Moore-Penrose Pseudo-Inverse Using Eigen

mp_psuedo_inv.cpp

// method for calculating the pseudo-Inverse as recommended by Eigen developers
template<typename _Matrix_Type_>
_Matrix_Type_ pseudoInverse(const _Matrix_Type_ &a, double epsilon = std::numeric_limits<double>::epsilon())
{

	Eigen::JacobiSVD< _Matrix_Type_ > svd(a ,Eigen::ComputeFullU | Eigen::ComputeFullV);
        // For a non-square matrix
        // Eigen::JacobiSVD< _Matrix_Type_ > svd(a ,Eigen::ComputeThinU | Eigen::ComputeThinV);
	double tolerance = epsilon * std::max(a.cols(), a.rows()) *svd.singularValues().array().abs()(0);
	return svd.matrixV() *  (svd.singularValues().array().abs() > tolerance).select(svd.singularValues().array().inverse(), 0).matrix().asDiagonal() * svd.matrixU().adjoint();
}

Thank you for sharing.

It gives the following error for a non-square matrix:

Assertion `lhs.cols() == rhs.rows() && "invalid matrix product" && "if you wanted a coeff-wise or a dot product use the respective explicit functions"' failed.

Replacing Eigen::ComputeFullU | Eigen::ComputeFullV above with Eigen::ComputeThinU | Eigen::ComputeThinV solves this issue as suggested here.

Non-square matrix fork

Glad you found it helpful, @gokhansolak! And thanks for the info about non-square matrices. I've added a comment line with this info.

Hi, thanks for the share.
I am using it with an Eigen::Matrix<double, 6, 9>, but in return get the same shape instead of an Eigen::Matrix<double, 9, 6>.
Is it normal behavior?
Thanks

Hi @muttistefano! As @gokhansolak noted above, this implementation doesn't seem to work for a non-square matrix. Perhaps you could give the version linked above a try?

Hi @pshriwise , i tried both versions and they both have problems.
I actually need to use Eigen::ComputeFullU | Eigen::ComputeFullV cause I need the full matrices of the svd.
If it's useful, I can post here a working version, based on the Eigen::BDCSVD class.
If I will have time I will dig more into this.
For now, I will stick to the working version.
I post it here cause if you look up for eigen pseudoinverse you might end up here.
Thanks

template<typename MatType>
PseudoInverseType<MatType> pseudoInverse(const MatType &a, double epsilon = std::numeric_limits<double>::epsilon())
{
	using WorkingMatType = Eigen::Matrix<typename MatType::Scalar, Eigen::Dynamic, Eigen::Dynamic, 0,
																			 MatType::MaxRowsAtCompileTime, MatType::MaxColsAtCompileTime>;
  Eigen::BDCSVD<WorkingMatType> svd(a, Eigen::ComputeFullU | Eigen::ComputeFullV);
	svd.setThreshold(epsilon*std::max(a.cols(), a.rows()));
	Eigen::Index rank = svd.rank();
	Eigen::Matrix<typename MatType::Scalar, Eigen::Dynamic, MatType::RowsAtCompileTime,
								0, Eigen::BDCSVD<WorkingMatType>::MaxDiagSizeAtCompileTime, MatType::MaxRowsAtCompileTime>
		tmp = svd.matrixU().leftCols(rank).adjoint();
	tmp = svd.singularValues().head(rank).asDiagonal().inverse() * tmp;
	return svd.matrixV().leftCols(rank) * tmp;
}

Thanks for posting this @muttistefano! If I have time I'll try this version in the application where I applied the inverse in this gist to ensure it also has the behavior I'd expect.