docs/source/parallel/parallel_multiengine.txt

.. _parallelmultiengine:

===============================
IPython's multiengine interface
===============================

The multiengine interface represents one possible way of working with a set of
IPython engines. The basic idea behind the multiengine interface is that the
capabilities of each engine are directly and explicitly exposed to the user.
Thus, in the multiengine interface, each engine is given an id that is used to
identify the engine and give it work to do. This interface is very intuitive
and is designed with interactive usage in mind, and is thus the best place for
new users of IPython to begin.

Starting the IPython controller and engines
===========================================

To follow along with this tutorial, you will need to start the IPython
controller and four IPython engines. The simplest way of doing this is to use
the :command:`ipcluster` command::

	$ ipcluster local -n 4
	
For more detailed information about starting the controller and engines, see
our :ref:`introduction <ip1par>` to using IPython for parallel computing.

Creating a ``MultiEngineClient`` instance
=========================================

The first step is to import the IPython :mod:`IPython.kernel.client` module
and then create a :class:`MultiEngineClient` instance:

.. sourcecode:: ipython

	In [1]: from IPython.kernel import client
	
	In [2]: mec = client.MultiEngineClient()

This form assumes that the :file:`ipcontroller-mec.furl` is in the
:file:`~./ipython/security` directory on the client's host. If not, the
location of the FURL file must be given as an argument to the
constructor:

.. sourcecode:: ipython

    In [2]: mec = client.MultiEngineClient('/path/to/my/ipcontroller-mec.furl')

To make sure there are engines connected to the controller, use can get a list
of engine ids:

.. sourcecode:: ipython

	In [3]: mec.get_ids()
	Out[3]: [0, 1, 2, 3]

Here we see that there are four engines ready to do work for us.

Quick and easy parallelism
==========================

In many cases, you simply want to apply a Python function to a sequence of objects, but *in parallel*.  The multiengine interface provides two simple ways of accomplishing this:  a parallel version of :func:`map` and ``@parallel`` function decorator.

Parallel map
------------

Python's builtin :func:`map` functions allows a function to be applied to a
sequence element-by-element. This type of code is typically trivial to
parallelize. In fact, the multiengine interface in IPython already has a
parallel version of :meth:`map` that works just like its serial counterpart:

.. sourcecode:: ipython

	In [63]: serial_result = map(lambda x:x**10, range(32))

	In [64]: parallel_result = mec.map(lambda x:x**10, range(32))

	In [65]: serial_result==parallel_result
	Out[65]: True

.. note::

    The multiengine interface version of :meth:`map` does not do any load
    balancing.  For a load balanced version, see the task interface.

.. seealso::

    The :meth:`map` method has a number of options that can be controlled by
    the :meth:`mapper` method.  See its docstring for more information.

Parallel function decorator
---------------------------

Parallel functions are just like normal function, but they can be called on sequences and *in parallel*.  The multiengine interface provides a decorator that turns any Python function into a parallel function:

.. sourcecode:: ipython

    In [10]: @mec.parallel()
       ....: def f(x):
       ....:     return 10.0*x**4
       ....: 

    In [11]: f(range(32))    # this is done in parallel
    Out[11]: 
    [0.0,10.0,160.0,...]

See the docstring for the :meth:`parallel` decorator for options.

Running Python commands
=======================

The most basic type of operation that can be performed on the engines is to
execute Python code. Executing Python code can be done in blocking or
non-blocking mode (blocking is default) using the :meth:`execute` method.

Blocking execution
------------------

In blocking mode, the :class:`MultiEngineClient` object (called ``mec`` in
these examples) submits the command to the controller, which places the
command in the engines' queues for execution. The :meth:`execute` call then
blocks until the engines are done executing the command:

.. sourcecode:: ipython

	# The default is to run on all engines
	In [4]: mec.execute('a=5')
	Out[4]: 
	<Results List>
	[0] In [1]: a=5
	[1] In [1]: a=5
	[2] In [1]: a=5
	[3] In [1]: a=5

	In [5]: mec.execute('b=10')
	Out[5]: 
	<Results List>
	[0] In [2]: b=10
	[1] In [2]: b=10
	[2] In [2]: b=10
	[3] In [2]: b=10

Python commands can be executed on specific engines by calling execute using
the ``targets`` keyword argument:

.. sourcecode:: ipython

	In [6]: mec.execute('c=a+b',targets=[0,2])
	Out[6]: 
	<Results List>
	[0] In [3]: c=a+b
	[2] In [3]: c=a+b


	In [7]: mec.execute('c=a-b',targets=[1,3])
	Out[7]: 
	<Results List>
	[1] In [3]: c=a-b
	[3] In [3]: c=a-b


	In [8]: mec.execute('print c')
	Out[8]: 
	<Results List>
	[0] In [4]: print c
	[0] Out[4]: 15

	[1] In [4]: print c
	[1] Out[4]: -5

	[2] In [4]: print c
	[2] Out[4]: 15

	[3] In [4]: print c
	[3] Out[4]: -5

This example also shows one of the most important things about the IPython
engines: they have a persistent user namespaces. The :meth:`execute` method
returns a Python ``dict`` that contains useful information:

.. sourcecode:: ipython

	In [9]: result_dict = mec.execute('d=10; print d')

	In [10]: for r in result_dict:
	   ....:     print r
	   ....:     
	   ....:     
	{'input': {'translated': 'd=10; print d', 'raw': 'd=10; print d'}, 'number': 5, 'id': 0, 'stdout': '10\n'}
	{'input': {'translated': 'd=10; print d', 'raw': 'd=10; print d'}, 'number': 5, 'id': 1, 'stdout': '10\n'}
	{'input': {'translated': 'd=10; print d', 'raw': 'd=10; print d'}, 'number': 5, 'id': 2, 'stdout': '10\n'}
	{'input': {'translated': 'd=10; print d', 'raw': 'd=10; print d'}, 'number': 5, 'id': 3, 'stdout': '10\n'}

Non-blocking execution
----------------------

In non-blocking mode, :meth:`execute` submits the command to be executed and
then returns a :class:`PendingResult` object immediately. The
:class:`PendingResult` object gives you a way of getting a result at a later
time through its :meth:`get_result` method or :attr:`r` attribute. This allows
you to quickly submit long running commands without blocking your local
Python/IPython session:

.. sourcecode:: ipython

	# In blocking mode
	In [6]: mec.execute('import time')
	Out[6]:
	<Results List>
	[0] In [1]: import time
	[1] In [1]: import time
	[2] In [1]: import time
	[3] In [1]: import time

	# In non-blocking mode
	In [7]: pr = mec.execute('time.sleep(10)',block=False)

	# Now block for the result
	In [8]: pr.get_result()
	Out[8]:
	<Results List>
	[0] In [2]: time.sleep(10)
	[1] In [2]: time.sleep(10)
	[2] In [2]: time.sleep(10)
	[3] In [2]: time.sleep(10)

	# Again in non-blocking mode
	In [9]: pr = mec.execute('time.sleep(10)',block=False)

	# Poll to see if the result is ready
	In [10]: pr.get_result(block=False)

	# A shorthand for get_result(block=True)
	In [11]: pr.r
	Out[11]:
	<Results List>
	[0] In [3]: time.sleep(10)
	[1] In [3]: time.sleep(10)
	[2] In [3]: time.sleep(10)
	[3] In [3]: time.sleep(10)

Often, it is desirable to wait until a set of :class:`PendingResult` objects
are done. For this, there is a the method :meth:`barrier`. This method takes a
tuple of :class:`PendingResult` objects and blocks until all of the associated
results are ready:

.. sourcecode:: ipython

	In [72]: mec.block=False

	# A trivial list of PendingResults objects
	In [73]: pr_list = [mec.execute('time.sleep(3)') for i in range(10)]

	# Wait until all of them are done
	In [74]: mec.barrier(pr_list)

	# Then, their results are ready using get_result or the r attribute
	In [75]: pr_list[0].r
	Out[75]: 
	<Results List>
	[0] In [20]: time.sleep(3)
	[1] In [19]: time.sleep(3)
	[2] In [20]: time.sleep(3)
	[3] In [19]: time.sleep(3)


The ``block`` and ``targets`` keyword arguments and attributes
--------------------------------------------------------------

Most methods in the multiengine interface (like :meth:`execute`) accept
``block`` and ``targets`` as keyword arguments. As we have seen above, these
keyword arguments control the blocking mode and which engines the command is
applied to. The :class:`MultiEngineClient` class also has :attr:`block` and
:attr:`targets` attributes that control the default behavior when the keyword
arguments are not provided. Thus the following logic is used for :attr:`block`
and :attr:`targets`:

* If no keyword argument is provided, the instance attributes are used.
* Keyword argument, if provided override the instance attributes.

The following examples demonstrate how to use the instance attributes:

.. sourcecode:: ipython

	In [16]: mec.targets = [0,2]

	In [17]: mec.block = False

	In [18]: pr = mec.execute('a=5')

	In [19]: pr.r
	Out[19]: 
	<Results List>
	[0] In [6]: a=5
	[2] In [6]: a=5

	# Note targets='all' means all engines
	In [20]: mec.targets = 'all'

	In [21]: mec.block = True

	In [22]: mec.execute('b=10; print b')
	Out[22]: 
	<Results List>
	[0] In [7]: b=10; print b
	[0] Out[7]: 10

	[1] In [6]: b=10; print b
	[1] Out[6]: 10

	[2] In [7]: b=10; print b
	[2] Out[7]: 10

	[3] In [6]: b=10; print b
	[3] Out[6]: 10

The :attr:`block` and :attr:`targets` instance attributes also determine the
behavior of the parallel magic commands.


Parallel magic commands
-----------------------

We provide a few IPython magic commands (``%px``, ``%autopx`` and ``%result``)
that make it more pleasant to execute Python commands on the engines
interactively. These are simply shortcuts to :meth:`execute` and
:meth:`get_result`. The ``%px`` magic executes a single Python command on the
engines specified by the :attr:`targets` attribute of the
:class:`MultiEngineClient` instance (by default this is ``'all'``):

.. sourcecode:: ipython

	# Make this MultiEngineClient active for parallel magic commands
	In [23]: mec.activate()

	In [24]: mec.block=True

	In [25]: import numpy

	In [26]: %px import numpy
	Executing command on Controller
	Out[26]:
	<Results List>
	[0] In [8]: import numpy
	[1] In [7]: import numpy
	[2] In [8]: import numpy
	[3] In [7]: import numpy


	In [27]: %px a = numpy.random.rand(2,2)
	Executing command on Controller
	Out[27]:
	<Results List>
	[0] In [9]: a = numpy.random.rand(2,2)
	[1] In [8]: a = numpy.random.rand(2,2)
	[2] In [9]: a = numpy.random.rand(2,2)
	[3] In [8]: a = numpy.random.rand(2,2)


	In [28]: %px print numpy.linalg.eigvals(a)
	Executing command on Controller
	Out[28]:
	<Results List>
	[0] In [10]: print numpy.linalg.eigvals(a)
	[0] Out[10]: [ 1.28167017  0.14197338]

	[1] In [9]: print numpy.linalg.eigvals(a)
	[1] Out[9]: [-0.14093616  1.27877273]

	[2] In [10]: print numpy.linalg.eigvals(a)
	[2] Out[10]: [-0.37023573  1.06779409]

	[3] In [9]: print numpy.linalg.eigvals(a)
	[3] Out[9]: [ 0.83664764 -0.25602658]

The ``%result`` magic gets and prints the stdin/stdout/stderr of the last
command executed on each engine. It is simply a shortcut to the
:meth:`get_result` method:

.. sourcecode:: ipython

	In [29]: %result
	Out[29]:
	<Results List>
	[0] In [10]: print numpy.linalg.eigvals(a)
	[0] Out[10]: [ 1.28167017  0.14197338]

	[1] In [9]: print numpy.linalg.eigvals(a)
	[1] Out[9]: [-0.14093616  1.27877273]

	[2] In [10]: print numpy.linalg.eigvals(a)
	[2] Out[10]: [-0.37023573  1.06779409]

	[3] In [9]: print numpy.linalg.eigvals(a)
	[3] Out[9]: [ 0.83664764 -0.25602658]

The ``%autopx`` magic switches to a mode where everything you type is executed
on the engines given by the :attr:`targets` attribute:

.. sourcecode:: ipython

	In [30]: mec.block=False

	In [31]: %autopx
	Auto Parallel Enabled
	Type %autopx to disable

	In [32]: max_evals = []
	<IPython.kernel.multiengineclient.PendingResult object at 0x17b8a70>

	In [33]: for i in range(100):
	   ....:     a = numpy.random.rand(10,10)
	   ....:     a = a+a.transpose()
	   ....:     evals = numpy.linalg.eigvals(a)
	   ....:     max_evals.append(evals[0].real)
	   ....:
	   ....:
	<IPython.kernel.multiengineclient.PendingResult object at 0x17af8f0>

	In [34]: %autopx
	Auto Parallel Disabled

	In [35]: mec.block=True

	In [36]: px print "Average max eigenvalue is: ", sum(max_evals)/len(max_evals)
	Executing command on Controller
	Out[36]:
	<Results List>
	[0] In [13]: print "Average max eigenvalue is: ", sum(max_evals)/len(max_evals)
	[0] Out[13]: Average max eigenvalue is:  10.1387247332

	[1] In [12]: print "Average max eigenvalue is: ", sum(max_evals)/len(max_evals)
	[1] Out[12]: Average max eigenvalue is:  10.2076902286

	[2] In [13]: print "Average max eigenvalue is: ", sum(max_evals)/len(max_evals)
	[2] Out[13]: Average max eigenvalue is:  10.1891484655

	[3] In [12]: print "Average max eigenvalue is: ", sum(max_evals)/len(max_evals)
	[3] Out[12]: Average max eigenvalue is:  10.1158837784


Moving Python objects around
============================

In addition to executing code on engines, you can transfer Python objects to
and from your IPython session and the engines. In IPython, these operations
are called :meth:`push` (sending an object to the engines) and :meth:`pull`
(getting an object from the engines).

Basic push and pull
-------------------

Here are some examples of how you use :meth:`push` and :meth:`pull`:

.. sourcecode:: ipython

	In [38]: mec.push(dict(a=1.03234,b=3453))
	Out[38]: [None, None, None, None]

	In [39]: mec.pull('a')
	Out[39]: [1.03234, 1.03234, 1.03234, 1.03234]

	In [40]: mec.pull('b',targets=0)
	Out[40]: [3453]

	In [41]: mec.pull(('a','b'))
	Out[41]: [[1.03234, 3453], [1.03234, 3453], [1.03234, 3453], [1.03234, 3453]]

	In [42]: mec.zip_pull(('a','b'))
	Out[42]: [(1.03234, 1.03234, 1.03234, 1.03234), (3453, 3453, 3453, 3453)]

	In [43]: mec.push(dict(c='speed'))
	Out[43]: [None, None, None, None]

	In [44]: %px print c
	Executing command on Controller
	Out[44]: 
	<Results List>
	[0] In [14]: print c
	[0] Out[14]: speed

	[1] In [13]: print c
	[1] Out[13]: speed

	[2] In [14]: print c
	[2] Out[14]: speed

	[3] In [13]: print c
	[3] Out[13]: speed

In non-blocking mode :meth:`push` and :meth:`pull` also return
:class:`PendingResult` objects:

.. sourcecode:: ipython

	In [47]: mec.block=False

	In [48]: pr = mec.pull('a')

	In [49]: pr.r
	Out[49]: [1.03234, 1.03234, 1.03234, 1.03234]


Push and pull for functions
---------------------------

Functions can also be pushed and pulled using :meth:`push_function` and
:meth:`pull_function`:

.. sourcecode:: ipython

    In [52]: mec.block=True

	In [53]: def f(x):
	   ....:     return 2.0*x**4
	   ....: 

	In [54]: mec.push_function(dict(f=f))
	Out[54]: [None, None, None, None]

	In [55]: mec.execute('y = f(4.0)')
	Out[55]: 
	<Results List>
	[0] In [15]: y = f(4.0)
	[1] In [14]: y = f(4.0)
	[2] In [15]: y = f(4.0)
	[3] In [14]: y = f(4.0)


	In [56]: px print y
	Executing command on Controller
	Out[56]: 
	<Results List>
	[0] In [16]: print y
	[0] Out[16]: 512.0

	[1] In [15]: print y
	[1] Out[15]: 512.0

	[2] In [16]: print y
	[2] Out[16]: 512.0

	[3] In [15]: print y
	[3] Out[15]: 512.0


Dictionary interface
--------------------

As a shorthand to :meth:`push` and :meth:`pull`, the
:class:`MultiEngineClient` class implements some of the Python dictionary
interface. This make the remote namespaces of the engines appear as a local
dictionary. Underneath, this uses :meth:`push` and :meth:`pull`:

.. sourcecode:: ipython

	In [50]: mec.block=True

	In [51]: mec['a']=['foo','bar']

	In [52]: mec['a']
	Out[52]: [['foo', 'bar'], ['foo', 'bar'], ['foo', 'bar'], ['foo', 'bar']]

Scatter and gather
------------------

Sometimes it is useful to partition a sequence and push the partitions to
different engines. In MPI language, this is know as scatter/gather and we
follow that terminology. However, it is important to remember that in
IPython's :class:`MultiEngineClient` class, :meth:`scatter` is from the
interactive IPython session to the engines and :meth:`gather` is from the
engines back to the interactive IPython session. For scatter/gather operations
between engines, MPI should be used:

.. sourcecode:: ipython

	In [58]: mec.scatter('a',range(16))
	Out[58]: [None, None, None, None]

	In [59]: px print a
	Executing command on Controller
	Out[59]: 
	<Results List>
	[0] In [17]: print a
	[0] Out[17]: [0, 1, 2, 3]

	[1] In [16]: print a
	[1] Out[16]: [4, 5, 6, 7]

	[2] In [17]: print a
	[2] Out[17]: [8, 9, 10, 11]

	[3] In [16]: print a
	[3] Out[16]: [12, 13, 14, 15]


	In [60]: mec.gather('a')
	Out[60]: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]

Other things to look at
=======================

How to do parallel list comprehensions
--------------------------------------

In many cases list comprehensions are nicer than using the map function. While
we don't have fully parallel list comprehensions, it is simple to get the
basic effect using :meth:`scatter` and :meth:`gather`:

.. sourcecode:: ipython

	In [66]: mec.scatter('x',range(64))
	Out[66]: [None, None, None, None]

	In [67]: px y = [i**10 for i in x]
	Executing command on Controller
	Out[67]: 
	<Results List>
	[0] In [19]: y = [i**10 for i in x]
	[1] In [18]: y = [i**10 for i in x]
	[2] In [19]: y = [i**10 for i in x]
	[3] In [18]: y = [i**10 for i in x]


	In [68]: y = mec.gather('y')

	In [69]: print y
	[0, 1, 1024, 59049, 1048576, 9765625, 60466176, 282475249, 1073741824,...]

Parallel exceptions
-------------------

In the multiengine interface, parallel commands can raise Python exceptions,
just like serial commands. But, it is a little subtle, because a single
parallel command can actually raise multiple exceptions (one for each engine
the command was run on). To express this idea, the MultiEngine interface has a
:exc:`CompositeError` exception class that will be raised in most cases. The
:exc:`CompositeError` class is a special type of exception that wraps one or
more other types of exceptions. Here is how it works:

.. sourcecode:: ipython

	In [76]: mec.block=True

	In [77]: mec.execute('1/0')
	---------------------------------------------------------------------------
	CompositeError                            Traceback (most recent call last)

	/ipython1-client-r3021/docs/examples/<ipython console> in <module>()

	/ipython1-client-r3021/ipython1/kernel/multiengineclient.pyc in execute(self, lines, targets, block)
	    432         targets, block = self._findTargetsAndBlock(targets, block)
	    433         result = blockingCallFromThread(self.smultiengine.execute, lines,
	--> 434             targets=targets, block=block)
	    435         if block:
	    436             result = ResultList(result)

	/ipython1-client-r3021/ipython1/kernel/twistedutil.pyc in blockingCallFromThread(f, *a, **kw)
	     72             result.raiseException()
	     73         except Exception, e:
	---> 74             raise e
	     75     return result
	     76 

	CompositeError: one or more exceptions from call to method: execute
	[0:execute]: ZeroDivisionError: integer division or modulo by zero
	[1:execute]: ZeroDivisionError: integer division or modulo by zero
	[2:execute]: ZeroDivisionError: integer division or modulo by zero
	[3:execute]: ZeroDivisionError: integer division or modulo by zero

Notice how the error message printed when :exc:`CompositeError` is raised has information about the individual exceptions that were raised on each engine.  If you want, you can even raise one of these original exceptions:

.. sourcecode:: ipython

	In [80]: try:
	   ....:     mec.execute('1/0')
	   ....: except client.CompositeError, e:
	   ....:     e.raise_exception()
	   ....:     
	   ....:     
	---------------------------------------------------------------------------
	ZeroDivisionError                         Traceback (most recent call last)

	/ipython1-client-r3021/docs/examples/<ipython console> in <module>()

	/ipython1-client-r3021/ipython1/kernel/error.pyc in raise_exception(self, excid)
	    156             raise IndexError("an exception with index %i does not exist"%excid)
	    157         else:
	--> 158             raise et, ev, etb
	    159 
	    160 def collect_exceptions(rlist, method):

	ZeroDivisionError: integer division or modulo by zero

If you are working in IPython, you can simple type ``%debug`` after one of
these :exc:`CompositeError` exceptions is raised, and inspect the exception
instance:

.. sourcecode:: ipython

	In [81]: mec.execute('1/0')
	---------------------------------------------------------------------------
	CompositeError                            Traceback (most recent call last)

	/ipython1-client-r3021/docs/examples/<ipython console> in <module>()

	/ipython1-client-r3021/ipython1/kernel/multiengineclient.pyc in execute(self, lines, targets, block)
	    432         targets, block = self._findTargetsAndBlock(targets, block)
	    433         result = blockingCallFromThread(self.smultiengine.execute, lines,
	--> 434             targets=targets, block=block)
	    435         if block:
	    436             result = ResultList(result)

	/ipython1-client-r3021/ipython1/kernel/twistedutil.pyc in blockingCallFromThread(f, *a, **kw)
	     72             result.raiseException()
	     73         except Exception, e:
	---> 74             raise e
	     75     return result
	     76 

	CompositeError: one or more exceptions from call to method: execute
	[0:execute]: ZeroDivisionError: integer division or modulo by zero
	[1:execute]: ZeroDivisionError: integer division or modulo by zero
	[2:execute]: ZeroDivisionError: integer division or modulo by zero
	[3:execute]: ZeroDivisionError: integer division or modulo by zero

	In [82]: %debug
	> 
	
	/ipython1-client-r3021/ipython1/kernel/twistedutil.py(74)blockingCallFromThread()
	     73         except Exception, e:
	---> 74             raise e
	     75     return result

	# With the debugger running, e is the exceptions instance.  We can tab complete
	# on it and see the extra methods that are available.
	ipdb> e.
	e.__class__         e.__getitem__       e.__new__           e.__setstate__      e.args
	e.__delattr__       e.__getslice__      e.__reduce__        e.__str__           e.elist
	e.__dict__          e.__hash__          e.__reduce_ex__     e.__weakref__       e.message
	e.__doc__           e.__init__          e.__repr__          e._get_engine_str   e.print_tracebacks
	e.__getattribute__  e.__module__        e.__setattr__       e._get_traceback    e.raise_exception
	ipdb> e.print_tracebacks()
	[0:execute]: 
	---------------------------------------------------------------------------
	ZeroDivisionError                         Traceback (most recent call last)

	/ipython1-client-r3021/docs/examples/<string> in <module>()

	ZeroDivisionError: integer division or modulo by zero

	[1:execute]: 
	---------------------------------------------------------------------------
	ZeroDivisionError                         Traceback (most recent call last)

	/ipython1-client-r3021/docs/examples/<string> in <module>()

	ZeroDivisionError: integer division or modulo by zero

	[2:execute]: 
	---------------------------------------------------------------------------
	ZeroDivisionError                         Traceback (most recent call last)

	/ipython1-client-r3021/docs/examples/<string> in <module>()

	ZeroDivisionError: integer division or modulo by zero

	[3:execute]: 
	---------------------------------------------------------------------------
	ZeroDivisionError                         Traceback (most recent call last)

	/ipython1-client-r3021/docs/examples/<string> in <module>()

	ZeroDivisionError: integer division or modulo by zero

.. note::

    The above example appears to be broken right now because of a change in 
    how we are using Twisted.

All of this same error handling magic even works in non-blocking mode:

.. sourcecode:: ipython

	In [83]: mec.block=False

	In [84]: pr = mec.execute('1/0')

	In [85]: pr.r
	---------------------------------------------------------------------------
	CompositeError                            Traceback (most recent call last)

	/ipython1-client-r3021/docs/examples/<ipython console> in <module>()

	/ipython1-client-r3021/ipython1/kernel/multiengineclient.pyc in _get_r(self)
	    170 
	    171     def _get_r(self):
	--> 172         return self.get_result(block=True)
	    173 
	    174     r = property(_get_r)

	/ipython1-client-r3021/ipython1/kernel/multiengineclient.pyc in get_result(self, default, block)
	    131                 return self.result
	    132         try:
	--> 133             result = self.client.get_pending_deferred(self.result_id, block)
	    134         except error.ResultNotCompleted:
	    135             return default

	/ipython1-client-r3021/ipython1/kernel/multiengineclient.pyc in get_pending_deferred(self, deferredID, block)
	    385 
	    386     def get_pending_deferred(self, deferredID, block):
	--> 387         return blockingCallFromThread(self.smultiengine.get_pending_deferred, deferredID, block)
	    388 
	    389     def barrier(self, pendingResults):

	/ipython1-client-r3021/ipython1/kernel/twistedutil.pyc in blockingCallFromThread(f, *a, **kw)
	     72             result.raiseException()
	     73         except Exception, e:
	---> 74             raise e
	     75     return result
	     76 

	CompositeError: one or more exceptions from call to method: execute
	[0:execute]: ZeroDivisionError: integer division or modulo by zero
	[1:execute]: ZeroDivisionError: integer division or modulo by zero
	[2:execute]: ZeroDivisionError: integer division or modulo by zero
	[3:execute]: ZeroDivisionError: integer division or modulo by zero