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How to write the sum of several matrices in Matlab ?

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Djamel
Djamel 2024-4-27
评论： Walter Roberson 2024-4-29
We have the sequence of matrices
B(i,j,n)=2/N exp⁡(-cn^2 ) sin⁡(nx_i ) sin⁡(n y_j )
where N and n are integers ,x_i and y_ji are real numbers in the
interval [0 ,1] and c is a real parameter strictly positive.
We pose
A(c)= ∑_B(n) for n=1,....,10
How to write in Matlab the sum A(c) ?

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回答（2 个）

Voss
Voss 2024-4-27 
A = sum(B,3);
  1 个评论
Voss
Voss 2024-4-27
Ran in:
I you don't have B already, here's how you can get it:
% your numbers go here:
N = 10;
nx = 7;
ny = 6;
x = rand(1,nx);
y = rand(1,ny);
c = rand();
n = reshape(1:N,1,1,[]);
B = 2/N.*exp(-c.*n.^2).*sin(n.*x(:)).*sin(n.*y(:).');
size(B)
ans = 1x3
7 6 10
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A = sum(B,3)
A = 7x6
0.0031 0.0035 0.0015 0.0018 0.0029 0.0033 0.0375 0.0429 0.0181 0.0225 0.0352 0.0411 0.0106 0.0121 0.0052 0.0064 0.0100 0.0116 0.0002 0.0002 0.0001 0.0001 0.0001 0.0002 0.0355 0.0406 0.0172 0.0213 0.0333 0.0389 0.0067 0.0077 0.0033 0.0041 0.0063 0.0074 0.0037 0.0043 0.0018 0.0023 0.0035 0.0041
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Walter Roberson
Walter Roberson 2024-4-27
Ran in:
syms c N
num_i = 3; %adjust as needed
num_j = 4; %adjust as needed
num_n = 10;
syms x [num_i 1]
syms y [1 num_j]
x = repmat(x, 1, num_j, num_n);
y = repmat(y, num_i, 1, num_n);
n = repmat(reshape(1:num_n, 1, 1, []), num_i, num_j, 1);
B = 2/N .* exp(-c .* n) .* sin(n .* x) .* sin(n .* y);
A = sum(B, 3)
A = 
  6 个评论
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Walter Roberson
Walter Roberson 2024-4-29
Ran in:
N = 7;
i = 1:N;
x_i = (i-1/2)/N * pi;
y_i = (i-1/2)/N * pi;
syms c
num_i = length(x_i);
num_j = length(y_i);
num_n = 10;
syms x [num_i 1]
syms y [1 num_j]
xG = repmat(x, 1, num_j, num_n);
yG = repmat(y, num_i, 1, num_n);
nG = repmat(reshape(1:num_n, 1, 1, []), num_i, num_j, 1);
B = 2/N .* exp(-c .* nG) .* sin(nG .* xG) .* sin(nG .* yG);
A = sum(B, 3)
A = 
Ad = vpa(subs(subs(A, x, x_i.'), y, y_i), 5)
Ad = 

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