问题
I wrote a inversion function for an n*n square matrix.
void inverseMatrix(int n, float **matrix)
{
float ratio,a;
int i, j, k;
for(i = 0; i < n; i++)
{
for(j = n; j < 2*n; j++)
{
if(i==(j-n))
matrix[i][j] = 1.0;
else
matrix[i][j] = 0.0;
}
}
for(i = 0; i < n; i++)
{
for(j = 0; j < n; j++)
{
if(i!=j)
{
ratio = matrix[j][i]/matrix[i][i];
for(k = 0; k < 2*n; k++)
{
matrix[j][k] -= ratio * matrix[i][k];
}
}
}
}
for(i = 0; i < n; i++)
{
a = matrix[i][i];
for(j = 0; j < 2*n; j++)
{
matrix[i][j] /= a;
}
}
//return matrix;
}
This works fine in almost all cases but is failing in some cases like the ones shown here:
1 1 1 0 1 1 1 0
1 1 2 0 1 1 2 0
1 2 0 1 1 2 1 0
1 2 0 2 1 2 0 2
What could be the case I am overlooking?
Thanks!
回答1:
see http://www.sourcecodesworld.com/source/show.asp?ScriptID=1086.
uses the Gauss Jordan algorithm
#include<stdio.h>
#include<stdlib.h>
int main()
{
float **A,**I,temp;
int i,j,k,matsize;
printf("Enter the size of the matrix(i.e. value of 'n' as size is
nXn):");
scanf("%d",&matsize);
A=(float **)malloc(matsize*sizeof(float *)); //allocate memory
dynamically for matrix A(matsize X matsize)
for(i=0;i<matsize;i++)
A[i]=(float *)malloc(matsize*sizeof(float));
I=(float **)malloc(matsize*sizeof(float *)); //memory allocation for
indentity matrix I(matsize X matsize)
for(i=0;i<matsize;i++)
I[i]=(float *)malloc(matsize*sizeof(float));
printf("Enter the matrix: "); // ask the user for matrix A
for(i=0;i<matsize;i++)
for(j=0;j<matsize;j++)
scanf("%f",&A[i][j]);
for(i=0;i<matsize;i++) //automatically initialize the unit matrix, e.g.
for(j=0;j<matsize;j++) // - -
if(i==j) // | 1 0 0 |
I[i][j]=1; // | 0 1 0 |
else // | 0 0 1 |
I[i][j]=0; // - -
/*---------------LoGiC starts here------------------*/ //procedure // to make the matrix A to unit matrix
for(k=0;k<matsize;k++) //by some row operations,and the same row operations of
{ //Unit mat. I gives the inverse of matrix A
temp=A[k][k]; //'temp'
// stores the A[k][k] value so that A[k][k] will not change
for(j=0;j<matsize;j++) //during the operation //A[i] //[j]/=A[k][k] when i=j=k
{
A[k][j]/=temp; //it performs // the following row operations to make A to unit matrix
I[k][j]/=temp; //R0=R0/A[0][0],similarly for I also
R0=R0/A[0][0]
} //R1=R1-R0*A[1][0] similarly for I
for(i=0;i<matsize;i++) //R2=R2-R0*A[2][0] ,,
{
temp=A[i][k]; //R1=R1/A[1][1]
for(j=0;j<matsize;j++) //R0=R0-R1*A[0][1]
{ //R2=R2-R1*A[2][1]
if(i==k)
break; //R2=R2/A[2][2]
A[i][j]-=A[k][j]*temp; //R0=R0-R2*A[0][2]
I[i][j]-=I[k][j]*temp; //R1=R1-R2*A[1][2]
}
}
}
/*---------------LoGiC ends here--------------------*/
printf("The inverse of the matrix is: "); //Print the //matrix I that now contains the inverse of mat. A
for(i=0;i<matsize;i++)
{
for(j=0;j<matsize;j++)
printf("%f ",I[i][j]);
printf(" ");
}
return 0;
}
回答2:
Diagonal elems have to be scaled to 1s first before zeroing lower triangle elems (your second nested loop). It turns out that diagonal contains 0 => no inverse exists OR we get a row echelon form. With a reversed iteration on diagonal we can reduce it and get the inverse. The code is far from optimal. When you have FPU, double could be a better choice than float for such numerical computations.
Note that zeroing submatrices, row swaps etc. could be replaced by far more optimal solutions. Matrix is a custom type and IsFloat0 is a custom function but all should be clear of naming and context. Enjoy code:
const uint sz = 4;
Matrix< double > mx;
mx.Resize( 2 * sz, sz );
mx.Zero();
for( uint rdx = 0; rdx < mx.NumRow(); ++rdx )
{
mx( rdx, rdx + mx.NumRow() ) = 1.0; // eye
}
mx( 0, 0 ) = 1.0; mx( 0, 1 ) = 1.0; mx( 0, 2 ) = 1.0; mx( 0, 3 ) = 0.0;
mx( 1, 0 ) = 1.0; mx( 1, 1 ) = 1.0; mx( 1, 2 ) = 2.0; mx( 1, 3 ) = 0.0;
mx( 2, 0 ) = 1.0; mx( 2, 1 ) = 2.0; mx( 2, 2 ) = 0.0; mx( 2, 3 ) = 1.0;
mx( 3, 0 ) = 1.0; mx( 3, 1 ) = 2.0; mx( 3, 2 ) = 0.0; mx( 3, 3 ) = 2.0;
// pivot iteration
uint idx;
for( idx = 0; idx < sz; ++idx )
{
// search for non-0 pivot
uint sdx = sz;
for( uint rdx = idx; rdx < sz; ++rdx )
{
if( !Util::IsFloat0( mx( rdx, idx ) ) ) { sdx = rdx; rdx = sz - 1; }
}
if( sdx < sz )
{
// swap rows
if( idx != sdx )
{
for( uint cdx = 0; cdx < ( sz << 1 ); ++cdx )
{
double swp;
swp = mx( idx, cdx );
mx( idx, cdx ) = mx( sdx, cdx );
mx( sdx, cdx ) = swp;
}
}
// 1 pivot and 0 col
{
double sc = 1.0 / mx( idx, idx );
for( uint cdx = 0; cdx < ( sz << 1 ); ++cdx )
{
mx( idx, cdx ) *= sc; // 1
}
for( uint rdx = 1 + idx; rdx < sz; ++rdx )
{
double sd = mx( rdx, idx );
for( uint cdx = 0; cdx < ( sz << 1 ); ++cdx )
{
mx( rdx, cdx ) -= sd * mx( idx, cdx ); // 0
}
}
}
}
else { idx = sz; }
}
if( sz < idx ) { mx.Zero(); }
else
{
for( idx = 0; idx < sz; ++idx )
{
uint ydx = sz - 1 - idx;
for( uint rdx = 0; rdx < ydx; ++rdx )
{
double sc = mx( rdx, ydx );
for( uint cdx = 0; cdx < ( sz << 1 ); ++cdx )
{
mx( rdx, cdx ) -= sc * mx( ydx, cdx ); // 0
}
}
}
}
来源：https://stackoverflow.com/questions/32043346/square-matrix-inversion-in-c