Inv
Inv
Compute the multiplicative inverse of a square invertible matrix by the Jordan-Gauss method.
matrix matrix::Inv()Return Value
Multiplicative inverse of the matrix.
Note
The product of the original matrix and the inverse matrix is the identity matrix.
If at least one matrix row or column is zero, the inverse matrix cannot be obtained.
If two or more matrix rows or columns are linearly dependent, the inverse matrix cannot be obtained.
Example
int TestInverse(const int size_m)
{
int i,j,errors=0;
matrix matrix_a(size_m,size_m);
//--- populate the square matrix
MatrixTestFirst(matrix_a);
//--- microseconds will be measured
ulong t1=GetMicrosecondCount();
//--- get the inverse matrix
matrix inverse=matrix_a.Inv();
//--- measure
ulong t2=GetMicrosecondCount();
//--- check the correctness
matrix identity=matrix_a.MatMul(inverse);
//---
for(i=0; i<size_m; i++)
{
for(j=0; j<size_m; j++)
{
double value;
//--- ones must be along the diagonal
if(i==j)
value=1.0;
else
value=0.0;
if(MathClassify(identity[i][j])>FP_ZERO)
errors++;
else
{
if(identity[i][j]!=value)
{
double diff=MathAbs(identity[i][j]-value);
//--- too many multiplications and devisions, so reduce the check accuracy
if(diff>1e-9)
errors++;
}
}
}
}
//---
double elapsed_time=double(t2-t1)/1000.0;
printf("Inversion of matrix %d x %d %s errors=%d time=%.3f ms",size_m,size_m,errors==0?"passed":"failed",errors,elapsed_time);
return(errors);
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