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Residual_1D_module.py
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"""
Created on Tue Jul 30 14:50:17 2019
@author: Neven Caplar
www.ncaplar.com
"""
import numpy as np
import matplotlib
import matplotlib.pyplot as plt
from mpl_toolkits.axes_grid1.inset_locator import inset_axes
def find_centroid_of_flux(image):
"""
function giving the position of weighted average of the flux in a square image
@array[in] sci_image numpy array with the values for the cutout of the science image (20x20 cutout)
"""
x_center=[]
y_center=[]
I_x=[]
for i in range(len(image)):
I_x.append([i,np.sum(image[:,i])])
I_x=np.array(I_x)
I_y=[]
for i in range(len(image)):
I_y.append([i,np.sum(image[i])])
I_y=np.array(I_y)
x_center=(np.sum(I_x[:,0]*I_x[:,1])/np.sum(I_x[:,1]))
y_center=(np.sum(I_y[:,0]*I_y[:,1])/np.sum(I_y[:,1]))
return(x_center,y_center)
def residual_1D(sci_image,var_image,model_image):
"""
@array[in] sci_image numpy array with the values for the cutout of the science image (20x20 cutout)
@array[in] var_image numpy array with the cutout for the cutout of the variance image (20x20 cutout)
@array[in] model_image model (20x20 image)
@array[out] init_lamda 1D extraction from the science image
@array[out] std_init_lamda error on the 1D extraction from the science image
@array[out] init_removal_lamda 1D extraction from the residual image
@array[out] std_init_removal_lamda error on 1D extraction from the residual image
"""
assert sci_image.shape==(20,20)
assert var_image.shape==(20,20)
assert sci_image.shape==(20,20)
cental_pixel_for_x_value_int=int(round(find_centroid_of_flux(sci_image)[0]))
multiplicative_factor_to_renormalize_to_40000=np.max(sci_image)/40000
sci_image_smaller=sci_image[:,cental_pixel_for_x_value_int-3:cental_pixel_for_x_value_int+3]/multiplicative_factor_to_renormalize_to_40000
var_image_smaller=var_image[:,cental_pixel_for_x_value_int-3:cental_pixel_for_x_value_int+3]/multiplicative_factor_to_renormalize_to_40000
residual_initial_smaller=sci_image_smaller-model_image[:,cental_pixel_for_x_value_int-3:cental_pixel_for_x_value_int+3]/multiplicative_factor_to_renormalize_to_40000
#################################
# step 5 from Horne (http://adsabs.harvard.edu/abs/1986PASP...98..609H), very simplified
inputimage_smaller=sci_image_smaller
Px=np.sum(inputimage_smaller,axis=0)/np.sum(inputimage_smaller)
var_inputimage_smaller=var_image_smaller
#################################
# Equation 8 from Horne with modification from Robert abut variance for extraction of signal
# note that this uses profile from full thing, and not "residual profile"
# nominator
weighted_inputimage_smaller=inputimage_smaller*Px/(1)
# denominator
weights_array=np.ones((inputimage_smaller.shape[0],inputimage_smaller.shape[1]))*Px**2
init_lamda=np.array(list(map(np.sum, weighted_inputimage_smaller)))/(np.array(list(map(np.sum,weights_array))))
init_lamda_boxcar=np.array(list(map(np.sum, inputimage_smaller)))
# Equation 8.5 from Horne
var_f_std_lamda=1/np.sum(np.array(Px**2/(var_inputimage_smaller)),axis=1)
std_init_lamda=np.sqrt(var_f_std_lamda)
std_init_lamda_boxcar=np.sqrt(np.array(list(map(np.sum, var_inputimage_smaller))))
#################################
# Equation 8 from Horne with modification from Robert abut variance for initial removal
# note that this uses profile from full thing, and not "residual profile"
# nominator
weighted_inputimage_smaller=residual_initial_smaller*Px/(1)
# denominator
weights_array=np.ones((residual_initial_smaller.shape[0],residual_initial_smaller.shape[1]))*Px**2
init_removal_lamda=np.array(list(map(np.sum, weighted_inputimage_smaller)))/(np.array(list(map(np.sum,weights_array))))
init_removal_lamda_boxcar=np.array(list(map(np.sum, residual_initial_smaller)))
# Equation 8.5 from Horne
var_init_removal_lamda=1/np.sum(np.array(Px**2/(var_inputimage_smaller)),axis=1)
std_init_removal_lamda=np.sqrt(var_init_removal_lamda)
return init_lamda,std_init_lamda,init_removal_lamda,std_init_removal_lamda
def chi_40000(sci_image,var_image,model_image):
"""
crude algorithm to modify chi**2 which one would expect if the max flux of the science image was at 40000 counts
@array[in] sci_image numpy array with the values for the cutout of the science image (20x20 cutout)
@array[in] var_image numpy array with the cutout for the cutout of the variance image (20x20 cutout)
@array[in] model_image model (20x20 image)
@float[out] chi**2
"""
sci_image_renormalized,var_image_renormalized,model_image_renormalized=add_artificial_noise(sci_image,var_image,model_image)
#multiplicative_factor_to_renormalize_to_40000=np.max(sci_image)/40000
#sci_image_renormalized=sci_image/multiplicative_factor_to_renormalize_to_40000
#var_image_renormalized=var_image/multiplicative_factor_to_renormalize_to_40000
#model_image_renormalized=model_image/multiplicative_factor_to_renormalize_to_40000
return np.mean((sci_image_renormalized-model_image_renormalized)**2/var_image_renormalized)
def add_artificial_noise(sci_image,var_image,model_image):
"""
add extra noise so that it has comparable noise as if the max flux in the image (in the single pixel) is 40000
@array[in] sci_image numpy array with the values for the cutout of the science image (20x20 cutout)
@array[in] var_image numpy array with the cutout for the cutout of the variance image (20x20 cutout)
@array[in] model_image model (20x20 image)
@array[out] sci_image if max flux smaller than 40000, unchanged science image (20x20 cutout)
if max flux larger than 40000, degraded science image
@array[out] modified variance image
@array[out] model_image unchagned model (20x20 image)
"""
# what is the ratio between the current science image and 40000 value
#multi_factor=np.max(sci_image)/40000
# signal to noise ratio in the brightess pixel
Max_SN_now=np.max(sci_image)/np.max(np.sqrt(var_image))
# what is the ratio between the SN ratio in the brightest pixel to what I expect (which is roughly np.sqrt(40000/1.2)=220)
# factor 1.2 in the previous line comes because variance is empirically a bit smaller than the signal
dif_in_SN=Max_SN_now/220
# prepare array which will contain artifically created noise
artifical_noise=np.zeros_like(model_image)
artifical_noise=np.array(artifical_noise)
# minimal value in the variance image
min_var_value=np.min(var_image)
# for each pixel create additional artifical random noise, drawing from the normal distribution
for i in range(len(artifical_noise)):
for j in range(len(artifical_noise)):
artifical_noise[i,j]=np.random.randn()*np.sqrt((dif_in_SN**2-1)*(var_image[i,j]-min_var_value))
# if you need to degrade image
# return science image with additional noise
# return variance image with stronger variance
if dif_in_SN>1:
return (sci_image+artifical_noise),((dif_in_SN**2)*(var_image-min_var_value)+min_var_value),model_image
else:
# if you need to ``improve image''
# return decreased variance image
return (sci_image),((dif_in_SN**2)*(var_image-min_var_value)+min_var_value),model_image
def plot_1D_residual(sci_image,var_image,model_image,title=None):
"""
@array[in] sci_image numpy array with the values for the cutout of the science image (20x20 cutout)
@array[in] var_image numpy array with the cutout for the cutout of the variance image (20x20 cutout)
@array[in] model_image model (20x20 image)
@string[in] title custom title to appear above the plot
@plot[out] diagnostic plot
"""
init_lamda,std_init_lamda,init_removal_lamda,std_init_removal_lamda=residual_1D(sci_image,var_image,model_image)
position_of_max_flux=np.where(init_lamda==np.max(init_lamda))[0][0]
difference_from_max=range(20)-position_of_max_flux
pixels_to_test=np.array(range(20))[(np.abs(difference_from_max)>2)&(np.abs(difference_from_max)<=6)]
Q=np.mean(np.abs(init_removal_lamda[pixels_to_test]/std_init_removal_lamda[pixels_to_test]))
plt.figure(figsize=(20,10))
plt.errorbar(np.array(range(len(init_lamda))),init_lamda,yerr=std_init_lamda,fmt='o',elinewidth=2,capsize=12,markeredgewidth=2,label='data',color='orange')
plt.errorbar(np.array(range(len(init_removal_lamda))),init_removal_lamda,yerr=std_init_removal_lamda,color='red',fmt='o',elinewidth=2,capsize=10,markeredgewidth=2,label='residual')
for i in range(20):
plt.text(-0.5+i, -1250, str("{:1.0f}".format(init_lamda[i])), fontsize=20,rotation=70.,color='orange')
for i in range(20):
plt.text(-0.5+i, -2050, str("{:1.1f}".format(init_removal_lamda[i]/std_init_removal_lamda[i])), fontsize=20,rotation=70.,color='red')
if title is None:
pass
else:
plt.title(str(title))
plt.legend(loc=2, fontsize=22)
plt.plot(np.zeros(20),'--',color='black')
plt.ylim(-2500,2500)
plt.ylabel('flux',size=25)
plt.xlabel('pixel',size=25)
plt.xticks(range(20))
sci_image_40000,var_image_40000,model_image_40000=add_artificial_noise(sci_image,var_image,model_image)
init_lamda,std_init_lamda,init_removal_lamda,std_init_removal_lamda=residual_1D(sci_image_40000,var_image_40000,model_image_40000)
position_of_max_flux=np.where(init_lamda==np.max(init_lamda))[0][0]
difference_from_max=range(20)-position_of_max_flux
pixels_to_test=np.array(range(20))[(np.abs(difference_from_max)>2)&(np.abs(difference_from_max)<=6)]
Q_40000=np.mean(np.abs(init_removal_lamda[pixels_to_test]/std_init_removal_lamda[pixels_to_test]))
plt.text(19.5,2300, '$Q_{'+str(np.int(np.round(np.max(sci_image))))+'}$='+str("{:1.2f}".format(Q)),
horizontalalignment='right',
verticalalignment='top',fontsize=26)
chi2=np.mean((model_image-sci_image)**2/var_image)
plt.text(19.5,2000, '$\chi^{2}_{'+str(np.int(np.round(np.max(sci_image))))+'}$='+str("{:1.2f}".format(chi2)),
horizontalalignment='right',
verticalalignment='top',fontsize=26)
chi2_40000=np.mean((model_image_40000-sci_image_40000)**2/var_image_40000)
plt.text(19.5,1650, '$Q_{40000}$='+str("{:1.2f}".format(Q_40000)),
horizontalalignment='right',
verticalalignment='top',fontsize=26)
plt.text(19.5,1300, '$\chi^{2}_{40000}$='+str("{:1.2f}".format(chi2_40000)),
horizontalalignment='right',
verticalalignment='top',fontsize=26)
plt.axvspan(pixels_to_test[0]-0.5, pixels_to_test[3]+0.5, alpha=0.3, color='grey')
plt.axvspan(pixels_to_test[4]-0.5, pixels_to_test[7]+0.5, alpha=0.3, color='grey')
def plot_1D_residual_custom(sci_image,var_image,model_image,title=None):
"""
@array[in] sci_image numpy array with the values for the cutout of the science image (20x20 cutout)
@array[in] var_image numpy array with the cutout for the cutout of the variance image (20x20 cutout)
@array[in] model_image model (20x20 image)
@string[in] title custom title to appear above the plot
@plot[out] diagnostic plot
"""
init_lamda,std_init_lamda,init_removal_lamda,std_init_removal_lamda=residual_1D(sci_image,var_image,model_image)
position_of_max_flux=np.where(init_lamda==np.max(init_lamda))[0][0]
difference_from_max=range(20)-position_of_max_flux
pixels_to_test=np.array(range(20))[(np.abs(difference_from_max)>2)&(np.abs(difference_from_max)<=6)]
Q=np.mean(np.abs(init_removal_lamda[pixels_to_test]/std_init_removal_lamda[pixels_to_test]))
plt.figure(figsize=(20,10))
plt.errorbar(np.array(range(len(init_lamda)))[2:19],init_lamda[2:19],yerr=std_init_lamda[2:19],fmt='o',elinewidth=2,capsize=12,markeredgewidth=2,label='data',color='black')
plt.errorbar(np.array(range(len(init_removal_lamda)))[2:19],init_removal_lamda[2:19],yerr=std_init_removal_lamda[2:19],color='red',fmt='o',elinewidth=2,capsize=10,markeredgewidth=2,label='residual')
"""
for i in range(2,18):
plt.text(-0.5+i, -1250, str("{:1.0f}".format(init_lamda[i])), fontsize=20,rotation=70.,color='orange')
for i in range(2,18):
plt.text(-0.5+i, -2050, str("{:1.1f}".format(init_removal_lamda[i]/std_init_removal_lamda[i])), fontsize=20,rotation=70.,color='red')
if title is None:
pass
else:
plt.title(str(title))
"""
plt.legend(loc=2, fontsize=30)
plt.plot(np.zeros(20),'--',color='black')
plt.ylim(-700,1500)
plt.xlim(1.5,18.5)
plt.ylabel('flux',size=35)
plt.xlabel('pixel',size=35)
plt.xticks(range(20)[2:19])
sci_image_40000,var_image_40000,model_image_40000=add_artificial_noise(sci_image,var_image,model_image)
init_lamda,std_init_lamda,init_removal_lamda,std_init_removal_lamda=residual_1D(sci_image_40000,var_image_40000,model_image_40000)
position_of_max_flux=np.where(init_lamda==np.max(init_lamda))[0][0]
difference_from_max=range(20)-position_of_max_flux
pixels_to_test=np.array(range(20))[(np.abs(difference_from_max)>2)&(np.abs(difference_from_max)<=6)]
Q_40000=np.mean(np.abs(init_removal_lamda[pixels_to_test]/std_init_removal_lamda[pixels_to_test]))
"""
plt.text(19.5,2300, '$Q_{'+str(np.int(np.round(np.max(sci_image))))+'}$='+str("{:1.2f}".format(Q)),
horizontalalignment='right',
verticalalignment='top',fontsize=26)
chi2=np.mean((model_image-sci_image)**2/var_image)
plt.text(19.5,2000, '$\chi^{2}_{'+str(np.int(np.round(np.max(sci_image))))+'}$='+str("{:1.2f}".format(chi2)),
horizontalalignment='right',
verticalalignment='top',fontsize=26)
chi2_40000=np.mean((model_image_40000-sci_image_40000)**2/var_image_40000)
plt.text(19.5,1650, '$Q_{40000}$='+str("{:1.2f}".format(Q_40000)),
horizontalalignment='right',
verticalalignment='top',fontsize=26)
plt.text(19.5,1300, '$\chi^{2}_{40000}$='+str("{:1.2f}".format(chi2_40000)),
horizontalalignment='right',
verticalalignment='top',fontsize=26)
"""
plt.axvspan(pixels_to_test[0]-0.5, pixels_to_test[3]+0.5, alpha=0.3, color='grey')
plt.axvspan(pixels_to_test[4]-0.5, pixels_to_test[7]+0.5, alpha=0.3, color='grey')
def plot_1D_residual_custom_large(sci_image,var_image,model_image,title=None):
"""
@array[in] sci_image numpy array with the values for the cutout of the science image (20x20 cutout)
@array[in] var_image numpy array with the cutout for the cutout of the variance image (20x20 cutout)
@array[in] model_image model (20x20 image)
@string[in] title custom title to appear above the plot
@plot[out] diagnostic plot
"""
init_lamda,std_init_lamda,init_removal_lamda,std_init_removal_lamda=residual_1D(sci_image,var_image,model_image)
position_of_max_flux=np.where(init_lamda==np.max(init_lamda))[0][0]
difference_from_max=range(20)-position_of_max_flux
pixels_to_test=np.array(range(20))[(np.abs(difference_from_max)>2)&(np.abs(difference_from_max)<=6)]
Q=np.mean(np.abs(init_removal_lamda[pixels_to_test]/std_init_removal_lamda[pixels_to_test]))
fig, ax = plt.subplots(figsize=[20, 10])
ax.errorbar(np.array(range(len(init_lamda)))[2:19],init_lamda[2:19],yerr=std_init_lamda[2:19],fmt='o',elinewidth=2,capsize=12,markeredgewidth=2,label='data',color='black',ls='--')
ax.errorbar(np.array(range(len(init_removal_lamda)))[2:19],init_removal_lamda[2:19],yerr=std_init_removal_lamda[2:19],color='red',fmt='o',elinewidth=2,capsize=10,markeredgewidth=2,label='residual')
"""
for i in range(2,18):
plt.text(-0.5+i, -1250, str("{:1.0f}".format(init_lamda[i])), fontsize=20,rotation=70.,color='orange')
for i in range(2,18):
plt.text(-0.5+i, -2050, str("{:1.1f}".format(init_removal_lamda[i]/std_init_removal_lamda[i])), fontsize=20,rotation=70.,color='red')
if title is None:
pass
else:
plt.title(str(title))
"""
ax.legend(loc=2, fontsize=35)
ax.plot(np.zeros(20),'--',color='grey')
ax.set_ylim(-10000,135000)
ax.set_xticks(range(18))
ax.set_xlim(1.5,18.5)
ax.set_ylabel('flux',size=45)
ax.set_xlabel('pixel',size=45)
sci_image_40000,var_image_40000,model_image_40000=add_artificial_noise(sci_image,var_image,model_image)
init_lamda,std_init_lamda,init_removal_lamda,std_init_removal_lamda=residual_1D(sci_image_40000,var_image_40000,model_image_40000)
position_of_max_flux=np.where(init_lamda==np.max(init_lamda))[0][0]
difference_from_max=range(20)-position_of_max_flux
pixels_to_test=np.array(range(20))[(np.abs(difference_from_max)>2)&(np.abs(difference_from_max)<=6)]
Q_40000=np.mean(np.abs(init_removal_lamda[pixels_to_test]/std_init_removal_lamda[pixels_to_test]))
"""
plt.text(19.5,2300, '$Q_{'+str(np.int(np.round(np.max(sci_image))))+'}$='+str("{:1.2f}".format(Q)),
horizontalalignment='right',
verticalalignment='top',fontsize=26)
chi2=np.mean((model_image-sci_image)**2/var_image)
plt.text(19.5,2000, '$\chi^{2}_{'+str(np.int(np.round(np.max(sci_image))))+'}$='+str("{:1.2f}".format(chi2)),
horizontalalignment='right',
verticalalignment='top',fontsize=26)
chi2_40000=np.mean((model_image_40000-sci_image_40000)**2/var_image_40000)
plt.text(19.5,1650, '$Q_{40000}$='+str("{:1.2f}".format(Q_40000)),
horizontalalignment='right',
verticalalignment='top',fontsize=26)
plt.text(19.5,1300, '$\chi^{2}_{40000}$='+str("{:1.2f}".format(chi2_40000)),
horizontalalignment='right',
verticalalignment='top',fontsize=26)
"""
#ax.axvspan(pixels_to_test[0]-0.5, pixels_to_test[3]+0.5, alpha=0.3, color='grey')
#ax.axvspan(pixels_to_test[4]-0.5, pixels_to_test[7]+0.5, alpha=0.3, color='grey')
axins = inset_axes(ax, width="100%", height="100%", loc=1,bbox_to_anchor=(0.63,0.55,0.35,0.38), bbox_transform=ax.transAxes)
axins.errorbar(np.array(range(len(init_lamda)))[2:19],init_lamda[2:19],yerr=std_init_lamda[2:19],fmt='o',elinewidth=2,capsize=12,markeredgewidth=2,label='data',color='black',ls='--')
axins.errorbar(np.array(range(len(init_removal_lamda)))[2:19],init_removal_lamda[2:19],yerr=std_init_removal_lamda[2:19],color='red',fmt='o',elinewidth=2,capsize=10,markeredgewidth=2,label='residual')
axins.set_ylim(-400,1400)
axins.set_xlim(1.5,18.5)
axins.plot(np.zeros(20),'--',color='grey')
axins.axvspan(pixels_to_test[0]-0.5, pixels_to_test[3]+0.5, alpha=0.3, color='grey')
axins.axvspan(pixels_to_test[4]-0.5, pixels_to_test[7]+0.5, alpha=0.3, color='grey')
fig.savefig('/Users/nevencaplar/Documents/PFS/Poster/Poster2019/' + '1d.png', bbox_inches='tight')