bool pinv_damped(const MatrixD &A, MatrixD *invA, Scalar lambda_max, Scalar eps) {
//A (m x n) usually comes from a redundant task jacobian, therfore we consider m<n
int m = A.rows() - 1;
VectorD sigma; //vector of singular values
Scalar lambda2;
int r = 0;
JacobiSVD<MatrixD> svd_A(A.transpose(), ComputeThinU | ComputeThinV);
sigma = svd_A.singularValues();
if (((m > 0) && (sigma(m) > eps)) || ((m == 0) && (A.array().abs() > eps).any())) {
for (int i = 0; i <= m; i++) {
sigma(i) = 1.0 / sigma(i);
}
(*invA) = svd_A.matrixU() * sigma.asDiagonal() * svd_A.matrixV().transpose();
return true;
} else {
lambda2 = (1 - (sigma(m) / eps) * (sigma(m) / eps)) * lambda_max * lambda_max;
for (int i = 0; i <= m; i++) {
if (sigma(i) > EPSQ)
r++;
sigma(i) = (sigma(i) / (sigma(i) * sigma(i) + lambda2));
}
//only U till the rank
MatrixD subU = svd_A.matrixU().block(0, 0, A.cols(), r);
MatrixD subV = svd_A.matrixV().block(0, 0, A.rows(), r);
(*invA) = subU * sigma.asDiagonal() * subV.transpose();
return false;
}
}
bool pinv(const MatrixD &A, MatrixD *invA, Scalar eps) {
//A (m x n) usually comes from a redundant task jacobian, therfore we consider m<n
int m = A.rows() - 1;
VectorD sigma; //vector of singular values
JacobiSVD<MatrixD> svd_A(A.transpose(), ComputeThinU | ComputeThinV);
sigma = svd_A.singularValues();
if (((m > 0) && (sigma(m) > eps)) || ((m == 0) && (A.array().abs() > eps).any())) {
for (int i = 0; i <= m; i++) {
sigma(i) = 1.0 / sigma(i);
}
(*invA) = svd_A.matrixU() * sigma.asDiagonal() * svd_A.matrixV().transpose();
return true;
} else {
return false;
}
}