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//Eg-3.3
//pg-71
clear
clc
// Matrix dimensions for a 3*3 coefficient matrix
n=3;
//First pass
k=0;
//Number of divisions per pass i.e for a particular value of 'k'
ndiv=n-k-1;
//Number of multiplications
nmul=(n-k)*(n-k-1);
//Total number of multiplications and divisions
ntot=nmul+ndiv;
//Displaying result
disp("total number of divisions and multiplications from formulae derived")
disp(ntot)
//Verifying result from example 3.2 by taking k=1(first pass)
// Matrices A and B (AX=B)
a=[1 1 -1;1 2 -2;-2 1 1];
[n,n]=size(a);
b=[1;0;1];
//Augumented matrix of A and B
auga=[a b];
//initialising nm(no of multiplications),nd(no. of divisions)
nd=0;
nm=0;
//Forward elimination
for k=1//only first pass is considered
for i=(k+1):n
factr=auga(i,k)/auga(k,k);
nd=nd+1;
auga(i,:)=auga(i,:)-factr*auga(k,:);
nm=nm+3;//since each row has 3 elements of A,hence 3 multiplications
end
end
//Total number of divisions and multiplications
nt=nd+nm;
//Verifying result
disp("total number of divisions and multiplications from code of example 3.2")
disp(nt)
disp("both are same")
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