def testSineEqualWeights():
scatter = 0.1
window = 15
order = 4
x = np.arange(0.0, 10.0, 0.2)
xx = np.arange(0.0, 10.0, 0.01)
y_true = np.sin(xx)
y = np.sin(x)
np.random.seed(152)
s = np.random.normal(0.0, scatter, (len(x)))
y = y + s
q_err = np.ones((len(x)), np.float) * scatter
sg = scipy.signal.savgol_filter(y, window, order, deriv = 0)
sg_err = savitzky_golay_werrors.savgol_filter_werror(y, window, order, q_err, deriv=None)
plt.figure()
plt.errorbar(x, y, yerr = q_err, fmt = '.', marker = 'o', ms = 3.0, label = 'data')
plt.plot(xx, y_true, ':', label = 'True')
plt.plot(x, sg, '-', label = 'SG')
plt.plot(x, sg_err, '--', label = 'SG new')
ax.legend(loc = 3, frameon=0, ncol=2, fontsize=13)
plt.savefig('Test_Sine_EqualWeights.pdf')
return
def testSpeed():
scatter = 0.1
window = 15
order = 4
N = 1000
x = np.arange(0.0, 10.0, 0.2)
y = np.sin(x)
np.random.seed(152)
s = np.random.normal(0.0, scatter, (len(x)))
y = y + s
q_err = np.ones((len(x)), np.float) * scatter
t1 = time.clock()
for dummy in range(N):
_ = scipy.signal.savgol_filter(y, window, order, deriv = 0)
print('Numpy: %.2f s' % (time.clock() - t1))
t1 = time.clock()
for dummy in range(N):
_ = savitzky_golay_werrors.savgol_filter_werror(y, window, order, q_err, deriv=None)
print('New: %.2f s' % (time.clock() - t1))
return
def testSine_wcov():
scatter_av = 0.1
scatter_sigma = 0.05
window = 15
order = 4
xx = np.arange(0.0, 10.0, 0.01)
y_true = np.sin(xx)
x = np.arange(0.0, 10.0, 0.2)
y = np.sin(x)
np.random.seed(250)
q_err = (np.abs(np.random.normal(scatter_av, scatter_sigma,
(len(x)))))
cov = np.diag(np.ones(q_err.size))
# A block diagonal covariance matrix where the correlation coefficient
# falls as a function of offset from the diagonal
for i in range(q_err.size):
for offset in range(1, q_err.size):
if i+offset >= q_err.size:
continue
cov[i, i+offset] = 0.3/offset**2
cov[i+offset, i] = 0.3/offset**2
for i in range(q_err.size):
for j in range(i, q_err.size):
cov[i, j] = cov[i, j] * q_err[i] * q_err[j]
cov[j, i] = cov[i, j]
y = np.random.multivariate_normal(y, cov)
sg = scipy.signal.savgol_filter(y, window, order, deriv = 0)
sg_err = savitzky_golay_werrors.savgol_filter_werror(y, window, order, cov=cov, deriv=None)
fig = plt.figure()
ax = fig.add_subplot(2, 1, 1)
ax.set_ylim([-2, 2])
import palettable
ax.set_color_cycle(palettable.colorbrewer.qualitative.Dark2_8.mpl_colors)
ax.errorbar(x, y, yerr = q_err, fmt = '.', marker = 'o', ms = 3.0,
label = 'Noisy data with covariant errors')
ax.plot(x, sg_err, '-', label = 'This work')
ax.plot(x, sg, '-', label = 'Traditional SG')
ax.plot(xx, y_true, '-', label = 'Noiseless')
ax.legend(loc = 3, frameon=0, ncol=2, fontsize=13)
ax.set_ylabel("y(x)")
ax.set_xticklabels([])
# Let us compute chisquare from the truth
# Chi-squared values compared to the underlying truth
print ("Chi-squared values compared to truth")
chisq_trad_truth = (np.dot(np.dot((sg-np.sin(x)).T, inv(cov)), (sg-np.sin(x))))
print ("Traditional: %.2f " % chisq_trad_truth )
chisq_new_truth = (np.dot(np.dot((sg_err-np.sin(x)).T, inv(cov)), (sg_err-np.sin(x))))
print ("This work: %.2f " % chisq_new_truth )
print ("Chi-squared values compared to data")
chisq_trad_data = (np.dot(np.dot((sg-y).T, inv(cov)), (sg-y)) )
print ("Traditional: %.2f " % chisq_trad_data)
chisq_new_data = (np.dot(np.dot((sg_err-y).T, inv(cov)), (sg_err-y)))
print ("This work: %.2f " % chisq_new_data)
ax = fig.add_subplot(2, 1, 2)
ax.set_color_cycle(palettable.colorbrewer.qualitative.Dark2_8.mpl_colors)
ax.errorbar(x, (y-np.sin(x))/q_err, q_err/q_err, fmt = '.', marker = 'o', ms = 3.0)
ax.plot(x, (sg_err-np.sin(x))/q_err, '-', label = r'This work $\chi^2=%.2f$' % chisq_new_truth)
ax.plot(x, (sg-np.sin(x))/q_err, '-', label= "Traditional SG $\chi^2=%.2f$" % chisq_trad_truth)
ax.axhline(0.0, color='grey')
ax.set_xlabel("x")
ax.set_ylabel(r"[y-sin(x)]/$\sigma_y$")
ax.legend(loc = 3, frameon=0, ncol=2, fontsize=13)
ax.set_ylim([-3, 3])
plt.tight_layout()
plt.savefig('Test_Sine_wcov.pdf')
return
def testSine():
scatter_av = 0.1
scatter_sigma = 0.05
window = 15
order = 4
xx = np.arange(0.0, 10.0, 0.01)
y_true = np.sin(xx)
x = np.arange(0.0, 10.0, 0.2)
y = np.sin(x)
np.random.seed(250)
q_err = np.abs(np.random.normal(scatter_av, scatter_sigma, (len(x))))
for i in range(len(x)):
y[i] += np.random.normal(0.0, q_err[i])
sg = scipy.signal.savgol_filter(y, window, order, deriv = 0)
sg_err = savitzky_golay_werrors.savgol_filter_werror(y, window, order, q_err, deriv=None)
fig = plt.figure()
ax = fig.add_subplot(2, 1, 1)
ax.set_ylim([-2, 2])
import palettable
ax.set_color_cycle(palettable.colorbrewer.qualitative.Dark2_8.mpl_colors)
ax.errorbar(x, y, yerr = q_err, fmt = '.', marker = 'o', ms = 3.0,
label = 'Noisy data, independent errors')
ax.plot(x, sg_err, '-', label = 'This work')
ax.plot(x, sg, '-', label = 'Traditional SG')
ax.plot(xx, y_true, '-', label = 'Noiseless')
ax.legend(loc = 3, frameon=0, ncol=2, fontsize=13)
ax.set_ylabel("y(x)")
ax.set_xticklabels([])
cov = np.diag(q_err**2.0)
print ("Chi-squared values compared to data")
chisq_trad_data = (np.dot(np.dot((sg-y).T, inv(cov)), (sg-y)) )
print ("Traditional: %.2f " % chisq_trad_data)
chisq_new_data = (np.dot(np.dot((sg_err-y).T, inv(cov)), (sg_err-y)))
print ("This work: %.2f " % chisq_new_data)
print ("Chi-squared values compared to truth")
chisq_trad_truth = (np.dot(np.dot((sg-np.sin(x)).T, inv(cov)), (sg-np.sin(x))) )
print ("Traditional: %.2f " % chisq_trad_truth)
chisq_new_truth = (np.dot(np.dot((sg_err-np.sin(x)).T, inv(cov)), (sg_err-np.sin(x))))
print ("This work: %.2f " % chisq_new_truth)
ax = fig.add_subplot(2, 1, 2)
ax.set_color_cycle(palettable.colorbrewer.qualitative.Dark2_8.mpl_colors)
ax.errorbar(x, (y-np.sin(x))/q_err, q_err/q_err, fmt = '.', marker = 'o', ms = 3.0)
ax.plot(x, (sg_err-np.sin(x))/q_err, '-', label = 'This work $\chi^2=%.2f$' % chisq_new_truth)
ax.plot(x, (sg-np.sin(x))/q_err, '-', label = 'Traditional SG $\chi^2=%.2f$' % chisq_trad_truth)
ax.axhline(0.0, color='grey')
ax.set_xlabel("x")
ax.set_ylabel("(y-sin(x))/$\sigma_y$")
ax.set_ylim([-3, 3])
ax.legend(loc = 3, frameon=0, ncol=2, fontsize=13)
plt.tight_layout()
plt.savefig('Test_Sine.pdf')
return
