def annular_PCA_by_lintrick( nod_beam, x_cen, y_cen, n_PCA, side):
side={0:'S',1:'D'}[side]
#////////////////////////////////////////////////////////
#Make polar and cartisian coordinate systems
#////////////////////////////////////////////////////////
X_DIM=300
Y_DIM=300
y,x=np.indices((Y_DIM,X_DIM))
#polar
radius=np.abs((x-x_cen)+1j*(y-y_cen))
radius_1d=radius.flatten()
#////////////////////////////////////////////////////////
#Get the data
#////////////////////////////////////////////////////////
if (nod_beam == 0) and (side == 'D'):
filenames=sorted(os.listdir('../../processed_data/sat/cxsxbcponlm/DX_0/*.fits'))
directory='../../processed_data/sat/cxsxbcponlm/DX_0/'
if (nod_beam == 1) and (side == 'D'):
filenames=sorted(os.listdir('../../processed_data/sat/cxsxbcponlm/DX_1/*.fits'))
directory='../../processed_data/sat/cxsxbcponlm/DX_1/'
if (nod_beam == 0) and (side == 'S'):
filenames=sorted(os.listdir('../../processed_data/sat/cxsxbcponlm/SX_0/*.fits'))
directory='../../processed_data/sat/cxsxbcponlm/SX_0/'
if (nod_beam == 1) and (side == 'S'):
filenames=sorted(os.listdir('../../processed_data/sat/cxsxbcponlm/SX_1/*.fits'))
directory='../../processed_data/sat/cxsxbcponlm/SX_1/'
n_images=len(filenames)
#data=fltarr(X_DIM,Y_DIM,n_images)
#////////////////////////////////////////////////////////
#start a loop to do region-by-region
#////////////////////////////////////////////////////////
n_r=140
r_subt_in=np.arange(n_r)*1.+3.
r_subt_out=np.arange(n_r)*1.+3.+1.
r_opt_in=r_subt_in-7.
r_opt_out=r_subt_in+9.
r_opt_in[r_opt_in < 6)]=5
#////////////////////////////////////////////////////////
#Do the whole thing in loops for memory allocation
#////////////////////////////////////////////////////////
combined_median=np.zeros(Y_DIM,X_DIM)
combined_data=fltarr(X_DIM,Y_DIM,n_images)
for l in xrange(n_r):
print, l
data=[]
for fn in xrange(filenames):
data.append(fits.open(fn)[0].data)
data=np.array(data)
data-=np.median(data,axis=0)[None,:,:]
#////////////////////////////////////////////////////////
#construct a masked region
#////////////////////////////////////////////////////////
#opt_mask=np.zeros(X_DIM*Y_DIM)
opt_mask=np.logical_and(radius_1d>r_opt_in[l],radius_1d<=r_opt_out[l])#bool
#opt_mask[where(radius_1d lt r_opt_in[l])]=1
#opt_mask[where(radius_1d ge r_opt_out[l])]=1
n_pix_opt_masked=np.sum(opt_mask.astype(int))
#sub_mask=fltarr(X_DIM*Y_DIM)
sub_mask=np.logical_and(radius_1d>r_subt_in[l],radius_1d<=r_subt_out[l])#bool
#sub_mask[where(radius_1d lt r_subt_in[l])]=1
#sub_mask[where(radius_1d ge r_subt_out[l])]=1
n_pix_sub_masked=np.sum(sub_mask.astype(int))
#////////////////////////////////////////////////////////
#make matrix of non-opt_masked pixels for PCA
#////////////////////////////////////////////////////////
A=[]
for h in xrange(n_images):
data_1d=data[h,:,:].flatten()
A.append(data_1d[opt_mask]#the shape has changed here compared to Andy's...
A=np.array(A)
#////////////////////////////////////////////////////////
#Find the principal components (eigenvectors)
#////////////////////////////////////////////////////////
mean_image=np.mean(A,axis=0)
A-=mean_image[None,:] #subtract off the mean image(the median is already gone JMS)
#linear algebra described on the wiki page for eigenfaces
#https://en.wikipedia.org/wiki/Eigenface#Computing_the_eigenvectors
AT_A=np.dot(A.T,A)
eigenvalues, eigenvectors = np.linalg.eig(AT_A)
idx=np.argsort(eigenvalues)[::-1]#python doesn't sort like idl...
eigenvectors=eigenvectors[:,idx]
eigenvectors=np.dot(A,eigenvectors)
#normalize the eigenvectors
for h in xrange(n_images):
eigenvectors[:,h]/=(np.sum(eigenvectors[:,h]**2.))**0.5#vector in rows for idl, columns in python...
#////////////////////////////////////////////////////////
#Fit the individual images and reform to 2d
#////////////////////////////////////////////////////////
#loop through image by image
for h in xrange(n_images):
#fit the image
#project each image onto each (requested) eigenvector
PCA_image_1d=np.zeros(n_pix_opt_masked)
for k in xrange(n_PCA):
coefficient=np.dot(A[:,h],eigenvectors[:,k])
PCA_image_1d+=(eigenvectors[:,k]*coefficient)
#subtract from original
PCA_subtracted_image=A[:,h]-PCA_image_1d
#insert the opt_masked pixels back in
PCA_subtracted_with_opt_mask_1d=np.zeros(X_DIM*Y_DIM,dtype=float)
PCA_subtracted_with_opt_mask_1d[opt_mask]=PCA_subtracted_image
#only save the subtraction region (not the opt region)
#PCA_subtracted_image*=sub_mask
#reform to 2-d
#overwriting data...
data[h,:,:]=PCA_subtracted_with_opt_mask_1d.reshape(Y_DIM,X_DIM)
#////////////////////////////////////////////////////////
#rotate and combine
#////////////////////////////////////////////////////////
fo=open('../../processed_data/sat/cxsxbcponlm/'+side+'X_'+str(nod_beam)+'_PA.sav','rb')
combined_images_PA=pickle.load(fo)
for h in xrange(n_images):
# wrote in python, works for integer pivot coords JMS
# rotating in the correct direction? JMS
data[h,:,:]=rot(data[h,:,:],combined_images_PA[h], (x_cen, y_cen))
#median combine and save
sub_mask_2d=sub_mask.reshape(Y_DIM,X_DIM)
combined_median+=np.median(data,axis=0)*(sub_mask_2d.astype(int)) #only save the subtraction region, not the optimization region
save_filename='../../processed_data/sat/PCA/'+side+'X_'+str(nod_beam)+'/median_annular_'+str(n_PCA)+'.fits'
fits.writeto(save_filename,combined_median)