Using logically indexed vector in a loop to create another vector

I have a vector `p=[-3 -2 -1 0 1 2 3]`, and an expression for and for ; and c have values. I want to create a vector . How to write a `for` loop to implement the above statement? The code I wrote to implement the first part of the statement is

k=2; p=[-3 -2 -1 0 1 2 3]; c=1; a=5; b=9;
L=logical(p);
p(L);
  for K = 1:numel(L)
      if L(K) < 1
          L(K) = a*exp(1i*K*k)+b*exp(-1i*K*k)
      end
  end

However, it returns error "Complex values cannot be converted to logicals". Secondly, the output for p(L) doesn't have the value 0 in it. I did it with a direct way which is not convenient for large vectors.

psi_33 = a*exp(-1i*3*k)+b*exp(1i*3*k);
psi_22 = a*exp(-1i*2*k)+b*exp(1i*2*k);
psi_11 = a*exp(-1i*1*k)+b*exp(1i*1*k);
psi_0 = a+b;
psi_1 = c*exp(1i*k);
psi_2 = c*exp(1i*2*k);
psi_3 = c*exp(1i*3*k);
phi11=[psi_33,psi_22,psi_11,psi_0,psi_1,psi_2,psi_3];

Answer 1

[KSSV]

p=[-3 -2 -1 0 1 2 3] ;

phi = zeros(size(p)) ;
for i = 1:length(p)
    if -3<p(i)<1
        % phi(i) = your expression
    elseif 1<=p(i)<=3
        % phi(i) = your expression
    end
end

[AtoZ]

@KSSV thanks. So the extra zeros won't effect? e.g., the first element is

phi = 13.4424 - 1.1177i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i

Secondly, how to call a specific `phi` to use it at a later stage? simply using `phi(i)`?

So essentially there was no need to do the logical indexing because of negative and zero elements in p?

[KSSV]

YOu can call by phi(i).....yes you need to go for logical indexing.....using logical indexing, you can vectorize the code and avoid loop.

[AtoZ]

@KSSV with your code, I won't need a logical indexing?

[AtoZ]

@KSSV For example, for p=-2 using your following code, and comparing the results of phi(2) (from your code) with the manually calculated phi(2) do not match?

Manual

phi_22 = a*exp(-1i*2*k)+b*exp(1i*2*k)

your code:

p=[-3 -2 -1 0 1 2 3] ;
phi = zeros(size(p)) ;
for i = 1:length(p)
    if -3<p(i)<1
         phi(i) = a*exp(1i*p(i)*k)+b*exp(-1i*p(i)*k);
    elseif 1<=p(i)<=3
         phi(i) = c*exp(p(i)*k);
    end
end
phi(2)

Answer 2

[Andrei Bobrov]

a = 5;
b = 9;
c = 1;
p = (-3:3)';
k = 2;

out = psifun(a,b,c,k,p);

here psifun - function:

function out = psifun(a,b,c,k,p)
    a = [a;c];
    b = [b;0];
    ii = (p >= 1) + 1;
    x = 1i*k.*p;
    out = a(ii).*exp(x) + b(ii).*exp(-x);
end