Question

2. Suppose we want to multiply two N-by-N matrices, C-A B, by following the componentwise formula に1 (a) What are the operation counts? (b) In floating-point arithmetic, for which of these operations does the order matter? (c) Write a Matlab program that implements this formula.

Answer 1

Matlab code for matrix multiplication clear all close all Matrix of order N h-5; %1st matrix A-rand (N,N); fprintf'1st matrix is A-n disp(A) 2nd matrix B-rand (N,N); fprintf2nd Matrix is B-n) disp (B) %code for matrix multipl iction CNT-0; for i= 1:N for j-l:N sum=0; for k-1:N sum-sum-A ( i, k)" B ( k, j ) ; end c(i,j)-sum; end end fprintf( The matrix C A*Bn') disp (C) fprintf(,\n\tTotal number of ope ration count fprint f("AtAmong which %d are sum operations is %d\n',2*N*N*N); and %d are multiplications.\n ,NWN N,N N*N) fprintftFor multiplication operation order matters.\n') 용욤욤응%号号%%号号%%号号%%号号%% End of Code 응용욤응응용욤응응용욤응융욤욤응응용 1st matrix is A- 0.1041.4 0.057777 0.74319 0.87497 0.86187 0.90507 0. 20399 0.41756 0. 76974 0.62697 0.61866 0. 79554 0.18574 0.50936 0.8942.1 0.075046 0. 75218 0.40398 0.1147 0. 26997 0.06444 0.39493 0.6837 0.70347 0.087424

2nd Matrix is B= 0. 92047 0.85471 0. 96215 0.45747 0.22997 0.74021 0. 75424 0.029836 0.53637 0.028759 0.20939 0.22189 0.091843 0.18745 0.93267 0.56841 0.71087 0.53549 0.17975 0.025744 0.57587 0.58466 0.8645.1 0.58422 0.35414 The matrix C-A B 0.50076 0.97229 0.98386 1.1192 1.2974 0.59932 0.87258 1.0888 1.4399 1.3849 1.0158 0.51277 0.7585 1.1611 1.0044 0. 8402 1.4451 1.438 1.5876 1.5253 0.9683 1.7329 1.6037 1.8259 2.0037 Total number of operation count is 250 Among which 125 are sum operations and 125 are multiplications. For multiplication operation order matters Published with MATLABE R2018a

%Matlab code for matrix multiplication
clear all
close all

%Matrix of order N
N=5;

%1st matrix
A=rand(N,N);

fprintf('1st matrix is A=\n')
disp(A)

%2nd matrix
B=rand(N,N);

fprintf('2nd Matrix is B=\n')
disp(B)

%Code for matrix multipliction
CNT=0;
for i=1:N
  
    for j=1:N
      
        sum=0;
      
        for k=1:N
            sum=sum+A(i,k)*B(k,j);
          
        end
      
        C(i,j)=sum;
    end
end

fprintf('The matrix C=A*B= \n')
disp(C)

fprintf('\n\tTotal number of operation count is %d\n',2*N*N*N);
fprintf('\tAmong which %d are sum operations and %d are multiplications.\n',N*N*N,N*N*N)
fprintf('\tFor multiplication operation order matters.\n')

%%%%%%%%%%%%%%%%%%%%% End of Code %%%%%%%%%%%%%%%%%%