apply a function to vector

I have a function like

fn=@(a) [a(1,:).^2 ; a(2,:).^2 ; 1]

i want to apply it to matrix

w=[2 3 4 5; 1 2 3 4]

but i is giving error CAT dimensions must agree.

i can evaluate it in a loop for every column of 'w'

but since 'fn' has third row as a constant, it cannot extend it to vector

ny idea how to vectorise this fn(w)

or what could i have done had i got a function like

fn=@(a)[a(1)^2;a(2)^2;1]

ie it cannot be vectorized, but i want to evaluate fn for a matrix of size 2xN

Answer 1

[Walter Roberson]

a(1,:)^2 will not generally work. It means a(1,:) * a(1,:) which is matrix multiplication of a 1xN by a 1xN but in matrix multiplication the inner dimensions must agree so a(1,:)^2 can only work if "a" only has a single row. Perhaps you mean .^2 instead of ^2 ?

Anyhow: ones(1, size(a,2))

[Archit]

I am getting this fn from somewhere.. i cannot modify it later on. So i have to do with what i have.

Answer 2

[Sargondjani]

you can loop for the second equation you gave for fn (the one with ^2):

fn=@(a)[a(1)^2;a(2)^2;1];
w=...

for iw=1:size(w,2));
y(iw)=fn(w(:,iw));
end

this should give you the answer in 3x1 vector. but i would still recommend using the other function (after adjusting it):

fn=@(a) [a(1,:).^2 ; a(2,:).^2 ; ones(1, size(a,2))];

(as Walter suggested)

and then

y=fn(w)

should give the same result (but faster)