate Averaging — `MDAnalysis.transformations.positionaveraging`
- 9.6.4. Fitting transformations — `MDAnalysis.transformations.fit`
- 9.6.5. Wrap/unwrap transformations — `MDAnalysis.transformations.wrap`
- 9.6.6. No Jump Trajectory Unwrapping — `MDAnalysis.transformations.nojump`
- 9.6.7. Set box dimensions — `MDAnalysis.transformations.boxdimensions`