Matrix manipulation code performing unknown operations -


i having trouble understanding of following code. think middle section of code point out performing multiplication, not sure, can please explain me middle part of code trying accomplish?

i understand input , output parts of array elements, not actual manipulations.

i understand this: 

 #include "stdafx.h"     #include<iostream>     using namespace std;     int main()     {        int i,j,k,n;        float a[100][200],t;        cout<<"enter order of matrix-";        cin>>n;        cout<<"enter elements of matrix"<<endl;        for(i=0;i<n;i++)           for(j=0;j<n;j++)              cin>>a[i][j];

but following lines confusing:

      for(i=0;i<n;i++)        {           for(j=n;j<2*n;j++)           {               if(i==j-n)                  a[i][j]=1;              else                  a[i][j]=0;            }        }        for(i=0;i<n;i++)        {           t=a[i][i];           for(j=i;j<2*n;j++)               a[i][j]=a[i][j]/t;           for(j=0;j<n;j++)           {              if(i!=j)              {                 t=a[j][i];                 for(k=0;k<2*n;k++)                     a[j][k]=a[j][k]-t*a[i][k];               }           }        }

again, following lines understandable:

cout<<"\n\ninverse matrix\n\n";        for(i=0;i<n;i++)        {           for(j=n;j<2*n;j++)              cout<<"\t"<<a[i][j];           cout<<"\n";         }     return 0;     }

your code attempting invert matrix. here code doing.

assuming have nxn matrix a, can create new nx2n matrix

b = ai

where nxn identity matrix. creation of b these lines trying do:

for(i=0;i<n;i++)        {           for(j=n;j<2*n;j++) // makes sure accessing columns in right hand part of matrix           {               if(i==j-n)                  a[i][j]=1;              else                  a[i][j]=0;            }        }

you perform series of row operations on 2n wide matrix identity matrix on left hand side resulting in third matrix

c=id

where again nxn identity matrix. creation of c through row operations part of code trying do: (though won't speak correctness of algorithm being used has been while since have done , typically use svd algorithm inverses)

for(i=0;i<n;i++) //transform b matrix c matrix        {           t=a[i][i];           for(j=i;j<2*n;j++)               a[i][j]=a[i][j]/t;           for(j=0;j<n;j++)           {              if(i!=j)              {                 t=a[j][i];                 for(k=0;k<2*n;k++)                     a[j][k]=a[j][k]-t*a[i][k];               }           }        }

now when complete row operations , identity matrix on left hand side of c matrix, turns out nxn d matrix makes right hand side of c matrix inverse of a. have

ad = i

which why last bit of code grabs right hand side of called c matrix.

that's code trying do. if want understand more theory behind it, take @ "numerical recipes in c" book. it's gold standard kind of thing , freely available online. http://www.nrbook.com/a/bookcpdf.html


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