UNSCRAM - DECONVOLUTE MULTIPLES
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INTRODUCTION
 
UNSCRAM serves a similar purpose to AFSCALE, except that it processes the
wavelength-overlapped spots. For each wavelength overlap, it uses the
different film-film ratios between intensity measurements on succesive
films at different wavelengths to calculate (`unscramble') the individual
single-wavelength components. The program accepts a generate file
containing intensities and a set of Victoreen coefficients (eg. as produced
by AFSCALE) describing the scale factors as a function of wavelength,
between films in a pack. The output of the program is in the same format as
that from AFSCALE. The program was written by M.Z. Papiz and I.J. Clifton,
Daresbury Laboratory.
 
List of sections:
 
   Running the Program
   Using UNSCRAM
   Input and Output Files
   Method
 
RUNNING THE PROGRAM
 
Use the command 'laue unscram'
 
The program runs in an interactive manner and prompts the user for input as
needed.
 
 
USING UNSCRAM
 
Generally, running UNSCRAM is similar to just using the 'Define' and
'Output} options in AFSCALE - however there is no main menu in UNSCRAM.
 
 * UNSCRAM has intensity and sigma rejection criteria that select spots to
   go into the unscrambling process.
 
 * There are also intensity, lambda and sigma rejection criteria which
   apply to the unscrambled values on output.
 
 * Different classes of spots (all spots, singlets, doublets etc.) can be
   output in separate batches.
 
 * UNSCRAM applies the same final scalings as AFSCALE (see its
   documentation for details) - LP, paper absorption, overall factor.
 
 * UNSCRAM can input Victoreen coefficients from the same sources as
   AFSCALE (.vc file, default settings etc.) but there is no way of doing
   refinement.
 
 * UNSCRAM does symmetry R-factor analyses similar to AFSCALE's.
 
 
 
INPUT AND OUTPUT FILES
 
The input files are as follows:
 
a) The .ge1/.ge2 pair of files
 
b) A victoreen coefficients file
 
The output file is:
 
a) A scaled intensities output file (type = .afout)
 
   This is a card image file with one record per reflection (scaled but
   unmerged, and unsorted data) containing the items: h k l lambda theta
   intensity sig(intensity) x and y in format (3I5,2F10.5,2I10,2F8.3).
 
 
 
METHOD
 
UNSCRAM solves a wavelength-overlap spot of order 'n' as follows: Assume
for simplicity the spot is measured properly on all six films (this is
unlikely to happen in practice) and let the wavelengths of the individual
components be lambda_1, lambda_2, ... lambda_n. Then from the given
Victoreen coefficients, scaling factors s_2,lambda_1, s_3,lambda_1, ...
s_6,lambda_1, s_2,lambda_2, ... s_6,lambda_n can be evaluated.
(s_i,lambda_j scales the A film down to the i'th film at lambda_j. The
problem is to calculate the 'n' components I_lambda_1 ... I_lambda_n
(intensities on the A film). On each film, each measured intensity is the
sum of its single-wavelength components, i.e.
 
    I_a = I_lambda_1 + ... + I_lambda_n

    I_b = s_2,lambda_1*I_lambda_1 + ... + s_2,lambda_n*I_lambda_n
    .   = .
    .   = .
    .   = .
    I_f = s_6,lambda_1*I_lambda_1 + ... + s_6,lambda_n*I_lambda_n
 
This is a set of (six) linear simultaneous equations in the 'n' unknowns
I_lambda_i and if n<=6 (Strictly 'n' should be equal to the `rank' of the
equations) a least-squares solution can be calculated. In practice, there
are only 'm' good measurements, m<=6, and unscrambling is usually only
worth while for doublets and perhaps triplets.
 
See S. Brandt, `Statistical and Computational Methods in Data Analysis',
chapter 9, paragraph 2. The program finds the least-squares solution of:
 
   A.I_lambda + Iobs = 0
 
by solving the (1/sigma**2 weighted) `normal equations'
 
     A(T).G_y.A.I_lambda + A(T).G_y.A.Iobs = 0
 
where Acontains (-s_(i,j)) and G_yis a weighting matrix:
 
   G_y = diag(1/sigma_1**2,...,1/sigma_m**2).
 
A(T)indicates the transpose of A. The normal equation is solved by matrix
inversion as the matrices involved are small.}