Source code :: CalcIonProjections

#!/usr/bin/env python 
# -*- coding: utf-8 -*-

"""
           calculate nonegative projections of the spectral basis to the 
           measured spectra. Projection basis was found as nonnegative sparse 
           decomposition of about 3500 spectra to 11 components. 

           In the first part of the algoritm is remove stray light and  made a corrections of the instrumental function
           It is very important because highly subpixel precision is necassary. 
           First correction is made as a blind deconvolution  of shape and then a zero and first 
           order of the wavelength polynome are made. Than a projections even with realible estimate of the 
           statistical errors are made. 

           In the second part of the script is Integrated data analyzis of the radiation. 
           Data from spectrometer with low time but very high wavelength resolution van be combinated
           with higt time, but low wavelength resoltion from othe diagnostics as photodiodes, cameras etc..


           Advantages: extremly high sensitivity, can be identified even weak lines lost between 
           strong surrounding lines of other ions. Immune agains line overburning. 
           (Relatively) fast caculaton. It can never missidentified one of the strong lines. 
           Disadvantage: In  rare cases there can happend something interesting which 
           can not be described by these limited number of components, 
           one kind of event is here:7307,7960;9298,9156;10097
           and also probably a new iont from unknow element can occure 
            9664,9665,9670,9839,9906,10131,10136. And finally a molecular spectrum 9504
            On the other hand, without this algoritm it would by imposible to find that 
            there is something interesting in this discharges. 



	Autor: Tomas Odstrcil
	date:12.12.2012

"""



from numpy import *
import matplotlib 
matplotlib.rcParams['backend'] = 'Agg'

from matplotlib.pyplot import *
from  SpectrometerControl  import *
from  scipy.linalg import  norm, inv,qr,pinv
from scipy.special import erfinv, erf
from scipy.stats.mstats import mquantiles
from scikits.sparse.cholmod import cholesky, analyze, cholesky_AAt,CholmodError
from scipy.signal import fftconvolve,convolve,gaussian,order_filter
from numpy import linalg
import time
from scipy import sparse
from scipy.sparse import *
from scipy.optimize import minimize_scalar,nnls,fmin_powell,fmin_cg,fmin_bfgs,fmin_ncg
from scipy.fftpack import fft,ifft
from fftshift import fftshift
from pygolem_lite.modules import save_adv,load_adv
from scipy.sparse import block_diag
from pygolem_lite import saveconst
from scipy.interpolate import interp1d



names =  ('HI','OI','OII', 'OIII', 'HeI', 'CII', 'CIII', 'NI','NII', 'NIII','Mystery1', 'OIV' )
styles = ('b-','r-','r--', 'r-.' , 'g-' ,  'k--', 'k-.' ,  'y-','y--', 'y-.' , 'c-'     , 'm:'      )

def Shift(x,s,win,lam):
    #místo přímého posuvu udělám inverzi posuvu zpět, je to stabilnější

    
    s-= 0.5  # systematický posuv, aby se to shodovalo s lineární interpolací
    s*= -1  #invezní posuv
    win = (win/2)*2

    diag_data = ones((2,win))
    diag_data[1,:] *=s-floor(s)
    diag_data[0,:] *=floor(s)+1-s
    S = spdiags(diag_data, (-floor(s),-floor(s)-1), win, win,format='csr')
 
    f0 = zeros(win)
    f0[win/2] = 1
    factor = cholesky_AAt(S.T,beta = lam)
    g = squeeze(factor(S.T*f0))    
 
    Sx = fftconvolve(x,g,mode = 'same')

    return Sx


def GapsFilling(signal,win = 100, lam = 1e-1):  #BUG loadovat to z pygolema
    """
    ===============================  Gaps Filling Filter 0.1 =====================
     reconstruct the corrupted data (data with nans)  by tikhonov-philips regularization with regulariting by laplace operator. And return smoothed retrofit
    Reconstruction is based on the invertation of the identical operator with zeros at the lines corresponding to the mising signal.
     due to memory and speed limitation the reconstruction is done on the overalaping intervals with width "win"
     signal - long data vector
     win - width of the recosntruction interval - it mas be much bigger than the gaps width
     lam - regularization parameter, dependes on the noise in data

    Autor: Tomas Odstrcil 2012
    """


    from scikits.sparse.cholmod import cholesky, analyze,cholesky_AAt
    from scipy.sparse import spdiags, eye


    n = len(signal)
    # signal extension -- avoid boundary effects
    n_ext = (n/win+3)*win
    ext_signal = ones(n_ext)*nan
    side = (n_ext-n)/2
    ext_signal[side:-side-n%2] = signal
    ext_signal[:side+1] = median(signal[~isnan(signal)][:win/2])
    ext_signal[-side-1:] = median(signal[~isnan(signal)][-win/2:])


    intervals = arange(0,n_ext, win/2)


    ind_nan = isnan(ext_signal)
    ext_signal[ind_nan] = 0


    recon = copy(ext_signal)

    diag_data = ones((2,win))
    diag_data[1,:]*=-1
    D = spdiags(diag_data, (0,1), win, win,format='csr')
    DD = D.T*D
    I = eye(win,win,format='csc')
    Factor = cholesky_AAt(DD, 1./lam)

    for i in range(len(intervals)-2):
	gaps = spdiags( int_(ind_nan[intervals[i]:intervals[i+2]]),0, win, win,format='csc')   # use overlapping intervals !!!
	Factor.update_inplace(gaps/sqrt(lam), subtract=True) # speed up trick
	g = Factor(ext_signal[intervals[i]:intervals[i+2]]/lam)
	Factor.update_inplace(gaps/sqrt(lam), subtract=False)  # speed up trick
	recon[(intervals[i]+intervals[i+1])/2:(intervals[i+1]+intervals[i+2])/2] = g[len(g)/4:-len(g)/4,0]

    #plot(recon,'r')
    #plot(ext_signal,'b')

    #savefig('gapsfill.png')
    #clf()
    chi2 = sum((ext_signal-recon)[~ind_nan]**2)/n

    recon = recon[(n_ext-n)/2:-(n_ext-n)/2]
    return recon, chi2


def Resample(tvec,vec,n,t_min = None,t_max = None,left = 0,right = 0):

    if t_min == None:
	t_min = amin(tvec)
    if t_max == None:
	t_max = amax(tvec) 
	
    std = (t_max-t_min)/(tvec[1]-tvec[0])/n/2
    std = max(std,1)
    gauss_win = gaussian(std*3,std)
    gauss_win/= sum(gauss_win)
    vec_smooth = fftconvolve(vec,gauss_win, mode = 'same')

    tvec_new = linspace(t_min,t_max,n)
    vec_new  = interp(tvec_new,tvec, vec_smooth, left=left, right=right)

    return tvec_new,vec_new


def downsample(data,  sampleInteg = False, downsample = 1):
    downsampled  = reshape(data, (-1,downsample), order = 'C')
    
    if sampleInteg:
	downsampled = sum(downsampled, axis = 1)/downsample
    else:
	downsampled = downsampled[:,0]

    return downsampled

def upsample_smooth(data, win,lam, sampleInteg = False, upsample = 1):
 
    win = 2*(win/2)
    n = len(data)
    npix = upsample*win
    n_ext = (n/win+1)*win
    
    ext_signal = empty(n_ext)
    ext_signal[(n_ext-n)/2:-(n_ext-n)/2] = data
    ext_signal[:(n_ext-n)/2+1] = 0#median(data[:win/2]) 
    ext_signal[-(n_ext-n)/2-1:] = 0#median(data[win/2:])
    

    retrofit =  zeros(n_ext*upsample)    


    #solve the upsamling problem only for short interval win
    diag_data = ones((2,npix))
    diag_data[1,:]*=-1
    D = spdiags(diag_data, (0,1), npix, npix,format='csr')
    D = D.T*D
    DD = D.T*D
  
    if sampleInteg:
	ReductMatrix =  kron(eye(win,win),ones((1,upsample))/upsample,format='csr')
    else:
	ReductMatrix =  kron(eye(win,win),eye(1,upsample),format='csr')

    T = ReductMatrix   
    f = ext_signal

    
    f0 =zeros(win)
    f0[win/2] = 1
    

    factor = cholesky(T.T*T+lam*DD)
    g = squeeze(factor(T.T*f0))
   

    #apply the single point solution g on the whole data vector 
    
    T_Tf = zeros((n_ext,upsample))
    T_Tf[:,0] = f    

    T_Tf  = squeeze(reshape(T_Tf, (-1,1), order = 'C'))

    if win*upsample > 100: #choose the faster way
	upsampled = fftconvolve(T_Tf,g,mode = 'same')
    else:
	upsampled = convolve(T_Tf,g,mode = 'same')

    retrofit[:-1] = upsampled[1:] #I don't know why but this must by done. 
    
    retrofit = reshape(retrofit, (-1,upsample), order = 'C')
   
    if sampleInteg:
	retrofit = mean(retrofit, axis = 1)
    else:
	retrofit = retrofit[:,0]
    
    upsampled = upsampled[(n_ext-n)/2*upsample:-(n_ext-n)/2*upsample]
    retrofit = retrofit[(n_ext-n)/2:-(n_ext-n)/2]
    
    #print 'error ',sum(abs(data-retrofit))

    return upsampled,retrofit
 
 

  



def removeStrayLight(data):
    #experimentálně ověřeno, lepší algoritmus mě nenapadl
    m = len(data)
    win = 101
    quantile = 0.1
    shift  = 1.4*(10*erfinv((quantile-0.5)*2))

    domain = ones(win)
    rank = int(win*quantile)
    background = order_filter(data-shift,domain,rank)

    
    gauss = exp(-linspace(-1,1,win)**2)
    gauss-= min(gauss)
    gauss/= sum(gauss)

    background = fftconvolve(background,gauss , mode = 'same')

    data-= background*0.8
    return data

import pyfftw

def deconv_opt(spectra,retrofit,overburned,lam,ker0=None):
    n = len(spectra)
    normal = fftconvolve(overburned, ones(5),mode='same') < 1./5

    fr = fft(retrofit[normal], n)/sqrt(n)
    fs = fft( spectra[normal], n)/sqrt(n)
    
    ker_full  = pyfftw.n_byte_align_empty(n, 16,dtype=complex)
    Fker_full = pyfftw.n_byte_align_empty(n, 16,dtype=complex)

    fft_forward = pyfftw.FFTW(ker_full,Fker_full, direction='FFTW_FORWARD', flags=['FFTW_ESTIMATE','FFTW_DESTROY_INPUT'])
    doF = sum(normal)*5.
    
    def f(ker):
	ker_full[:]=0
	
	ker_full[n/2-(len(ker))/2+1:n/2+(len(ker))/2+1] = ker
	ker_full[:] = fftshift(ker_full)
        fft_forward()

	chi2 = norm(fs-fr*Fker_full)**2/doF
        
	return chi2+norm(ker)*lam
    
    
    if ker0 == None:
	L = 10
	ker0 = zeros(L)
	ker0[L/2-1] = 1
    else:
	L = len(ker0)
	
    #t = time.time()
    #y = fmin_powell(f, ker0, xtol=1e-5,ftol=1e-5,maxfun=1e6,disp=True)
    y= fmin_bfgs(f, ker0, gtol=1e-1,maxiter=1e6,disp=False)

    #print time.time()-t
    #exit()
    ker_full = zeros(n)    
    
    ker_full[n/2-L/2:n/2+(L+1)/2] = real(y)
   
    return real(y),ker_full


def optim_fun(noise,spectra,retrofit,overburned,lim):

    dec = deconv(noise,spectra,retrofit,overburned,lim)

    chi2 = norm(spectra-fftconvolve(retrofit,dec,mode='same'))**2/size(spectra)/5
    return exp(abs(log(chi2)))




def CalcProjections(spectrometr,shot, plasma_start,plasma_end):

    shot_number = 100000
    #BUG!!!!
	
    tvec = shot.time_stamps/1000.
    
    wavelength, intensities = shot.getData()


    MaxIntensity = 32000  # hodnota po korekci nelinearity detektoru!
    if shot_number < 8500:
	MaxIntensity = 18200
    overburned = intensities > MaxIntensity
    if shot_number < 7625: #koukali jsme se skrze sklo
	overburned[wavelength < 330,:] = True
    if shot_number > 10300: #koukali jsme se skrze sklo
	overburned[wavelength < 330,:] = True
    overburned[spectrometr.black_pixels,:] = False

    if spectrometr.hotPixels != []:
	overburned[spectrometr.hotPixels,:] = True

    data = load('SpectraComponents2.npz')  #the most critical part, weeks of my work
    components = data['components']
    
    

    intensities-=  mean((intensities[spectrometr.black_pixels,:]))


    
    n_features    = size(components,1)
    n_components  = size(components,0)
    n_measurement = size(intensities,1)
    upsample = 10


    projection = zeros((n_measurement, n_components))
    projectionError = zeros((n_measurement, n_components))

    dataSTD = shot.readoutNoiseRMS 


    #detect plasma
    plasma = nanmax(intensities, axis = 0) > 10*dataSTD   #překročení této hranice šumem je sttaisticky vellmi nepravděpodobné
    
    
    save_adv('./data/plasma', tvec,plasma)

    if not any(plasma):
	return True
    
    imin = amin(where(plasma)[0])-1
    imax = amax(where(plasma)[0])
    #print plasma
    #print 'tvec',imin,imax, isfinite(plasma_start), isfinite(plasma_end)
    #if isfinite(plasma_start) and isfinite(plasma_end):
	##print 'tvec ', (arange(n_measurement)-imin)*(plasma_end-plasma_start)/(imax-imin)+plasma_start
	#tvec = (arange(n_measurement)-imin)*(plasma_end-plasma_start)/(imax-imin)+plasma_start+shot.integ_time/2000
    
    
    
    plasma[1:]  = plasma[1:] | plasma[:-1]
    plasma[:-1] = plasma[1:] | plasma[:-1]

    


    ##preprocess 
    for i in where(plasma)[0]:
	intensities[:,i] = removeStrayLight(intensities[:,i])

    intensities /= dataSTD   #normalize by staistical error

    components_reshaped  = reshape(components.T, (1,-1), order = 'F')[0,:]
    upsampled, retrofit = upsample_smooth(components_reshaped, 30,1, sampleInteg = True, upsample = upsample)
    upsampled_components  = reshape(upsampled, (n_features*upsample,-1), order = 'F').T


    spect_lines  = sum(components,axis = 0) != 0   #TODO 60% je nulových => jde to tím urychlit
   
    
    def estimateResid(components ):

	resid = zeros(n_measurement)
	for j in where(plasma)[0]:
	    normalPx = ~overburned[:,j]
	    _,resid[j] = nnls(components[:,normalPx].T,intensities[normalPx,j])
	    
	chi2 = norm(resid)**2/(sum(plasma)*size(intensities,0))
	return chi2

	
    def shiftSpectra(components,(s1,s2)):
	n = size(components,1)
	shift_components = interp1d(linspace(s2,n-s2-1,n),components,
                    bounds_error=False,fill_value=0)(s1+arange(n))

	return shift_components
	


    def fitfun(params):
	shift_components = shiftSpectra(components_corr, params)
	chi2 = estimateResid(shift_components)
	#print chi2
	return chi2





    total_intens = sum( intensities[:,plasma], axis = 1)
    L = 10
    ker = zeros(L)
    ker[L/2-1] = 1
    ker_full = zeros(n_features)
    ker_full[n_features/2] = 1
    normalPx = sum(overburned ,1) == 0
    components_corr = zeros_like(components)
    print 'calc inst fun'
    for i in range(5):
	for j in range(n_components):
	    components_corr[j,:] = fftconvolve(components[j,:],ker_full,mode='same')
	proj, resid = nnls(components_corr[:,normalPx].T,total_intens[normalPx])
	retrofit = dot(proj.T,components).T

	ker,ker_full = deconv_opt(total_intens,retrofit,~normalPx,2,ker)
   
    t = time.time()
    par0 = [0,0]
    #print par0, [components_corr,]
    
    y = fmin_powell(fitfun,par0, xtol=1e-4,ftol=1e-3,maxfun=1e6,disp=False)

    components_corr = shiftSpectra(components_corr, y)

    proj, resid = nnls(components_corr[:,normalPx].T,total_intens[normalPx])
    #print resid**2/n_features/sum(plasma)
    print 'calc inst fun finished'
	
 
    components = components_corr
    components[components < 0] = 0



    difference = zeros(n_features)    
    chi2ion = zeros(n_components)
    resid = ones(n_measurement)*sqrt(n_features)

    q,r = qr(components.T,mode =  'economic')
    F = matrix(dot(inv(r),q.T))
    
    for j in where(plasma)[0]:
	normalPx = ~overburned[:,j]
	projection[j, :], resid[j] = nnls(components[:,normalPx].T, intensities[normalPx,j])
	
	#try to account error  nonstatistical errors in fit
	difference[normalPx]  = intensities[normalPx,j]-dot(components.T,projection[j, :])[normalPx]
	difference[~normalPx] = amax(difference[normalPx] )   #prostě tam bude velká chyba
	DataError = sqrt(difference**2+1)-(sqrt(2)-1)
	projectionError[j, :] = sqrt(diag(F*diag(DataError**2)*F.T))
	for i in range(n_components):
	    chi2ion[i] += norm(difference*(components[i,:]/(1e-3+sum(components,axis = 0))))**2/n_features
	    
	    
	#plot(wavelength, (dot(diag(projection[j, :]),components)).T,linewidth = 0.2)
	#plot(wavelength, intensities[:,j],'b-.')
	#plot(wavelength,dot(components.T,projection[j, :]), 'k')
	#plot(wavelength[:], intensities[:,j]-dot(components.T,projection[j, :]), 'r:' )   #ylim(-2, 100)
	#show()
    spectra = sum( intensities[:,plasma], axis = 1)
    retrofit = sum( dot(projection,components).T, axis = 1)
    chi2 = norm(spectra-retrofit)**2/n_features/sum(plasma)
    print 'standart chi2',chi2
    normalPx = sum(overburned ,1) == 0
    
    

    
     



 


    #calculate global charasteristics of the fit and spectra
    chi2 = sum(resid**2)/(n_measurement*n_features)

    print chi2, resid**2/n_features
    print chi2,chi2ion
    savetxt('./results/IonChi2'+'.txt',chi2ion)
    savetxt('./results/TimeChi2'+'.txt',resid**2/n_features)
    save('./results/TotalChi2',chi2)


    energy_constants  = zeros(n_components)

    for i in range(n_components):
	norm_comp = spectrometr.convertCountToPhotons(shot.wavelength,
				copy(components[i,:]),shot.integ_time)
	energy_constants[i] = sum(norm_comp)
    abs_calibration = loadtxt('absolute_calibration.txt')
    energy_constants *= abs_calibration


    
    


    
    rel_proj = copy(projection)
    rel_proj_err = copy(projectionError)
    projection*= energy_constants
    projectionError *= energy_constants
    
    P_total = sum(projection,1)
    P_total_error = sqrt(sum(projectionError**2,1))
    
    if isfinite(plasma_start) and isfinite(plasma_end):
	
	mean_tvec = sum(P_total*tvec)/sum(P_total)
	print mean_tvec
	print (plasma_start+plasma_end)/2
	tvec = tvec-mean_tvec+(plasma_start+plasma_end)/2-shot.integ_time/1e3/2
    
    
    save_adv('./data/TotalPower',tvec,P_total,data_err=P_total_error, tvec_err = 1e-3 )
    n_frames = (plasma_end-plasma_start)/(shot.integ_time/1000)
    saveconst('./HistoricalAnalysis/meanPower',sum(P_total[plasma])/n_frames)
    save_adv('./data/projection', tvec,rel_proj, data_err=rel_proj_err, tvec_err=1e-3 )
    save_adv('./data/intensities', tvec,intensities)
    save_adv('./data/components', wavelength,components)
    save_adv('./data/plasma', tvec,plasma)

    save('./data/energy_constants',energy_constants)