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example2_unbounded.m
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example2_unbounded.m
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% Copyright Mohamed Nasser 2017
% Please cite this MATLAB functions as:
%
% When citing this software please mention the URL of the master repository
% (https://github.com/mmsnasser/CircularMap), and the paper
% M.M.S. Nasser,Fast Computation of the Circular Map, Computational Methods
% and Function Theory, 15 (2015) 187-223.
%
%
% PLEASE note that this toolbox contains the files:
% zfmm2dpart.m
% fmm2d_r2012a.mexw32
% fmm2d_r2012a.mexw64
% pthreadGC2-w32.dll
% pthreadGC2-w64.dll
% From the Toolbox:
% L. G REENGARD AND Z. G IMBUTAS , FMMLIB2D: A MATLAB toolbox for
% fast multipole method in two dimensions, Version 1.2, 2012.
% http://www.cims.nyu.edu/cmcl/fmm2dlib/fmm2dlib.html
% PLEASE also cite the FMMLIB2D toolbox.
clear
clc
%%
n = 2^10
ratio = 0.2;
t = (0:2*pi/n:2*pi-2*pi/n).';
%%
Mat_coef = [
0.0 2.0 0.1
0.3+0.35i 0.1 0.5
-0.3+0.35i 0.1 0.5
0.0+0.20i 0.4 0.1
0.0+0.40i 0.4 0.1
0.0+0.65i 0.6 0.1
];
cent = Mat_coef(:,1);
radx = Mat_coef(:,2);
rady = Mat_coef(:,3);
m = length(cent)
%%
for k=1:m
et(1+(k-1)*n:k*n,1) = cent(k)+0.5.*(+radx(k).*cos(t)-i*rady(k).*sin(t));
etp(1+(k-1)*n:k*n,1) = 0.5.*(-radx(k).*sin(t)-i*rady(k).*cos(t));
end
%%
[zet,zetp,cntd,rad]=circmap(et,etp,inf,n);
%%
%%
[xh,yh]=meshgrid(-2:0.001:2,-1.5:0.1:1.5);
zeh=xh+i.*yh;
[mh,nh] = size(zeh);
for k=1:m
zho=(zeh-cent(k))./0.5;
zeh((real(zho)./radx(k)).^2+(imag(zho)./rady(k)).^2<=1)=NaN+i*NaN;
end
z_ind = 1;
for k=1:mh
for j=1:nh
if (abs(zeh(k,j))>=0)
zehv(z_ind)=zeh(k,j);
z_ind = z_ind+1;
end
end
end
wehv = (zehv-cent(1)).*(fcau(et,etp,zet./(et-cent(1)),zehv,n,1));
z_ind = 1;
for k=1:mh
for j=1:nh
if (abs(zeh(k,j))>=0)
weh(k,j)=wehv(z_ind);
z_ind = z_ind+1;
else
weh(k,j) = NaN+i*NaN;
end
end
end
%%
[xv,yv]=meshgrid(-2:0.1:2,-1.5:0.001:1.5);
zev=xv+i.*yv;
[mv,nv] = size(zev);
for k=1:m
zvo=(zev-cent(k))./0.5;
zev((real(zvo)./radx(k)).^2+(imag(zvo)./rady(k)).^2<=1)=NaN+i*NaN;
end
z_ind = 1;
for k=1:mv
for j=1:nv
if (abs(zev(k,j))>=0)
zevv(z_ind)=zev(k,j);
z_ind = z_ind+1;
end
end
end
wevv = (zevv-cent(1)).*(fcau(et,etp,zet./(et-cent(1)),zevv,n,1));
z_ind = 1;
for k=1:mv
for j=1:nv
if (abs(zev(k,j))>=0)
wev(k,j)=wevv(z_ind);
z_ind = z_ind+1;
else
wev(k,j) = NaN+i*NaN;
end
end
end
%%
%%
figure;
hold on
box on
for k=1:mh
plot(real(zeh(k,:)),imag(zeh(k,:)),'r')
end
for k=1:nv
plot(real(zev(:,k)),imag(zev(:,k)),'b')
end
for k=1:m
c_cr = et((k-1)*n+1:k*n,1); c_cr(n+1) = c_cr(1);
plot(real(c_cr),imag(c_cr),'k')
end
axis equal
axis off
set(gca,'LooseInset',get(gca,'TightInset'))
%%
figure;
hold on
box on
for k=1:mh
plot(real(weh(k,:)),imag(weh(k,:)),'r')
end
for k=1:nv
plot(real(wev(:,k)),imag(wev(:,k)),'b')
end
for k=1:m
c_cr = zet((k-1)*n+1:k*n,1); c_cr(n+1) = c_cr(1);
plot(real(c_cr),imag(c_cr),'k')
end
axis equal
axis off
set(gca,'LooseInset',get(gca,'TightInset'))
%%
%%
[xhi,yhi]=meshgrid(-2:0.001:2,-1.5:0.1:1.5);
wehi=xhi+i.*yhi;
[mhi,nhi] = size(wehi);
for k=1:m
wehi(abs(wehi-cntd(k))<=rad(k)) = NaN+i*NaN;
end
z_ind = 1;
for k=1:mhi
for j=1:nhi
if (abs(wehi(k,j))>=0)
wehiv(z_ind)=wehi(k,j);
z_ind = z_ind+1;
end
end
end
zehvi = (wehiv-cntd(1)).*(fcau(zet,zetp,et./(zet-cntd(1)),wehiv,n,1));
z_ind = 1;
for k=1:mhi
for j=1:nhi
if (abs(wehi(k,j))>=0)
zehi(k,j)=zehvi(z_ind);
z_ind = z_ind+1;
else
zehi(k,j) = NaN+i*NaN;
end
end
end
%%
[xvi,yvi]=meshgrid(-2:0.1:2,-1.5:0.001:1.5);
wevi=xvi+i.*yvi;
[mvi,nvi] = size(wevi);
for k=1:m
wevi(abs(wevi-cntd(k))<=rad(k)) = NaN+i*NaN;
end
z_ind = 1;
for k=1:mvi
for j=1:nvi
if (abs(wevi(k,j))>=0)
weviv(z_ind)=wevi(k,j);
z_ind = z_ind+1;
end
end
end
zevvi = (weviv-cntd(1)).*(fcau(zet,zetp,et./(zet-cntd(1)),weviv,n,1));
z_ind = 1;
for k=1:mvi
for j=1:nvi
if (abs(wevi(k,j))>=0)
zevi(k,j)=zevvi(z_ind);
z_ind = z_ind+1;
else
zevi(k,j) = NaN+i*NaN;
end
end
end
%%
%%
figure;
hold on
box on
for k=1:mhi
plot(real(wehi(k,:)),imag(wehi(k,:)),'r')
end
for k=1:nvi
plot(real(wevi(:,k)),imag(wevi(:,k)),'b')
end
for k=1:m
c_cr = zet((k-1)*n+1:k*n,1); c_cr(n+1) = c_cr(1);
plot(real(c_cr),imag(c_cr),'k')
end
axis equal
axis off
set(gca,'LooseInset',get(gca,'TightInset'))
%%
figure;
hold on
box on
for k=1:mhi
plot(real(zehi(k,:)),imag(zehi(k,:)),'r')
end
for k=1:nvi
plot(real(zevi(:,k)),imag(zevi(:,k)),'b')
end
for k=1:m
c_cr = et((k-1)*n+1:k*n,1); c_cr(n+1) = c_cr(1);
plot(real(c_cr),imag(c_cr),'k')
end
axis equal
axis off
set(gca,'LooseInset',get(gca,'TightInset'))
%%