maximum entropy calculation engine

The 1984 Skilling and Bryan paper is available online [1] through the SAO/NASA ADS Astronomy Abstract Service:

[1]	http://adsabs.harvard.edu/abs/1984MNRAS.211..111S

sbmaxent

Entropy maximization routine as described in the article J Skilling and RK Bryan; MNRAS 211 (1984) 111 - 124. (“MNRAS”: “Monthly Notices of the Royal Astronomical Society”)

license:Copyright (c) 2013, UChicago Argonne, LLC license:This file is distributed subject to a Software License Agreement found in the file LICENSE that is included with this distribution.

References:

1. J Skilling and RK Bryan; MON NOT R ASTR SOC 211 (1984) 111 - 124.
2. JA Potton, GJ Daniell, and BD Rainford; Proc. Workshop Neutron Scattering Data Analysis, Rutherford Appleton Laboratory, UK, 1986; ed. MW Johnson, IOP Conference Series 81 (1986) 81 - 86, Institute of Physics, Bristol, UK.
3. ID Culverwell and GP Clarke; Ibid. 87 - 96.
4. JA Potton, GK Daniell, & BD Rainford, J APPL CRYST 21 (1988) 663 - 668.
5. JA Potton, GJ Daniell, & BD Rainford, J APPL CRYST 21 (1988) 891 - 897.

SB_MaxEnt.sbmaxent.ChiNow(ax, c1, c2, s1, s2)

Returns tuple:(ChiNow computation of w, beta)

SB_MaxEnt.sbmaxent.ChoSol(a, b)

ChoSol: ? chop the solution vectors ?

Returns:new vector beta

SB_MaxEnt.sbmaxent.Dist(s2, beta)

measure the distance of this possible solution

SB_MaxEnt.sbmaxent.EllipsoidVolume(r, aspect=1.0)

Volume of an ellipsoid with diameters: \(2r\times2r\times2r\beta\)

• \(\beta\): aspect ratio

SB_MaxEnt.sbmaxent.G_term(q, r, V, rhosq)

Calculates the response matrix \(G(Q,r)\)

Parameters:

• q (double) – \(Q\)
• r (double) – \(r\)
• rhosq (double) – \(|\Delta\rho|^2\), the scattering contrast

Returns double:

G(Q,r)

class SB_MaxEnt.sbmaxent.MaxEnt(data, sigma, base, IterMax, image_to_data, data_to_image, G)

manage the iterative method described by Skilling and Bryan

MaxEnt_iteration()

one iteration of the MaxEnt algorithm

chi_squared()

returns \(\sum{z^2}\)

compute_beta()

beta vector: ... meaning ...

standardized_residuals()

returns vector \(\vec{z}\) of standardized_residuals

where:

• \(\vec{z} = (\vec{y} - \hat{\vec{y}}) / \vec{\sigma}\)
• \(\vec{y}\): measured data
• \(\hat{\vec{y}} = opus(\vec{f}, G)\)
• \(\vec{\sigma}\): estimated uncertainties of \(\vec{y}\)

sum_f()

returns \(\sum_i{f_i}\)

exception SB_MaxEnt.sbmaxent.MaxEntException

Any exception from this module

SB_MaxEnt.sbmaxent.MaxEntMove(fSum, blank, chisq, chizer, c1, c2, s1, s2)

move beta one step closer towards the solution

SB_MaxEnt.sbmaxent.MaxEnt_SB(datum, sigma, base, IterMax, image_to_data, data_to_image, G, report=True)

do the complete Maximum Entropy algorithm of Skilling and Bryan

Parameters:

• datum[] (float) –
• sigma[] (float) –
• base[] (float) –
• IterMax (int) –
• image_to_data (obj) – opus function
• data_to_image (obj) – tropus function
• G (float[][]) – transformation matrix

Returns float[]:  

\(f(r) dr\)

SB_MaxEnt.sbmaxent.opus(image, G)

opus: transform solution-space -> data-space: [G]^tr * image

default definition, caller can use this definition or provide an alternative

Parameters:

• image (float[N]) – solution, ndarray of shape (N)
• G (float[M][N]) – transformation matrix, ndarray of shape (M,N)

Returns float[M]:  

calculated data, ndarray of shape (M)

SB_MaxEnt.sbmaxent.print_arr(text, a)

print the contents of an array to the console

SB_MaxEnt.sbmaxent.print_vec(text, a)

print the contents of a vector to the console

SB_MaxEnt.sbmaxent.readTextData(filename)

return q, I, dI from a 3-column text file

SB_MaxEnt.sbmaxent.test_ChiNow()

test routine for ChiNow()

test values obtained from C version of sizes program

SB_MaxEnt.sbmaxent.test_ChoSol()

test routine for ChoSol()

test values obtained from C version of sizes program

SB_MaxEnt.sbmaxent.test_Dist()

test routine for Dist()

test values obtained from C version of sizes program

SB_MaxEnt.sbmaxent.test_EllipsoidVolume()

test routine for EllipsoidVolume()

SB_MaxEnt.sbmaxent.test_G_term()

test routine for G_term()

test values are trivial checks comparison values computed from C code

SB_MaxEnt.sbmaxent.test_MaxEntMove()

test routine for MaxEntMove()

test values obtained from C version of sizes program

SB_MaxEnt.sbmaxent.test_opus_tropus()

test routine for Dist()

test values are trivial checks

SB_MaxEnt.sbmaxent.tropus(data, G)

tropus: transform data-space -> solution-space: [G] * data

default definition, caller can use this definition or provide an alternative

Parameters:

• data (float[M]) – observations, ndarray of shape (M)
• G (float[M][N]) – transformation matrix, ndarray of shape (M,N)

Returns float[N]:  

calculated image, ndarray of shape (N)