def test_random_odd(self):
for h in [0.1,0.5,1,5.5,10]:
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(itilbert(tilbert(f,h),h),f)
assert_array_almost_equal(tilbert(itilbert(f,h),h),f)
def test_random_odd(self):
for h in [0.1, 0.5, 1, 5.5, 10]:
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(itilbert(tilbert(f, h), h), f)
assert_array_almost_equal(tilbert(itilbert(f, h), h), f)
def test_definition(self):
for h in [0.1, 0.5, 1, 5.5, 10]:
for n in [16, 17, 64, 127]:
x = arange(n) * 2 * pi / n
y = tilbert(sin(x), h)
y1 = direct_tilbert(sin(x), h)
assert_array_almost_equal(y, y1)
assert_array_almost_equal(tilbert(sin(x), h),
direct_tilbert(sin(x), h))
assert_array_almost_equal(tilbert(sin(2 * x), h),
direct_tilbert(sin(2 * x), h))
def test_definition(self):
for h in [0.1,0.5,1,5.5,10]:
for n in [16,17,64,127]:
x = arange(n)*2*pi/n
y = tilbert(sin(x),h)
y1 = direct_tilbert(sin(x),h)
assert_array_almost_equal(y,y1)
assert_array_almost_equal(tilbert(sin(x),h),
direct_tilbert(sin(x),h))
assert_array_almost_equal(tilbert(sin(2*x),h),
direct_tilbert(sin(2*x),h))
def bench_random(self):
print()
print(' Tilbert transform of periodic functions')
print('=========================================')
print(' size | optimized | 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, end=' ')
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(tilbert(f,1),direct_tilbert(f,1))
print('| %9.2f' % measure('tilbert(f,1)',repeat), end=' ')
sys.stdout.flush()
print('| %9.2f' % measure('direct_tilbert(f,1)',repeat), end=' ')
sys.stdout.flush()
print(' (secs for %s calls)' % (repeat))
def bench_random(self):
print
print ' Tilbert transform of periodic functions'
print '========================================='
print ' size | optimized | 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(tilbert(f,1),direct_tilbert(f,1))
print '| %9.2f' % measure('tilbert(f,1)',repeat),
sys.stdout.flush()
print '| %9.2f' % measure('direct_tilbert(f,1)',repeat),
sys.stdout.flush()
print ' (secs for %s calls)' % (repeat)
def test_tilbert_relation(self):
for n in [16, 17, 64, 127]:
x = arange(n) * 2 * pi / n
f = sin(x) + cos(2 * x) * sin(x)
y = hilbert(f)
y1 = direct_hilbert(f)
assert_array_almost_equal(y, y1)
y2 = tilbert(f, h=10)
assert_array_almost_equal(y, y2)
def test_tilbert_relation(self):
for n in [16,17,64,127]:
x = arange(n)*2*pi/n
f = sin(x)+cos(2*x)*sin(x)
y = hilbert(f)
y1 = direct_hilbert(f)
assert_array_almost_equal(y,y1)
y2 = tilbert(f,h=10)
assert_array_almost_equal(y,y2)
def time_tilbert(self, size, soltype):
if soltype == 'fft':
tilbert(self.f, 1)
else:
direct_tilbert(self.f, 1)
def time_tilbert(self, size, soltype):
if soltype == 'fft':
tilbert(self.f, 1)
else:
direct_tilbert(self.f, 1)
