More Recursion Help Needed

Hi again everyone,

I became stuck on another section of my lab saying this:

Error in ==> pnm at 6
if ((n ~= 0 && m ~= 0) || (n~=0 && m==0) || (n==0 && m~=0))

??? Output argument "values" (and maybe others) not assigned
during call to "E:\Matlab\ENGO423-Lab2\pnm.m>pnm".

Error in ==> pnm at 19
            pnmCurrentn =
            ((2*n-1)/(n-m)).*cos(theta).*pnm(n-1,m,theta,norm)-((n+m-1)/(n-m))*pnm(n-2,m,theta,norm);

Error in ==> main at 24
set2non = pnm(3,1,theta,0);

Here are my codes:

Main:

    close all
  clear all
  clc
theta = [-pi:pi/100:pi]';
plotValues = cos(theta);

set1 = pnm(1,1,theta,1);
set2 = pnm(3,1,theta,1);
set3 = pnm(5,1,theta,1);
set4 = pnm(7,1,theta,1);

hold on
plot(plotValues,set1,'g');
plot(plotValues,set2,'r');
plot(plotValues,set3,'m');
plot(plotValues,set4,'b');
axis([-1 1 -4 4]);

legend('n=1; m=1','n=3; m=1', 'n=5; m=1', 'n=7; m=1')

set1non = pnm(1,1,theta,0);
set2non = pnm(3,1,theta,0);
%set3non = pnm(5,1,theta,0);
%set4non = pnm(7,1,theta,0);

pnm:

    function [ values ] = pnm( n,m,theta,norm )
%What to do...

if ((n ~= 0 && m ~= 0) || (n~=0 && m==0) || (n==0 && m~=0))

      if (norm == 0 )
          if (m >= 2)
              pnmCurrentn = 2*(m-1)*((cos(theta)/sqrt(1-cos(theta)^2)))*pnm(n,m-1,theta,norm)-(n-m+2)*(n+m-1)*pnm(n,m-2,theta,norm);
              values = pnmCurrentn;
          elseif (norm == 0 && m == 0)
              pn = -((n-1)/n)*pnm(n-2,0,theta,norm)+((2*n-1)/n)*(cos(theta))*pnm(n-1,0,theta,norm);
              values = pn;
          elseif ( norm == 0 && n >= m+2)
              pnmCurrentn = ((2*n-1)/(n-m)).*cos(theta).*pnm(n-1,m,theta,norm)-((n+m-1)/(n-m))*pnm(n-2,m,theta,norm);
              values = pnmCurrentn;
          elseif (norm == 0 && n==1 && m==1)
              values = sin(theta);
          end
      elseif ( norm == 1)
          if ( n == 1 && m == 1)
              w11 = sqrt(3);
              values = w11*sqrt((1-cos(theta).^2))*pnm(m-1,m-1,theta,norm);
          elseif (( n==0 && m==0) || (n==0 && m~=0) || (n~=0 && m==0))
              values = 1;
          elseif ( n == m  )
          wmm = sqrt((2*m-1)/(2*m));
          values = wmm*(1-cos(theta)^2)^(1/2)*pnm(m-1,m-1,theta,norm);
          elseif ( (n ~= m) && (n~=0 || m~=0) )
          wnm = sqrt(((2*n+1)*(2*n-1))/((n+m)*(n-m)));
          wnmB = sqrt(((2*(n-1)+1)*(2*(n-1)-1))/(((n-1)+m)*((n-1)-m)));
          values = wnm*(cos(theta).*pnm(n-1,m,theta,norm)-inv(wnmB)*pnm(n-2,m,theta,norm));        
          end
      end
elseif ((n == 0 && m == 0))

      if (norm ~= 1)
          values = 1; 
      elseif (norm == 1)
          values = 1;
      end
end

end

If anyone can assist me in finding my error again that would be greatly appreciated.

Answer 1

[Amin Bashi]

see the 11th and 12th lines of pnm function elseif ( norm == 0 && n >= m+2) pnmCurrentn = ((2*n-1)/(n-m)).*cos(theta).*pnm(n-1,m,theta,norm)-((n+m-1)/(n-m))*pnm(n-2,m,theta,norm);

when u call pnm with pnm(3,1,theta,0), it call pnm again with (2,1,theta,0) in line 12; but u don't have this condition in your code