//==========================================================================
// Class: Matrix
// Function: GetPsuedoInverse
//
// Description: Returns the pseudo-inverse of this matrix.
//
// Input Arguments:
// None
//
// Output Arguments:
// inverse = Matrix&, inverse of this
//
// Return Value:
// bool, true for success, false otherwise
//
//==========================================================================
bool Matrix::GetPsuedoInverse(Matrix &inverse) const
{
// Use singular value decomposition to compute the inverse
// SVD algorithm interpreted from Numerical Recipies in C
Matrix U;
Matrix W;
Matrix V;
if (!GetSingularValueDecomposition(U, V, W))
return false;
inverse = V * W.GetDiagonalInverse() * U.GetTranspose();
return true;
}
//==========================================================================
// Class: Matrix
// Function: LeftDivide
//
// Description: Performs division from the left. For example, to solve
// Ax=b for x, left divide x = A \ b, where this matrix is A.
// Same as A^-1 * b.
//
// Input Arguments:
// b = const Matrix& vector to divide this into
//
// Output Arguments:
// x = Matrix&
//
// Return Value:
// bool, true for success, false otherwise
//
//==========================================================================
bool Matrix::LeftDivide(const Matrix &b, Matrix &x) const
{
// Normal equations solution (not very robust?)
//return GetInverse() * b;
// Use singular value decomposition
Matrix U;
Matrix V;
Matrix W;
if (!GetSingularValueDecomposition(U, V, W))
return false;
x = V * W.GetDiagonalInverse().GetTranspose() * U.GetTranspose() * b;
return true;
}