Error: Incorrect dimensions for matrix multiplication

Question

Janee 2023-10-13

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https://ww2.mathworks.cn/matlabcentral/answers/2032769-error-incorrect-dimensions-for-matrix-multiplication

评论： Torsten 2023-10-13

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I have the following code which is an iterative solver that solves for a linear poisson's equation as a simple test:

clearvars; clc; close all;

N=30;

[D,x] = cheb(N); D2 = D^2;

D2(N+1,:) = D(N+1,:); %Neumann BC at left endpoint (x=-1), esp w/ D

D2 = D2(2:N+1,2:N+1); %Dirichlet BC at right endpoint (x=1)

u = (exp(4*x) - 4*exp(-4)*(x-1)-exp(4))/16; %w/ BCs ux(-1)=u(1)=0

n =ones(size(u));

%build source term

dndx = D *n;

dudx = D *u;

prod1 = dndx .* dudx;

du2dx = D * dudx;

prod2 = n .*du2dx;

invN = (1./n) ;

source = prod1(2:N) + prod2(2:N);

uold = ones(size(u(2:N)));

max_iter =500;

err_max = 1e-8;

for iterations = 1:max_iter

phikmax_old = (max(abs(uold)));

duoldx = D(2:N,2:N) *uold;

dnudx = dndx(2:N) .* duoldx;

ffh = source;

RHS = ffh - dnudx;

Stilde = invN(2:N) .* RHS;

unew = D2\[Stilde;0];

phikmax = (max(abs(unew)));

if phikmax < err_max

it_error = err_max /2;

else

it_error = abs( phikmax - phikmax_old) / phikmax;

end

if it_error < err_max

break;

end

uold = unew;

end

unew = [0;unew];

figure

plot(x,unew,'--rs',x,(u));

legend('Num solution','Exact solution')

Function cheb:

function [ D, x ] = cheb ( N )
  if ( N == 0 )
    D = 0.0;
    x = 1.0;
    return
  end
  x = cos ( pi * ( 0 : N ) / N )'; 
  c = [ 2.0; ones(N-1,1); 2.0 ] .* (-1.0).^(0:N)';
  X = repmat ( x, 1, N + 1 );
  dX = X - X';
  D = ( c * (1.0 ./ c )' ) ./ ( dX + ( eye ( N + 1 ) ) );
  D = D - diag ( sum ( D' ) );
  return
end

I get the correct solution at the first iteraion " for iterations = 1 %1:max_iter" then after that I get the error:

Error using  * 
Incorrect dimensions for matrix multiplication. Check that the number of columns in the first matrix matches the number of
rows in the second matrix. To perform elementwise multiplication, use '.*'.
Error in Filename (line 298)
    duoldx = D(2:N,2:N) *uold;