# How can I vectorize a function?

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David Franco on 1 Mar 2018
Commented: Star Strider on 24 Mar 2018
The function I want to vectorize is Cross-in-Tray Function (2-D):
f(X,Y) = -0.0001*(abs(sin(X)*sin(Y)*exp(abs(100-sqrt(X^2+Y^2)/pi)))+1)^0.1;
I want to use the command (to plot the function):
fsurf(@(x,y) crossintrayfcn([x,y]))
I have this two function codes:
function z = crossintrayfcn(xx)
x = xx(:,1);
y = xx(:,2);
expcomponent = abs(100-(sqrt(x.^2 + y.^2)/pi));
z = -0.0001*((abs(sin(x).*sin(y).*exp(expcomponent))+1).^0.1);
end
And:
function [y] = crossintrayfcn(xx)
x1 = xx(1);
x2 = xx(2);
fact1 = sin(x1)*sin(x2);
fact2 = exp(abs(100 - sqrt(x1^2 + x2^2)/pi));
y = -0.0001 * (abs(fact1*fact2) + 1)^0.1;
end
But they plot nothing!
Thanks!

Star Strider on 1 Mar 2018
Vectorising it simply requires using element-wise operations:
f = @(X,Y) -0.0001*(abs(sin(X).*sin(Y).*exp(abs(100-sqrt(X.^2+Y.^2)/pi)))+1).^0.1;
[x,y] = meshgrid(linspace(-10, 10, 49));
figure
surfc(x, y, f(x,y))
grid on
See the documentation on Array vs. Matrix Operations (link) and Vectorization (link) for details.
Star Strider on 24 Mar 2018
@Yair — My pleasure.

### More Answers (1)

David Franco on 5 Mar 2018
Because of the above problems I'm using my own function with surfc to replace fsurf:
function z = plotfcn(fcn,range,grid,shad)
% PLOTFCN evaluate and plot a 3D function
% INPUT:
% FCN - @myFunction (function handle)
% RANGE - [x1min x1 max x2min x2max] (default = [-10 10 -10 10])
% GRID - grid size for the function evaluation (default = 101)
% SHAD - set color shading properties (default = 0)
% 0 = faceted (continued colormap with black mesh lines)
% 1 = interp (interpolated colormap)
% 2 = flat (continued colormap)
% OUTPUT:
% Z - function eval (GRID x GRID)
% EXAMPLE:
% z = plotfcn2(@ackleyfcn, [-32 32; -32 32], 200, 1);
switch nargin
case 4
case 3
case 2
grid = 101;
case 1
grid = 101;
range = [-10 10 -10 10];
otherwise
disp('Not enough input arguments. Function required.')
return
end
x1 = meshgrid(linspace(range(1,1), range(1,2), grid));
x2 = meshgrid(linspace(range(1,3), range(1,4), grid))';
xx = [x1(:),x2(:)];
f = fcn(xx);
f = reshape(f,size(x1));
if nargout == 1
z = f;
end
figure
surfc(x1,x2,f)
title([func2str(fcn), ' [x,y]'])
colormap jet
if shad == 1
elseif shad == 2
end
end

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