def bolEstm(obj, sig, width):
'''
peakFinder.bolEstm(obj, sig, width)
=============================
Performs a SN estimation at each wavelength following the max-likelihood
approach of Bolton et al. (2012).
Parameters:
obj: The SDSS object/spectra on which applied the subtraction
sig: Width of the gaussian kernel
width: Width of the convolutional window
Returns:
SN: The SN at each wavelength as an array. Beginning and end are filled
with null values due to the convolution.
'''
NormGauss = gauss(np.linspace(-width * 0.5, width * 0.5, width), 0.0, 1.0,
sig**2.0)
NormGauss = NormGauss / np.sum(NormGauss)
Cj1 = np.array([
np.sum(
kernel(j + 0.5 * width, width, NormGauss, len(obj.wave)) *
obj.reduced_flux * obj.ivar)
for j in range(int(len(obj.wave) - width))
])
Cj2 = np.array([
np.sum(obj.ivar *
kernel(j + 0.5 * width, width, NormGauss, len(obj.wave))**2.0)
for j in range(int(len(obj.wave) - width))
])
SN = np.zeros(len(obj.wave))
SN[int(width * 0.5):int(width * 0.5 + len(Cj1))] = Cj1 / np.sqrt(Cj2)
return SN
def bolEstm(obj, sig, width):
'''
peakFinder.bolEstm(obj, sig, width)
=============================
Performs a SN estimation at each wavelength following the max-likelihood
approach of Bolton et al. (2012).
Parameters:
obj: The SDSS object/spectra on which applied the subtraction
sig: Width of the gaussian kernel
width: Width of the convolutional window
Returns:
SN: The SN at each wavelength as an array. Beginning and end are filled
with null values due to the convolution.
'''
NormGauss = gauss(np.linspace(-width * 0.5, width * 0.5, width), 0.0, 1.0,
sig ** 2.0)
NormGauss = NormGauss / np.sum(NormGauss)
Cj1 = np.array([np.sum(kernel(j + 0.5 * width, width, NormGauss,
len(obj.wave)) * obj.reduced_flux * obj.ivar)
for j in range(int(len(obj.wave) - width))])
Cj2 = np.array([np.sum(obj.ivar * kernel(j + 0.5 * width, width, NormGauss,
len(obj.wave)) ** 2.0)
for j in range(int(len(obj.wave) - width))])
SN = np.zeros(len(obj.wave))
SN[int(width * 0.5): int(width * 0.5 + len(Cj1))] = Cj1 / np.sqrt(Cj2)
return SN
def qsoContfit(obj, peak, searchLyA, sig, window_width=40):
'''
peakFinder.qsoContfit(obj, peak, searchLyA, window_width)
=============================
A function to fit the QSO continuum near a peak with a 3rd order polynomial
and subtract it. Add the new SN of the peak in its class.
Parameters:
obj: The SDSS object/spectra on which applied the subtraction
peak: The inquired peak
sig: Sigma of gaussian to perform SN max-likelihood
searchLyA: True if we search for background LAE, False for backgroung ELGs
window_width: Half-width (Angstroms) on which the polynomial is fitted
Returns:
accept: True if the SN is still high after subtraction. False otherwise.
'''
x0 = peak.wavelength
window = np.linspace(obj.wave2bin(x0) - window_width,
obj.wave2bin(x0) + window_width,
2 * window_width + 1,
dtype=np.int16)
median_local = np.median(obj.reduced_flux[window])
fit_QSO = np.poly1d(np.polyfit(x=obj.wave[window],y=obj.reduced_flux[window],deg=3, \
w=(np.abs(obj.reduced_flux[window]-median_local)<5)*np.sqrt(obj.ivar[window])) )
new_flux = obj.reduced_flux[window] - fit_QSO(obj.wave[window])
NormGauss = gauss(
np.linspace(-window_width * 0.5, window_width * 0.5, window_width),
0.0, 1.0, sig**2.0)
NormGauss = NormGauss / np.sum(NormGauss)
cj1_new = np.sum(
new_flux *
kernel(int(len(window) / 2), window_width, NormGauss, len(new_flux)) *
obj.ivar[window])
cj2_new = np.sum(
obj.ivar[window] *
kernel(int(len(window) / 2), window_width, NormGauss, len(window))**2)
SN_fitted = cj1_new / np.sqrt(cj2_new)
if searchLyA and SN_fitted < 6:
return False #Reject
elif searchLyA and SN_fitted > 6:
peak.reduced_sn = SN_fitted
obj.reduced_flux_QSO[window] = new_flux
elif searchLyA == False and SN_fitted < 6:
return False # Reject
elif searchLyA == False and SN_fitted > 6:
peak.reduced_sn = SN_fitted
obj.reduced_flux_QSO[window] = new_flux
return True # Accept
def bolEstm(obj, sig, width):
NormGauss = gauss(np.linspace(-width * 0.5, width * 0.5, width), 0.0, 1.0,
sig ** 2.0)
NormGauss = NormGauss / np.sum(NormGauss)
Cj1 = np.array([np.sum(kernel(j + 0.5 * width, width, NormGauss,
len(obj.wave)) * obj.reduced_flux * obj.ivar)
for j in range(int(len(obj.wave) - width))])
Cj2 = np.array([np.sum(obj.ivar * kernel(j + 0.5 * width, width, NormGauss,
len(obj.wave)) ** 2.0)
for j in range(int(len(obj.wave) - width))])
SN = np.zeros(len(obj.wave))
SN[int(width * 0.5): int(width * 0.5 + len(Cj1))] = Cj1 / np.sqrt(Cj2)
return SN
def _generate_table(self, max_rng):
"""
Workhorse of GenCoeffs class, compute kernel
and separate into rng specific coefficients.
"""
# Calculate combined kernel of rng from 1 to max_rng:
kers = kernel(max_rng)
# Separate into kernels of each rng and flatten them:
self._coeffs = [
*reversed([
*map(
GenCoeffs.flattened_rim,
map(
lambda slices: kers[slices],
zip(
repeat(...),
*tee(
chain((slice(None, None), ),
map(lambda i: slice(i, -i),
range(1, max_rng)))),
))),
])
]
self._g_scalers = [
*map(
lambda coeffs: 255.9 / (255 * np.hypot(*coeffs)),
accumulate(
map(
lambda coeffs: np.maximum(coeffs, 0).sum(axis=1),
self._coeffs,
)))
]
return self
def update_nn_weights_derivative_free_old(cloud, cost, lr, N, kernel_a, alpha,
beta, gamma):
#get flattened weights, nn shape and weight names
cloudf, nn_shape, weight_names = flatten_weights(cloud, N)
#compute kernels
kernels = [[kernel(cloudf[i], cloudf[j], kernel_a) for j in range(N)]
for i in range(N)]
gkernels = [[gkernel(cloudf[i], cloudf[j], kernel_a) for j in range(N)]
for i in range(N)]
#plt.imshow(kernels,vmin=0,vmax=1)
#plt.colorbar()
#compute mean and standart deviation
cloud_mean = np.mean(cloudf, axis=0)
cloud_var = get_var(cloudf, cloud_mean)
#compute gradient flows
updates = []
for nn in range(N):
R = 0
P = 0
S = 0
Q = [
gkernels[nn][j] * cost[j] + kernels[nn][j] * cost[j] * np.divide(
(cloudf[j] - cloud_mean), cloud_var) for j in range(N)
]
Q = np.mean(Q, axis=0)
if alpha > 0:
R = [[kernels[nn][j] * (cloudf[j] - cloudf[k]) for j in range(N)]
for k in range(N)]
R = [item for sublist in R
for item in sublist] #Flatten list of lists
R = np.sum(R, axis=0) * float(1 / N**2)
if beta > 0:
P = [gkernels[nn][j] for j in range(N)]
P = np.mean(P, axis=0)
if gamma > 0:
S = [
kernels[nn][j] * np.divide((cloudf[j] - cloud_mean), cloud_var)
for j in range(N)
]
S = np.mean(S, axis=0)
updates.append(-lr * (Q + alpha * R + beta * P + gamma * S))
#update flattened tensors
for nn in range(N):
cloudf[nn] = cloudf[nn] + updates[nn]
#restore NN weight shapes
new_nn_weights = unflatten_weights(cloudf, nn_shape, weight_names, N)
return new_nn_weights, cloud_var
def qsoContfit(obj, peak, searchLyA, sig, window_width = 40):
'''
peakFinder.qsoContfit(obj, peak, searchLyA, window_width)
=============================
A function to fit the QSO continuum near a peak with a 3rd order polynomial
and subtract it. Add the new SN of the peak in its class.
Parameters:
obj: The SDSS object/spectra on which applied the subtraction
peak: The inquired peak
sig: Sigma of gaussian to perform SN max-likelihood
searchLyA: True if we search for background LAE, False for backgroung ELGs
window_width: Half-width (Angstroms) on which the polynomial is fitted
Returns:
accept: True if the SN is still high after subtraction. False otherwise.
'''
x0 = peak.wavelength
window = np.linspace(obj.wave2bin(x0)-window_width,obj.wave2bin(x0)+window_width,2*window_width+1,dtype = np.int16)
median_local = np.median(obj.reduced_flux[window])
fit_QSO = np.poly1d(np.polyfit(x=obj.wave[window],y=obj.reduced_flux[window],deg=3, \
w=(np.abs(obj.reduced_flux[window]-median_local)<5)*np.sqrt(obj.ivar[window])) )
new_flux = obj.reduced_flux[window] - fit_QSO(obj.wave[window])
NormGauss = gauss(np.linspace(-window_width * 0.5, window_width * 0.5, window_width), 0.0, 1.0,sig ** 2.0)
NormGauss = NormGauss / np.sum(NormGauss)
cj1_new = np.sum(new_flux*kernel(int(len(window)/2),window_width,NormGauss,len(new_flux))*obj.ivar[window])
cj2_new = np.sum(obj.ivar[window]*kernel(int(len(window)/2),window_width,NormGauss,len(window))**2)
SN_fitted = cj1_new/np.sqrt(cj2_new)
if searchLyA and SN_fitted < 6:
return False #Reject
elif searchLyA and SN_fitted > 6:
peak.reduced_sn = SN_fitted
obj.reduced_flux_QSO[window]=new_flux
elif searchLyA == False and SN_fitted < 6:
return False # Reject
elif searchLyA == False and SN_fitted > 6:
peak.reduced_sn = SN_fitted
obj.reduced_flux_QSO[window]=new_flux
return True # Accept