How can I vectorize this function with nested FOR loop?

The function is:

x = -10:10;
y = -5:5;

for j = 1:21
    for i = 1:11
        f(i) = - 20 * exp( - 0.2 * sqrt( ( 1/2 ) * sum( x(j)^2 + y(i)^2 ) ) );
    end
    z(j,:) = f;
end

Thanks!

Answer 1

[Andrei Bobrov]

% MATLAB >= R2016b

z = - 20 * exp( - 0.2 * sqrt( .5 * sum( x(:).^2 + y(:)'.^2 ) ) );

% MATLAB <= R2016a

[xx,yy] = ndgrid(x,y);
z = - 20 * exp( - 0.2 * sqrt( .5 * sum( xx.^2 + yy.^2 ) ) );

[David Franco]

Thanks for the answer Andrei, but the results are different:

In the original code z = 21x11

In your codes z = 1x11

Any suggestions on how to fix this?

[David Franco]

I figured out:

Removing the sum command the results are the same.

Thanks!

Answer 2

[per isakson]

Yes, try this

>> max( cssm, [], 1 )
ans =
     0     0     0     0     0     0     0     0     0     0     0
>>

where

function    dz = cssm()
    x = -10:10;
    y = -5:5;
    f = nan(1,11);
    z = nan(21,11);
    %
    for j = 1:21
        for i = 1:11
            f(i) = - 20 * exp( - 0.2 * sqrt( ( 1/2 ) * sum( x(j)^2 + y(i)^2 ) ) );
        end
        z(j,:) = f;
    end

vectorized version

    x02 = repmat( reshape( x, [], 1 ), 1,length(y) );
    y02 = repmat( y, length(x),1 );
    z02 = - 20 * exp( - 0.2 * sqrt( ( 1/2 ) * ( x02.^2 + y02.^2 ) ) );
    %
    dz  = abs( z02 - z );
end

on R2016a

btw: Isn't true that sum in this case has no effect?

[David Franco]

It worked, but how can I extrapolate to higher dimensions?

Ackley's Function:

z = -20*exp(-0.2*sqrt((1/d)*sum(x^2)))-exp((1/d)*sum(cos(2*pi*x)))+20+exp(1);

where d is the dimension of the input.

Thanks!

[per isakson]

See the FEX submission Traditionalized Ackley by George Evers

[David Franco]

Thanks per isakson!