def test_smooth_nd():
for edge in ['m', 'c']:
a = rand(20, 2, 3) + 10
for M in [5, 20, 123]:
print("nd", edge, "M=%i" %M)
kern = gaussian(M, 2.0)
asm = smooth(a, kern[:,None,None], axis=0, edge=edge)
assert asm.shape == a.shape
for jj in range(asm.shape[1]):
for kk in range(asm.shape[2]):
assert np.allclose(asm[:,jj,kk], smooth(a[:,jj,kk], kern,
edge=edge))
mn = a[:,jj,kk].min()
mx = a[:,jj,kk].max()
smn = asm[:,jj,kk].min()
smx = asm[:,jj,kk].max()
assert smn >= mn, "min: data=%f, smooth=%f" %(mn, smn)
assert smx <= mx, "max: data=%f, smooth=%f" %(mx, smx)
def test_smooth_nd():
for edge in ['m', 'c']:
a = rand(20, 2, 3) + 10
for M in [5, 20, 123]:
print "nd", edge, "M=%i" %M
kern = gaussian(M, 2.0)
asm = smooth(a, kern[:,None,None], axis=0, edge=edge)
assert asm.shape == a.shape
for jj in range(asm.shape[1]):
for kk in range(asm.shape[2]):
assert np.allclose(asm[:,jj,kk], smooth(a[:,jj,kk], kern,
edge=edge))
mn = a[:,jj,kk].min()
mx = a[:,jj,kk].max()
smn = asm[:,jj,kk].min()
smx = asm[:,jj,kk].max()
assert smn >= mn, "min: data=%f, smooth=%f" %(mn, smn)
assert smx <= mx, "max: data=%f, smooth=%f" %(mx, smx)
def test_smooth_1d():
for edge in ['m', 'c']:
for N in [20,21]:
# values in [9.0,11.0]
x = rand(N) + 10
mn = 9.0
mx = 11.0
for M in range(18,27):
print("1d", edge, "N=%i, M=%i" %(N,M))
xsm = smooth(x, gaussian(M,2.0), edge=edge)
assert len(xsm) == N
# (N,1) case
xsm2 = smooth(x[:,None], gaussian(M,2.0)[:,None], edge=edge)
assert np.allclose(xsm, xsm2[:,0], atol=1e-14, rtol=1e-12)
# Smoothed signal should not go to zero if edge effects are handled
# properly. Also assert proper normalization (i.e. smoothed signal
# is "in the middle" of the noisy original data).
assert xsm.min() >= mn
assert xsm.max() <= mx
assert mn <= xsm[0] <= mx
assert mn <= xsm[-1] <= mx
# convolution with delta peak produces same data exactly
assert np.allclose(smooth(x, np.array([0.0,1,0]), edge=edge),x, atol=1e-14,
rtol=1e-12)
def test_smooth_1d():
for edge in ['m', 'c']:
for N in [20,21]:
# values in [9.0,11.0]
x = rand(N) + 10
mn = 9.0
mx = 11.0
for M in range(18,27):
print "1d", edge, "N=%i, M=%i" %(N,M)
xsm = smooth(x, gaussian(M,2.0), edge=edge)
assert len(xsm) == N
# (N,1) case
xsm2 = smooth(x[:,None], gaussian(M,2.0)[:,None], edge=edge)
assert np.allclose(xsm, xsm2[:,0], atol=1e-14, rtol=1e-12)
# Smoothed signal should not go to zero if edge effects are handled
# properly. Also assert proper normalization (i.e. smoothed signal
# is "in the middle" of the noisy original data).
assert xsm.min() >= mn
assert xsm.max() <= mx
assert mn <= xsm[0] <= mx
assert mn <= xsm[-1] <= mx
# convolution with delta peak produces same data exactly
assert np.allclose(smooth(x, np.array([0.0,1,0]), edge=edge),x, atol=1e-14,
rtol=1e-12)
if nrand % 2 == 1:
nrand += 1
y[npoints/2-nrand/2:npoints/2+nrand/2] = np.random.rand(nrand) + 2.0
# Sum of Lorentz functions at data points. This is the same as convolution
# with a Lorentz function withOUT end point correction, valid if data `y`
# is properly zero at both ends, else edge effects are visible: smoothed
# data always goes to zero at both ends, even if original data doesn't. We
# need to use a very wide kernel with at least 100*std b/c of long
# Lorentz tails. Better 200*std to be safe.
sig = np.zeros_like(y)
for xi,yi in enumerate(y):
sig += yi * std / ((x-xi)**2.0 + std**2.0)
sig = scale(sig)
plt.plot(sig, label='sum')
# convolution with wide kernel
klen = 200*std
klen = klen+1 if klen % 2 == 0 else klen # odd kernel
kern = lorentz(klen, std=std)
plt.plot(scale(convolve(y, kern/float(kern.sum()), 'same')),
label='conv, klen=%i' %klen)
# Convolution with Lorentz function with end-point correction.
for klen in [10*std, 100*std, 200*std]:
klen = klen+1 if klen % 2 == 0 else klen # odd kernel
kern = lorentz(klen, std=std)
plt.plot(scale(smooth(y, kern)), label='conv+egde, klen=%i' %klen)
plt.title("npoints=%i" %npoints)
plt.legend()
plt.show()
nrand += 1
y[npoints // 2 - nrand // 2:npoints // 2 +
nrand // 2] = np.random.rand(nrand) + 2.0
# Sum of Lorentz functions at data points. This is the same as convolution
# with a Lorentz function withOUT end point correction, valid if data `y`
# is properly zero at both ends, else edge effects are visible: smoothed
# data always goes to zero at both ends, even if original data doesn't. We
# need to use a very wide kernel with at least 100*std b/c of long
# Lorentz tails. Better 200*std to be safe.
sig = np.zeros_like(y)
for xi, yi in enumerate(y):
sig += yi * std / ((x - xi)**2.0 + std**2.0)
sig = scale(sig)
plt.plot(sig, label='sum')
# convolution with wide kernel
klen = 200 * std
klen = klen + 1 if klen % 2 == 0 else klen # odd kernel
kern = lorentz(klen, std=std)
plt.plot(scale(convolve(y, kern / float(kern.sum()), 'same')),
label='conv, klen=%i' % klen)
# Convolution with Lorentz function with end-point correction.
for klen in [10 * std, 100 * std, 200 * std]:
klen = klen + 1 if klen % 2 == 0 else klen # odd kernel
kern = lorentz(klen, std=std)
plt.plot(scale(smooth(y, kern)), label='conv+egde, klen=%i' % klen)
plt.title("npoints=%i" % npoints)
plt.legend()
plt.show()
