Speeding up autowrap from Sympy - python

I'm trying to convert a large number of Sympy expressions using the autowrap function. It is however a slow process.
I've tried parallelizing with some Python packages, but I keep getting errors.
My question is, is it possible to speed up the autowrapping process? Like with parallelization or something?
If it is necessary, I can post parts of my script to show how my particular case can be solved, but I'd like to try something more general.
EDIT: The way my code works is (probably not the best way) it creates some expressions from a general expression and its derivatives (Euler-Lagrange equations for those interested). Said expressions are then stored in an array (list of lists) from where they are being called to be autowrapped. Once that is done, they are saved in another array.
This I can do with a simple for loop. It is very very slow for when I have, let's say 400 (aka 20^2) of those expressions.
I've tried using ProcessPoolExecutor from concurrent.futures because I'm already using it in another part of my code. But that throws a BrokenProcessPool: A process in the process pool was terminated abruptly while the future was running or pending. error, unless I try to wrap only one function. Then it works fine.
ThreadPoolExecutor does the same thing (or it complains about a wrapper_module_# missing which sometimes is on the tempdir I indicated).
From multiprocessing.Pool I only get Exception in thread Thread-#: and then it keeps running forever unless I stop it. Then it says ModuleNotFoundError: No module named 'wrapper_module_#'.
So I'm not sure why those modules are missing when they are really not.
I'll try to shorten my code as much as possible and I'll post it in a few hours.
EDIT 2: So here's a piece of code that throws the same or similar errors.
# This is the setup (declaring equations and such)
import sympy as sp
from sympy.utilities.autowrap import autowrap
import itertools
import os # <- To change directories because it appears that it changes automatically when using Process and ThreadPoolExecutor
from concurrent.futures import ProcessPoolExecutor,ThreadPoolExecutor
cwd = os.getcwd()
x,y,dx,dy = sp.var('x y dx dy')
eq = list()
eq.append(sp.cos(x)*dx + y*dy) # <- Some random equations
eq.append(3*x*dx + dy) # equations as examples.
coeff1 = [eq[0].coeff(dx),eq[0].coeff(dy)] # <- Coefficients of eq[0]
coeff2 = [eq[1].coeff(dx),eq[1].coeff(dy)] # <- Coefficients of eq[1]
coeff = [coeff1,coeff2] # <- This is my list of lists of coefficients
# (currently Sympy expressions)
arguments = [x,y] # <- Arguments for my equations.
Here comes the fun part:
Using list comprehension to call autowrap for every entry of my coeff array works just fine.
coeffComp = [[autowrap( coeff[i][j] , backend='cython', tempdir=cwd+'/CoefficientsComprehension',args=arguments) for j in range(2)] for i in range(2)]
# To visualize:
print(coeff)
# returns [[cos(x), y], [3*x, 1]]
# If I evaluate in (x=1,y=0)
print([[coeffComp[i][j](1,0) for j in range(2)] for i in range(2)])
# returns [[0.5403023058681398, 0.0], [3.0, 1]], which is correct.
However, trying to work with ProcessPoolExecutor or ThreadPoolExecutor
def AutoWrapCoefficients(Index): # <- Function to map
i,j = Index
return autowrap( coeff[i][j] , backend='cython', tempdir='./CoefficientsPoolExecutor',args=arguments)
def ToPyOfArray(): # <- Mapping function
TempArr = list()
with ThreadPoolExecutor() as executor:
results = executor.map(AutoWrapCoefficients, itertools.product(range(2),repeat=2))
for res in results:
os.chdir(cwd)
TempArr.append(res)
return TempArr
if __name__ == '__main__':
coeffFunctions = ToPyOfArray() # <- Throws described errors
And with multiprocessing:
from multiprocessing import Pool
if __name__ == '__main__':
with Pool() as p:
p.map( AutoWrapCoefficients, itertools.product(range(2),repeat=2)) # <- Throws described errors

Related

Multiprocessing Z3 in Python

I have a large list of various types of objects I would like Z3 to synthesize in my Python project. Since constraints associated with each object to be synthesized are independent, this process can be completely parallelized. That is, instead of synthesizing one value at a time, if I have a machine with 4 cores, I can synthesize 4 values at the same time. To do this, we must use Python's multiprocessing package instead of threading (due to GIL and the fact that the workload should be CPU-bound).
For simplicity, say I have a simple str synthesizer that synthesizes a new str that is lexicographically less than a given input value, something like this:
def lt_constraint(value):
solver = Solver()
# do a number of processing on 'value', which is an input string
# ... define char and _chars in code here
template = Concat(Re(StringVal(value[:offset])), char, Star(_chars))
solver.add(InRe(String("var"), template))
if solver.check() == sat:
value = solver.model()[self.var]
return convert_to_str(value)
Now if I have a number of values, I want to run the function above in parallel:
from pathos.multiprocessing import ProcessingPool as Pool
with Pool(processes=4) as pool:
value_list = ['This', 'is', 'an', 'example']
synthesized_strs = pool.map(lt_constraint, value_list)
I use pathos hoping that it will handle pickling issue, but I still received this error:
TypeError: cannot pickle 're.Match' object
which I believe is because Z3 uses methods in re and they need to be pickled when pickling lt_constraint(), but dill cannot pickle those.
Is there any other way to parallelize Z3 for my case (other than implementing pickling myself for re or what not)?
Thanks!
Stack-overflow works the best when you include your whole code, so people can experiment with it. Having said that, I had good luck with the following:
from z3 import *
import concurrent.futures
def getVal(value):
solver = Solver()
var = Int('var')
solver.add(var > value)
if solver.check() == sat:
return solver.model()[var].as_long()
else:
return 'CANT SOLVE'
with concurrent.futures.ThreadPoolExecutor() as executor:
futures = [executor.submit(getVal, i) for i in [1, 2, 3]]
results = [f.result() for f in futures]
print(results)
This prints:
$ python3.9 a.py
[2, 3, 4]
Without actually having the details of how you constructed your lt_constraint, it's hard to tell whether this'll work for your case. But it seems using the concurrent.futures library works well with z3; so far as simple constraints are used. Give this a try and see if it handles your case as well. If not; please post the full-code as an minimal-reproducible example. See https://stackoverflow.com/help/minimal-reproducible-example

Pass arguments to objective function in scipy differential evolution with multiple workers

For some optimization problem I am using differential evolution from scipys optimization toolbox.
I'd like to use several CPUs to speed up the process, but I would like to pass several additional arguments to the objective function. However, these are not just some scalars but some datasets which are required for the optimization to evaluate the models.
When I try to pass the arguments to the objective function directly in the usual way, python complains that the objective function is not pickable. When I put my data into a dictionary and pass that to the objective function, python complains about
" File "/usr/lib64/python3.6/multiprocessing/connection.py", line 393, in _send_bytes
header = struct.pack("!i", n)
struct.error: 'i' format requires -2147483648 <= number <= 2147483647
"
How can I pass nontrivial data to the objective function of differential evolution when using multiple workers? I have yet to find a way.
Something like
par02 = {'a':2,'b':3, "data":train_data}
# Define optimization bounds.
bounds = [(0, 10), (0, 10)]
# Attempt to optimize in series.
# series_result = differential_evolution(rosenbrock, bounds, args=(par02,))
# print(series_result.x)
# Attempt to optimize in parallel.
parallel_result = differential_evolution(rosenbrock, bounds, args=(par02,),
updating='deferred', workers=-1)
does not work for example.
Anyone got an idea? Or do I really have to load the data from disk everytime the objective function is called? That would slow down the optimization considerably I believe.
It always helps if a MWE is provided. For parallel processing to be used the objective function and args need to be picklable.
The following illustrates the problem:
-------stuff.py--------
from scipy.optimize import rosen
def obj(x, *args):
return rosen(x)
-------in the CLI-------
import numpy as np
import pickle
from scipy.optimize import differential_evolution, rosen
from stuff import obj
train_data = "123"
par02 = {'a':2,'b':3, "data":train_data}
bounds = [(0, 10), (0, 10)]
# This will work because `obj` is importable in
# the __main__ context.
differential_evolution(obj, bounds, args=(par02,),
updating='deferred', workers=-1)
def some_other_func(x, *args):
pass
wont_work = {'a':2,'b':3, "data":some_other_func}
# look at the output here. ` some_other_func` is referenced with
# respect to __main__
print(pickle.dumps(wont_work))
# the following line will hang because `some_other_func`
# is not importable by the main process; to get it
# to work the function has to reside in an importable file.
parallel_result = differential_evolution(obj, bounds, args=(wont_work,),
updating='deferred', workers=-1)
Basically you can't use classes/functions that are defined in the main context (i.e. the CLI), they have to be importable by main.
https://docs.python.org/3/library/multiprocessing.html#multiprocessing-programming

Python: ValueError: not enough values to unpack (expected 3, got 1)

I am kinda new to multiprocessing library in python. I have watched couple of lectures on youtube and have implemented basic instances of process from multiprocessing. My problem is, I want to speed up my code by utilizing all the 8 available cores. I asked a similar question in this regard a couple of days back but couldnt elicit a reasonable answer. I went back and did thorough homework and now after having understood the basics of pool(among other things in multiprocessing), I am kinda stuck in a peculier situation. I went through similar problems that were posed here at SO for instance this one-(Python multiprocessing pool map with multiple arguments) and (Python multiprocessing pool.map for multiple arguments). I even implemented the solution mentioned in former. However my code is still throwing this error-
File "minimal_example_so.py", line 84, in <module>
X,u,t=pool.starmap(solver,[args])
ValueError: not enough values to unpack (expected 3, got 1)
My code looks something like this-
import time
ti=time.time()
import matplotlib.pyplot as plt
from scipy.integrate import ode
import numpy as np
from numpy import sin,cos,tan,zeros,exp,tanh,dot,array
from matplotlib import rc
import itertools
from const_for_drdo_mod4 import *
plt.style.use('bmh')
import mpltex
from functools import reduce
from multiprocessing import Pool
import multiprocessing
linestyles=mpltex.linestyle_generator()
def zetta(x,spr,c):
num=len(x)*len(c)
Mu=[[] for i in range(len(x))]
for i in range(len(x)):
Mu[i]=np.zeros(len(c))
m=[]
for i in range(len(x)):
for j in range(len(c)):
Mu[i][j]=exp(-.5*((x[i]-c[j])/spr)**2)
b=list(itertools.product(*Mu))
for i in range(len(b)):
m.append(reduce(lambda x,y:x*y,b[i]))
m=np.array(m)
S=np.sum(m)
return m/S
def f(t,Y,a,b,spr,tim,so,k,K,C):
x1,x2=Y[0],Y[1]
e=x1-2
de=-2*x1+a*x2+b*sin(x1)
s=de+2*e
xx=[e,de]
sold,ti=so,tim
#import pdb;pdb.set_trace()
theta=Y[2:2+len(C)**len(xx)]
Z=zetta(xx,spr,C)
u=dot(Z,theta)
Z1=list(Z)
dt=time.time()-ti
ti=time.time()
sodt=(s-sold)/dt
x1dot=de
x2dot=-x2*cos(x1)+cos(2*x1)*u
xdot=[x1dot,x2dot]
thetadot=[-20*number*(sodt+k*s+K*tanh(s))-20*.1*number2 for number,number2 in zip(Z1,theta)]
sold=s
ydot=xdot+thetadot
return [ydot,u]
def solver(t0,y0,t1,dt,a,b,spr,tim,so,k,K,C):
num=2
x,t=[[] for i in range(2+len(C)**num)],[]
u=[]
r=ode(lambda t,y,a,b,spr,tim,so,k,K,C: f(t,y,a,b,spr,tim,so,k,K,C)[0]).set_integrator('dopri5',method='bdf')
r.set_initial_value(y0,t0).set_f_params(a,b,spr,tim,so,k,K,C)
while r.successful() and r.t<t1:
r.integrate(r.t+dt)
for i in range(2+len(C)**num):
x[i].append(r.y[i])
u.append(f(r.t,r.y,a,b,spr,tim,so,k,K,C)[1])
t.append(r.t)
return x,u,t
if __name__=='__main__':
spr,C=1.5,[-3,-1.5,0,1.5,3]
num=2
k,K=2,5
tim,so=0,0
a,b=1,2
y0,T=[0.1,0],100
x1=[0 for i in range(len(C)**num)]
x0=y0+x1
args=(0,x0,T,1e-2,a,b,spr,tim,so,k,K,C)
pool=multiprocessing.Pool(3)
X,u,t=pool.starmap(solver,[args])
#X,u,t=solver(0,x0,T,1e-2,a,b,spr,tim,so,k,K,C)
nam=["x1","x2"]
pool.close()
pool.join()
plt.figure(1)
for i in range(len(X[0:2])):
plt.plot(t,X[i],label=nam[i])
plt.legend(loc='upper right')
plt.figure(2)
for i in range(len(X[2:])):
plt.plot(t,X[i])
plt.figure(3)
plt.plot(t,u)
plt.show()
Here I wish to tell that all my arguments are either plain numbers or lists/array of numbers which needs to be passed to the solver method. I tried couple of ways to pass my arguments to the pool using map and even starmap, but all of them were in vain. Kindly help, thanks in advance.
PS- my code is working absolutely fine without pool.
You're calling starmap with a list of just one tuple of arguments. The return value will therefore also be a list containing one element - the tuple returned by one call to solver. So you're effectively saying
X, u, t = [(x1, u1, t1)]
which is why you get the exception you're getting: you can't unpack one value (the returned tuple) into three variables. If you want to use starmap here you'll need to do something like:
[(X,u,t)] = pool.starmap(solver,[args])
instead. But for only one set of arguments it makes more sense to use apply, since it's designed for a single invocation:
X,u,t = pool.apply(solver, args)

Running rpy2 in parallel using multiprocessing raises weird exception that cannot be caught

So this is a problem that I have not been able to solve, and neither do I know of a good way to make a MCVE out of. Essentially, it has been briefly discussed here, but as the comments show, there was some disagreement, and the final verdict is still out. Hence I am posting a similar question again, hoping to get a better answer.
Background
I have sensor data from a couple of thousand sensors, that I get every minute. My interest lies in forecasting the data. For this I am using the ARIMA family of forecasting models. Long story short, after discussion with the rest of my research group, we decided to use the Arima function available in the R package forecast, instead of the statsmodels implementation of the same.
Problem Definition
Since, I have data from a few thousand sensors, for which I would like to at least analyse a whole week's worth of data (to begin with), and since a week has 7 days, I have 7 times the number of sensors data with me. Essentially a some 14k sensor-day combinations. Finding the best ARIMA order (which minimizes BIC) and forecasting the next day of week data takes about 1 minute for each sensor-day combination. Which means upwards of 11 days to just process one week data on a single core!
This is obviously a waste, when I have 15 more cores just idling away the whole time. So, obviously, this is a problem for parallel processing. Note that each sensor-day combination does not influence any other sensor-day combination. Also, the rest of my code is fairly well profiled, and optimized.
Issue
The issue is that I get this weird error that I cannot catch anywhere. Here is the error reproduced:
Exception in thread Thread-3:
Traceback (most recent call last):
File "/home/kartik/miniconda3/lib/python3.5/threading.py", line 914, in _bootstrap_inner
self.run()
File "/home/kartik/miniconda3/lib/python3.5/threading.py", line 862, in run
self._target(*self._args, **self._kwargs)
File "/home/kartik/miniconda3/lib/python3.5/multiprocessing/pool.py", line 429, in _handle_results
task = get()
File "/home/kartik/miniconda3/lib/python3.5/multiprocessing/connection.py", line 251, in recv
return ForkingPickler.loads(buf.getbuffer())
File "/home/kartik/miniconda3/lib/python3.5/site-packages/rpy2/robjects/robject.py", line 55, in _reduce_robjectmixin
rinterface_level=rinterface_factory(rdumps, rtypeof)
ValueError: Mismatch between the serialized object and the expected R type (expected 6 but got 24)
Here are a few characteristics of this error that I have discovered:
It is raised in the rpy2 package
It has something to do with Thread 3. Since Python is zero indexed, I am guessing this is the fourth thread. Therefore, 4x6 = 24, which adds up to the numbers shown in the final error statement
rpy2 is being used in only one place in my code where it might have to recode returned values into Python types. Protecting that line in try: ... except: ... does not catch that exception
The exception is not raised when I ditch the multiprocessing and call the function within a loop
The exception does not crash the program, just suspends it forever (till I Ctrl+C it into terminating)
All that I tried till now, have had no effect in resolving the error
Things Tried
I have tried everything from extreme procedural coding, with functions to deal with the least cases (that is only one function to be called in parallel), to extreme encapsulation, where the executable block in the if __name__ == '__main__': calls a function which reads in the data, does the necessary grouping, then passes the groups to another function, which imports multiprocessing and calls another function in parallel, which imports the processing module that imports rpy2, and passes the data to the Arima function in R.
Basically, it doesn't matter if rpy2 is called and initialized deep inside function nests, such that it has no idea another instance might be initialized, or if it is called and initialized once, globally, the error is raised if multiprocessing is involved.
Pseudo Code
Here is an attempt to present at least some basic pseudo code such that the error might be reproduced.
import numpy as np
import pandas as pd
def arima_select(y, order):
from rpy2 import robjects as ro
from rpy2.robjects.packages import importr
from rpy2.robjects import pandas2ri
pandas2ri.activate()
forecast = importr('forecast')
res = forecast.Arima(y, order=ro.FloatVector(order))
return res
def arima_wrapper(data):
data = data[['tstamp', 'val']]
data.set_index('tstamp', inplace=True)
return arima_select(data, (1,1,1))
def applyParallel(groups, func):
from multiprocessing import Pool, cpu_count
with Pool(cpu_count()) as p:
ret_list = p.map(func, [group for _, group in groups])
return pd.concat(ret_list, keys=[name for name, _ in groups])
def wrapper():
df = pd.read_csv('file.csv', parse_dates=[1], infer_datetime_format=True)
df['day'] = df['tstamp'].dt.day
res = applyParallel(df.groupby(['sensor', 'day']), arima_wrapper)
print(res)
Obviously, the above code can be encapsulated further, but I think it should reproduce the error quite accurately.
Data Sample
Here is the output of print(data.head(6)) when placed immediately below data.set_index('tstamp', inplace=True) in arima_wrapper from the pseudo code above:
Or alternatively, data for a sensor, for a whole week can be generated simply with:
def data_gen(start_day):
r = pd.Series(pd.date_range('2016-09-{}'.format(str(start_day)),
periods=24*60, freq='T'),
name='tstamp')
d = pd.Series(np.random.randint(10, 80, 1440), name='val')
s = pd.Series(['sensor1']*1440, name='sensor')
return pd.concat([s, r, d], axis=1)
df = pd.concat([data_gen(day) for day in range(1,8)], ignore_index=True)
Observations and Questions
The first observation is that this error is only raised when multiprocessing is involved, not when the function (arima_wrapper) is called in a loop. Therefore, it must be associated somehow with multiprocessing issues. R is not very multiprocess friendly, but when written in the way shown in the pseudo code, each instance of R should not know about the existence of the other instances.
The way the pseudo code is structured, there must be an initialization of rpy2 for each call inside the multiple subprocesses spawned by multiprocessing. If that were true, each instance of rpy2 should have spawned its own instance of R, which should just execute one function, and terminate. That would not raise any errors, because it would be similar to the single threaded operation. Is my understanding here accurate, or am I completely or partially missing the point?
Were all instances of rpy2 to somehow share an instance of R, then I might reasonably expect the error. What is true: is R shared among all instances of rpy2, or is there an instance of R for each instance of rpy2?
How might this issue be overcome?
Since SO hates question threads with multiple questions in them, I will prioritize my questions such that partial answers will be accepted. Here is my priority list:
How might this issue be overcome? A working code example that does not raise the issue will be accepted as answer even if it does not answer any other question, provided no other answer does better, or was posted earlier.
Is my understanding of Python imports accurate, or am I missing the point about multiple instances of R? If I am wrong, how should I edit the import statements such that a new instance is created within each subprocess? Answers to this question are likely to point me towards a probable solution, and will be accepted, provided no answer does better, or was posted earlier
Is R shared among all instances of rpy2 or is there an instance of R for each instance of rpy2? Answers to this question will be accepted only if they lead to a resolution of the problem.
(...) Long story short (...)
Really ?
How might this issue be overcome? A working code example that does not
raise the issue will be accepted as answer even if it does not answer
any other question, provided no other answer does better, or was
posted earlier.
Answers may leave a quite bit of work on your end...
Is my understanding of Python imports accurate, or am
I missing the point about multiple instances of R? If I am wrong, how
should I edit the import statements such that a new instance is
created within each subprocess? Answers to this question are likely to
point me towards a probable solution, and will be accepted, provided
no answer does better, or was posted earlier
Python packages/modules are "uniquely" imported across your process which means that all code using the package/module within the process is using the same single import (you don't have a copy per import in a given block).
Because of this, I'd recommend to use an initialization function when creating your Pool rather than repeatedly import rpy2 and setup the conversion each time a task is sent to a worker. You may also gain in performance if each task is short.
def arima_select(y, order):
# FIXME: check whether the rpy2.robjects package
# should be (re) imported as ro to be visible
res = forecast.Arima(y, order=ro.FloatVector(order))
return res
forecast = None
def worker_init():
from rpy2 import robjects as ro
from rpy2.robjects.packages import importr
from rpy2.robjects import pandas2ri
pandas2ri.activate()
global forecast
forecast = importr('forecast')
def applyParallel(groups, func):
from multiprocessing import Pool, cpu_count
with Pool(cpu_count(), worker_init) as p:
ret_list = p.map(func, [group for _, group in groups])
return pd.concat(ret_list, keys=[name for name, _ in groups])
Is R shared among all
instances of rpy2 or is there an instance of R for each instance of
rpy2? Answers to this question will be accepted only if they lead to a
resolution of the problem.
rpy2 is making R available by linking its C shared library. One such library per Python process, and that's as a stateful library (R not able to handle concurrency). I think that your issue has more to do with object serialization (see http://rpy2.readthedocs.io/en/version_2.8.x/robjects_serialization.html#object-serialization) than with concurrency.
What is happening is some apparent confusion when reconstructing the R objects after Python pickled the rpy2 object. More specifically, when looking that the R object types mentioned in the error message:
>>> from rpy2.rinterface import str_typeint
>>> str_typeint(6)
'LANGSXP'
>>> str_typeint(24)
'RAWSXP'
I am guessing that the R object returned by forecast.Arima contains an unevaluated R expression (for example the call that lead to that result object) and when serializing and unserializing it is coming back as something different (a raw vector of bytes). This is possibly a bug with R's own serialization mechanism (since rpy2 is using it behind the hood). For now, and solve your issue, you may want to extract what forecast.Arima what you care most about and only return that from the function call ran by the worker.
The following changes to the arima_select function in the pesudo code presented in the question work:
import numpy as np
import pandas as pd
from rpy2 import rinterface as ri
ri.initr()
def arima_select(y, order):
def rimport(packname):
as_environment = ri.baseenv['as.environment']
require = ri.baseenv['require']
require(ri.StrSexpVector([packname]),
quiet = ri.BoolSexpVector((True, )))
packname = ri.StrSexpVector(['package:' + str(packname)])
pack_env = as_environment(packname)
return pack_env
frcst = rimport("forecast")
args = (('y', ri.FloatSexpVector(y)),
('order', ri.FloatSexpVector(order)),
('include.constant', ri.StrSexpVector(const)))
return frcst['Arima'].rcall(args, ri.globalenv)
Keeping the rest of the pseudo code the same. Note that I have since optimized the code further, and it does not require all the functions presented in the question. Basically, the following is necessary and sufficient:
import numpy as np
import pandas as pd
from rpy2 import rinterface as ri
ri.initr()
def arima(y, order=(1,1,1)):
# This is the same as arima_select above, just renamed to arima
...
def applyParallel(groups, func):
from multiprocessing import Pool, cpu_count
with Pool(cpu_count(), worker_init) as p:
ret_list = p.map(func, [group for _, group in groups])
return pd.concat(ret_list, keys=[name for name, _ in groups])
def main():
# Create your df in your favorite way:
def data_gen(start_day):
r = pd.Series(pd.date_range('2016-09-{}'.format(str(start_day)),
periods=24*60, freq='T'),
name='tstamp')
d = pd.Series(np.random.randint(10, 80, 1440), name='val')
s = pd.Series(['sensor1']*1440, name='sensor')
return pd.concat([s, r, d], axis=1)
df = pd.concat([data_gen(day) for day in range(1,8)], ignore_index=True)
applyParallel(df.groupby(['sensor', pd.Grouper(key='tstamp', freq='D')]),
arima) # Note one may use partial from functools to pass order to arima
Note that I also do not call arima directly from applyParallel since my goal is to find the best model for the given series (for a sensor and day). I use a function arima_wrapper to iterate through the order combinations, and call arima at each iteration.

How to use IPython.parallel for functions with multiple inputs?

This is my first attempt at using IPython.parallel so please bear with me.
I read this question
Parfor for Python
and am having trouble implementing a simple example as follows:
import gmpy2 as gm
import numpy as np
from IPython.parallel import Client
rc = Client()
lview = rc.load_balanced_view()
lview.block = True
a = 1
def L2(ii,jj):
out = []
out.append(gm.fac(ii+jj+a))
return out
Nloop = 100
ii = range(Nloop)
jj = range(Nloop)
R2 = lview.map(L2, zip(ii, jj))
The problems I have are:
a is defined outside the loop and I think I need to do something like "push" but am a bit confused by that. Do I need to "pull" after?
there are two arguments that are required for the function and I don't know how to pass them correctly. I tried things like zip(ii,jj) but got some errors.
Also,, I assume the fact that I'm using a random library gmpy2 shouldn't affect things. Is this correct? Do I need to do anything special for this?
Ideally I would like your help so on this simple example the code runs error free.
If you think it would be beneficial to post my failed attempts at #2 let me know. I'm in the dark with #1.
I found two ways that make this work:
One is pushing the variable to the cores. There is no need to pull it. The variable will simply be defined in the namespace of each process-engine.
rc.client[:].push({'a':a})
R2 = lview.map(L2, ii, jj)
The other way is as to redefine L2 to take a as an input and pass an array of a's to the map function:
def L2(ii,jj,a):
out = []
out.append(gm.fac(ii+jj+a))
return out
R2 = lview.map(L2, ii, jj, [a]*Nloop)
With regards to the import as per this website:
http://ipython.org/ipython-doc/dev/parallel/parallel_multiengine.html#non-blocking-execution
You simply import the required libraries in the function:
Note the import inside the function. This is a common model, to ensure
that the appropriate modules are imported where the task is run. You
can also manually import modules into the engine(s) namespace(s) via
view.execute('import numpy')().
Or you can do as per this link
http://ipython.org/ipython-doc/dev/parallel/parallel_multiengine.html#remote-imports

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