%%Attempt to solve a multiple scattering problem with a TRIANGULAR LATTICE

%General Options
movie=2; %If movie=1, a .avi file is created
intensedouble=1; %multiply intensity on right side
yoffset=0; %Move offcenter=1
posneg=1; %1=peaks/troughs 2=weak/strong
%Angular Momentum value %Paramaters for crystal
nmax=2; %filling factor
nvals=[-nmax:nmax];
a=.1; %radius of cylinder (m)
pho_scat=7.67; pho_air=1.29*10^-3; %density of steel/air (g/cm^3
g_i=pho_scat/pho_air; %density ratio
cl_scat=6010; cl_air=340; %long. sound steel/vel. in air (m/s)
symmetric=1; h_i=cl_scat/cl_air; %long.sound vel. ratio

%User enters index of refraction
nind=input('enter index of refraction:');

if nind==-.7
f=.47; %Filling Fraction
lat_a=sqrt(2*pi*a^2/(sqrt(3)*f)); %Lattice Constant
xo=6*lat_a; %First x value
lambda=1.54*lat_a; %Wavelength
kwav=2*pi/lambda; %Wavevector
elseif nind==-1
f=.906;
lat_a=sqrt(2*pi*a^2/(sqrt(3)*f));
xo=.5*lat_a;
lambda=2.74*lat_a;
kwav=2*pi/lambda;
end

%Set up for the cylinders----source is at rx=0,ry=0 -----lattice constant a
%This is a triangular lattice so that every other column is offset by a/2
%I is number of columns J is the number of rows
%Total number of cylinders=floor(I/2)*J+ceil((I-1)/2)*(J-1)
I=6; Imax=I; J=35;
N=ceil(I/2)*J+ceil((I-1)/2)*(J-1);

%Values for the columns
index=(1:N); col1=ones(J,1); col2=zeros(J-1,1);
subcols=cat(1,col1,col2);
rx=xo-sqrt(3)/2*lat_a+(sqrt(3)/2)*lat_a*(2*ceil(index/(2*J-1))'-repmat(subcols,I/2,1));
%This will add an extra column to make it symmetric about the middle
if symmetric==1
rx=cat(1,rx,(I+1)*sqrt(3)/2*lat_a+(xo-sqrt(3)/2*lat_a)*col1);
end

%Values for the Rows;
row1=(lat_a)*(-floor(J/2):floor(J/2)); row2=row1(1:J-1)+lat_a/2;
subrows=cat(1,row1',row2');
ry=repmat(subrows,I/2,1);
%Add extra column y values if symmetric about the middle
if symmetric==1
ry=cat(1,ry,row1');
end

%Move the whole array up one notch to set it off from zero
if yoffset==1
ry=ry+lat_a/2;
end

%If the extra column has been added N will be different, update anyway
[N,meaningless]=size(rx);

%Boundaries for Field
xright=ceil(max(rx)+10*lat_a);
ytop=ceil(max(ry)+2*lat_a);
ybot=floor(min(ry)-2*lat_a);

%The Matrix will have Columns------ N*(2*nmax+1)
% Rows--------- N*(2*nmax+1)
num_columns=N*(2*nmax+1);
j=[1:num_columns];
k=[1:num_columns];

%Index each column by l and each row by n
l_lr=repmat(nvals,1,N); l_ud=l_lr'; n_ud=l_ud;
n=ceil(j/(2*nmax+1))';
[J,I]=meshgrid(n,n); [l_ind,n_ind]=meshgrid(l_lr,l_ud);
l_minus_n=l_ind-n_ind; del_i_j=I~=J;

%Arguments of the bessel function
ka=kwav.*a.*ones(num_columns,1);
kah=ka/h_i;
gh=g_i*h_i*ones(num_columns,1); %Assumes that all cylinders are the same

ri=sqrt(rx(n).^2+ry(n).^2); %Get Magnitude of ri
phi_ri=atan2(ry(n),rx(n)); %Get Angle of ri
ri_rj=sqrt((rx(I)-rx(J)).^2+(ry(I)-ry(J)).^2); %Calculate Mag Differences
phi_ri_rj_temp=atan2(del_i_j.*(ry(I)-ry(J)),(rx(I)-rx(J))); %Get angles
phi_ri_rj=zeros(num_columns); %Create array for phi vals
phi_ri_rj(find(del_i_j==1))=phi_ri_rj_temp(find(del_i_j==1)); %Keep i!=j

%Here are the coefficients for the matrix multiplication to solve
% i i N nmax i,j j i
%gamma A - sum sum G A = T
% n n j,j~=i l=-nmax l,n l nr
Gamma_i_n=(besselh(l_ud,ka).*.5.*(besselj(l_ud-1,kah)-besselj(l_ud+1,kah))-...
gh.*.5.*(besselh(l_ud-1,ka)-besselh(l_ud+1,ka)).*besselj(l_ud,kah))./...
(gh.*.5.*(besselj(l_ud-1,ka)-besselj(l_ud+1,ka)).*besselj(l_ud,kah)-...
besselj(l_ud,ka).*.5.*(besselj(l_ud-1,kah)-besselj(l_ud+1,kah)));

Gamma_i_n_mat=diag(Gamma_i_n);

T_i_n=besselh(-n_ud,kwav*ri).*exp(-i.*n_ud.*phi_ri);

Gijln_temp=besselh(l_minus_n,kwav.*ri_rj).*exp(i.*l_minus_n.*phi_ri_rj);
Gijln=zeros(num_columns);
Gijln(find(del_i_j==1))=Gijln_temp(find(del_i_j==1)); %Keep i!=j

%%Solve for the Coeeficients Alj
Ain=(Gamma_i_n_mat-Gijln)^-1*T_i_n;

clear('T_i_n','Gamma_i_n_mat','Gamma_i_n','Gijln_temp','Gijln','del_i_j','phi_ri_rj',...
'phi_ri_rj_temp','J','K','j','k');

%%Assuming I didn't screw up big time

revx=[-1:0.02:xright]; revy=[ybot:0.02:ytop];
maxrx=max(revx); maxry=max(revy);
minrx=min(revx); minry=min(revy);

[revX,revY]=meshgrid(revx,revy);
rev=(sqrt(revX.^2+revY.^2));
pho_source_r=i*pi*besselh(0,kwav.*rev);

%Create the 3 dimensional array to get this done. Summing Ani terms
% i designates num of cyliner n designates order of hankel function
[length,width]=size(revX);

%Use for loop this time because computer can't handle the memory storage
term_sum=zeros(size(revX));
inside_cyls=[];

for in=1: num_columns

if mod(in,2*nmax+1)==1
r_ri=sqrt((revX-rx(n(in))).^2+(revY-ry(n(in))).^2);
phi_ri=zeros(size(r_ri));
phi_ri=atan2((revY-ry(n(in))),(revX-rx(n(in))));
%Don't care about values inside cyls
inside_cyls=cat(1,inside_cyls,find(r_ri <=a));
outside_cyls=find(r_ri >a);
phi_ri(outside_cyls)=atan2((revY(outside_cyls)-ry(n(in))),...
(revX(outside_cyls)-rx(n(in))));

end

term_sum(outside_cyls)=term_sum(outside_cyls)+...
i*pi.*Ain(in).*besselh(l_lr(in),kwav*r_ri(outside_cyls)).*...
exp(i.*l_lr(in).*phi_ri(outside_cyls));
end

pho_r=pho_source_r+term_sum;
pho_r(inside_cyls)=-.5;

%For pretty picture purposes---make length x width x 3 true color image
if posneg==1
inside_cyls=repmat(inside_cyls,[1 1 3]);
if intensedouble==1
pho_r(find(revX > (max(rx)-a)))=...
6*pho_r(find(revX > (max(rx)-a)));
end
pho_r_scaled=(real(pho_r)-min(real(pho_r(:))))/(max(real(pho_r(:)))-min(real(pho_r(:))));
pho_r3_scaled=repmat(pho_r_scaled,[1 1 3]);
pho_r3_scaled(inside_cyls(:,:,1))=1;
pho_r3_scaled(inside_cyls(:,:,2))=0;
pho_r3_scaled(inside_cyls(:,:,3))=1;
else
inside_cyls=repmat(inside_cyls,[1 1 3]);
if intensedouble==1
pho_r(find(revX > (Imax+1)*sqrt(3)/2*lat_a+xo+a))=...
6*pho_r(find(revX > (Imax+1)*sqrt(3)/2*lat_a+xo+a));
end
pho_r_scaled=abs(real(pho_r))/(max(abs(real(pho_r(:)))));
pho_r3_scaled=repmat(pho_r_scaled,[1 1 3]);
pho_r3_scaled(inside_cyls(:,:,1))=1;
pho_r3_scaled(inside_cyls(:,:,2))=0;
pho_r3_scaled(inside_cyls(:,:,3))=1;
end

filename=['C:\Documents and Settings\Lance\Desktop\School\Qual\Square_Lat_Space_N_',num2str(nmax),...
'_r_',num2str(a),'_a_'];
filename=[filename,num2str(lat_a),'_f_',num2str(f),'_xo_',num2str(xo),'_k_'];
filename=[filename,num2str(kwav),'.tif'];

imname=['C:\Documents and Settings\Lance\Desktop\School\Qual\im_MST_Square_Lattice_N_',...
num2str(nmax),'_r_',num2str(a)];
imname=[imname,'_a_',num2str(lat_a),'_f_',num2str(f),'_xo_',num2str(xo)];
imname=[imname,'_k_',num2str(kwav),'.tif'];

newfig=figure;
imagesc([minrx,maxrx],[minry,maxry],real(pho_r3_scaled));
text(0,1.05,['\lambda=',num2str(lambda),'m'],'units','normalized');
text(0.25,1.03,['r_{o}=',num2str(a),'m'],'units','normalized');
text(0.5,1.03,['a_{lat}=',num2str(lat_a),'m'],'units','normalized');
text(0.75,1.05,['N=',num2str(nmax)],'units','normalized');

imwrite(abs(pho_r3_scaled),imname,'tif');
saveas(newfig,filename,'tif');
pause;
%Attempt at a movie?
%Attempt at a movie?i

if movie==1
avistring=['/nfs/slac/g/ki/ki08/lsst/CPanalysis/Phononic_Crys/','MST_Tri_Lat_lat_a',num2str(lat_a),'_f_',num2str(f),...
'_lambda_',num2str(lambda),'.avi'];
aviobj=avifile(avistring);

tmax=80; omega=.65;
set(gcf,'doublebuffer','on');
for t=0:tmax
pho_movie=exp(-i*omega*t).*pho_r;
pho_movie(inside_cyls)=-.5;
if intensedouble==1
pho_movie(find(revX > (Imax+1)*sqrt(3)/2*lat_a+xo+a))=...
6*pho_movie(find(revX > (Imax+1)*sqrt(3)/2*lat_a+xo+a));
end
imagesc([minrx,maxrx],[minry,maxry],real(pho_movie),[-15 15]);colormap(gray);
if movie==1
frame=getframe(gca);
for frames=1:10
aviobj=addframe(aviobj,frame);
end
end
pause(0.1);

aviobj=close(aviobj);

end

end