How to solve this equation with two variables in one equation ?

A = 1;
B = 1;
for n=0.0:0.1:1.0
    for  c = 0.0:0.1:1.0
        c0  = 1.13e-4;
        w   = -A*(c-c0)^2*(n^4-3*n^2+2*n)+B.*(c-1)^2*n^2;
    end
end

Answer 1

[Adam Danz]

Loop through index values rather than a vector of values.

Store each iteration in w(n,c) and pre-allocate w with NaNs.

A = 1;
B = 1;
c0  = 1.13e-4;

% Vectors to loop through
nVec=0.0:0.1:1.0;  
cVec = 0.0:0.1:1.0;

w = nan(numel(nVec),numel(cVec)); %pre-allocate with NaNs

% Loop through each element of nVec
for n=1:numel(nVec)
    % Loop through each element of cVec
    for  c = 1:numel(cVec)
        w(n,c) = -A*(cVec(c)-c0)^2*(nVec(n)^4-3*nVec(n)^2+2*nVec(n))+B.*(cVec(c)-1)^2*nVec(n)^2;
    end
end

w(n,c) is the result for inputs nVec(n) and cVec(c)

[Robert101]

Thanks man. It works. However, if i use that code and try to get contour plot i don't get like that

in my program.Apparently everything looks good in the code.

KB  = 8.617e-5; 
T   = 1276;
Efv = 3.14;
A = 1;
B = 1;
c0  = 1.13e-4;

% Vectors to loop through

nVec = 0.0:0.1:1.0;  
cVec = 0.0:0.1:1.0;

% h = n.^4-2*n.^2+1;
w    = nan(numel(nVec),numel(cVec)); %pre-allocate with NaNs
f    = nan(numel(nVec),numel(cVec)); %pre-allocate with NaNs

% Loop through each element of nVec
for n=1:numel(nVec)
    % Loop through each element of cVec
    for  c = 1:numel(cVec)
        w(n,c) = -A*(cVec(c)-c0)^2*(nVec(n)^4-3*nVec(n)^2+2*nVec(n))+B.*(cVec(c)-1)^2*nVec(n)^2;
        f(n,c) = (nVec(n)^4-2*nVec(n)^2+1)*cVec(c)*Efv/(KB*T)+cVec(c)*log(cVec(c))+(1.-cVec(c)).*log(1.-cVec(c));
    end
end

E = f+w;
contour(cVec,nVec,E)

[Adam Danz]

Two quick things I noticed off the bat.

1. If you want a filled contour, use contourf(). You're using contour() which only draws the contour lines. https://www.mathworks.com/help/matlab/ref/contourf.html
2. The first column of f are all NaNs. This is because you're computing log(0) when n=1 and that produces a -inf which ends up being NaN.

[Robert101]

Thanks man for the swift reply.

i got it the NaN. But still, i think, countour is supposed to be the way it is shown in the attachment.

In current code it seems far away from that one. And the values are also different here.

Apparently everything is being computed in the right way.

[Adam Danz]

Check out the documentation for controur() and controurf() and check out the examples provided. I already provided the link to controurf(). Here's the link to contour().

https://www.mathworks.com/help/matlab/ref/contour.html

You might notice that controur() only plots controur lines (no fill). controurf() does the filling.

Also check out the properties for contour objects. There is a 'fill' option that can be used with either function.

https://www.mathworks.com/help/matlab/ref/matlab.graphics.chart.primitive.contour-properties.html

Here's the result of using contourf() along with some other additions.

contourf(cVec,nVec,E,20)  %20 contour lines
axis equal
colormap('jet')
colorbar()

If you want something smoother and without the black contour lines,

contourf(cVec,nVec,E,200, 'LineColor','None')

The axes roughly span from 0 to 1 as in your picture. The missing values along the x axis are likely due to the NaNs in the data (I haven't looked deeper but that's my hunch).

More importantly, the color bar values have a much larger range than in your image. That might be a hint at where to start troublshooting your algorithm if you expect the plot to look like the example you shared.

[Robert101]

Thanks man. You are great

[Adam Danz]

Glad I could help and learn along with ya!