How to write the sum of several matrices in Matlab ?

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) ?

[Dyuman Joshi]

What are i and j?

Answer 1

[Voss]

A = sum(B,3);

[Voss]

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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Answer 2

[Walter Roberson]

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 = 

[Walter Roberson]

Note that the repmat() is needed for symbolic work, as symbolic work does not fully support implicit expansion.

[Djamel]

Thanks Walter.I still can't adapt the crip to my problem.

I specify that x_i and y_j come from the discretization of the interval [0 ,π].

We choose the following scheme

x_i = y_i = (i-1/2) . π/N ,i=1,…,N

The matrices B and the matrix A are therefore of dimension N×N.

[Djamel]

When I do sum(B,10) I get 10 matrices not the sum of ten matrices.

[Voss]

sum(B,10) sums B across the 10th dimension. The result is B since B is only 3-dimensional. You should do sum(B,3) to sum B across the 3rd dimension.

[Djamel]

Thank you so much. It worked

[Walter Roberson]

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 =