Is this the correct implementation of the total variation algorithm?

I need to compute the total variation of an image based on the algorithm presented here

I have implemented the following code using the l1 norm of the spatial fist-order derivatives:

function TV = compute_total_variation1(y)
% y is the image
nbdims = 2;

% check number of channels in an image
if size(y,1)==1 || size(y,2)==1
    % we have one dimension
    nbdims = 1;
end

if size(y,1)>1 && size(y,2)>1 && size(y,3)>1
    % we have three dimensions
    nbdims = 3;
end

if nbdims==1
    TV = sum(abs(diff(y)));
    return;
end

% the total variation weight is 1
% weight_tv = ones(size(y));

[gx gy] = gradient(y);
% compute using the l1 norm of the first order derivatives
% horizontal
TVgx = sum( abs(gx),nbdims+1);
% vertical
TVgy = sum( abs(gy),nbdims+1);
% TV = TV .* weight_tv;
TV = sum(TVgx(:)) + sum(TVgy(:));

Is the above implementation valid or not?