Error with matrix size

I have a very confusing problem when working on Matlab Web version, by checking that the matrix A has a size of 9x9 but when running the program, the compiler reports an error at line 43 that the size of the matrix A is is 1x0. Please help me. Thank.

Here is my entire code:

clear all

close all

h=0.1;

k=0.01;

x=0:h:1;

n=length(x);

t=0:k:0.01;

m=length(t);

c=1;

r=(c^2*k)/h^2;

%Khai báo hàm điều kiện đầu

f=@(x) sin(pi*x)+sin(3*pi*x);

%khai báo hàm điều kiện biên

g=@(t) 0;

%khởi tạo ma trận mạng lưới

u=zeros(m,n);

%Khai báo điều kiện đầu cho mạng lưới

for j=2:n-1

u(1,j)= f(x(j));

end

%Khai báo điều kiện biên cho 2 bên lưới

for i=1:m

u(i,1)= g(x(i));

u(i,n)= g(x(i));

end

d1=zeros(n-2,1);

d2=zeros(n-2,1);

for i=1:n-2

d2(i,1)=-1;

d1(i,1)=2/r+2;

end

A=spdiags([d2 d1 d2],-1:1,n-2,n-2);

B=zeros(m-1,n-2);

for i=2:11

for j=2:n-1

B(j-1,i-1)=r*u(i-1,j-1)+(2-2*r)*u(i-1,j)+r*u(i-1,j+1)+r*u(i,j-1);

end

u(i,2:(m-1))=A\B(:,i-1);

end

surf(u)

colorbar

Answer 1

[Stephen23]

The size of the matrix A is not important. The size of the RHS of the "=" is important. Lets check that size:

A = rand(9,9);
B = rand(9,1);
A\B(:,1) % this is what you actually have on the RHS, a 9x1 array

ans = 9×1

0.7286 16.1988 2.4267 -8.6586 -11.1960 8.6900 -12.4435 -5.6568 3.2342

Apparently the colon on the LHS evaluates to an empty list (most likely because m<3), so the indexing on the LHS is allocating to a 1x0 area of u. So far everything is very simple to explain, there are no surprises here.

"I have a very confusing problem when working on Matlab Web version"

It is unclear what the confusion is: the RHS is 9x1 and the LHS is 1x0. It is not possible to allocate 9 element into 0 elements.

The only confusing thing seems to be that you have not checked to see what your code is actually doing.

" the compiler reports an error at line 43 that the size of the matrix A is is 1x0."

No, it definitely does not say that. Read it again: the error message does not mention the array "A" anywhere. The RHS is always the result of the final operation performed, which in this case is an MLDIVIDE operation, and not your array A.

[VINH]

I really don't understand, I'm remaking a program to solve the heat equation using the Crank Nicholson method that I did 3 years ago.

clc
clear all
close all
h=0.1;
k=0.01;
x=0:h:1;
t=0:k:0.1;
n=length(t);
m=length(x);
r=1;
%Khai báo hàm điều kiện đầu
f=@(x) sin(pi*x)+sin(3*pi*x);
%Khai báo hàm điều kiện biên
g=@(t) 0;

u=zeros(n,m);

%dieu kien bien
for i=1:n
    u(i,1)=g(t(i));
    u(i,m)=g(t(i));
end
%dieu kien dau

for j=2:m-1
    u(1,j)=f(x(j));
end
for i=1:m-2
    s2(i,1)=-r;
    s1(i,1)=2*r+2;
end
A=spdiags([s2 s1 s2],-1:1,m-2,m-2);
full(A) 
for i=2:n
    for j=2:m-1
    B(j-1,i-1)=r*u(i-1,j-1)+(2-2*r)*u(i-1,j)+r*u(i-1,j+1)+r*u(i,j-1);
    end
    u(i,2:n-1)=A\B(:,i-1);
end
u(:,2:n-1)
 surf(u)
colorbar

This is the code I did and gave the correct result

[VINH]

I figured it out, I mistakenly typed an additional 0 in the t array declaration line, it should be t=0:k:0.1, it's just a simple thing but it took me a day to think about it without considering these things. The simple thing

[VINH]

Your comment was really helpful, I didn't realize the matrix u didn't have enough size to fit the right side. Thank you for taking the time to answer my stupid question.