// matrix inversion
// the result is put in Y
void Camera::MatrixInversion(float **A, int order, float **Y)
{
// get the determinant of a
double det = 1.0/CalcDeterminant(A,order);
// memory allocation
float *temp = new float[(order-1)*(order-1)];
float **minor = new float*[order-1];
for(int i=0;i<order-1;i++)
minor[i] = temp+(i*(order-1));
for(int j=0;j<order;j++)
{
for(int i=0;i<order;i++)
{
// get the co-factor (matrix) of A(j,i)
GetMinor(A,minor,j,i,order);
Y[i][j] = det*CalcDeterminant(minor,order-1);
if( (i+j)%2 == 1)
Y[i][j] = -Y[i][j];
}
}
// release memory
//delete [] minor[0];
delete [] temp;
delete [] minor;
}
// Calculate the determinant recursively.
double Camera::CalcDeterminant( float **mat, int order)
{
// order must be >= 0
// stop the recursion when matrix is a single element
if( order == 1 )
return mat[0][0];
// the determinant value
float det = 0;
// allocate the cofactor matrix
float **minor;
minor = new float*[order-1];
for(int i=0;i<order-1;i++)
minor[i] = new float[order-1];
for(int i = 0; i < order; i++ )
{
// get minor of element (0,i)
GetMinor( mat, minor, 0, i , order);
// the recusion is here!
det += (i%2==1?-1.0:1.0) * mat[0][i] * CalcDeterminant(minor,order-1);
//det += pow( -1.0, i ) * mat[0][i] * CalcDeterminant( minor,order-1 );
}
// release memory
for(int i=0;i<order-1;i++)
delete [] minor[i];
delete [] minor;
return det;
}
// Calculate the determinant recursively.
double CalcDeterminant( float **mat, int s)
{
//Señal que detiene la recursividad
if( s == 1 )
return mat[0][0];
float det = 0;
// Generamos espacio temporal para almacenar la menor
float **minor;
minor = new float*[s-1];
for(int i=0;i<s-1;i++)
minor[i] = new float[s-1];
//Siempre obtiene la determinante usando la primer fila
for(int i = 0; i < s; i++ )
{
GetMinor( mat, minor, 0, i , s); //Sobreescribe la matriz menor
//Aqui obtenemos el cofactor, multiplicamos por el elemento en la posicion i y ahora por la determinante
det += (i%2==1?-1.0:1.0) * mat[0][i] * CalcDeterminant(minor,s-1);
}
// Quitamos el espacio usado
for(int i=0;i<s-1;i++)
delete [] minor[i];
delete [] minor;
return det;
}
int main(int argc, const char * argv[])
{
int size=3; //Definir tamaño
float **matrix = new float*[size];
for(int i =0;i<size;++i)
matrix[i]=new float[size];
matrix[0][0]=0; matrix[0][1]=2; matrix[0][2]=0;
matrix[1][0]=2; matrix[1][1]=1; matrix[1][2]=1;
matrix[2][0]=2; matrix[2][1]=1; matrix[2][2]=2; //LLENAMOS LA MATRIX COMO EL EJEMPLO DEL PDF
std::cout<<CalcDeterminant(matrix, size)<<"\n"; //PRINTEAMOS DETERMINANTE
float **inv=MatrixInversion(matrix, size); //El apuntador Inv se llena aqui
std::cout<<"\nOriginal\n";
//PRINTEAR MATRIX
for(int i =0;i<size;++i)
{
for(int j =0;j<size;++j)
std::cout<<matrix[i][j]<<"\t";
std::cout<<"\n";
}
//PRINTEAR MATRIX INV
std::cout<<"\nInversa\n";
for(int i =0;i<size;++i)
{
for(int j =0;j<size;++j)
std::cout<<inv[i][j]<<"\t";
std::cout<<"\n";
}
return 0;
}
void MatrixInversion(float **A, int order, float **Y)
/*< matrix inversion main interface >*/
{
/* calculate determinant */
double det = 1.0/CalcDeterminant(A,order);
/* allocate memory for co-factor matrix */
float **minor = sf_floatalloc2(order-1,order-1);
for(int j=0; j < order; j++) {
for(int i=0; i < order; i++) {
/* get the co-factor matrix of A(j,i) */
GetMinor(A,minor,j,i,order);
Y[i][j] = det*CalcDeterminant(minor,order-1);
if((i+j)%2 == 1)
Y[i][j] = -Y[i][j];
}
}
}
//逆行列を計算する
Matrix Matrix::CalcInverseMatrix()
{
if (this->xSize != this->ySize) //正方行列ではない場合
return Matrix(0, 0);
double Determinant = CalcDeterminant(); //行列式の値を計算する
if (Determinant == 0.0) //行列式が0の場合
return Matrix(0, 0); //逆行列は存在しない
Matrix mtrxCofactor = CalcCofactorMatrix(); //余因子行列を計算
return mtrxCofactor * (1.0 / Determinant); //余因子行列を行列式の値で割る
}
double CalcDeterminant(float **mat, int order)
/*< recursive calculation of determinant >*/
{
/* stop recursion when matrix is a single element */
if(order == 1)
return mat[0][0];
/* the determinant value */
float det = 0.;
/* allocate memory for cofactor matrix */
float **minor = sf_floatalloc2(order-1,order-1);
for(int i=0; i < order; i++)
{
/* get minor of element (0,i) */
GetMinor(mat,minor,0,i,order);
/* recursion */
det += (i%2==1?-1.0:1.0) * mat[0][i] * CalcDeterminant(minor,order-1);
}
return det;
}
