def differences_testing ( RULE , logger ) :
a = 1.5
fun = lambda x : math.sin ( a * x )
exact_ders = ( fun , ## 0
lambda x : math.cos ( a * x ) * a , ## 1
lambda x : - math.sin ( a * x ) * a * a , ## 2
lambda x : - math.cos ( a * x ) * pow ( a , 3 ) , ## 3
lambda x : math.sin ( a * x ) * pow ( a , 4 ) , ## 4
lambda x : math.cos ( a * x ) * pow ( a , 5 ) , ## 4
lambda x : - math.sin ( a * x ) * pow ( a , 6 ) ) ## 4
h0 = 0
hmax = 1.2
N = 1000
cd = SE ()
cp = SE ()
ch = SE ()
for D in range ( 1 , RULE.DMAX + 1 ) :
table = [ ( 'I' , '#' , 'step' , '' , 'delta' , '' , 'pull' ) ]
for I in range ( RULE.IMAX ( D ) ) :
rule = RULE ( D , I , with_error = True )
for ik in range ( N ) :
z = random.uniform ( -math.pi , math.pi )
h , _ = rule.optimal_step ( fun , z , h0 , hmax )
r = rule ( fun , z , h )
exact = exact_ders [ D ] ( z )
dd = float ( r ) - exact
cd += abs ( dd )
cp += dd / r.error()
ch += h
hh = ch.mean()
dd = cd.mean()
hh , nh = pretty_ve ( hh , width = 4 , precision = 3 , parentheses = False )
dd , nd = pretty_ve ( dd , width = 4 , precision = 3 , parentheses = False )
row = '%2d' % I , \
'%2d' % len( rule.stencil) , \
hh , '' if not nh else '[10^%-3d]' % nh , \
dd , '' if not nd else '[10^%-3d]' % nd , \
"%-.2f" % cp.rms()
table.append ( row )
title = 'Finite differences test for D=%s derivative' % D
table = T.table ( table , title = title , prefix = '# ' , alignment = 'rrlclcr' )
logger.info ('%s\n%s' % ( title , table ) )
def test_derivative_4 ():
logger = getLogger ( 'test_derivative_4' )
functions = (
( lambda x : cos(10.*x) , lambda x : -10*sin(10.*x) ) ,
( lambda x : x**3 , lambda x : 3.0*x*x ) ,
( lambda x : exp(x) , lambda x : exp(x) ) ,
( lambda x : x**8 , lambda x : 8.0*x**7 ) ,
( lambda x : tanh(2.*x) , lambda x : 2*(1.-tanh(2.*x)**2) ) ,
( lambda x : 1.11*x , lambda x : 1.11 ) ,
( lambda x : 1.11111 , lambda x : 0.0 ) ,
( lambda x : x**10 , lambda x : 10.*x**9 ) ,
)
from ostap.core.core import SE
counters = {}
from ostap.utils.progress_bar import progress_bar
IMAX = 8
table = [ ['Function'] + [ 'I=%d' % i for i in range ( IMAX ) ] ]
for i , o in enumerate ( progress_bar ( functions ) ) :
fun = o [ 0 ] ## function
der = o [ 1 ] ## derivative
row = [ '%2d' % (i+1) ]
for I in range ( IMAX ) :
cnt1 = SE ()
cnt2 = SE ()
dd = Derivative ( fun , step = 0.001 , calc = I , with_error = True )
for j in range ( 1000 ) :
x = random.uniform ( 0.05 , 1.5 )
res = dd ( x )
dif = float ( res ) - der ( x )
cnt1 += dif
if res.cov2() > 0 : cnt2 += dif/res.error()
mmax1 = abs ( cnt1.max () *10**12 )
if 2 < cnt2.nEntries() :
mmax2 = cnt2.max()
row.append ( '%7.3f / %-5.2fs' % ( mmax1, mmax2 ) )
else :
mmax2 = 0
row.append ( '%7.3f / %-5.2fs' % ( mmax1, mmax2 ) )
table.append ( row )
table = T.table ( table , prefix = '# ' , alignment=9*'c' )
logger.info ('Numerical differentiation: Max difference [10^12]\n%s' % table )
def test_interpolation():
"""Test spline interpolation
"""
if 62006 <= root_version_int:
logger.warning("Test_interpolation segfaults for ROOT %s" %
root_version_int)
return
from math import sin, pi, sqrt
fun = lambda x: sin(2 * pi * x)
bs = ostap.math.bspline.interpolate(
fun, None, [0] + [random.uniform(0.01, 0.99) for i in range(50)] + [1],
2)
from ostap.stats.counters import SE
s = SE()
for i in range(10000):
x = random.uniform(0, 1)
vf = fun(x)
vb = bs(x)
s += vf - vb
logger.info('Interpolation quality %s' % s)
def derivative_testing ( der_type , func , der_exact , logger , **kwargs ) :
IMAX = der_type.IMAX
cnt1 = {}
for i in range ( IMAX ) : cnt1 [i] = SE()
ders = [ der_type ( func , I , **kwargs ) for I in range ( IMAX ) ]
with timing ( 'derivative test' , logger = logger ) :
for i in range(10000) :
x = random.uniform ( 0 , pi )
d_true = der_exact ( x )
for I , dd in enumerate ( ders ) :
delta = dd ( x ) - d_true
cnt1 [I] += delta
rows = [ ('I' , 'rms' , 'min' , 'max' ) ]
for i,c in cnt1.items() :
row = '%d' % i , '% .4g' % c.rms () , '% .4g' % c.min() , '% .4g' % c.max()
rows.append ( row )
table = T.table ( rows ,
title = 'Test numerical derivatives' ,
prefix = '# ' , alignment = 'clll' )
logger.info ( 'Test numerical derivatives\n%s' % table )
def stat(self, *args):
""" Get the full statistic over all categories
>>> method = ...
>>> pt, eta, phi = 5 , 3.0 , 0 ## variables
>>> print 'Response statistic is %s' % method.stat ( pt , eta , phi )
"""
from ostap.stats.counters import SE
se = SE()
for i in range(self.__N):
se += self.evaluate(i, *args)
return se
def test_derivative():
from math import sin, cos, pi
from ostap.math.derivative import derivative, iszero
import random
from ostap.stats.counters import SE
from ostap.utils.timing import timing
cnt = {}
cntE = {}
for I in range(1, 9):
cnt[I] = SE()
func = lambda x: sin(10 * x) + x
deri = lambda x: 10 * cos(10 * x) + 1
func = lambda x: sin(x) / x
deri = lambda x: (cos(x) - sin(x) / x) / x
## func = lambda x : x**9
## deri = lambda x : 9*x**8
## from math import sinh, cosh
## func = lambda x : sinh(2*x)
## deri = lambda x : 2*cosh(2*x)
## from math import tanh,cosh
## func = lambda x : tanh(3*x)
## deri = lambda x : 3./(cosh(3*x)**2)
with timing():
for i in range(50000):
x = random.uniform(0, pi)
d_true = deri(x)
for I in range(1, 9):
delta = derivative(func, x, I=I, err=True) - d_true
## delta = derivative ( sin , x , I = I ) - d_true
## cnt [I] += delta*1.e+10
## cnt [I] += abs(delta/d_true)*1.e+10
if not iszero(delta.cov2()):
cnt[I] += abs(delta.value()) / delta.error()
for I in range(1, 9):
print I, cnt[I]
def test_interpolation ():
"""Test bernstein interpolation
"""
from math import sin,pi, sqrt
fun = lambda x : sin(2*pi*x)
bs = ostap.math.bernstein.interpolate ( fun , [0] + [ random.uniform(0.01,0.99) for i in range(25) ] + [1] , 0 , 1 )
from ostap.stats.counters import SE
s = SE()
for i in range(10000) :
x = random.uniform ( 0 , 1 )
vf = fun(x)
vb = bs (x)
s += vf-vb
logger.info ('Interpolation quality %s' % s )
def test_approximation():
"""Test spline approximation
"""
from math import sin, pi, sqrt
fun = lambda x: sin(2 * pi * x)
bs = ostap.math.bspline.approximate(
fun, [0] + [random.uniform(0.01, 0.99) for i in range(50)] + [1], 2)
from ostap.stats.counters import SE
s = SE()
for i in range(10000):
x = random.uniform(0, 1)
vf = fun(x)
vb = bs(x)
s += vf - vb
logger.info('Approximation quality %s' % s)
def test_derivative_2():
logger = getLogger('test_derivative_2')
cnt = {}
cntE = {}
for I in range(1, 9):
cnt[I] = SE()
func = lambda x: sin(10 * x) + x
deri = lambda x: 10 * cos(10 * x) + 1
with timing():
for i in range(10000):
x = random.uniform(0, pi)
d_true = deri(x)
for I in range(1, 9):
delta = derivative(func, x, I=I) - d_true
cnt[I] += delta
rows = [('Order', '#', 'min', 'max')]
for i in cnt:
c = cnt[I]
row = '%d' % i, '%d' % c.nEntries(), '%+.5g' % c.min(
), '%+.5g' % c.max()
rows.append(row)
table = T.table(rows,
title='Test numerical derivatives',
prefix='# ',
alignment='crll')
logger.info('Test numerical derivatives\n%s' % table)
if not hasattr(random, 've_gauss'): random.ve_gauss = random._inst.ve_gauss
if not hasattr(random.Random, 'poisson'): random.Random.poisson = _poisson_
if not hasattr(random, 'poisson'): random.poisson = random._inst.poisson
if not hasattr(random.Random, 'cauchy'): random.Random.cauchy = _cauchy_
if not hasattr(random, 'cauchy'): random.cauchy = random._inst.cauchy
bifur = random.bifur
ve_gauss = random.ve_gauss
poisson = random.poisson
cauchy = random.cauchy
# =============================================================================
if '__main__' == __name__:
from ostap.utils.docme import docme
docme(__name__, logger=logger)
from ostap.stats.counters import SE
cnt = SE()
mu = 0.4
for i in range(10000):
cnt += poisson(0.4)
logger.info('Poisson(mu=%s) : %s' % (mu, cnt))
logger.info(80 * '*')
# =============================================================================
# The END
# =============================================================================