Kindly help me understand this code, it is a user defined function for multiplying two polynomials

User-defined function:

p1 = [2 5 3];
p2 = [4 0 5 8 12];
p = polymult(p1,p2)

p = 1×7

8 20 22 41 79 84 36

p_matlab = conv(p1,p2)

p_matlab = 1×7

8 20 22 41 79 84 36

function p = polymult(p1,p2) 
%Multiply polynomials 
na=length(p1); nb=length(p2);
if nb > na d=p1; p1=p2;
    clear b 
    p2=d; nd=na; na=nb; nb=nd; 
end
for k=1:nb 
    p(k)=0;
    for i=1:k
        p(k)=p(k)+p1(i)*p2(k+1-i); 
    end 
end
for k=nb+1:na 
    p(k)=0; for i=k-nb+1:k 
        p(k)=p(k)+p1(i)*p2(k+1-i);
    end 
end 
for k=na+1:na+nb-1
    p(k)=0; for i=k-nb+1:na 
        p(k)=p(k)+p1(i)*p2(k+1-i); 
    end 
end
end

[John D'Errico]

Are you asking why the user written code does the same thing as conv (though poorly written IMHO), for multiplying two polynomials? Are you asking how that godawful code works at all?

Note that a well written code to perform the multiply need use only one set of loops not three separate sets of loops. As well, a well written code would actually have more than one comment line, so as to be self-documenting. I could make a few more points in this. But if you got that code for free, then it is likely worth exactly what you paid for it: nothing.

Answer 1

[John D'Errico]

I'm sorry, but that code is complete crapola. Better code might look something like that below.

Test it out.

p1 = [2 5 3];
p2 = [4 0 5 8 12];
p12 = polymult(p1,p2)

p12 = 1×7

8 20 22 41 79 84 36

pconv = conv(p1,p2)

pconv = 1×7

8 20 22 41 79 84 36

function pprod = polymult(P1,P2)
  % simple polynomial multiply code
  n1 = numel(P1); n2 = numel(P2);
  
  % known length of the result
  nprod = n1 + n2 - 1;
  
  % pre-allocate final result as all zeros
  pprod = zeros(1,nprod);
  
  % single loop to perform the multiply, though it is actually
  % an implicit double loop, since a scalar*vector multiply is employed
  for i1 = 1:n1
    ind = i1+(0:n2-1);
    % just multiply every element of P1 with all of the elements of P2,
    % and sum them up.
    pprod(ind) = pprod(ind) + P1(i1)*P2;
  end
end

Note that the explanation of why and how the code works is complete, and inside the code. I would expect that the use of conv would be faster, since conv will be compiled code.

[Tanui Redempter]

The question actually is,write a user defined function that multiplies two polynomials,function name,p=polymult(p1,p2) The input arguments p1 and p2 are vectors of coefficients of the two polynomials.The output argument is the resulting polynomial.

[Tanui Redempter]

But thanks 😊

[John D'Errico]

So let me see. I did write exactly that, no? Is that not true?

[Tanui Redempter]

Thank you John