Calculate pi using monte-Carlo simulation with logical vector

I want to know how to model the script for calculating pi using Monte-Carlo simulation with using logical vectors

I already know the method using for/if, but does not know the method with logical vector

Please let me know how to do it

the below script is for the method using for/if

clear
clc

inside = 0;
nmax = 10000;

for n = 1:nmax
    x = rand;
    y = rand;

      x1=x-0.5;
      y1=y-0.5;

      if sqrt(x1^2+y1^2) <= 0.5
          plot(x1,y1,'b.');
          inside = inside + 1;
      else
          plot(x1,y1,'r.');
      end

      if ( mod(n,1000) == 0 )
          pi = 4 * inside / n;
          fprintf('%8.4f\n',pi);
      end

      hold on;
  end
  hold off;

pi = 4 * inside / nmax;

fprintf('%8.4f\n',pi);

Answer 1

[KSSV]

nmax = 10000;
x = rand(nmax,1);
y = rand(nmax,1);
x1=x-0.5;
y1=y-0.5;
r = sqrt(x1.^2+y1.^2) ;
% get logicals 
inside = r<=0.5 ;
outside = r>0.5 ;
% plot 
plot(x1(inside),y1(inside),'b.');
hold on
plot(x1(outside),y1(outside),'r.');
% get pi value 
thepi = 4*sum(inside)/nmax ;  
fprintf('%8.4f\n',thepi)

Answer 2

[David Contreras]

This might be a little faster by making all random points X and Y on a single function call.

nmax = 10000;
%Make x and y positions for all points
points = rand(nmax,2);
r=0.5;
%Translate to the origin
P1 = points-r;

%Check which points are insisde
inside = P1(:,1).^2+P1(:,2).^2 <= r.^2;

%Separate points in two sets, inside and outisde
IN = points(inside,:);
OUT = points(not(inside),:);

%Calculate PI
PI = 4*mean(inside);

%Plot blue inside pionts and redo outside points
plot(IN(:,1),IN(:,2),'b.',OUT(:,1),OUT(:,2),'r.')
title(['\pi = ', num2str(PI)])
axis([0 1 0 1], "equal")

Answer 3

[Fuat Yilmaz]

hi can you make a animation for this ?:)

[Rajan Prasad]

Try this for simulation using frame capture

clc;
clear;
%---------% starts from here__________________________
a=char({'\pi'});
n=(0:10:1000)*100;
n(1)=100;

for i=1:length(n)
np=n(i);
x=rand(np,1);
y=rand(np,1);
dis=x.^2+y.^2;
%----------Points separation---------------
in_p = dis<=1;
out_p=dis>1;
%---------------Points plot------------------
plot(x(in_p),y(in_p),'.r');
hold on;
plot(x(out_p),y(out_p),'.b');
%---------------Estimating pi----------------
tpi(i)=4*sum(in_p)/np;
str1=sprintf('n=%d,%s =%.5f',np,a,tpi(i));
title(str1,'FontName','Times New Roman');
clear x y dis in_p out_p

drawnow;

frame = getframe(gcf);
% im(i)=frame;
im2{i} = frame2im(frame);
clf;

end
filename = 'montecarlo.gif'; % Specify the output file name
for i = 1:length(n)
    [A1,map] = rgb2ind(im2{i},256);
    if i == 1
        imwrite(A1,map,filename,'gif','LoopCount',Inf,'DelayTime',0.4);
    else
        imwrite(A1,map,filename,'gif','WriteMode','append','DelayTime',0.4);
    end
end