def VminusdIvar(Islicedata, Vslicedata, dispersion, alpha, f, B, col):
"""NAME: VminusdIvar
PURPOSE: Returns noise of data
INPUTS: Islicedata - The array of information for stokes I at a horizontal slice
Vslicedata - The array of information for stokes V at a horizontal slice (is divided by I)
dispersion - The number of angstroms/wavelength pixel
alpha - Constant alpha returned by function Alpha above
f - The value of the filling factor
B - The value of the LOS B field n iron core region
col - The col of the full disk image, from 0 to 2047
OUTPUTS: sigma - The noise to be plugged into the Generalized Posterior
EXAMPLE:
"""
Iflux=np.array(v9s.LoadedDataSpectrum(Islicedata=Islicedata, slicedata=Islicedata, xpos=col)) #loads in array of stokes I intensities over wavelength for a spatial pixel
Vflux=np.array(v9s.LoadedDataSpectrum(Islicedata=Islicedata, slicedata=Vslicedata, xpos=col)) #loads in array of stokes V intensities over wavelength for a spatial pixel
Vcontinuum=Vflux[97:115] #picks out the wavelengths at which there is continuum
Icontinuum=Iflux[97:115] #picks out the wavelengths at which there is continuum
deriv=np.gradient(Icontinuum)/dispersion #the wavelength derivative of Intensity, calculated by chain rule: dI/dpixel * dpixel/dAngstrom
dIvar=np.var(deriv) #variance of the derivative
Vvar=np.var(Vcontinuum) #variance in V
cov=np.cov((Vcontinuum,deriv))[0][1] #the covariance is a matrix, the terms on the opposite diagonal are the cross terms
#var=Vvar+(alpha*f*B)**2.*dIvar-2.*(alpha*f*B)*cov #based on Var(X+Y)=Var(X)+Var(Y)-2*Cov(X,Y) - for Var(dI) the constants come out twice
var=Vvar #simplest case
sigma=np.sqrt(var) #noise/st. dev. is sqrt(variance)
return sigma #in Asensios Sec. 3.1 on the left side middle paragraph: "variance of terms inside the parentheses"
def A1A2A3(Islicedata, Vslicedata, f, B, col, dispersion, alpha, ironloc):
"""NAME: A1A2A3
PURPOSE: Returns A1, A2, A3, N defined on page 3 of Asensios
INPUTS: Islicedata - The array of information for stokes I at a horizontal slice
Vslicedata - The array of information for stokes V at a horizontal slice (is divided by I)
col - The col of the full disk image, from 0 to 2047
f - The value of the filling factor
B - The value of the LOS B field
dispersion - The number of angstroms/wavelength pixel
alpha - Constant alpha returned by function Alpha above
ironloc - Index of iron absorption core
OUTPUTS: A1 - A1 is the sum of squared stokes V values in iron core region
A2 - A2 is the sum of stokes V * derivative of I in iron core region
A3 - A3 is the sum derivative of I squared in iron core region
N - N is the number of wavelength pixels around the core region included
EXAMPLE:
"""
Iflux=np.array(v9s.LoadedDataSpectrum(Islicedata=Islicedata, slicedata=Islicedata, xpos=col)) #loads in array of stokes I intensities over wavelength for a spatial pixel
Vflux=np.array(v9s.LoadedDataSpectrum(Islicedata=Islicedata, slicedata=Vslicedata, xpos=col)) #loads in array of stokes V intensities over wavelength for a spatial pixel
ironloc=np.int(ironloc) #the iron absorption core loc for the single pixel
core=np.arange(ironloc-2, ironloc+3,1) #the indices of the region of the absorption line in the spectrum
Icore=Iflux[core] #selects out the region of iron absorption in the spectrum
Vcore=Vflux[core] #selects out the region of iron absorption in the spectrum
gradI=np.gradient(Icore)/dispersion #dI/dlambda
sigma=VminusdIvar(Islicedata=Islicedata,Vslicedata=Vslicedata,dispersion=dispersion,alpha=alpha,f=f,B=B,col=col) #calculate noise value
A1=np.ndarray.sum(Vcore**2.)/(2.*sigma**2.) #as defined on page 3 of Asensios Ramos
A2=np.ndarray.sum(Vcore*gradI)/(2.*sigma**2.) #as defined on page 3 of Asensios Ramos, but I keep alpha outside it
A3=np.ndarray.sum(gradI**2.)/(2.*sigma**2.) #as defined on page 3 of Asensios Ramos, but I keep alpha outside it
N=len(core) #number of wavelength pixels included in summation
return A1, A2, A3, N
def PixelIndices(slicedata, array, row, col, line='Iron'):
"""NAME: PixelIndices
PURPOSE: Assigns the value to the element of the array of index locations for a pixel.
INPUTS: slicedata - The array of intensities for a horizontal slice of the sun.
array - The array which will hold the index information.
row - The row which is being operated upon.
col - The column which is being operated upon.
line - The absorption line to look at: Calcium or Oxygen
OUTPUTS: N/A - Only reassigns the value of the array element.
EXAMPLE:
In [6]: datapath='k4v9s160517t213238_oid114635206372132_cleaned'
disk=fits.getdata('/Users/jhamer/Research/Output/k4v9s160517t213238/FullDiskPlots /k4v9s160517t213238_oid114635206372132_cleanedI80fulldisk.fits')
stokesslice=v9s.SingleStokes(datapath, 'I', slicenumber=400)
indexmap=np.zeros((len(disk), len(disk)))
CL.PixelIndices(stokesslice, indexmap, 400, 700)
polyminloc=CL.PolyMinLoc(flux, xs)
In [7]: indexmap[400][700]
Out[7]: 61.789999999999999
"""
flux = v9s.LoadedDataSpectrum(Islicedata=slicedata,
slicedata=slicedata,
xpos=col)
if line == 'Iron':
xs = IronCoreRegion(flux)
elif line == 'Oxygen1':
xs = Oxygen1CoreRegion(flux)
elif line == 'Oxygen2':
xs = Oxygen2CoreRegion(flux)
loc = PolyMinLoc(flux, xs)
array[row][col] = loc