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+math/decompose_affine_matrix.m
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% DECOMPOSE_AFFINE_MATRIX calculate rotation, shear, asymmetry and scale from affine matrix
%
% [scale, asymmetry, rotation, shear] = decompose_affine_matrix(affine_mat)
%
% Inputs:
% ** affine_mat affine matrix = A1*A2*A3*A4
%
% returns:
% ++scale A1 = [scale, 0; 0, scale]
% ++asymmetry A2 = [1+asymmetry/2,0; 0,1-asymmetry/2]
% ++rotation A3 = [cosd(rotation), sind(rotation); -sind(rotation), cosd(rotation)]
% ++shear A4 = [1,0;tand(shear),1];
%
%*-----------------------------------------------------------------------*
%|                                                                       |
%|  Except where otherwise noted, this work is licensed under a          |
%|  Creative Commons Attribution-NonCommercial-ShareAlike 4.0            |
%|  International (CC BY-NC-SA 4.0) license.                             |
%|                                                                       |
%|  Copyright (c) 2017 by Paul Scherrer Institute (http://www.psi.ch)    |
%|                                                                       |
%|      Author: CXS group, PSI  |
%*-----------------------------------------------------------------------*
% You may use this code with the following provisions:
%
% If the code is fully or partially redistributed, or rewritten in another
% computing language this notice should be included in the redistribution.
%
% If this code, or subfunctions or parts of it, is used for research in a
% publication or if it is fully or partially rewritten for another
% computing language the authors and institution should be acknowledged
% in written form in the publication: “Data processing was carried out
% using the “cSAXS matlab package” developed by the CXS group,
% Paul Scherrer Institut, Switzerland.”
% Variations on the latter text can be incorporated upon discussion with
% the CXS group if needed to more specifically reflect the use of the package
% for the published work.
%
% A publication that focuses on describing features, or parameters, that
% are already existing in the code should be first discussed with the
% authors.
%
% This code and subroutines are part of a continuous development, they
% are provided “as they are” without guarantees or liability on part
% of PSI or the authors. It is the user responsibility to ensure its
% proper use and the correctness of the results.
function [scale, asymmetry, rotation, shear] = decompose_affine_matrix(affine_mat)
err_fun = @(x)(affine_mat - x(1)*[1+x(2)/2,0; 0,1-x(2)/2]*[cosd(x(3)), sind(x(3)); -sind(x(3)), cosd(x(3))] * [1,0;tand(x(4)),1]);
options = optimoptions('lsqnonlin','Display','off');
xopt = lsqnonlin( err_fun, [1,0,0,0],[],[],options);
scale = xopt(1);
asymmetry = xopt(2);
rotation = xopt(3);
shear = xopt(4);
end