Script for making simulations

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%Simulation of generic function (e.g. peaks) and S(Q,w) models

%========= S(Q,w) model simulations ========================

%simulate on sqw objects using S(Q,w) model for the physics

%Use sqw_eval for S(Q,w) models

%Here my_slice is an sqw object. We have a Matlab function on our path called my_sqw_model.m, and there are
%some parameters associated with this model, [1,2,3,4].
%The form (1st line) of my_sqw_model.m should be:
% function weight=my_sqw_model(h,k,l,e,pars)
% the pars are the vector of input parameters we used above
% An example of an S(Q,w) model is given in the Horace "functions" directory, in the Matlab m-file
% "demo_FM_spinwaves_2dSlice_sqw.m

%Simulating a dnd and an sqw that are notionally the same gives different results, since for the sqw all of the contributing
%detector pixels are simulated and then re-summed, whereas for the dnd just single points at the centre of bins are used
%So if the intensity varies across a bin the dnd simulation will not capture this

%========== Generic function simulation ==================

%Use func_eval for generic functions

%Here the function mgauss is included in the Horace distribution (in the functions directory). It only works on 1-dimensional cuts, and simulates multiple
%gaussians. The syntax is the same as for the sqw_eval function, so the vector argument is a list of input parameters for the function
%In the case of mgauss, they are [amplitude1, centre1, width1, amplitude2, centre2, width2, ...., amplitudeM, centreM, widthM]
%for M gaussians

Plotting dispersion


rlp=[0,0,0; 1/2,0,0; 1/2,1/2,0; 1/2,1/2,1/2; 0,0,0; 0,0,1/2;]; 

%The dispersion function has different (but similar) form to cross section functions
% The inputs are h,k,l and parameters; the outputs are the energy (i.e. dispersion) and spectral weight at that point

%Here is an example dispersion function
function [wdisp1,s_yy]=sr122_disp(qh,qk,ql,p)
% SrFe2As2 cross-section, from Tobyfit

%  Spin waves for FeAs, from Ewings et al., PRB 78 
%  Lattice parameters as for orthorhombic lattice i.e. a ~= b ~5.6Ang
% 	p(1)	S_eff
% 	p(2)	SK_ab
% 	p(3)	SK_c
%    If ircoss=201:
% 	p(4)	SJ_1a
% 	p(5)	SJ_1b
% 	p(6)	SJ_2
%    If icross=202
% 	p(4)	S(2J2+J_1a)
% 	p(5)	S(2J2-J_1b)
% 	p(6)	SJ1a-SJ1b
% 	p(7)	SJ_c
% 	p(8)	inverse lifetime gamma (= energy half-width)
% 	p(19)	0 if S(Q,w) as theory, =1 if multiply S(Q,w) by energy transfer
% 	p(20)	0 if twinned; 1 if twin #1 ; -1 if twin #2

% If icross=207
% As cross-section 204, but deal with J1a, J1b, J2 directly.

s_eff = p(1);
sj_1a = p(4);
sj_1b = p(5);
sj_2  = p(6);
sj_c  = p(7);
sjplus = sj_1a+(2.*sj_2);
sjminus = (2.*sj_2)-sj_1b;
sk_ab = 0.5.*(sqrt((sjplus+sj_c).^2 + 10.5625) - (sjplus+sj_c));
sk_c  = sk_ab;
gam   = p(8);

qsqr = (qh*arlu(1)).^2 + (qk*arlu(2)).^2 + (ql*arlu(3)).^2;


%First twin:
a_q = 2.*( sj_1b.*(cos(pi.*qk)-1) + sj_1a + 2.*sj_2 + sj_c ) + (3.*sk_ab+sk_c);
d_q = 2.*( sj_1a.*cos(pi.*qh) + 2.*sj_2.*cos(pi.*qh).*cos(pi.*qk) + sj_c.*cos(pi.*ql) );
c_anis = sk_ab-sk_c;

wdisp1 = sqrt(abs(a_q.^2-(d_q+c_anis).^2));
%wdisp2 = sqrt(abs(a_q.^2-(d_q-c_anis).^2));

s_yy = s_eff.*((a_q-d_q-c_anis)./wdisp1);