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

Question

Tom 2014-7-2

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/139891-arrayfun-once-with-4-variables-or-twice-with-2-in-each-then-mult-why-do-these-two-approaches-give

评论： Tom 2014-7-3

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'