Write a MATLAB function called zgemm that computes the generalized matrix multip

Question

Write a MATLAB function called zgemm that computes the generalized matrix multiplication alphaAB + betaC using loops, where A, B, and C are matrices and alpha and beta are scalar values. The input order should be (alpha, A, B, beta, C). Check for proper dimensions on each input, report any error and return an empty matrix if they are incorrect. Do not use MATLAB's matrix multiply functions inside this function. Use alpha=0.1, A=[5 7;11 9;0 2], B=[1 2 3 4; 9 8 7 6], C=eye(n,m), beta=0.9 to test zgemm and compare to MATLAB matrix multiply (>>alpha*A*B+beta*C)

Explanation / Answer

% This function computes alpha*A*B+ beta*C without using matlab's inbuilt multiplication.

function mul = zgemm(alpha,A,B,beta,C)
D=multiply(alpha,A);
D=multiply(D,B);
mul=multiply(beta,C);
mul=D+mul;
end

function mul=multiply(A,B)
[m n]=size(A);
[p q]=size(B);

sum=0;
mul=zeros(m,q);
if(m~=1 || n~=1)
  
if(n~=p) 'Matrix dimensions do not match'
else
for c=1:m
for d=1:q
for k=1:p
sum = sum + A(c,k)*B(k,d);
end
mul(c,d)=sum;
sum=0;
end
end
end
else
for i=1:p
for j=1:q
B(i,j)=A*B(i,j);
end
end
mul=B;
end

end

OUTPUT:

alpha=0.1; A=[5 7;11 9;0 2]; B=[1 2 3 4; 9 8 7 6]; C=eye(3,4); beta=0.9;
>> alpha*A*B+beta*C

ans =

7.7000 6.6000 6.4000 6.2000
9.2000 10.3000 9.6000 9.8000
1.8000 1.6000 2.3000 1.2000

>> zgemm(alpha,A,B,beta,C)

ans =

7.7000 6.6000 6.4000 6.2000
9.2000 10.3000 9.6000 9.8000
1.8000 1.6000 2.3000 1.2000

>>

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