Why do I get wrong multiplication result?
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Dear Community members,
I am trying to implement this equation in Matlab:
Here is the code (I instead of A):
lambda = 0.01;
k = 2*pi/lambda;
N = 46;
M = 37;
dx = lambda/2;
dy = lambda/2;
teta=-pi/2:.01:pi/2;
phi =0:.01:pi;
F1 = zeros(length(teta),length(teta));
% Array
for m=1:M
for n=1:N
F1 = F1+I(m,n)*exp(1i*k*sin(teta).*(m*dx*cos(phi)+n*dy*sin(phi)));
end
end
% 10th value of phi
plot(teta*360/pi,F1(10,:))
The problem I experience is the wrong F1 matrix, where all the rows are the same, while it should vary because of different teta and phi:
Could you please explain what is wrong? I matrix is attached
Accepted Answer
1 vote
teta and phi are row vectors of the same length, so this expression:
exp(1i*k*sin(teta).*(m*dx*cos(phi)+n*dy*sin(phi)));
is also a row vector of that same length (because everything else in there is a scalar).
To demonstrate this fact:
lambda = 0.01;
k = 2*pi/lambda;
dx = lambda/2;
dy = lambda/2;
teta = -pi/2:0.01:pi/2;
phi = 0:0.01:pi;
m = 1;
n = 1;
temp = exp(1i*k*sin(teta).*(m*dx*cos(phi)+n*dy*sin(phi)));
size(teta)
ans = 1×2
1 315
size(phi)
ans = 1×2
1 315
size(temp)
ans = 1×2
1 315
Therefore, each iteration of the two nested loops calculates a row vector of that form, multiplies it by the scalar I(m,n), and adds that product to F1, which is a square matrix (specifically 315x315). Adding a row vector to a matrix adds the row vector to each row of the matrix, assuming they have compatible sizes, which they do in this case:
F1 = zeros(numel(teta),numel(phi));
F1 = F1+temp
F1 =
-1.0000 - 0.0000i -0.9995 + 0.0311i -0.9981 + 0.0615i -0.9958 + 0.0912i -0.9927 + 0.1202i -0.9889 + 0.1484i -0.9844 + 0.1758i -0.9793 + 0.2024i -0.9736 + 0.2282i -0.9675 + 0.2531i -0.9608 + 0.2771i -0.9539 + 0.3002i -0.9466 + 0.3225i -0.9390 + 0.3439i -0.9313 + 0.3643i -0.9234 + 0.3839i -0.9154 + 0.4026i -0.9073 + 0.4204i -0.8993 + 0.4374i -0.8913 + 0.4534i -0.8834 + 0.4686i -0.8757 + 0.4829i -0.8681 + 0.4964i -0.8607 + 0.5090i -0.8536 + 0.5209i -0.8468 + 0.5319i -0.8403 + 0.5420i -0.8342 + 0.5514i -0.8285 + 0.5601i -0.8231 + 0.5679i -0.8182 + 0.5750i -0.8137 + 0.5813i -0.8097 + 0.5869i -0.8061 + 0.5917i -0.8031 + 0.5958i -0.8006 + 0.5992i -0.7986 + 0.6019i -0.7971 + 0.6039i -0.7961 + 0.6051i -0.7957 + 0.6057i -0.7958 + 0.6055i -0.7965 + 0.6046i -0.7977 + 0.6031i -0.7994 + 0.6008i -0.8017 + 0.5978i -0.8044 + 0.5940i -0.8077 + 0.5896i -0.8115 + 0.5844i -0.8157 + 0.5785i -0.8204 + 0.5718i -0.8255 + 0.5644i -0.8311 + 0.5562i -0.8370 + 0.5472i -0.8433 + 0.5375i -0.8499 + 0.5269i -0.8569 + 0.5155i -0.8641 + 0.5033i -0.8716 + 0.4903i -0.8792 + 0.4764i -0.8870 + 0.4617i -0.8950 + 0.4461i -0.9030 + 0.4297i -0.9110 + 0.4123i -0.9191 + 0.3941i -0.9270 + 0.3750i -0.9349 + 0.3550i -0.9425 + 0.3341i -0.9500 + 0.3124i -0.9571 + 0.2897i -0.9639 + 0.2661i -0.9703 + 0.2417i -0.9763 + 0.2164i -0.9817 + 0.1903i -0.9866 + 0.1633i -0.9908 + 0.1355i -0.9943 + 0.1070i -0.9970 + 0.0777i -0.9989 + 0.0476i -0.9999 + 0.0169i -0.9999 - 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Notice all the rows of F1 are the same because temp was added to each row, which initially were all zeros. F1 is going to be updated, as the loops iterate, by doing this same type of matrix and row-vector addition, so all the rows of F1 are always going to be the same. That's why F1 is like that.
What you really mean to be doing is, on each iteration of the loops, generate a matrix of elements that vary with both teta and phi rather than a row vector. To do that, make one of teta or phi into a column vector when you use them (or define it to be a column vector) - it makes sense to make teta the column vector, since that's how you've defined the size of F1.
temp = exp(1i*k*sin(teta(:)).*(m*dx*cos(phi)+n*dy*sin(phi)));
size(temp)
ans = 1×2
315 315
Now you get a 315-by-315 matrix each time, with elements that vary in both dimensions.
temp
temp =
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(One reason it might have been difficult to see that you were constructing row vectors when you meant to be constructing matrices is that teta and phi are the same length as each other. If you had tried the code with teta a different length than phi, you would've run into an error that would've been an indication that things were not working as expected.)
For completeness, this is how the code might look:
load('matlab.mat')
whos I
Name Size Bytes Class Attributes
I 37x46 13616 double
lambda = 0.01;
k = 2*pi/lambda;
dx = lambda/2;
dy = lambda/2;
% teta = -pi/2:0.01:pi/2;
% phi = 0:0.01:pi;
% I'm using smaller vectors
teta = -pi/2:0.05:pi/2;
phi = 0:0.05:pi;
F1 = zeros(numel(teta),numel(phi));
N = 46;
M = 37;
for m=1:M
for n=1:N
F1 = F1+I(m,n)*exp(1i*k*sin(teta(:)).*(m*dx*cos(phi)+n*dy*sin(phi)));
end
end
size(F1)
ans = 1×2
63 63
disp(F1)
1.0e+04 *
Columns 1 through 10
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0.0004 + 0.0138i 0.0008 - 0.0094i -0.0064 - 0.0138i 0.0009 + 0.0070...
and now it works with teta and phi being different lengths:
teta = -pi/2:0.05:pi/2;
phi = 0:0.1:pi;
F1 = zeros(numel(teta),numel(phi));
for m=1:M
for n=1:N
F1 = F1+I(m,n)*exp(1i*k*sin(teta(:)).*(m*dx*cos(phi)+n*dy*sin(phi)));
end
end
size(F1)
ans = 1×2
63 32
disp(F1)
1.0e+04 *
Columns 1 through 10
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Columns 31 through 32
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-0.0285 + 0.0477i 0.0898 - 0.1952i
-0.0632 - 0.0895i 0.1390 - 0.0898i
0.0819 + 0.0344i -0.0987 + 0.0691i
-0.0565 + 0.2057i -0.2862 + 0.0044i
-0.2135 - 0.0099i -0.1307 - 0.1828i
-0.2341 - 0.1754i -0.1230 - 0.2745i
1.0795 + 1.9059i 0.7669 + 2.0595i
0.1655 - 1.9176i -0.2636 - 1.9192i
0.0132 + 0.0743i 0.0452 + 0.0545i
-0.1077 + 0.1067i 0.0296 + 0.1492i
-0.1457 - 0.1391i -0.2354 + 0.1386i
0.0488 - 0.1069i -0.1914 + 0.0019i
0.0081 + 0.0933i 0.0939 - 0.0022i
-0.0460 - 0.0111i 0.1748 + 0.1332i
0.0529 - 0.0259i 0.0228 + 0.0892i
0.0400 - 0.0004i -0.0168 - 0.1341i
0.0337 - 0.0508i 0.1264 - 0.1088i
0.0184 - 0.0369i -0.0397 + 0.0327i
0.0090 - 0.0750i -0.1257 - 0.0919i
-0.0057 - 0.0410i 0.0142 - 0.0067i
-0.0448 - 0.0466i -0.0735 + 0.1008i
0.0024 - 0.0189i -0.0136 - 0.0319i
-0.0473 - 0.0304i 0.0329 + 0.1011i
-0.0108 - 0.0054i -0.0099 - 0.0129i
-0.0414 + 0.0009i 0.0794 + 0.0441i
0.0168 + 0.0277i -0.0109 - 0.0516i
0.0123 - 0.0241i 0.0372 + 0.0345i
-0.0021 - 0.0028i 0.0146 - 0.0643i
0.0195 - 0.0153i -0.0280 + 0.0186i
0.0013 - 0.0297i 0.0488 - 0.0098i
-0.0028 - 0.0152i -0.0163 - 0.0617i
0.0112 - 0.0192i -0.0520 + 0.0067i
0.0083 - 0.0369i 0.0037 + 0.0363i
-0.0080 - 0.0431i 0.0333 - 0.0033i
-0.0206 - 0.0368i 0.0119 - 0.0361i
-0.0247 - 0.0279i -0.0185 - 0.0368i
-0.0241 - 0.0219i -0.0354 - 0.0230i
-0.0227 - 0.0191i -0.0407 - 0.0115i
but before (using teta and phi as row vectors of different lengths, i.e., without converting one of them to a column vector) it would not have run:
teta = -pi/2:0.05:pi/2;
phi = 0:0.1:pi;
F1 = zeros(numel(teta),numel(phi));
for m=1:M
for n=1:N
F1 = F1+I(m,n)*exp(1i*k*sin(teta).*(m*dx*cos(phi)+n*dy*sin(phi)));
end
end
Arrays have incompatible sizes for this operation.
More Answers (1)
Image Analyst
on 21 May 2022
0 votes
You're not indexing F1. You're just overwriting the same F1 scalar on every iteration.
2 Comments
Begginer201
on 21 May 2022
Could you please tell me how I should index F1 using different phi values?
Image Analyst
on 21 May 2022
teta and phi should be constants, not vectors.
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