error "Inner matrix dimensiion must Agree"
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Please I'm trying to plot graphs and varying parameter Gr and t which is temperature. But i keep getting an error "Inner matrix dimensiion must Agree"
>> Gr = [5:5:25];
>> t = [0.2:0.2:1];
>> H = 1;
>> n = 1;
>> N = 5;
>> Pr = 0.72;
>> S = 0.2;
% This is my code
>> U = -Gr*(t.^2/2 + Pr*(N-n)*(t.^4/24 - t.^2/4) + (Pr*(N-n))^2*(t.^6/720 - t.^4/48 + 5*t.^2)...
+ (Pr*(N-n))^3*(t.^8/40320 - t.^6/1440 + 5*t.^4/576 - 61*t.^2/1440) + (Pr*(N-n))^4*(t.^10/36288000 - t.^8/80640 + 5*t.^6/17280 -61*t.^4/17280 + 1385*t.^2/806400)...
- 1/2 + Pr*(N-n)*5/24 - (Pr*(N-n))^2*61/720 + (Pr*(N-n))^3*277/8064 - (Pr*(N-n)^4*(0.014))...
-(S + H - n)*Gr*(t.^4/24 * Pr*(N-n)*(t.^6/720 - t.^4/48) + (Pr*(N - n))^2*(t.^8/40320 - t.^6/1440 + 5*t.^4/576)...
+ (Pr*(N-n))^3*(t.^10/32688000 - t.^8/80640 + 5*t.^6/17280 + 61*t.^4/17280) + (Pr*(N-n))^4*(t.^12/479001600 - t.^10/7257600 + 5*t.^8/967680 - 61*t.^6/518400 + 1385*t.^4/967680)...
- t.^2/4 + Pr*(N-n)*5*t.^2/48 - (Pr*(N-n))^2*61*t.^2/1440 + (Pr*(N-n))^3*277*t.^2/16128 - (Pr*(N-n))^4*(7*t.^2/1000))...
-(1/24 + Pr*(N-n)*(1/720 -1/48) + (Pr*(N-n))^2*(1/40320 - 1/1440 + 5/576) + (Pr*(N-n))^3*(1/36288000 - 1/80640 + 5/17280 - 61/17280) + (Pr*(N-n))^4*(1/479001600 - 1/7257600 + 5/967680 - 61/518400 + 1385/967680)...)
-1/4 + Pr*(N-n)*5/48 - (Pr*(N-n))^2*61/1440 + (Pr*(N-n))^3*277/16128-(Pr*(N-n))^4*(7/100)))
Error using *
Inner matrix dimensions must agree.
>>
>>
Accepted Answer
You're trying to do matrix multiplication with arrays of incompatible size. You probably mean to do .* elementwise multiplication.
Also, those exponentiations are probably all wrong as well. For example:
1^2/3
1^(2/3)
EDIT: also, this improperly-continued line means that the trailing ) isn't being used. Since the parentheses are balanced, that means that another parentheses is either added or missing somewhere. It's impossible to know where.
+ A^3*(1/36288000 - 1/80640 + 5/17280 - 61/17280) + A^4*(1/479001600 - 1/7257600 + 5/967680 - 61/518400 + 1385/967680)...)
10 Comments
Maduka
on 17 Dec 2022
Try this. I make no guarantees that I haven't missed something. EDIT: I've gone back and checked this against the paper as given. I found a few more mistakes, but the expression as printed is still ambiguous.
Gr = 5:5:25; % vectors are orthogonal, allowing implicit expansion to 2D
t = (0.2:0.2:1).';
H = 1;
n = 1;
N = 5;
Pr = 0.72;
S = 0.2;
% pull out common terms
B = Pr*(N-n);
% pull out term blocks
% note that the terms of TB1 begin with an imbalanced (Pr*(N-n)^k, so it's unclear what that means
% i'm going to assume that means (Pr*(N-n))^k, not Pr*(N-n)^k
TB1 = t.^2/2 ...
+ B*(t.^4/24 - t.^2/4) ...
+ B^2*(t.^6/720 - t.^4/48 + 5*t.^2/48)... % 5*t^2/48
+ B^3*(t.^8/40320 - t.^6/1440 + 5*t.^4/576 - 61*t.^2/1440) ...
+ B^4*(t.^10/36288000 - t.^8/80640 + 5*t.^6/17280 - 61*t.^4/17280 + 1385*t.^2/806400) - 1/2 ...
+ B*5/24 ...
- B^2*61/720 ...
+ B^3*277/8064 ...
- B^4*(0.014);
TB2 = t.^4/24 ... % + not *
+ B.*(t.^6/720 - t.^4/48) ...
+ B^2*(t.^8/40320 - t.^6/1440 + 5*t.^4/576)...
+ B^3*(t.^10/32688000 - t.^8/80640 + 5*t.^6/17280 - 61*t.^4/17280) ...
+ B^4*(t.^12/479001600 - t.^10/7257600 + 5*t.^8/967680 - 61*t.^6/518400 + 1385*t.^4/967680) - t.^2/4 ...
+ B*5*t.^2/48 ...
- B^2*61*t.^2/1440 ...
+ B^3*277*t.^2/16128 ...
- B^4*(7*t.^2/1000);
TB3 = 1/24 ...
+ B*(1/720 - 1/48) ...
+ B^2*(1/40320 - 1/1440 + 5/576) ...
+ B^3*(1/36288000 - 1/80640 + 5/17280 - 61/17280) ...
+ B^4*(1/479001600 - 1/7257600 + 5/967680 - 61/518400 + 1385/967680) - 1/4 ...
+ B*5/48 ...
- B^2*61/1440 ...
+ B^3*277/16128 ...
- B^4*7/100;
U = -Gr.*TB1 - (S + H - n)*Gr.*(TB2 - TB3); % elementwise multiply
% plot everything
figure
contourf(Gr,t,U)
colorbar
figure;
hp = plot(t,U,'-d');
lstr = cell(numel(Gr),1);
for k = 1:numel(Gr)
lstr{k} = sprintf('Gr = %d',Gr(k));
end
legend(hp,lstr,'location','southwest')
Obviously that doesn't look like the given plot, but I don't know what else to say. This is how I marked out the expression as I transcribed it:
Each blue term is a product of the form (Pr*(N-n))^p*(subexpression). I'm assuming that this pattern extends to the terms in TB1. Outside the three major terms marked in yellow, the expression is plainly U = -Gr.*TB1 - (S + H - n)*Gr.*(TB2 - TB3);
If I've missed more transcription errors, I don't know where they'd be. If the printed formula is incorrect, I wouldn't know.
Torsten
on 19 Dec 2022
Obviously, there are mistakes in the formula for U (e.g. missing or misplaced brackets).
So if you give us the correct U, we can replicate your graph.
I guess you can just plot it if that's the correct data.
Gr = 5:5:25; % vectors are orthogonal, allowing implicit expansion to 2D
t = (0:0.2:1).';
U = [0 0 0 0 0;
-0.1015 -0.203 -0.3045 -0.406 -0.5075;
-0.4167 -0.8334 -1.2501 -1.6667 -2.0834;
-0.9861 -1.9722 -2.9583 -3.9444 -4.9305;
-1.8796 -3.7592 -5.6388 -7.5184 -9.398;
-3.2068 -6.4137 -9.6205 -12.8274 -16.0342];
hp = plot(t,U,'-d');
lstr = cell(numel(Gr),1);
for k = 1:numel(Gr)
lstr{k} = sprintf('Gr = %d',Gr(k));
end
legend(hp,lstr,'location','southwest')
Maduka
on 20 Dec 2022
DGM
on 20 Dec 2022
hp = plot(t,U,'-d') % solid line with diamond markers
hp = plot(t,U,'-') % solid line with no markers
Maduka
on 23 Dec 2022
Maduka
on 23 Dec 2022
If you just want to smooth the curve and still have it go through the original points, you can do some sort of spline interpolation.
N = [5:5:10 20:30:80];
torig = (0:0.2:1).'; % original t
U = [0 0 0 0 0;
-0.203 -0.2045 -0.2094 -0.2248 -0.2411;
-0.8334 -0.8742 -0.9593 -1.2573 -1.6266;
-1.9722 -2.1899 -2.6840 -4.737 -7.9306;
-3.7592 -4.51 -6.3789 -16.1119 -35.5583;
-6.4136 -8.4597 -14.1636 -52.4222 -148.671];
% interpolate U using a finer t
t = (0:0.05:1).';
U = interp1(torig,U,t,'spline'); % use spline interpolation to smooth the curve
hp = plot(t,U,'-');
lstr = cell(numel(N),1);
title('Effect of Radiation on Velocity')
for k = 1:numel(N)
lstr{k} = sprintf('N = %d',N(k));
end
legend(hp,lstr,'location','southwest')
More Answers (1)
GR = [5:5:25];
T = [0.2:0.2:1];
H = 1;
n = 1;
N = 5;
Pr = 0.72;
S = 0.2;
for i = 1:numel(GR)
Gr = GR(i);
for j = 1: numel(T)
t = T(j);
U(i,j) = -Gr*(t.^2/2 + Pr*(N-n)*(t.^4/24 - t.^2/4) + (Pr*(N-n))^2*(t.^6/720 - t.^4/48 + 5*t.^2)...
+ (Pr*(N-n))^3*(t.^8/40320 - t.^6/1440 + 5*t.^4/576 - 61*t.^2/1440) + (Pr*(N-n))^4*(t.^10/36288000 - t.^8/80640 + 5*t.^6/17280 -61*t.^4/17280 + 1385*t.^2/806400)...
- 1/2 + Pr*(N-n)*5/24 - (Pr*(N-n))^2*61/720 + (Pr*(N-n))^3*277/8064 - (Pr*(N-n)^4*(0.014))...
-(S + H - n)*Gr*(t.^4/24 * Pr*(N-n)*(t.^6/720 - t.^4/48) + (Pr*(N - n))^2*(t.^8/40320 - t.^6/1440 + 5*t.^4/576)...
+ (Pr*(N-n))^3*(t.^10/32688000 - t.^8/80640 + 5*t.^6/17280 + 61*t.^4/17280) + (Pr*(N-n))^4*(t.^12/479001600 - t.^10/7257600 + 5*t.^8/967680 - 61*t.^6/518400 + 1385*t.^4/967680)...
- t.^2/4 + Pr*(N-n)*5*t.^2/48 - (Pr*(N-n))^2*61*t.^2/1440 + (Pr*(N-n))^3*277*t.^2/16128 - (Pr*(N-n))^4*(7*t.^2/1000))...
-(1/24 + Pr*(N-n)*(1/720 -1/48) + (Pr*(N-n))^2*(1/40320 - 1/1440 + 5/576) + (Pr*(N-n))^3*(1/36288000 - 1/80640 + 5/17280 - 61/17280) + (Pr*(N-n))^4*(1/479001600 - 1/7257600 + 5/967680 - 61/518400 + 1385/967680)...)
-1/4 + Pr*(N-n)*5/48 - (Pr*(N-n))^2*61/1440 + (Pr*(N-n))^3*277/16128-(Pr*(N-n))^4*(7/100)));
end
end
contourf(GR,T,U)
colorbar
3 Comments
- (Pr*(N-n))^4*(0.014)
instead of
- (Pr*(N-n)^4*(0.014))
The printed formula is full of imbalanced parentheses, so that's just the way I read it.
EDIT: also, the way U is addressed is transposed with respect to how it's plotted. It's easy to miss since the vectors have the same length.
Maduka
on 18 Dec 2022
Maduka
on 18 Dec 2022
@DGM please can you help structure the code, this is the nature of graph I’m expecting
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