Please help me with syntax error on line 52

function [e1, e2] = spand_hw7(mesh, d, f, dfdx)
% Check if input arguments are provided
if nargin < 4
    error('Insufficient input arguments. Please provide all required inputs.');
end


% Initialize error norms
e1 = 0;
e2 = 0;

% Define Gauss quadrature points and weights
x_quad = [-sqrt(5 + 2*sqrt(10/7))/3, 0, sqrt(5 + 2*sqrt(10/7))/3];
w_quad = [5/9, 8/9, 5/9];

% Loop over elements
for el = 1:size(mesh.conn, 2)
    % Element nodes
    nodes = mesh.conn(:, el);
    
    % Element coordinates
    xe = mesh.x(nodes);
    
    % Element displacements
    de = d(nodes);
    
    % Jacobian matrix
    J = (xe(end) - xe(1)) / 2;
    
    % Initialize element error norms
    e1_el = 0;
    e2_el = 0;
    
    % Loop over quadrature points
    for q = 1:length(x_quad)
        % Quadrature point
        xq = (xe(end) + xe(1)) / 2 + x_quad(q) * J;
        
        % Interpolated solution at quadrature point
        u_interp = sum(N(xq, xe) .* de');
        
        % Exact solution and its derivative at quadrature point
        u_exact = f(xq);
        du_exact = dfdx(xq);
        
        % Compute L2 error norm
        e1_el = e1_el + w_quad(q) * (u_exact - u_interp)^2;
        
        % Compute energy error norm
        e2_el = e2_el + w_quad(q) * sum((du_exact - de' .* dNdx(xq, xe)).^2);
    end
    
    % Add element error norms to total error norms
    e1 = e1 + e1_el * J;
    e2 = e2 + e2_el * J;
end

% Normalize error norms
e1 = sqrt(e1);
e2 = sqrt(e2);
end
% Shape functions
function N_val = N(x, xe)
N_val = [(x - xe(2)) .* (x - xe(3)) / ((xe(1) - xe(2)) * (xe(1) - xe(3)));
    (x - xe(1)) .* (x - xe(3)) / ((xe(2) - xe(1)) * (xe(2) - xe(3)));
    (x - xe(1)) .* (x - xe(2)) / ((xe(3) - xe(1)) * (xe(3) - xe(2)))];
end
% Derivative of shape functions
function dNdx_val = dNdx(x, xe)
dNdx_val = [(2*x - xe(2) - xe(3)) / ((xe(1) - xe(2)) * (xe(1) - xe(3)));
    (2*x - xe(1) - xe(3)) / ((xe(2) - xe(1)) * (xe(2) - xe(3)));
    (2*x - xe(1) - xe(2)) / ((xe(3) - xe(1)) * (xe(3) - xe(2)))];
end

Syntax error at line 52: Incorrect dimensions for raising a matrix to a power. Check that the matrix is square and the power is a scalar. To operate on each element of the matrix individually, use POWER (.^) for elementwise power.

% Example inputs before calling the function
ne = 10;
nn = 2*ne + 1;
mesh.x = linspace(0, 6, nn);
mesh.conn = [1:2:nn-2; 2:2:nn-1; 3:2:nn];
f = @(x) 1.0./((x-3).^2+0.2);
dfdx = @(x) -2.0*(x-3.0) ./ ((x-3).^2 + 0.2).^2;
d = f(mesh.x)';

Answer 1

[Walter Roberson]

% Example inputs before calling the function
ne = 10;
nn = 2*ne + 1;
mesh.x = linspace(0, 6, nn);
mesh.conn = [1:2:nn-2; 2:2:nn-1; 3:2:nn];
f = @(x) 1.0./((x-3).^2+0.2);
dfdx = @(x) -2.0*(x-3.0) ./ ((x-3).^2 + 0.2).^2;
d = f(mesh.x)';

[E1,E2] = spand_hw7(mesh, d, f, dfdx)

de = 3×1

0.1087 0.1335 0.1678

  Name      Size            Bytes  Class     Attributes

  Nxq       3x1                24  double              

  Name          Size            Bytes  Class     Attributes

  u_exact       1x1                 8  double              
  u_interp      1x3                24  double              

Error using ^
Incorrect dimensions for raising a matrix to a power. Check that the matrix is square and the power is a scalar. To operate on each element of the matrix individually, use POWER (.^) for elementwise power.

Error in solution>spand_hw7 (line 61)
e1_el = e1_el + w_quad(q) * (u_exact - u_interp)^2;

function [e1, e2] = spand_hw7(mesh, d, f, dfdx)
% Check if input arguments are provided
if nargin < 4
    error('Insufficient input arguments. Please provide all required inputs.');
end


% Initialize error norms
e1 = 0;
e2 = 0;

% Define Gauss quadrature points and weights
x_quad = [-sqrt(5 + 2*sqrt(10/7))/3, 0, sqrt(5 + 2*sqrt(10/7))/3];
w_quad = [5/9, 8/9, 5/9];

% Loop over elements
for el = 1:size(mesh.conn, 2)
    % Element nodes
    nodes = mesh.conn(:, el);
    
    % Element coordinates
    xe = mesh.x(nodes);
    
    % Element displacements
    de = d(nodes)
    
    % Jacobian matrix
    J = (xe(end) - xe(1)) / 2;
    
    % Initialize element error norms
    e1_el = 0;
    e2_el = 0;
    
    % Loop over quadrature points
    for q = 1:length(x_quad)
        % Quadrature point
        xq = (xe(end) + xe(1)) / 2 + x_quad(q) * J;
        
        % Interpolated solution at quadrature point
        Nxq = N(xq, xe);
        whos Nxq
        u_interp = sum(N(xq, xe) .* de');
        
        % Exact solution and its derivative at quadrature point
        u_exact = f(xq);
        du_exact = dfdx(xq);
        
        whos u_exact u_interp
        % Compute L2 error norm
        e1_el = e1_el + w_quad(q) * (u_exact - u_interp)^2;
        
        % Compute energy error norm
        e2_el = e2_el + w_quad(q) * sum((du_exact - de' .* dNdx(xq, xe)).^2);
    end
    
    % Add element error norms to total error norms
    e1 = e1 + e1_el * J;
    e2 = e2 + e2_el * J;
end

% Normalize error norms
e1 = sqrt(e1);
e2 = sqrt(e2);
end
% Shape functions
function N_val = N(x, xe)
N_val = [(x - xe(2)) .* (x - xe(3)) / ((xe(1) - xe(2)) * (xe(1) - xe(3)));
    (x - xe(1)) .* (x - xe(3)) / ((xe(2) - xe(1)) * (xe(2) - xe(3)));
    (x - xe(1)) .* (x - xe(2)) / ((xe(3) - xe(1)) * (xe(3) - xe(2)))];
end
% Derivative of shape functions
function dNdx_val = dNdx(x, xe)
dNdx_val = [(2*x - xe(2) - xe(3)) / ((xe(1) - xe(2)) * (xe(1) - xe(3)));
    (2*x - xe(1) - xe(3)) / ((xe(2) - xe(1)) * (xe(2) - xe(3)));
    (2*x - xe(1) - xe(2)) / ((xe(3) - xe(1)) * (xe(3) - xe(2)))];
end

[Walter Roberson]

u_interp = sum(N(xq, xe) .* de');

N(xq, xe) is 3 x 1

de is 3 x 1

de' is 1 x 3

3 x 1 .* 1 x 3 gives 3 x 3

sum(3 x 3) gives 1 x 3

So u_interp comes out 1 x 3.