Matrix inversion algorithm and program implementation (c + +)

In the course of doing the project, we encountered the problem of finding polynomial, and used the method of seeking inverse. Matrix inversion generally uses a simple algorithm, there are fast algorithms such as the full selection of the main element Gauss-Jordan elimination method, but this program mainly wrote a simple matrix inverse algorithm definition method of the adjoint matrix inverse formula is as follows, where a reversible:

, where the adjoint matrix is:

1. Given a square, non-singular (not also can, the procedure is considered);

2. The matrix gets its determinant, the value such as | a|;

3. To seek its adjoint matrix;

4. Get its inverse matrix.

The main functions are as follows:

1 //the inverse matrix of the given matrix SRC is saved to Des. 2 BOOLGetmatrixinverse (DoubleSrc[n][n],intNDoubleDes[n][n])3 {4     Doubleflag=Geta (src,n);5     DoubleT[n][n];6     if(flag==0)7     {8         return false;9     }Ten     Else One     { A Getastart (src,n,t); -          for(intI=0; i<n;i++) -         { the              for(intj=0; j<n;j++) -             { -des[i][j]=t[i][j]/Flag; -             } +  -         } +     } A  at  -     return true; -  -}

Calculation | a|:

1 //expand calculation by First line | a|2 DoubleGeta (DoubleArcs[n][n],intN)3 {4     if(n==1)5     {6         returnarcs[0][0];7     }8     DoubleAns =0;9     Doubletemp[n][n]={0.0};Ten     inti,j,k; One      for(i=0; i<n;i++) A     { -          for(j=0; j<n-1; j + +) -         { the              for(k=0; k<n-1; k++) -             { -Temp[j][k] = arcs[j+1[(k>=i) K +1: K]; -  +             } -         } +         Doublet = Geta (temp,n-1); A         if(i%2==0) at         { -Ans + = arcs[0][i]*T; -         } -         Else -         { -Ans-= arcs[0][i]*T; in         } -     } to     returnans; +}

To compute the adjoint matrix:

1 //calculates the cofactor for each element of each column of each row, forming a *2 voidGetastart (DoubleArcs[n][n],intNDoubleAns[n][n])3 {4     if(n==1)5     {6ans[0][0] =1;7         return;8     }9     inti,j,k,t;Ten     DoubleTemp[n][n]; One      for(i=0; i<n;i++) A     { -          for(j=0; j<n;j++) -         { the              for(k=0; k<n-1; k++) -             { -                  for(t=0; t<n-1; t++) -                 { +Temp[k][t] = arcs[k>=i?k+1: k][t>=j?t+1: t]; -                 } +             } A  at  -Ans[j][i] = Geta (temp,n-1); -             if((i+j)%2==1) -             { -Ans[j][i] =-Ans[j][i]; -             } in         } -     } to}

These three functions constitute the inverse matrix of the steps, the author calls and successful use, no fault, in this mutual encouragement. If you have any questions, please leave a message. Thank you

Other matrix inverse good algorithm and code please share.

Matrix inversion algorithm and program implementation (c + +)