def bench_random(self,level=5):
print
print 'Differentiation of periodic functions'
print '====================================='
print ' size | convolve | naive'
print '-------------------------------------'
for size,repeat in [(100,1500),(1000,300),
(256,1500),
(512,1000),
(1024,500),
(2048,200),
(2048*2,100),
(2048*4,50),
]:
print '%6s' % size,
sys.stdout.flush()
x = arange (size)*2*pi/size
if size<2000:
f = sin(x)*cos(4*x)+exp(sin(3*x))
else:
f = sin(x)*cos(4*x)
assert_array_almost_equal(diff(f,1),direct_diff(f,1))
assert_array_almost_equal(diff(f,2),direct_diff(f,2))
print '| %9.2f' % self.measure('diff(f,3)',repeat),
sys.stdout.flush()
print '| %9.2f' % self.measure('direct_diff(f,3)',repeat),
sys.stdout.flush()
print ' (secs for %s calls)' % (repeat)
def check_int(self):
n = 64
x = arange(n)*2*pi/n
assert_array_almost_equal(diff(sin(x),-1),-cos(x))
assert_array_almost_equal(diff(sin(x),-2),-sin(x))
assert_array_almost_equal(diff(sin(x),-4),sin(x))
assert_array_almost_equal(diff(2*cos(2*x),-1),sin(2*x))
def check_period(self):
for n in [17,64]:
x = arange(n)/float(n)
assert_array_almost_equal(diff(sin(2*pi*x),period=1),
2*pi*cos(2*pi*x))
assert_array_almost_equal(diff(sin(2*pi*x),3,period=1),
-(2*pi)**3*cos(2*pi*x))
def check_random_odd(self):
for k in [0,1,2,3,4,5,6]:
for n in [33,65,55]:
f=random ((n,))
af=sum(f,axis=0)/n
f=f-af
assert_almost_equal(sum(f,axis=0),0.0)
assert_array_almost_equal(diff(diff(f,k),-k),f)
assert_array_almost_equal(diff(diff(f,-k),k),f)
def check_random_even(self):
for n in [32,64,56]:
f=random ((n,))
af=sum(f,axis=0)/n
f=f-af
# zeroing Nyquist mode:
f = diff(diff(f,1),-1)
assert_almost_equal(sum(f,axis=0),0.0)
assert_array_almost_equal(direct_hilbert(direct_ihilbert(f)),f)
assert_array_almost_equal(hilbert(ihilbert(f)),f)
def check_expr_large(self):
for n in [2048,4096]:
x = arange(n)*2*pi/n
f=sin(x)*cos(4*x)+exp(sin(3*x))
df=cos(x)*cos(4*x)-4*sin(x)*sin(4*x)+3*cos(3*x)*exp(sin(3*x))
ddf=-17*sin(x)*cos(4*x)-8*cos(x)*sin(4*x)\
-9*sin(3*x)*exp(sin(3*x))+9*cos(3*x)**2*exp(sin(3*x))
assert_array_almost_equal(diff(f),df)
assert_array_almost_equal(diff(df),ddf)
assert_array_almost_equal(diff(ddf,-1),df)
assert_array_almost_equal(diff(f,2),ddf)
def check_expr(self):
for n in [64,77,100,128,256,512,1024,2048,4096,8192][:5]:
x = arange(n)*2*pi/n
f=sin(x)*cos(4*x)+exp(sin(3*x))
df=cos(x)*cos(4*x)-4*sin(x)*sin(4*x)+3*cos(3*x)*exp(sin(3*x))
ddf=-17*sin(x)*cos(4*x)-8*cos(x)*sin(4*x)\
-9*sin(3*x)*exp(sin(3*x))+9*cos(3*x)**2*exp(sin(3*x))
d1 = diff(f)
assert_array_almost_equal(d1,df)
assert_array_almost_equal(diff(df),ddf)
assert_array_almost_equal(diff(f,2),ddf)
assert_array_almost_equal(diff(ddf,-1),df)
def check_sin(self):
for n in [32,64,77]:
x = arange(n)*2*pi/n
assert_array_almost_equal(diff(sin(x)),cos(x))
assert_array_almost_equal(diff(cos(x)),-sin(x))
assert_array_almost_equal(diff(sin(x),2),-sin(x))
assert_array_almost_equal(diff(sin(x),4),sin(x))
assert_array_almost_equal(diff(sin(4*x)),4*cos(4*x))
assert_array_almost_equal(diff(sin(sin(x))),cos(x)*cos(sin(x)))
def check_zero_nyquist (self):
for k in [0,1,2,3,4,5,6]:
for n in [32,33,64,56,55]:
f=random ((n,))
af=sum(f,axis=0)/n
f=f-af
# zeroing Nyquist mode:
f = diff(diff(f,1),-1)
assert_almost_equal(sum(f,axis=0),0.0)
assert_array_almost_equal(diff(diff(f,k),-k),f)
assert_array_almost_equal(diff(diff(f,-k),k),f)
def check_definition(self):
for n in [16,17,64,127,32]:
x = arange(n)*2*pi/n
assert_array_almost_equal(diff(sin(x)),direct_diff(sin(x)))
assert_array_almost_equal(diff(sin(x),2),direct_diff(sin(x),2))
assert_array_almost_equal(diff(sin(x),3),direct_diff(sin(x),3))
assert_array_almost_equal(diff(sin(x),4),direct_diff(sin(x),4))
assert_array_almost_equal(diff(sin(x),5),direct_diff(sin(x),5))
assert_array_almost_equal(diff(sin(2*x),3),direct_diff(sin(2*x),3))
assert_array_almost_equal(diff(sin(2*x),4),direct_diff(sin(2*x),4))
assert_array_almost_equal(diff(cos(x)),direct_diff(cos(x)))
assert_array_almost_equal(diff(cos(x),2),direct_diff(cos(x),2))
assert_array_almost_equal(diff(cos(x),3),direct_diff(cos(x),3))
assert_array_almost_equal(diff(cos(x),4),direct_diff(cos(x),4))
assert_array_almost_equal(diff(cos(2*x)),direct_diff(cos(2*x)))
assert_array_almost_equal(diff(sin(x*n/8)),direct_diff(sin(x*n/8)))
assert_array_almost_equal(diff(cos(x*n/8)),direct_diff(cos(x*n/8)))
for k in range(5):
assert_array_almost_equal(diff(sin(4*x),k),direct_diff(sin(4*x),k))
assert_array_almost_equal(diff(cos(4*x),k),direct_diff(cos(4*x),k))