def test_corresponds_ac_first_loop():
"""
numpy correlation:
G_m = sum_i(a_i*a_{i+m})
multipletau correlation 2nd order:
b_j = (a_{2i} + a_{2i+1} / 2)
G_m = sum_j(b_j*b_{j+1})
= 1/4*sum_i(a_{2i} * a_{2i+m} +
a_{2i} * a_{2i+m+1} +
a_{2i+1} * a_{2i+m} +
a_{2i+1} * a_{2i+m+1}
)
The values after the first m+1 lag times in the multipletau
correlation differ from the normal correlation, because the
traces are averaged over two consecutive items, effectively
halving the size of the trace. The multiple-tau correlation
can be compared to the regular correlation by using an even
sized sequence (here 222) in which the elements 2i and 2i+1
are equal, as is done in this test.
"""
myframe = sys._getframe()
myname = myframe.f_code.co_name
print("running ", myname)
a = [arr / np.average(arr) for arr in get_sample_arrays_cplx()]
a = np.concatenate(a)[:222]
# two consecutive elements are the same, so the multiple-tau method
# corresponds to the numpy correlation for the first loop.
a[::2] = a[1::2]
for m in [2, 4, 6, 8, 10, 12, 14, 16]:
restau = multipletau.correlate(a=a,
v=a.imag + 1j * a.real,
m=m,
copy=True,
normalize=False,
dtype=np.complex_)
reslin = multipletau.correlate_numpy(a=a,
v=a.imag + 1j * a.real,
copy=True,
normalize=False,
dtype=np.complex_)
idtau = np.where(restau[:, 0] == m + 2)[0][0]
tau3 = restau[idtau, 1] #m+1 initial bins
idref = np.where(reslin[:, 0] == m + 2)[0][0]
tau3ref = reslin[idref, 1]
assert np.allclose(tau3, tau3ref)
def test_corresponds_ac_first_loop():
"""
numpy correlation:
G_m = sum_i(a_i*a_{i+m})
multipletau correlation 2nd order:
b_j = (a_{2i} + a_{2i+1} / 2)
G_m = sum_j(b_j*b_{j+1})
= 1/4*sum_i(a_{2i} * a_{2i+m} +
a_{2i} * a_{2i+m+1} +
a_{2i+1} * a_{2i+m} +
a_{2i+1} * a_{2i+m+1}
)
The values after the first m+1 lag times in the multipletau
correlation differ from the normal correlation, because the
traces are averaged over two consecutive items, effectively
halving the size of the trace. The multiple-tau correlation
can be compared to the regular correlation by using an even
sized sequence (here 222) in which the elements 2i and 2i+1
are equal, as is done in this test.
"""
myframe = sys._getframe()
myname = myframe.f_code.co_name
print("running ", myname)
a = [ arr / np.average(arr) for arr in get_sample_arrays_cplx() ]
a = np.concatenate(a)[:222]
# two consecutive elements are the same, so the multiple-tau method
# corresponds to the numpy correlation for the first loop.
a[::2] = a[1::2]
for m in [2,4,6,8,10,12,14,16]:
restau = multipletau.correlate(a=a,
v=a.imag+1j*a.real,
m=m,
copy=True,
normalize=False,
dtype=np.complex256)
reslin = multipletau.correlate_numpy(a=a,
v=a.imag+1j*a.real,
copy=True,
normalize=False,
dtype=np.complex256)
idtau = np.where(restau[:,0]==m+2)[0][0]
tau3 = restau[idtau, 1] #m+1 initial bins
idref = np.where(reslin[:,0]==m+2)[0][0]
tau3ref = reslin[idref, 1]
assert np.allclose(tau3, tau3ref)
def test_corresponds_ac_nonormalize():
myframe = sys._getframe()
myname = myframe.f_code.co_name
print("running ", myname)
a = np.concatenate(get_sample_arrays_cplx()).real
m = 16
restau = multipletau.autocorrelate(a=1 * a,
m=m,
copy=True,
normalize=False,
dtype=np.float_)
reslin = multipletau.correlate_numpy(a=1 * a,
v=1 * a,
copy=True,
normalize=False,
dtype=np.float_)
idx = np.array(restau[:, 0].real, dtype=int)[:m + 1]
assert np.allclose(reslin[idx, 1], restau[:m + 1, 1])
def test_corresponds_ac_nonormalize():
myframe = sys._getframe()
myname = myframe.f_code.co_name
print("running ", myname)
a = np.concatenate(get_sample_arrays_cplx()).real
m=16
restau = multipletau.autocorrelate(a=1*a,
m=m,
copy=True,
normalize=False,
dtype=np.float128)
reslin = multipletau.correlate_numpy(a=1*a,
v=1*a,
copy=True,
normalize=False,
dtype=np.float128)
idx = np.array(restau[:,0].real, dtype=int)[:m+1]
assert np.allclose(reslin[idx, 1], restau[:m+1,1])
def test_corresponds_cc():
myframe = sys._getframe()
myname = myframe.f_code.co_name
print("running ", myname)
a = np.concatenate(get_sample_arrays_cplx())
m = 16
restau = multipletau.correlate(a=a,
v=a.imag + 1j * a.real,
m=m,
copy=True,
normalize=True,
dtype=np.complex_)
reslin = multipletau.correlate_numpy(a=a,
v=a.imag + 1j * a.real,
copy=True,
normalize=True,
dtype=np.complex_)
idx = np.array(restau[:, 0].real, dtype=int)[:m + 1]
assert np.allclose(reslin[idx, 1], restau[:m + 1, 1])
def test_corresponds_cc():
myframe = sys._getframe()
myname = myframe.f_code.co_name
print("running ", myname)
a = np.concatenate(get_sample_arrays_cplx())
m=16
restau = multipletau.correlate(a=a,
v=a.imag+1j*a.real,
m=m,
copy=True,
normalize=True,
dtype=np.complex256)
reslin = multipletau.correlate_numpy(a=a,
v=a.imag+1j*a.real,
copy=True,
normalize=True,
dtype=np.complex256)
idx = np.array(restau[:,0].real, dtype=int)[:m+1]
assert np.allclose(reslin[idx, 1], restau[:m+1,1])
