arrayfun once with 4 variables, or twice with 2 in each, then mult. Why do these two approaches give different solutions?

I have the following code to achieve W_n

%%CONSTANTS & VARIABLES

clear all; close all;

L_x             = 27.4e-3;              % membrane width (m)
L_y             = 27.4e-3;              % membrane height (m)
N_x             = 3;                    % no. of x dim. eigenfreqs
N_y             = 3;                    % no. of y dim. eigenfreqs
N               = N_x*N_y;              % total no. of eigenfreqs
numX            = 101;                  % no. of x-dir. mapping points
numY            = 101;                  % no. of y-dir. mapping points
xs              = linspace(0,L_x,numX); % x-dir. membrane mapping points
ys              = linspace(0,L_y,numY); % y-dir. membrane mapping points

%%SET UP MESHES

[X,Y]           = meshgrid(ys,xs);      % create X and Y array in 2d
XFull           = repmat(X, [1 1 N]);   % modify X and Y array for 3d
YFull           = repmat(Y, [1 1 N]);   % modify X and Y array for 3d

R               = ones(numX, numY, N_x);% create mode array for X
RFull           = [];                   % create an empty array (0 by 0)
for n = 1:N_x
    RFull = cat(3, RFull, n*R);
end

S               = ones(numX, numY);     % create mode array for Y
SFull           = [];                   % create an empty array (0 by 0)
for n = 1:N_y
    SFull = cat(3, SFull, n*S);
end
SFull           = repmat(SFull, [1 1 N_x]);

A               = ones(numX, numY, N_x);% create mode array for X
AFull           = [];                   % create an empty array (0 by 0)
for n = 1:N_x
    AFull = cat(3, AFull, n*A);
end

B               = ones(numX, numY);     % create mode array for Y
BFull           = [];                   % create an empty array (0 by 0)
for n = 1:N_y
    BFull = cat(3, BFull, n*B);
end
BFull           = repmat(BFull, [1 1 N_x]);

%%W_n 

% 1st method

W_n_i           = arrayfun(@(x,r,y,s)sin(x.*r*pi/L_x).*sin(y.*s*pi/L_y)...
                  ,XFull,RFull,YFull,SFull);

% 2nd method

% W_n_x           = arrayfun(@(x,r)sin(x.*(r*pi/L_x)), XFull, RFull); 
% W_n_y           = arrayfun(@(y,s)sin(y.*(s*pi/L_y)), YFull, SFull); 
% W_n_ii          = W_n_x .* W_n_y;       % mode superposition

W_n             = W_n_i;                % choose 'i' or 'ii'

I can't work out why W_n_i is different to W_n_ii.

Could anyone help me to see why this is?

Many thanks in advance.

Answer 1

[Robert Cumming]

Your calculations are not the same, in the second method you have:

 sin(x.*(r*pi/L_x))
 sin(y.*(s*pi/L_y))

in the first you have:

 sin(x.*r*pi/L_x)
 sin(y.*s*pi/L_y)

Note the extra brackets in the first method.

[Tom]

Well spotted!

If there were no . before the * sign, this would not matter. So why does it matter here?

[Robert Cumming]

its important due to the order of how operations are performed see the official documentation.

[Tom]

Okay, many thanks for this.