Loop over two variables

I have a formula

U(x,y) = some formula that depends on x and y

x and y are Cartesian coordinates and U is the output that depends on x and y.

I want to create an array U that contains the value of U for many x and y. Usually, I would use meshgrid, but do not want to do this (for particular reasons..).

The domain of x and y is something like x from -x to +x in small definable increments y from -y to +y in small definable increments

So I guess I will have two loops one nested in another?

So it might be y = -y then calculate all values of U for all x and for fixed y = -y

then increase the value of y incrementally and calculate all values of U for all x and y+increment of y

This seems simple, but I am getting confused!

thanks for your help W

[dpb]

Well, the end result will be same as if you had used meshgrid so why not?

ic=0;        
x=-xL:dx:xH
for y=-yL:dy:yH
  U(:,ic)=fnU(x,y);
end

vectorizes over x for each y. NB: fnU must return column vector and you'll want to preallocate before the loop based on length() two X,_Y_ vectors.

[William White]

Meshgrid is failing. There is a term in the function that changes depending on the relationship between x,y and a host of other variables. Say this term is called T. I have to run IF statements to define T for every x and y before I calculate U. This fails using the meshgrid approach.

[dpb]

That means your vectorized function fails, not meshgrid

Can you illustrate the problem in a reasonably short function? Generally there's a way to vectorize even with if

[William White]

The function U is complicated and has many variables.

One such variable, T is

T = atan a + atan b

where a and b are functions of x and y too.

So the function is something along the lines of

U = x,y,T, etc.etc.

I have to determine the relationship between a and b along the lines of

If a>0 and ab<-1 then T = something else

etc. etc.

So using the meshgrid a and b are arrays rather than single values.

Once the programme runs through the logic for a single value of a and b, T is defined.

When a and b are arrays, T is not defined.

I can post the function in full here, but it is rather long (very long)

[dpb]

"If a>0 and b<-1 then T = ... So using the meshgrid a and b are arrays rather than single values."

Sure. But logical addressing can solve that dilemma...

isAB=(a>0 & b<-1);    % logical array of condition
T( isAB)=whatever(x(isAB),y(isAB),Q,R,S,...);       % compute those
T(~isAB)=thealternate(x(~isAB),y(~isAB),Q,R,S,...); % the rest

Answer 1

[Geoff Hayes]

William - you could do something like the following if you assume that you know your domains for x and y.

 numElementsX = length(x);
 numElementsY = length(y);
 U = zeros(numElementsX, numElementsY);
 for r=1:numElementsX
    for s=1:numElementsY
        U(r,s) = func(x(r),y(s));  % func is just some function that you have defined
    end
 end

So like you thought, we can use two loops to iterate over all elements contained in the x array and those in the y array. On each iteration of the outer loop, we fix the value of x to be x(r) and then iterate over each element in the y array. And then repeat for the next value of x.

[William White]

I'll give it a go. My domain for x and y is something like -3E-9 to +3E-9 with about 1000 increments (these are very small distances!).

Does this loop work for negative values of x and y?

[dpb]

I'm still not convinced you can't use meshgrid (with some rework of your function, of course), but for those kinds of numbers use linspace

x=linspace(xLo,xHi,1000);  % ditto for y

then as above iterate over x,_y_

The alternative as shown above still works as well altho again you would need to vectorize fnU(x,y) to make use of it.

BTW, it'll probably run noticeably faster if you switch order of for loops and iterate over r first; that is sequential memory storage order in Matlab. 1000x1000 is small enough may not make much difference, but...