How to write a function with logical condition which takes an array and turns back an array?

What I want to acheive is the following. Let's say I have the function if and .

I have two vectors with nodes: x and y and I would like to calculate the function mentioned abose as an array. I can do it straightforwardly as

A = zeros(length(x), length(y));

for i = 1 : length(x)

for j = 1 : length(y)

if (x(i) ~= y(j))

A(i,j) = sin(alpha*(x(i) - y(j))) / (alpha * (x(i) - y(j)));

else

A(i,j) = 1;

end

end

end

This way is not really fast. I would like to have a function that will produce similar output as this cycle. More precisely, I would like to have the output in the form which is applicable for the trapz() command to calculate the double integral after all

trapz(y, trapz(x, K, 2))

there K has been calculated previously

I was trying something loke this

function val = K(alp, x, y)

% [x, y] = meshgrid(x, y); %% I was trying different variants here

% [x, y] = ndgrid(x, y);

if (x ~= y)

val = sin(alp * (x - y)) ./ ( alp * (x - y) );

else

val = 1;

end

end

but, of course, it did not work. Could you tell me, please, how shall I rewrite this function to achieve what I mentioned?

Answer 1

[Matt J]

K=sinc(alpha/pi*(x-y.'));

[Bogdan MP]

Thank you for the answer. In fact, I have a more fancy function that cannot be written as one function. Could you tell me please if the same structure can be rewritten in the form I used in my example? With the following logical construction:

if (x ~= y)

K = one story

else

K = another store

end

?

[Matt J]

No, not without a loop. You could do

mask=(x=y.');

K=K1.* mask+K2.*(~mask);

[Bogdan MP]

Unfortunately, looks like it doesn't work even for the sinc() case (or, probably, I didn't get you correct). I considered

function val = Ker(x, y)

mask = (x == y.');

K1 = sin(pi * (x - y.')) ./ ( pi * (x - y.') );

K2 = 1;

val = K1.* mask + K2.*(~mask);

end

And runned

x = [1 : 1 : 5] / pi;

y = [3 : 1 : 7] / pi;

Ker(x, y)

The result was

1 1 NaN 1 1

1 1 1 NaN 1

1 1 1 1 NaN

1 1 1 1 1

1 1 1 1 1

I tried exchange them (val = K2.* mask + K1.*(~mask); ) and got

0.4546 0.8415 NaN 0.8415 0.4546

0.0470 0.4546 0.8415 NaN 0.8415

-0.1892 0.0470 0.4546 0.8415 NaN

-0.1918 -0.1892 0.0470 0.4546 0.8415

-0.0466 -0.1918 -0.1892 0.0470 0.4546

[Matt J]

x = (1:5) / pi;
y = (3:7) / pi;

K = sin(pi * (x - y.')) ./ ( pi * (x - y.') );
K(x == y.')=1       

K = 5×5

0.4546 0.8415 1.0000 0.8415 0.4546 0.0470 0.4546 0.8415 1.0000 0.8415 -0.1892 0.0470 0.4546 0.8415 1.0000 -0.1918 -0.1892 0.0470 0.4546 0.8415 -0.0466 -0.1918 -0.1892 0.0470 0.4546

[Bogdan MP]

Thank you very much!