Hello Philipp,
The ‘potential()’ function in MATLAB is used to compute the scalar potential of a vector field. Given a vector field ‘V’ and its coordinates ‘X’, the function integrates the vector field to find the scalar potential field.
For your scenario, the partial derivatives ‘dR_dx’ and ‘dR_dy’ represent the ‘x’ and ‘y’ components of the density gradient vector field. These should be input to ‘potential()’ function to find the scalar field Rho you seek.
Here's a modified version of your code.
% Assuming dR_dx and dR_dy are the m-by-n matrices of partial derivatives
% X and Y are the vectors representing the coordinates in the image
[m, n] = size(dR_dx); % Assuming dR_dx and dR_dy have the same size
X = linspace(x_start, x_end, n); % Define the X coordinates
Y = linspace(y_start, y_end, m); % Define the Y coordinates
% Convert the matrices to symbolic form for the potential function
dRdx_sym = sym(dR_dx, 'f');
dRdy_sym = sym(dR_dy, 'f');
% Create symbolic variables for x and y
syms x y
% Initialize the matrix to hold the potential values
Rho_pot = zeros(m, n);
% Compute the potential
for i = 1:m
for j = 1:n
% Compute the potential at each point
Rho_sym = potential([dRdx_sym(i, j), dRdy_sym(i, j)], [x, y], [X(1), Y(1)]);
% Substitute the symbolic variables with the actual coordinates
Rho_pot(i, j) = double(subs(Rho_sym, {x, y}, {X(j), Y(i)}));
end
end
Please replace ‘x_start’, ‘x_end’, ‘y_start’, and ‘y_end’ with the actual coordinate limits of x and y components respectively. Also, the code presumes that gradient field is conservative; otherwise, the ‘potential' function may not apply.
Hope this helps.
Best Regards,
Sachin
