MATLAB: Can this be written in a much better way for fast computations

for loopparfor


coast=magic(14400)
di_max=100;
mx=14400;
my=14400;
for ix=1:mx
    for iy=1:my
        %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

        for dx=-di_max:di_max
            for dy=-di_max:di_max
                jx=ix+dx;
                jy=iy+dy;
                if((jx>=1) && (jx<=mx) && (jy>=1) && (jy<=my))
                    dd=sqrt(dx^2+dy^2);
                    coast(jx,jy) = min([coast(jx,jy),dd]);
                end
            end
        end
        %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    end
end

Best Answer

The code below will do what you are asking without needing a loop.

coast=magic(14400);
di_max=100;
mx=14400;
my=14400;
[ix dx] = meshgrid(1:mx, -di_max:di_max);
[iy dy] = meshgrid(1:my, -di_max:di_max);
jx = ix+dx;
jy = iy+dy;
dd= sqrt(dx.^2+dy.^2);
mask = ((jx(:)>=1) & (jx(:)<=mx) & (jy(:)>=1) & (jy(:)<=my));
idx = sub2ind(size(coast), jx(mask), jy(mask));
coast(idx) = min(coast(idx),dd(mask));

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Here is how i see solution for this question

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[X,Y] = meshgrid(x,y);              % create grid
    
R = 1;                              % circle radius
plot(lat,long,'.r')                 % plot data
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MATLAB: Bad result in 2D Transient Heat Conduction Problem Using BTCS Finite Difference Method implicitly

%2-D Transient Heat Conduction With No Heat Generation [FDM][BTCS]
clc;
clear all;
%% Variable Declaration
n = 21;                 %number of nodes
L = 1;                  %length of domain
W = 1;                  %width of domain
alpha = 1e-4;           %thermal diffusivity (m^2/s)
m =(n-2)*(n-2);         %variable used to construct penta diagonal matrix
sm = sqrt(m);
dx = L/(n-1);           %delta x domain 
dy = W/(n-1);           %delta y domain
x = linspace(0,L,n);    %linearly spaced vectors x direction
y = linspace(0,W,n);    %linearly spaced vectors y direction
[X,Y]=meshgrid(x,y);
Tin = 200;              %internal temperature
T  = ones(m,1)* Tin;    %initilizing Space
Ta = zeros(n,n);
A  = zeros(m,m);         
Ax = zeros(m,1);
B  = zeros(sm,sm);
dt = 0.1;                %time step
tmax = 500;              %total Time steps (s)
t = 0 : dt : tmax;
r = alpha * dt /(dx^2);  %for stability, must be 0.5 or less
Tt = 100;                %Top Wall

Tb = 100;                %Bottom Wall

Tl = 100;                %Left Wall

Tr = 100;                %Right Wall

%% Boundry Conditions
Ta(1,1:n) = Tt;         %Top Wall
Ta(n,1:n) = Tb;         %Bottom Wall
Ta(1:n,1) = Tl;         %Left Wall
Ta(1:n,n) = Tr;         %Right Wall
%% Setup Matrix
for ix = 1 : 1 : m
    
    for jx =1 : 1 : m
        
        if (ix == jx)
                A(ix,jx) = (1 + 4*r); 
                
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        elseif ( (ix == jx - 1) && ( ix ~= sm*round(ix/sm) ) )
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                A(ix,jx) = -r;
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                A(ix,jx) = 0;
        end
    end
end
 
for iy = 1 : 1 : sm
    
    for jy = 1 : 1 : sm
        
        if (iy == 1) && (jy == 1)
            B(iy,jy) = r * (Tl + Tt);
            
        elseif (iy == 1) && (jy == sm)
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            B(iy,jy) = r * Tl;
        else
            B(iy,jy) = 0;
        end
                    
    end
end
 Bx = reshape(B,[],1);  %Convert matrix to vector
 
%% Solution
for l = 2 : length(t)   %time steps
    
     Xx = ( T + Bx );
     
           Ax = A \ Xx;
           
                 T( 1 : m ) = Ax( 1 : m );
                       fprintf('Time t=%d\n',l-1);
    
end
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for i = 2 : 1 : n-1
    
    for j = 2 : 1 :n-1
        
        Ta(i,j) = Tx ( i-1 , j-1 );
        
    end
    
end
%% Plot
   contourf(X,Y,Ta,50,'edgecolor','none');
        h = colorbar;
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        colormap jet
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            yyaxis right
            ylabel(['Right (Tr)= ',num2str(Tr),'°C'])

Best Answer

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MATLAB: How to calculate distance between a point in a given radius inside a geographic coordinate grid

MATLAB: Bad result in 2D Transient Heat Conduction Problem Using BTCS Finite Difference Method implicitly

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