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_QR_Z(const MatrixD &A, const MatrixD &Z0, MatrixD *invA, MatrixD *Z, Scalar lambda_max, Scalar eps) {
VectorD sigma; //vector of singular values
Scalar lambda2;
MatrixD AZ0t = (A * Z0).transpose();
HouseholderQR < MatrixD > qr = AZ0t.householderQr();
int m = A.rows();
int p = Z0.cols();
MatrixD Rt = MatrixD::Zero(m, m);
bool invertible;
MatrixD hR = (MatrixD) qr.matrixQR();
MatrixD Y = ((MatrixD) qr.householderQ()).leftCols(m);
//take the useful part of R
for (int i = 0; i < m; i++) {
for (int j = 0; j <= i; j++)
Rt(i, j) = hR(j, i);
}
FullPivLU < MatrixD > invRt(Rt);
invertible = fabs(invRt.determinant()) > eps;
if (invertible) {
*invA = Z0 * Y * invRt.inverse();
*Z = Z0 * (((MatrixD) qr.householderQ()).rightCols(p - m));
return true;
} else {
MatrixD R = MatrixD::Zero(m, m);
//take the useful part of R
for (int i = 0; i < m; i++) {
for (int j = i; j < m; j++) // TODO: is starting at i correct?
R(i, j) = hR(i, j);
}
//perform the SVD of R
JacobiSVD<MatrixD> svd_R(R, ComputeThinU | ComputeThinV);
sigma = svd_R.singularValues();
lambda2 = (1 - (sigma(m - 1) / eps) * (sigma(m - 1) / eps)) * lambda_max * lambda_max;
for (int i = 0; i < m; i++) {
sigma(i) = sigma(i) / (sigma(i) * sigma(i) + lambda2);
}
(*invA) = Z0 * Y * svd_R.matrixU() * sigma.asDiagonal() * svd_R.matrixV().transpose();
*Z = Z0 * (((MatrixD) qr.householderQ()).rightCols(p - m));
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;
}
}