imaginary numbers slow down code

I am trying to build a complex matrix of size 1024x1024, and at each index evaluate the following function: , where phi is dependent on x and y which is calculated in a seperate function called 'Phasevector2D'. aX, bX, aY and bY represent the min and max values of my x and y values.

The code below runs fine when I take small values for aX, bX, aY and bY, such as -5 to 5, but when I take bigger values (-100 to 100) the code becomes terribly slow. When phi is put equal to zero, meaning that there is no contribution from the imaginary part, the code works fine, so I am suspecting it has something to do with the imaginary number.

Does anybody underestand why this is happening? Thanks

aX = -100;
bX = 100;
aY = -100;
bY = 100;

nX = 1024;
mY = 1024;

f = complex(zeros(nX, mY));
Phasevector = zeros(nX, mY);
ii = 1;
jj = 1;

Xrange = linspace(aX, bX, nX);
Yrange = linspace(aY, bY, mY);

for x = Xrange
     for y = Yrange
        f(jj, ii) = exp(-pi * (x^2 + y^2) + 1i * phasevector2D(x,y));
        jj = jj + 1; 
    end
    ii = ii + 1;
    jj = 1;
    disp(ii);
end

The function Phasevector2D looks like below, but eventually also needs no work for x^2+y^2, x^3+y^3, sin(x+y) and similar simple functions. The output value of Phasevector2D is always smaller than 2pi.

function  X = phasevector2D( x,y )
X = 50 * (x + y + 10);
X = X - fix(X/(2*pi)) * 2*pi;
end

[dpb]

If imaginary part is real (not zero), the optimizer may recognize it does not need to call phasevector2D so the overhead there goes away. We don't know what's in it...

You could vectorize your functional and remove the loop construct and might see some performance improvement as well.

Show us phasevector2D

[Isa Hendriks]

Phasevector2D looks like this:

function  X = phasevector2D( x,y )
X = 50 * (x + y + 10);
X = X - fix(X/(2*pi)) * 2*pi;
end

It basically returns a real value between 0 and 2pi

[Walter Roberson]

There are different library routines to deal with complex numbers

[Isa Hendriks]

Could you suggest a different one than the one that I am using right now? And explain how to implement it?

[dpb]

Walter just means the internal runtime libraries aren't the same for real and complex; not that you have a choice.

[Walter Roberson]

dpb is exactly right. The high performance internal libraries (used for larger arrays) are specialized into real-only and complex-valued versions. The real-only versions can store more array entries at a time into primary cache, so they can be faster.

Answer 1

[Steven Lord]

Your phasevector2D function can accept arrays of values for the x and y inputs. If you vectorize your expression for f, you don't even need the nested for loops. Hint:

x = [1 2];
y = [3; 4; 5];
z = x + y

This works as of release R2016b when implicit expansion was introduced.

[Isa Hendriks]

That solved my problem! Runs in an instant now, thanks so much!