double determinant(Matrix& A)
{
if ((A.m_rows != A.m_columns) || A.m_rows<1)//no need to check columns too for <1
{
return 0;
}
else if (A.m_rows == 1){ return A.mat[0]; }
//else if (A.m_rows == 2)
//{
// // A
// // [ 0 1 ]
// // [ 2 3 ]
// //
// return (A.mat[0] * A.mat[3] - A.mat[1] * A.mat[2]);
//}
else
{
double det=0;
for (int i = 0; i < A.m_columns; i++)
{
Matrix temp = A;
double coefficient = pow(-1.0, i)*A.mat[i];
temp.DeleteColumn(i);
temp.DeleteRow(0);
det += coefficient*determinant(temp);//recursion here :D
}
return det;
}
}
Matrix Matrix::inverse()
{
if (determinant(*this) == 0 || (m_rows != m_columns)) //Actually need to check too if max(Coffactors[])* 1/det ->OVERFLOW
{
return *this;//do nothing
}
else
{
Matrix Cofactors(m_rows, m_columns);
//Compute the Coffactor elementes
for (int i = 0; i < Cofactors.m_columns; i++)
{
for (int j = 0; j < Cofactors.m_rows; j++)
{
Matrix temp = *this;
double coefficient = pow(-1.0, i + j) /* *A.mat[j*A.m_columns + i]*/;
temp.DeleteColumn(i);
temp.DeleteRow(j);
Cofactors.mat[j*m_columns + i] = coefficient*determinant(temp);
}
}
Matrix Inverse = Cofactors.traspose() / determinant(*this);
return Inverse;
}
}
void invert(Matrix& A)
{
if (determinant(A) == 0 || (A.m_rows!=A.m_columns)) //Actually need to check too if max(Coffactors[])* 1/det ->OVERFLOW
{
}
else
{
Matrix Cofactors(A.m_rows, A.m_columns);
//Compute the Coffactor elementes
for (int i = 0; i < Cofactors.m_columns; i++)
{
for (int j = 0; j < Cofactors.m_rows; j++)
{
Matrix temp = A;
double coefficient = pow(-1.0, i + j) ;
temp.DeleteColumn(i);
temp.DeleteRow(j);
Cofactors.mat[j*A.m_columns + i] = coefficient*determinant(temp);
}
}
Matrix Inverse = Cofactors.traspose() / determinant(A);
A = Inverse;
}
}
void NormalEquations::Diagnostics()
{
CalculateResiduals();
CalculateCovariances();
cholesky.BackSubst(residuals);
rawQ = residuals.InnerProduct(cholesky.x);
Q = sqrt(2.0 * rawQ) - sqrt(2.0 * residuals.dim - 1.0);
Qi.Dimension(residuals.dim);
Matrix M;
Vector v, r;
Cholesky chol;
for (int i = 0; i < residuals.dim; i++)
{
M = varMatrix;
v = M[i];
M.DeleteColumn(i);
M.DeleteRow(i);
v.DeleteDimension(i);
chol.Decompose(M);
chol.BackSubst(v);
double var = varMatrix[i][i] - v.InnerProduct(chol.x);
r = residuals;
r.DeleteDimension(i);
chol.BackSubst(r);
Qi[i] = residuals[i] - v.InnerProduct(chol.x);
Qi[i] = Qi[i] * Qi[i] / var;
}
}