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