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benching_uncertainty.py
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benching_uncertainty.py
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"""
benchmark uncertainty methods with simple function
============================ ==============
method Benchmark [s]
============================ ==============
Numpy w/std-dev only 0.000866898
create ufloat w/std-dev only 0.00197498
Uncertainties w/std-dev only 0.00774529 ($)
Scipy w/std-dev only 0.00157711
statsmodels w/std-dev only 0.0441201
numdifftools w/std-dev only 0.104556
algopy w/std-dev 0.0277903 (*)
---------------------------- --------------
Numpy w/covariance 0.0770831
Jacobian estimate 0.0816991
statsmodels w/covariance 0.113367
numdifftools w/covariance 85.104
algopy w/covariance 0.156879
============================ ==============
Notes:
------
* Uncertainties covariance doesn't work with wrapped functions and not with
unumpy vectorized analytical derivatives either, fails comparison
* variance of all runtimes is large, from 10% up to 50%
($) total time for Uncertainties is 0.00972072[s]
(*) algopy derivative runtimes seems to vary by 10x, weird!
"""
import numpy as np
import numdifftools as nd
import numdifftools.nd_algopy as nda
from algopy import sin
from uncertainties import ufloat, umath, unumpy, correlated_values, wrap
#
# wrap only works on scalars
# from example in help(wrap)
# >>> f_wrapped = wrap(math.sin)
# >>> f_wrapped(ufloat(1.23, 0.45))
# 0.9424888019316975+/-0.15040697757063842
# try with np.array of Variable objects fails with
#
# TypeError: only length-1 arrays can be converted to Python scalars
#
from statsmodels.tools import numdiff
from scipy.misc import derivative
from jacobian_fun import jacobian, jacobs
from time import clock
import logging
logging.basicConfig()
LOGGER = logging.getLogger(__name__)
LOGGER.setLevel(logging.DEBUG)
AVG = np.random.rand(1000) * 11.
COV = np.random.rand(1000, 1000) / 11.
COV *= COV.T
TOL = 1e-6
COV = np.where(COV > TOL, COV, np.zeros((1000, 1000)))
STD = np.sqrt(COV.diagonal())
# test pure numpy implementation of uncertainty
def test_puro_cov(avg=AVG, cov=COV):
c = clock()
nobs = avg.size
LOGGER.debug('\t1> %g [s]', clock() - c)
j = np.eye(nobs) * np.cos(avg.flatten())
LOGGER.debug('\t2> %g [s]', clock() - c)
cov = np.dot(np.dot(j, cov), j.T)
LOGGER.debug('\t3> %g [s]', clock() - c)
avg = np.sin(avg)
LOGGER.debug('\t4> %g [s]', clock() - c)
cov = np.reshape(cov.diagonal(), avg.shape)
LOGGER.debug('\t5> %g [s]', clock() - c)
dt = np.dtype([('avg', float), ('cov', float)])
LOGGER.debug('\t6> %g [s]', clock() - c)
return np.array(zip(avg, cov), dtype=dt)
cstart = clock()
np.sin(AVG)
cstop = clock()
LOGGER.debug('calculate sin(avg):\n\telapsed time> %g [s]\n', cstop - cstart)
cstart = clock()
np.cos(AVG)
cstop = clock()
LOGGER.debug('calculate cos(avg):\nelapsed time> %g [s]\n', cstop - cstart)
cstart = clock()
r1 = test_puro_cov()
cstop = clock()
LOGGER.debug('test puro w/covariance:\n\telapsed time> %g [s]\n',
cstop - cstart)
def test_puro_std(avg=AVG, std=STD):
c = clock()
j = np.cos(avg)
LOGGER.debug('\t1> %g [s]', clock() - c)
std = np.abs(j*std) # np.sqrt(j*std*std*j)
LOGGER.debug('\t2> %g [s]', clock() - c)
avg = np.sin(avg)
LOGGER.debug('\t3> %g [s]', clock() - c)
dt = np.dtype([('avg', float), ('std', float)])
LOGGER.debug('\t4> %g [s]', clock() - c)
return np.array(zip(avg, std), dtype=dt)
cstart = clock()
r2 = test_puro_std()
cstop = clock()
LOGGER.debug('test puro w/std-dev only:\n\telapsed time> %g [s]\n',
cstop - cstart)
# test uncertainties package
cstart = clock()
X = unumpy.uarray(AVG, STD)
cstop = clock()
LOGGER.debug('create ufloat array w/std-dev only:\n\telapsed time> %g [s]\n',
cstop - cstart)
def test_uncertainties_std(x=X):
return unumpy.sin(x)
cstart = clock()
r3 = test_uncertainties_std()
cstop = clock()
LOGGER.debug('test uncertainties w/std-dev only:\n\telapsed time> %g [s]\n',
cstop - cstart)
cstart = clock()
Y = correlated_values(AVG, COV)
cstop = clock()
LOGGER.debug('create array of correlated values:\n\telapsed time> %g [s]\n',
cstop - cstart)
def test_uncertainties_cov(y=Y):
return unumpy.sin(y)
cstart = clock()
r4 = test_uncertainties_cov()
cstop = clock()
LOGGER.debug('test uncertainties w/ covariance:\n\telapsed time> %g [s]\n',
cstop - cstart)
F = lambda x: np.sin(x)
EPS = np.finfo(float).eps
DX = EPS ** (1. / 3.)
# test numerical differentiation methods
# scipy.misc.derivative
# * inputs to must be an array
# * can handle multiple observations but not multiple args
# * ie: f(x) must be a scalar function
# * however f(x) return can be an array
def test_scipy_derivative(avg=AVG, std=STD, f=F):
c = clock()
j = derivative(f, avg, dx=DX)
LOGGER.debug('\t1> %g [s]', clock() - c)
std = np.abs(j*std) # np.sqrt(j*std*std*j)
LOGGER.debug('\t2> %g [s]', clock() - c)
avg = F(avg)
LOGGER.debug('\t3> %g [s]', clock() - c)
dt = np.dtype([('avg', float), ('std', float)])
LOGGER.debug('\t4> %g [s]', clock() - c)
return np.array(zip(avg, std), dtype=dt)
# test Jacobian estimate
def test_jacobian_cov(avg=AVG, cov=COV, f=F):
c = clock()
avg = np.atleast_2d(avg)
LOGGER.debug('\t1> %g [s]', clock() - c)
j = jacobs(jacobian(f, avg))
LOGGER.debug('\t2> %g [s]', clock() - c)
cov = np.dot(np.dot(j, cov), j.T)
LOGGER.debug('\t3> %g [s]', clock() - c)
avg = f(avg)
LOGGER.debug('\t4> %g [s]', clock() - c)
cov = np.reshape(cov.diagonal(), avg.shape)
LOGGER.debug('\t5> %g [s]', clock() - c)
dt = np.dtype([('avg', float), ('cov', float)])
LOGGER.debug('\t6> %g [s]', clock() - c)
return np.array(zip(avg.squeeze(), cov.squeeze()), dtype=dt)
cstart = clock()
r12 = test_jacobian_cov()
cstop = clock()
LOGGER.debug('test jacobian estimate:\n\telapsed time> %g [s]\n',
cstop - cstart)
# statsmodels.tools.models
# * numdiff seems to have problems broadcasting despite what its docs say
# * x must be a 1-d array apparently
# * if it is 2-d or if indexing produces a sequence it fails
def test_statsmodels_numdiff_std(avg=AVG, std=STD, f=F):
c = clock()
j = numdiff.approx_fprime(avg, f, centered=True)
LOGGER.debug('\t1> %g [s]', clock() - c)
std = np.abs(j.diagonal()*std) # np.sqrt(j*std*std*j)
LOGGER.debug('\t2> %g [s]', clock() - c)
avg = f(avg)
LOGGER.debug('\t3> %g [s]', clock() - c)
dt = np.dtype([('avg', float), ('std', float)])
LOGGER.debug('\t4> %g [s]', clock() - c)
return np.array(zip(avg, std), dtype=dt)
def test_statsmodels_numdiff_cov(avg=AVG, cov=COV, f=F):
c = clock()
j = numdiff.approx_fprime(avg, f, centered=True)
LOGGER.debug('\t1> %g [s]', clock() - c)
cov = np.dot(np.dot(j, cov), j.T)
LOGGER.debug('\t2> %g [s]', clock() - c)
avg = f(avg)
LOGGER.debug('\t3> %g [s]', clock() - c)
cov = np.reshape(cov.diagonal(), avg.shape)
LOGGER.debug('\t4> %g [s]', clock() - c)
dt = np.dtype([('avg', float), ('cov', float)])
LOGGER.debug('\t5> %g [s]', clock() - c)
return np.array(zip(avg, cov), dtype=dt)
cstart = clock()
r5 = test_scipy_derivative()
cstop = clock()
LOGGER.debug('test scipy derivative w/std-dev only:\n\telapsed time> %g [s]\n',
cstop - cstart)
cstart = clock()
r6 = test_statsmodels_numdiff_std()
cstop = clock()
LOGGER.debug('test statsmodels numdiff w/std-dev only:\n\telapsed time> %g [s]\n',
cstop - cstart)
cstart = clock()
r7 = test_statsmodels_numdiff_cov()
cstop = clock()
LOGGER.debug('test statsmodels numdiff w/covariance:\n\telapsed time> %g [s]\n',
cstop - cstart)
# test numdifftools
def test_numdifftools_std(avg=AVG, std=STD, f=F):
c = clock()
jac = nd.Derivative(f)
LOGGER.debug('\t1> %g [s]', clock() - c)
j = jac(avg)
LOGGER.debug('\t2> %g [s]', clock() - c)
std = np.abs(j*std) # np.sqrt(j*std*std*j)
LOGGER.debug('\t3> %g [s]', clock() - c)
avg = f(avg)
LOGGER.debug('\t4> %g [s]', clock() - c)
dt = np.dtype([('avg', float), ('std', float)])
LOGGER.debug('\t5> %g [s]', clock() - c)
return np.array(zip(avg, std), dtype=dt)
def test_numdifftools_cov(avg=AVG, cov=COV, f=F):
c = clock()
jac = nd.Jacobian(f)
LOGGER.debug('\t1> %g [s]', clock() - c)
j = jac(avg)
LOGGER.debug('\t2> %g [s]', clock() - c)
cov = np.dot(np.dot(j, cov), j.T)
LOGGER.debug('\t3> %g [s]', clock() - c)
avg = f(avg)
LOGGER.debug('\t4> %g [s]', clock() - c)
cov = np.reshape(cov.diagonal(), avg.shape)
LOGGER.debug('\t5> %g [s]', clock() - c)
dt = np.dtype([('avg', float), ('cov', float)])
LOGGER.debug('\t6> %g [s]', clock() - c)
return np.array(zip(avg, cov), dtype=dt)
cstart = clock()
r8 = test_numdifftools_std()
cstop = clock()
LOGGER.debug('test numdifftools w/std-dev only:\n\telapsed time> %g [s]\n',
cstop - cstart)
cstart = clock()
r9 = test_numdifftools_cov()
cstop = clock()
LOGGER.debug('test numdifftools w/covariance:\n\telapsed time> %g [s]\n',
cstop - cstart)
# test numdifftools with algopy
G = lambda x: sin(x)
def test_algopy_std(avg=AVG, std=STD, f=G):
c = clock()
jac = nda.Derivative(f)
LOGGER.debug('\t1> %g [s]', clock() - c)
j = jac(avg)
LOGGER.debug('\t2> %g [s]', clock() - c)
std = np.abs(j*std) # np.sqrt(j*std*std*j)
LOGGER.debug('\t3> %g [s]', clock() - c)
avg = f(avg)
LOGGER.debug('\t4> %g [s]', clock() - c)
dt = np.dtype([('avg', float), ('std', float)])
LOGGER.debug('\t5> %g [s]', clock() - c)
return np.array(zip(avg, std), dtype=dt)
def test_algopy_cov(avg=AVG, cov=COV, f=G):
c = clock()
jac = nda.Jacobian(f)
LOGGER.debug('\t1> %g [s]', clock() - c)
j = jac(avg)
LOGGER.debug('\t2> %g [s]', clock() - c)
cov = np.dot(np.dot(j, cov), j.T)
LOGGER.debug('\t3> %g [s]', clock() - c)
avg = f(avg)
LOGGER.debug('\t4> %g [s]', clock() - c)
cov = np.reshape(cov.diagonal(), avg.shape)
LOGGER.debug('\t5> %g [s]', clock() - c)
dt = np.dtype([('avg', float), ('cov', float)])
LOGGER.debug('\t6> %g [s]', clock() - c)
return np.array(zip(avg, cov), dtype=dt)
cstart = clock()
r10 = test_algopy_std()
cstop = clock()
LOGGER.debug('test algopy w/std-dev only:\n\telapsed time> %g [s]\n',
cstop - cstart)
cstart = clock()
r11 = test_algopy_cov()
cstop = clock()
LOGGER.debug('test algopy w/covariance:\n\telapsed time> %g [s]\n',
cstop - cstart)
# compare averages
print "compare avg numpy to numpy: %s" % np.allclose(r1['avg'], r2['avg'])
print "compare avg numpy to numpy: %s" % np.allclose(
r1['avg'], [_.n for _ in r3])
print "compare avg numpy to Uncertainties: %s" % np.allclose(
r1['avg'], [_.n for _ in r4])
print "compare avg numpy to scipy: %s" % np.allclose(r1['avg'], r5['avg'])
print "compare avg numpy to statsmodels: %s" % np.allclose(r1['avg'], r6['avg'])
print "compare avg numpy to statsmodels: %s" % np.allclose(r1['avg'], r7['avg'])
print "compare avg numpy to numdifftools: %s" % np.allclose(r1['avg'], r8['avg'])
print "compare avg numpy to numdifftools: %s" % np.allclose(r1['avg'], r9['avg'])
print "compare avg numpy to algopy: %s" % np.allclose(r1['avg'], r10['avg'])
print "compare avg numpy to algopy: %s" % np.allclose(r1['avg'], r11['avg'])
print
# compare std-dev
print "compare std numpy to Uncertainties: %s" % np.allclose(
r2['std'], [_.s for _ in r3])
print "compare std numpy to scipy: %s" % np.allclose(r2['std'], r5['std'])
print "compare std numpy to statsmodels: %s" % np.allclose(r2['std'], r6['std'])
print "compare std numpy to numdifftools: %s" % np.allclose(r2['std'], r8['std'])
print "compare std numpy to algopy: %s" % np.allclose(r2['std'], r10['std'])
print
# compare covariance
print "compare cov numpy to Uncertainties: %s" % np.allclose(
r1['cov'], np.array([_.s for _ in r4]) ** 2)
# XXX: *** Uncertainties covariance doesn't match expected values ***
print "compare cov numpy to statsmodels: %s" % np.allclose(r1['cov'], r7['cov'])
print "compare cov numpy to numdifftools: %s" % np.allclose(r1['cov'], r9['cov'])
print "compare cov numpy to algopy: %s" % np.allclose(r1['cov'], r11['cov'])
print "compare cov numpy to jacobian estimate: %s" % np.allclose(
r1['cov'], r12['cov'])
print