# Introduction to PyZoltan

PyZoltan is as the name suggests, is a Python wrapper for the Zoltan data management library. Although it’s primary purpose is a tool for dynamic load balancing for PySPH, the features are general enough to warrant a separate discussion. In Using the PySPH library, we touched upon how to perform nearest neighbor queries in a distributed environment. In this document, we will introduce the PyZoltan interface in it’s native non-SPH format.

In PyZoltan, we wrap the specific routines and objects that we wish to use. The following features of Zoltan are currently supported:

> - Dynamic load balancing using geometric algorithms
> - Unstructured point-to-point communication
> - Distributed data directories

PyZoltan interfaces with Zoltan, which is itself a library that is called to perform specific tasks on the application data. Information about the application data is provided to Zoltan through the method of callbacks, whereby, query functions are registered with Zoltan. These query functions are called internally by Zoltan and are responsible to provide the correct information about the application data to the library. The user is responsible to make available this data in consonance with the application requirement.

## A simple example: Partitioning points

The following simple example demonstrates the partitioning of a random collection of points in the unit cube \([0,1]^3\). The objects to be partitioned in this case is therefore the points themselves which can be thought of as particles in an SPH simulation. We begin with some imports:

    # Imports
    import mpi4py.MPI as mpi
    from pyzoltan.core.carray import UIntArray, DoubleArray
    from pyzoltan.core import zoltan

    from numpy import random
    import numpy as np

    from mpl_toolkits.mplot3d import Axes3D
    import matplotlib.pyplot as plt

    comm = mpi.COMM_WORLD
    rank = comm.Get_rank()
    size = comm.Get_size()

    colors = ['r', 'g', 'b', 'y', 'm', 'k', 'c', 'burlywood']

### Creating the data

After the initial imports, we define the local data on each processor and broadcast this to the root node for plotting the initial assignment:

    numPoints = 1<<12

    x = random.random( numPoints )
    y = random.random( numPoints )
    z = random.random( numPoints )
    gid = np.arange( numPoints*size, dtype=np.uint32 )[rank*numPoints:(rank+1)*numPoints]

    X = np.zeros( size * numPoints )
    Y = np.zeros( size * numPoints )
    Z = np.zeros( size * numPoints )
    GID = np.arange( numPoints*size, dtype=np.uint32 )

    comm.Gather( sendbuf=x, recvbuf=X, root=0 )
    comm.Gather( sendbuf=y, recvbuf=Y, root=0 )
    comm.Gather( sendbuf=z, recvbuf=Z, root=0 )

Note

Each object (point) is assigned a unique global identifier (the gid array). The identifiers must be unique for a load balancing cycle.

Note

The data type of the global identifiers is of type ZOLTAN_ID_TYPE (default uint32). This is set at the time of building the Zoltan library.

### ZoltanGeometricPartitioner

The `ZoltanGeometricPartitioner` is a concrete sub-class of `PyZoltan`. This class defines all helper methods needed for a domain decomposition using a geometric algorithm. After the data has been initialized, we instantiate the `ZoltanGeometricPartitioner` object and set some parameters:

    xa = DoubleArray(numPoints); xa.set_data(x)
    ya = DoubleArray(numPoints); ya.set_data(y)
    za = DoubleArray(numPoints); za.set_data(z)
    gida = UIntArray(numPoints); gida.set_data(gid)

    pz = zoltan.ZoltanGeometricPartitioner(
        dim=3, comm=comm, x=xa, y=ya, z=za, gid=gida)

    pz.set_lb_method('RCB')
    pz.Zoltan_Set_Param('DEBUG_LEVEL', '1')

Note

We use CArrays internally to represent the data in PyZoltan. This is done mainly for compatibility with the PySPH particle data structure.

The complete list of parameters can be found in the Zoltan reference manual. All parameters are supported through the wrapper `PyZoltan.Zoltan_Set_Param()` method. In this example, we set the desired load balancing algorithm (Recursive Coordinate Bisection) and the output debug level.

### Calling the load balance function

Once all the parameters are appropriately set-up, we can ask Zoltan to provide new assignments for the particles:

    pz.Zoltan_LB_Balance()

This will call the chosen load balancing function internally and upon return, set a number of lists (arrays) indicating which objects need to be exported and which objects need to be imported. The data attributes for the export lists are:

> - numExport : Number of objects to be exported
> - exportLocalids : Local indices of the objects to be exported
> - exportGlobalids : Global indices of the objects to be exported
> - exportProcs : A list of size numExport indicating to which processor each object is exported

And similar arrays for the import lists. The import/export lists returned by Zoltan give an application all the information required to initiate the data transfer.

Note

Zoltan does not perform the data transfer. The data transfer must be done by the application or using the Unstructured communication utilities provided by Zoltan.

Given the new assignments, we once again broadcast this to the root to plot the final partition. The partition generated by this approach is shown below.

Point assignment to 4 processors where color indicates assignment.

We can see that the RCB method has resulted in cuts orthogonal to the domain axes. Each processor has exactly one fourth of the total number of particles.

The code for this example can be found in pyzoltan/core/tests/3d_partition.py

## Inverting the Import/Export lists

In the example above, Zoltan returned a list of objects that were to be imported and exported. There arise situations in applications however, when only one set of arrays is available. For example, a common scenario is that we might know which objects need to be exported to remote processors but do not know in advance which objects need to be imported. The matter is complicated for dynamic applications because without a knowledge of the number of objects to be imported, we cannot allocate buffers of appropriate size on the receiving end.

For these scenarios when only one set (either import or export) of arrays is available, we use the `PyZoltan.Zoltan_Invert_Lists()` method to get the other set.

`PyZoltan` exposes this important utility function from Zoltan by assuming that the export lists are known to the application. Upon return from this method, the relevant import lists are also known. Note that the behaviour of import and export lists can be interchanged from the application.

A simple example demonstrating this is given below:

    from pyzoltan.core import carray
    from pyzoltan.core import zoltan

    import numpy
    import mpi4py.MPI as mpi

    comm = mpi.COMM_WORLD; rank = comm.Get_rank(); size = comm.Get_size()

    if rank == 0:
        proclist = numpy.array( [1, 1, 2, 1], dtype=numpy.int32 )
        locids = numpy.array( [1, 3, 5, 7], dtype=numpy.uint32 )
        glbids = numpy.array( [1, 3, 5, 7], dtype=numpy.uint32 )

    if rank == 1:
        proclist = numpy.array( [0, 2, 0], dtype=numpy.int32 )
        locids = numpy.array( [1, 3, 5], dtype=numpy.uint32 )
        glbids = numpy.array( [11, 33, 55], dtype=numpy.uint32 )

    if rank == 2:
        proclist = numpy.array( [1, 1], dtype=numpy.int32 )
        locids = numpy.array( [1, 3], dtype=numpy.uint32 )
        glbids = numpy.array( [111, 333], dtype=numpy.uint32 )

    # create the Zoltan object
    zz = zoltan.PyZoltan(comm)

    # set the export lists
    numExport = proclist.size; zz.numExport = numExport
    zz.exportLocalids.resize(numExport); zz.exportLocalids.set_data(locids)
    zz.exportGlobalids.resize(numExport); zz.exportGlobalids.set_data(glbids)
    zz.exportProcs.resize(numExport); zz.exportProcs.set_data(proclist)

    print 'Proc %d to send %s to %s'%(rank, glbids, proclist)

    # Invert the lists
    zz.Zoltan_Invert_Lists()

    # get the import lists
    numImport = zz.numImport
    importlocids = zz.importLocalids.get_npy_array()
    importglbids = zz.importGlobalids.get_npy_array()
    importprocs = zz.importProcs.get_npy_array()

    print 'Proc %d to recv %s from %s'%(rank, importglbids, importprocs)

In this example (which is hard coded for up to 3 processors), each processor artificially creates a list of objects it knows it must send to remote processors, which is set-up as the export lists for the `PyZoltan` object. Thereafter, `PyZoltan.Zoltan_Invert_Lists()` is called to get the lists that must be imported by each processor. The output from this example is shown below:

    $ mpirun -n 3 python invert_lists.py
    Proc 2 to send [111 333] to [1 1]
    Proc 1 to send [11 33 55] to [0 2 0]
    Proc 0 to send [1 3 5 7] to [1 1 2 1]
    Proc 2 to recv [ 5 33] from [0 1]
    Proc 0 to recv [11 55] from [1 1]
    Proc 1 to recv [  1   3   7 111 333] from [0 0 0 2 2]

We can see that after a call to this method, each processor knows of remote data that must be received. In an application, this information can be used to effect the data transfer.

Another option is to use the unstructured communication utilities offered by Zoltan. This is described next.

## Unstructured point to point communication

In the previous section, we saw how to use the Zoltan library function to invert a set of export indices to get corresponding import indices. Naturally, with a little bit of work, we can structure the requisite communication (MPI send and receives) to exchange the data.

This set of operations is fairly common and Zoltan (PyZoltan) provides a very convenient utility called `ZComm` to perform such communication. The typical use case for `ZComm` is when we know the list of local objects to send to remote processors but have no information about the objects to be received. An example (pyzoltan/core/tests/zcomm.py) demonstrating the use of the `ZComm` object is outlined below.

The example can be run with an arbitrary number of processors. Each processor allocates some data locally and randomly picks \(5\) of these objects to be sent to remote processors. The remote processors are also picked randomly:

    import mpi4py.MPI as mpi
    import numpy as np
    from numpy import random

    # import the unstructured communication package
    from pyzoltan.core import zoltan_comm
    from pyzoltan.core import zoltan

    # MPI comm, rank and size
    comm = mpi.COMM_WORLD; rank = comm.Get_rank(); size = comm.Get_size()

    # each processor creates some random data
    numObjectsTotal = 1<<10

    x = random.random(numObjectsTotal)
    gids = np.array( np.arange(size * numObjectsTotal) )[rank*numObjectsTotal:(rank+1)*numObjectsTotal]
    gids = gids.astype(np.uint32)

    # arbitrarily assign some objects to be sent to some other processor
    nsend = np.int32( random.random_integers(low=1, high=10) )
    object_ids = random.random_integers( low=0, high=numObjectsTotal, size=nsend )
    proclist = random.random_integers(low=0, high=size-1, size=nsend).astype(np.int32)

    my_indices = np.where(proclist == rank)[0]
    proclist[my_indices] = (rank+1)%size

This information is sufficient enough to instantiate the `ZComm` object which will be used as the communication plan to exchange this data. Once the communication plan is setup, each processor knows of the data it must receive with the ZComm.nreturn attribute. This is used to allocate receive buffers:

    # create the ZComm object
    tag = np.int32(0)
    zcomm = zoltan_comm.ZComm(comm, tag=tag, nsend=nsend, proclist=proclist)

    # the data to send and receive
    senddata = x[ object_ids ]
    recvdata = np.ones( zcomm.nreturn )

With the send buffer and the allocated receive buffer, we can perform the communication using the `ZComm.Comm_Do()` method:

    # use zoltan to exchange doubles
    print "Proc %d, Sending %s to %s"%(rank, senddata, proclist)
    zcomm.Comm_Do(senddata, recvdata)
    print "Proc %d, Received %s"%(rank, recvdata)

Note that the user does not need to explicitly write the MPI send and receive calls. All that is required from the user is to correctly allocate the data on the receive side. The output from this example is (it will vary given the use of random numbers):

    $ mpirun  -n 3 python zcomm.py
    Proc 2, Sending [ 0.83476393  0.07041833  0.20059537  0.7722934   0.4529769 ] to [0 1 0 0 1]
    Proc 2, Received [ 0.50391764  0.40028207]
    Proc 0, Sending [ 0.50391764] to [2]
    Proc 1, Sending [ 0.29755463  0.40028207  0.69433472] to [0 2 0]
    Proc 1, Received [ 0.07041833  0.4529769 ]
    Proc 0, Received [ 0.29755463  0.69433472  0.83476393  0.20059537  0.7722934 ]

### Using the plan for similar communication

The `ZComm` object was used to send values of type float64 in this example. If the number of objects to be sent and their destinations are the same, we can modify the `ZComm` to send other objects. For example, the same object can be used to exchange the global indices (uint32) like so:

    senddata = gids[ object_ids ]
    recvdata = np.ones(zcomm.nreturn, dtype=np.uint32)
    zcomm.set_nbytes(recvdata.itemsize)

    print "Proc %d, Sending %s to %s"%(rank, senddata, proclist)
    zcomm.Comm_Do(senddata, recvdata)
    print "Proc %d, Received %s"%(rank, recvdata)

Note

The `ZComm.set_nbytes()` method is used to indicate the size of the individual objects that is communicated via `ZComm.Comm_Do()`

The output with this change is:

    $ mpirun  -n 3  python zcomm.py
    Proc 1, Sending [1054 1692 2034] to [0 2 0]
    Proc 0, Sending [214] to [2]
    Proc 2, Sending [2720 3034 2511 2412 2975] to [0 1 0 0 1]
    Proc 2, Received [ 214 1692]
    Proc 1, Received [3034 2975]
    Proc 0, Received [1054 2034 2720 2511 2412]

### Reversing the communication plan

It is often the case for dynamic applications that objects initially shared with remote processors have their values updated on remote processors. Subsequently, these updated values are required on the originating processor, necessitating them to be communicated back.

For such scenarios, the communication plan represented by `ZComm` can be used to reverse the communication. That is the data that was originally sent will be treated as a receive and vice-versa.

To illustrate the use of this feature, we continue with our example. The received data (array of unsigned ints) is modified on the remote processor and communicated back using the `ZComm.Comm_Do_Reverse()` method:

    recvdata[:] = rank

    updated_info = np.zeros(zcomm.nsend, dtype=senddata.dtype)
    print 'Proc %d, sending updated data %s'%(rank, recvdata)
    zcomm.Comm_Do_Reverse(recvdata, updated_info)
    print 'Proc %d, received updated data %s'%(rank, updated_info)

Note

The size of the buffer each processor will receive in the reverse communication phase is equal to the number of objects initially sent. This is available through the ZComm.send attribute

The output from this when run on 3 processors is:

    $ mpirun  -n 3  python zcomm.py
    Proc 1, Sending [1054 1692 2034] to [0 2 0]
    Proc 0, Sending [214] to [2]
    Proc 2, Sending [2720 3034 2511 2412 2975] to [0 1 0 0 1]
    Proc 2, Received [ 214 1692]
    Proc 1, Received [3034 2975]
    Proc 0, Received [1054 2034 2720 2511 2412]
    Proc 0, sending updated data [0 0 0 0 0]
    Proc 2, sending updated data [2 2]
    Proc 1, sending updated data [1 1]
    Proc 0, received updated data [2]
    Proc 1, received updated data [0 2 0]
    Proc 2, received updated data [0 1 0 0 1]

## Distributed data directories

The Zoltan Distributed Data Directory utility is a convenient way for a processor to locate remote data. It is implemented as a parallel hash map, keyed on the object identifiers (global indices) and with arbitrary user data associated with each entry.

The use of this feature is highly problem dependent since the user defined data will necessarily change for different applications. We use a simple example demonstrating it’s use. Each processor stores ownership of the object in the distributed directory without any user data associated with each entry.

We begin with the standard set of imports and create some data on each processor and assign each object a unique global identifier:

    import numpy
    import pyzoltan.api as pz
    import mpi4py.MPI as mpi

    comm = mpi.COMM_WORLD
    rank = comm.Get_rank()
    size = comm.Get_size()

    # every processor owns some data
    numObjectsTotal = 5
    my_indices = numpy.array( range( rank*numObjectsTotal,(rank+1)*numObjectsTotal ), dtype=numpy.uint32 )

    gid = pz.UIntArray(my_indices.size); gid.set_data( my_indices )

Additionally, each processor has an IntArray which denotes object assignment:

    part_assignment = numpy.array( [rank]*numObjectsTotal, dtype=numpy.int32 )
    part = pz.IntArray( part_assignment.size ); part.set_data( part_assignment )

This is sufficient data to create the distributed directory:

    # create a zoltan dd and store the object assignments
    dd = pz.Zoltan_DD(comm)

    # update the dd with the data
    dd.Zoltan_DD_Update(gid, part)

Note that after instantiation of the `Zoltan_DD` object, we call the `Zoltan_DD.Zoltan_DD_Update()` method to update the data associated with this directory. Now, given the shared data available with each processor, we can query for object assignments. In the example below, each processor queries for the objects with global indices numObjectsTotal + rank and numObjectsTotal - rank:

    # now we can query the dd
    owner_data = pz.IntArray()   # output array for the object data assignment
    owner_parts = pz.IntArray()  # output array for the object assignment

    # every processor requests for information about some data
    query_gids = pz.UIntArray(2); query_gids.set_data( numpy.array([numObjectsTotal+rank,
                                                                    numObjectsTotal-rank], dtype=numpy.uint32) )

    # use Zoltan_DD_Find to query the data
    dd.Zoltan_DD_Find(query_gids, owner_parts, owner_data)

The result from this quey with \(3\) processors is shown below:

    $ mpirun  -n 3 python zoltan_dd.py
    Processor 0, query_gids = [5 5], owner_parts = [1 1], owner_data = [1 1]
    Processor 1, query_gids = [6 4], owner_parts = [1 0], owner_data = [1 0]
    Processor 2, query_gids = [7 3], owner_parts = [1 0], owner_data = [1 0]