Controller::Controller(dynamics::SkeletonDynamics* _skel, const vector<int> &_actuatedDofs,
const VectorXd &_kP, const VectorXd &_kD, const vector<int> &_ankleDofs, const VectorXd &_anklePGains, const VectorXd &_ankleDGains) :
mSkel(_skel),
mKp(_kP.asDiagonal()),
mKd(_kD.asDiagonal()),
mAnkleDofs(_ankleDofs),
mAnklePGains(_anklePGains),
mAnkleDGains(_ankleDGains),
mTrajectory(NULL)
{
const int nDof = mSkel->getNumDofs();
mSelectionMatrix = MatrixXd::Zero(nDof, nDof);
for (int i = 0; i < _actuatedDofs.size(); i++) {
mSelectionMatrix(_actuatedDofs[i], _actuatedDofs[i]) = 1.0;
}
mDesiredDofs.resize(nDof);
for (int i = 0; i < nDof; i++) {
mDesiredDofs[i] = mSkel->getDof(i)->getValue();
}
Vector3d com = mSkel->getWorldCOM();
double cop = 0.0;
mPreOffset = com[0] - cop;
}
VectorXd lsq_weigh_nonneg(const MatrixXd& A, const VectorXd& b, const VectorXd& w)
{
const unsigned m = A.rows();
const unsigned n = A.cols();
if(b.size() != m || w.size() != m || n < 1 || m < 1)
{
std::cerr<<"#error in lsq_weigh_nonneg: If A is a m by n matrix, then b and w must have length m. We also want n >= 1 and m >= 1. A is "<< m <<" by "<< n <<", b has length "<< b.size() <<" and w has length "<< w.size() <<"."<<std::endl;
throw std::invalid_argument("lsq_weigh_nonneg: dimension mismatch");
}
// initialization
const MatrixXd H = A.transpose() * w.asDiagonal() * A;
const VectorXd f = - A.transpose() * w.asDiagonal() * b;
VectorXd x = VectorXd::Zero(n), mu = f;
// iterate
double relerr;
do
{
for(unsigned k = 0; k < n; ++k)
{
const double xtmp = x(k);
x(k) -= mu(k) / H(k,k);
if(x(k) < 0) x(k) = 0;
const double d = x(k) - xtmp;
if(d != 0) mu += d * H.col(k);
}
relerr = 0;
for(unsigned k = 0; k < n; ++k)
{
if(x(k) != 0)
{
double err = mu(k) / x(k);
if(err < 0) err = -err;
if(err > relerr) relerr = err;
}
}
}
while(relerr >= 1e-2);
// update non-zero columns with more costly, but also more precise calculation
const VectorXi p = find(x.array() > 0);
const VectorXd xp = lscov(pick_col(A, p), b, w);
if(find(xp.array() >= 0).all()) set_ind(x, p, xp);
return x;
}
VectorXd svdSolve( JacobiSVD<MatrixXd> & svd,VectorXd & ref, double * rankPtr = NULL, double EPS=1e-6 )
{
typedef JacobiSVD<MatrixXd> SVDType;
const JacobiSVD<MatrixXd>::MatrixUType &U = svd.matrixU();
const JacobiSVD<MatrixXd>::MatrixVType &V = svd.matrixV();
const JacobiSVD<MatrixXd>::SingularValuesType &s = svd.singularValues();
//std::cout << (MATLAB)U<< (MATLAB)s<<(MATLAB)V << std::endl;
const int N=V.rows(),M=U.rows(),S=std::min(M,N);
int rank=0;
while( rank<S && s[rank]>EPS ) rank++;
VectorXd sinv = s.head(rank).array().inverse();
//std::cout << "U = " << (MATLAB)U.leftCols(rank) << std::endl;
//std::cout << "V = " << (MATLAB)V.leftCols(rank) << std::endl;
//std::cout << "S = " << (MATLAB)(MatrixXd)sinv.asDiagonal() << std::endl;
VectorXd x;
x = V.leftCols(rank)
* sinv.asDiagonal()
* U.leftCols(rank).transpose()
* ref;
if(rankPtr!=NULL) *rankPtr = rank;
return x;
}
void Spectral::generate_kernel_matrix(){
// Fill kernel matrix
K.resize(X.rows(),X.rows());
for(unsigned int i = 0; i < X.rows(); i++){
for(unsigned int j = i; j < X.rows(); j++){
K(i,j) = K(j,i) = kernel(X.row(i),X.row(j));
//if(i == 0) cout << K(i,j) << " ";
}
}
// Normalise kernel matrix
VectorXd d = K.rowwise().sum();
for(unsigned int i = 0; i < d.rows(); i++){
d(i) = 1.0/sqrt(d(i));
}
auto F = d.asDiagonal();
MatrixXd l = (K * F);
for(unsigned int i = 0; i < l.rows(); i++){
for(unsigned int j = 0; j < l.cols(); j++){
l(i,j) = l(i,j) * d(i);
}
}
K = l;
}
void eigs_sym_Cpp(MatrixXd &M, VectorXd &init_resid, int k, int m,
double &time_used, double &prec_err)
{
double start, end;
start = get_wall_time();
DenseGenMatProd<double> op(M);
SymEigsSolver< double, LARGEST_MAGN, DenseGenMatProd<double> > eigs(&op, k, m);
eigs.init(init_resid.data());
int nconv = eigs.compute();
int niter = eigs.num_iterations();
int nops = eigs.num_operations();
VectorXd evals = eigs.eigenvalues();
MatrixXd evecs = eigs.eigenvectors();
/*
std::cout << "computed eigenvalues D = \n" << evals.transpose() << std::endl;
std::cout << "first 5 rows of computed eigenvectors U = \n" << evecs.topRows<5>() << std::endl;
std::cout << "nconv = " << nconv << std::endl;
std::cout << "niter = " << niter << std::endl;
std::cout << "nops = " << nops << std::endl;
*/
end = get_wall_time();
time_used = (end - start) * 1000;
MatrixXd err = M * evecs - evecs * evals.asDiagonal();
prec_err = err.cwiseAbs().maxCoeff();
}
SparseMatrix<double> compute_M2_topic( SparseMatrix<double> data ){
cout << "Computing M2 topic..." << endl;
int n = data.rows();
int na = data.cols();
SparseMatrix<double> M2(na,na);
for (int t = 0; t < n; ++t){
cout << t << endl;
VectorXd c = data.row(t);
SparseVector<double> c_sp = data.row(t);
MatrixXd temp = c.asDiagonal();
M2 += (c_sp*c_sp.transpose() - temp.sparseView());
}
M2 *= (alpha0+1.)/n;
SparseVector<double> M1 = compute_M1_topic(data).sparseView();
cout << M2.cols() << endl;
cout << M2.rows() << endl;
cout << M1.size() << endl;
SparseMatrix<double> aux = alpha0 * ( M1 * M1.transpose() );
cout << aux.cols() << endl;
cout << aux.rows() << endl;
M2 = M2 - aux;
return M2;
}
// ZCA of genotypes
void RandomPCA::zca_whiten(bool transpose)
{
verbose && std::cout << timestamp() << " Whitening begin" << std::endl;
VectorXd s = 1 / d.array();
MatrixXd Dinv = s.asDiagonal();
if(transpose)
W.noalias() = U * Dinv * U.transpose() * X.transpose();
else
W.noalias() = U * Dinv * U.transpose() * X;
verbose && std::cout << timestamp() << " Whitening done (" << dim(W) << ")" << std::endl;
}
void pseudoinverse(const MatrixXd& A, MatrixXd& P)
{
JacobiSVD<MatrixXd> svd(A, ComputeThinU | ComputeThinV);
VectorXd invSingularVals = svd.singularValues();
const double tolerance = 1e-6;
for (int i = 0; i < invSingularVals.size(); i++)
if (fabs(invSingularVals(i)) > tolerance)
invSingularVals(i) = 1.0/invSingularVals(i);
else
invSingularVals(i) = 0.0;
P = svd.matrixV() * invSingularVals.asDiagonal() * svd.matrixU().transpose();
}
MatrixXd CMT::pInverse(const MatrixXd& matrix) {
if(matrix.size() == 0)
return matrix.transpose();
JacobiSVD<MatrixXd> svd(matrix, ComputeThinU | ComputeThinV);
VectorXd svInv = svd.singularValues();
for(int i = 0; i < svInv.size(); ++i)
if(svInv[i] > 1e-8)
svInv[i] = 1. / svInv[i];
return svd.matrixV() * svInv.asDiagonal() * svd.matrixU().transpose();
}
//**************************************************************************************************
Eigen::MatrixRXd wholeBodyReach::pinvDampedEigen(const Eigen::Ref<Eigen::MatrixRXd> &A, double damp)
{
// allocate memory
int m = A.rows(), n = A.cols(), k = m<n?m:n;
VectorXd SpinvD = VectorXd::Zero(k);
// compute decomposition
JacobiSVD<MatrixRXd> svd(A, ComputeThinU | ComputeThinV); // default Eigen SVD
VectorXd sv = svd.singularValues();
// compute pseudoinverse of singular value matrix
double damp2 = damp*damp;
for (int c=0;c<k; c++)
SpinvD(c) = sv(c) / (sv(c)*sv(c) + damp2);
// compute damped pseudoinverse
return svd.matrixV() * SpinvD.asDiagonal() * svd.matrixU().transpose();
}
MatrixXd compute_w( SparseMatrix<double> M2, int KHID ){
cout << "Computing the whitening matrix..." << endl;
int m = M2.rows();
cout << "Calculating SVD..." << endl;
JacobiSVD<MatrixXd> svd( M2, ComputeThinU );
cout << "SVD successfully calculated" << endl;
VectorXd E = svd.singularValues();
E = E.head(KHID);
E = E.array().sqrt().inverse().matrix();
MatrixXd E_diag = E.asDiagonal();
MatrixXd U = svd.matrixU();
U = U.block(0,0,m,KHID);
cout << U.rows() << endl;
cout << U.cols() << endl;
return U*E_diag;
}
void LAR::train(const MatrixXd& data )
{
LINE; LINE;
cout << "Data Dimension : " << data.rows() << " X " << data.cols() << endl;
LINE;
cout << endl;
//Training data
double trainRatio = 2.8 / 3;
int breakPoint = (int)(data.rows() * trainRatio), col = data.cols(), row = data.rows();
MatrixXd X_(breakPoint, col);
X_ << data.block(0, 0, breakPoint, col - 1), MatrixXd::Ones(breakPoint, 1);
MatrixXd Y = data.block(0, col - 1, breakPoint, 1);
//testing
MatrixXd Xts(row - breakPoint, col);
Xts = data.block(breakPoint, 0, row - breakPoint, col - 1), MatrixXd::Ones(row - breakPoint, 1);
MatrixXd Yts = data.block(breakPoint, col - 1, row - breakPoint, 1);
//Least absolute error regression
//initialize the parameter
VectorXd beta_new = VectorXd::Zero(col);
VectorXd beta_old = VectorXd::Ones(col);
cout << "Iteratively weighted least square regression:" << endl << endl;
int i = 0;
while ((beta_new - beta_old).norm()>0.01)
{
beta_old = beta_new;
//Parameter estiamtion -- iteratively weighted least square
VectorXd weight = 1 / (Y - X_*beta_old).array().abs();
MatrixXd C = weight.asDiagonal();
beta_new = (X_.transpose()*C*X_).inverse()*X_.transpose()*C*Y;
cout << "Training iteration: " << setw(3) << ++i << " , current coefficients: " << beta_new.transpose() << endl;
}
//prediction on test set
LINE;
cout << "Result: " << endl << endl;
beta = beta_new.head(beta_new.size()-1);
cout << " Coefficients for X are: " << beta << endl;
offset = beta_new(beta_new.size() - 1);
cout << " Offset term is: " << offset << endl;
LINE; LINE;
}
MatrixXd rbf_kernel(MatrixXd& X, const double sigma, bool rbf_center,
bool verbose)
{
unsigned int n = X.rows();
VectorXd norms = X.array().square().rowwise().sum();
VectorXd ones = VectorXd::Ones(n);
MatrixXd R = norms * ones.transpose();
MatrixXd D = R + R.transpose() - 2 * X * X.transpose();
D = D.array() / (-1 * sigma * sigma);
MatrixXd K = D.array().exp();
if(rbf_center)
{
verbose && std::cout << timestamp() << " Centering RBF kernel" << std::endl;
MatrixXd M = ones * ones.transpose() / n;
MatrixXd I = ones.asDiagonal();
K = (I - M) * K * (I - M);
}
return K;
}
VectorXd
PatchFit::lls(MatrixXd J, VectorXd b)
{
// check input dimensions
if (J.rows() != b.rows())
cerr << "Wrong dimensions" << endl;
VectorXd a (J.cols()); //output parameters
JacobiSVD<MatrixXd> svd(J, ComputeThinU | ComputeThinV);
VectorXd sv = svd.singularValues();
MatrixXd V = svd.matrixV();
VectorXd pv = sv.array().inverse();
VectorXd pvSq = pv.array()*pv.array();
if (b.any())
a = V * pvSq.asDiagonal() * V.adjoint() * J.adjoint() * b;
else
a = V.rightCols(1);
return a;
}
MatrixXd sample_MME_multiple_diagR(
MatrixXd Y,
SpMat W,
SpMat chol_C,
VectorXd pe,
MSpMat chol_K_inv,
VectorXd tot_Eta_prec,
MatrixXd randn_theta,
MatrixXd randn_e
){
MatrixXd theta_star = chol_K_inv.triangularView<Upper>().solve(randn_theta);
MatrixXd e_star = randn_e * pe.cwiseSqrt().cwiseInverse().asDiagonal();
MatrixXd W_theta_star = W * theta_star;
MatrixXd Y_resid = Y - W_theta_star - e_star;
MatrixXd WtRiy = W.transpose() * (Y_resid * pe.asDiagonal());
MatrixXd theta_tilda = chol_C.transpose().triangularView<Upper>().solve(chol_C.triangularView<Lower>().solve(WtRiy));
MatrixXd theta = theta_tilda * tot_Eta_prec.cwiseInverse().asDiagonal() + theta_star;
return theta;
}
int setupAndSolveQP(NewQPControllerData *pdata, std::shared_ptr<drake::lcmt_qp_controller_input> qp_input, double t, Map<VectorXd> &q, Map<VectorXd> &qd, const Ref<Matrix<bool, Dynamic, 1>> &b_contact_force, QPControllerOutput *qp_output, std::shared_ptr<QPControllerDebugData> debug) {
// The primary solve loop for our controller. This constructs and solves a Quadratic Program and produces the instantaneous desired torques, along with reference positions, velocities, and accelerations. It mirrors the Matlab implementation in atlasControllers.InstantaneousQPController.setupAndSolveQP(), and more documentation can be found there.
// Note: argument `debug` MAY be set to NULL, which signals that no debug information is requested.
// look up the param set by name
AtlasParams *params;
std::map<string,AtlasParams>::iterator it;
it = pdata->param_sets.find(qp_input->param_set_name);
if (it == pdata->param_sets.end()) {
mexWarnMsgTxt("Got a param set I don't recognize! Using standing params instead");
it = pdata->param_sets.find("standing");
if (it == pdata->param_sets.end()) {
mexErrMsgTxt("Could not fall back to standing parameters either. I have to give up here.");
}
}
// cout << "using params set: " + it->first + ", ";
params = &(it->second);
// mexPrintf("Kp_accel: %f, ", params->Kp_accel);
int nu = pdata->B.cols();
int nq = pdata->r->num_positions;
// zmp_data
Map<Matrix<double, 4, 4, RowMajor>> A_ls(&qp_input->zmp_data.A[0][0]);
Map<Matrix<double, 4, 2, RowMajor>> B_ls(&qp_input->zmp_data.B[0][0]);
Map<Matrix<double, 2, 4, RowMajor>> C_ls(&qp_input->zmp_data.C[0][0]);
Map<Matrix<double, 2, 2, RowMajor>> D_ls(&qp_input->zmp_data.D[0][0]);
Map<Matrix<double, 4, 1>> x0(&qp_input->zmp_data.x0[0][0]);
Map<Matrix<double, 2, 1>> y0(&qp_input->zmp_data.y0[0][0]);
Map<Matrix<double, 2, 1>> u0(&qp_input->zmp_data.u0[0][0]);
Map<Matrix<double, 2, 2, RowMajor>> R_ls(&qp_input->zmp_data.R[0][0]);
Map<Matrix<double, 2, 2, RowMajor>> Qy(&qp_input->zmp_data.Qy[0][0]);
Map<Matrix<double, 4, 4, RowMajor>> S(&qp_input->zmp_data.S[0][0]);
Map<Matrix<double, 4, 1>> s1(&qp_input->zmp_data.s1[0][0]);
Map<Matrix<double, 4, 1>> s1dot(&qp_input->zmp_data.s1dot[0][0]);
// // whole_body_data
if (qp_input->whole_body_data.num_positions != nq) mexErrMsgTxt("number of positions doesn't match num_dof for this robot");
Map<VectorXd> q_des(qp_input->whole_body_data.q_des.data(), nq);
Map<VectorXd> condof(qp_input->whole_body_data.constrained_dofs.data(), qp_input->whole_body_data.num_constrained_dofs);
PIDOutput pid_out = wholeBodyPID(pdata, t, q, qd, q_des, ¶ms->whole_body);
qp_output->q_ref = pid_out.q_ref;
// mu
// NOTE: we're using the same mu for all supports
double mu;
if (qp_input->num_support_data == 0) {
mu = 1.0;
} else {
mu = qp_input->support_data[0].mu;
for (int i=1; i < qp_input->num_support_data; i++) {
if (qp_input->support_data[i].mu != mu) {
mexWarnMsgTxt("Currently, we assume that all supports have the same value of mu");
}
}
}
const int dim = 3, // 3D
nd = 2*m_surface_tangents; // for friction cone approx, hard coded for now
assert(nu+6 == nq);
vector<DesiredBodyAcceleration> desired_body_accelerations;
desired_body_accelerations.resize(qp_input->num_tracked_bodies);
Vector6d body_pose_des, body_v_des, body_vdot_des;
Vector6d body_vdot;
for (int i=0; i < qp_input->num_tracked_bodies; i++) {
int body_id0 = qp_input->body_motion_data[i].body_id - 1;
double weight = params->body_motion[body_id0].weight;
desired_body_accelerations[i].body_id0 = body_id0;
Map<Matrix<double, 6, 4,RowMajor>>coefs_rowmaj(&qp_input->body_motion_data[i].coefs[0][0]);
Matrix<double, 6, 4> coefs = coefs_rowmaj;
evaluateCubicSplineSegment(t - qp_input->body_motion_data[i].ts[0], coefs, body_pose_des, body_v_des, body_vdot_des);
desired_body_accelerations[i].body_vdot = bodyMotionPD(pdata->r, q, qd, body_id0, body_pose_des, body_v_des, body_vdot_des, params->body_motion[body_id0].Kp, params->body_motion[body_id0].Kd);
desired_body_accelerations[i].weight = weight;
desired_body_accelerations[i].accel_bounds = params->body_motion[body_id0].accel_bounds;
// mexPrintf("body: %d, vdot: %f %f %f %f %f %f weight: %f\n", body_id0,
// desired_body_accelerations[i].body_vdot(0),
// desired_body_accelerations[i].body_vdot(1),
// desired_body_accelerations[i].body_vdot(2),
// desired_body_accelerations[i].body_vdot(3),
// desired_body_accelerations[i].body_vdot(4),
// desired_body_accelerations[i].body_vdot(5),
// weight);
// mexPrintf("tracking body: %d, coefs[:,0]: %f %f %f %f %f %f coefs(", body_id0,
}
int n_body_accel_eq_constraints = 0;
for (int i=0; i < desired_body_accelerations.size(); i++) {
if (desired_body_accelerations[i].weight < 0)
n_body_accel_eq_constraints++;
}
MatrixXd R_DQyD_ls = R_ls + D_ls.transpose()*Qy*D_ls;
pdata->r->doKinematics(q,false,qd);
//---------------------------------------------------------------------
vector<SupportStateElement> available_supports = loadAvailableSupports(qp_input);
vector<SupportStateElement> active_supports = getActiveSupports(pdata->r, pdata->map_ptr, q, qd, available_supports, b_contact_force, params->contact_threshold, pdata->default_terrain_height);
int num_active_contact_pts=0;
for (vector<SupportStateElement>::iterator iter = active_supports.begin(); iter!=active_supports.end(); iter++) {
num_active_contact_pts += iter->contact_pts.size();
}
pdata->r->HandC(q,qd,(MatrixXd*)nullptr,pdata->H,pdata->C,(MatrixXd*)nullptr,(MatrixXd*)nullptr,(MatrixXd*)nullptr);
pdata->H_float = pdata->H.topRows(6);
pdata->H_act = pdata->H.bottomRows(nu);
pdata->C_float = pdata->C.head(6);
pdata->C_act = pdata->C.tail(nu);
bool include_angular_momentum = (params->W_kdot.array().maxCoeff() > 1e-10);
if (include_angular_momentum) {
pdata->r->getCMM(q,qd,pdata->Ag,pdata->Agdot);
pdata->Ak = pdata->Ag.topRows(3);
pdata->Akdot = pdata->Agdot.topRows(3);
}
Vector3d xcom;
// consider making all J's into row-major
pdata->r->getCOM(xcom);
pdata->r->getCOMJac(pdata->J);
pdata->r->getCOMJacDot(pdata->Jdot);
pdata->J_xy = pdata->J.topRows(2);
pdata->Jdot_xy = pdata->Jdot.topRows(2);
MatrixXd Jcom,Jcomdot;
if (x0.size()==6) {
Jcom = pdata->J;
Jcomdot = pdata->Jdot;
}
else {
Jcom = pdata->J_xy;
Jcomdot = pdata->Jdot_xy;
}
MatrixXd B,JB,Jp,Jpdot,normals;
int nc = contactConstraintsBV(pdata->r,num_active_contact_pts,mu,active_supports,pdata->map_ptr,B,JB,Jp,Jpdot,normals,pdata->default_terrain_height);
int neps = nc*dim;
VectorXd x_bar,xlimp;
MatrixXd D_float(6,JB.cols()), D_act(nu,JB.cols());
if (nc>0) {
if (x0.size()==6) {
// x,y,z com
xlimp.resize(6);
xlimp.topRows(3) = xcom;
xlimp.bottomRows(3) = Jcom*qd;
}
else {
xlimp.resize(4);
xlimp.topRows(2) = xcom.topRows(2);
xlimp.bottomRows(2) = Jcom*qd;
}
x_bar = xlimp-x0;
D_float = JB.topRows(6);
D_act = JB.bottomRows(nu);
}
int nf = nc*nd; // number of contact force variables
int nparams = nq+nf+neps;
Vector3d kdot_des;
if (include_angular_momentum) {
VectorXd k = pdata->Ak*qd;
kdot_des = -params->Kp_ang*k; // TODO: parameterize
}
//----------------------------------------------------------------------
// QP cost function ----------------------------------------------------
//
// min: ybar*Qy*ybar + ubar*R*ubar + (2*S*xbar + s1)*(A*x + B*u) +
// w_qdd*quad(qddot_ref - qdd) + w_eps*quad(epsilon) +
// w_grf*quad(beta) + quad(kdot_des - (A*qdd + Adot*qd))
VectorXd f(nparams);
{
if (nc > 0) {
// NOTE: moved Hqp calcs below, because I compute the inverse directly for FastQP (and sparse Hqp for gurobi)
VectorXd tmp = C_ls*xlimp;
VectorXd tmp1 = Jcomdot*qd;
MatrixXd tmp2 = R_DQyD_ls*Jcom;
pdata->fqp = tmp.transpose()*Qy*D_ls*Jcom;
// mexPrintf("fqp head: %f %f %f\n", pdata->fqp(0), pdata->fqp(1), pdata->fqp(2));
pdata->fqp += tmp1.transpose()*tmp2;
pdata->fqp += (S*x_bar + 0.5*s1).transpose()*B_ls*Jcom;
pdata->fqp -= u0.transpose()*tmp2;
pdata->fqp -= y0.transpose()*Qy*D_ls*Jcom;
pdata->fqp -= (params->whole_body.w_qdd.array()*pid_out.qddot_des.array()).matrix().transpose();
if (include_angular_momentum) {
pdata->fqp += qd.transpose()*pdata->Akdot.transpose()*params->W_kdot*pdata->Ak;
pdata->fqp -= kdot_des.transpose()*params->W_kdot*pdata->Ak;
}
f.head(nq) = pdata->fqp.transpose();
} else {
f.head(nq) = -pid_out.qddot_des;
}
}
f.tail(nf+neps) = VectorXd::Zero(nf+neps);
int neq = 6+neps+6*n_body_accel_eq_constraints+qp_input->whole_body_data.num_constrained_dofs;
MatrixXd Aeq = MatrixXd::Zero(neq,nparams);
VectorXd beq = VectorXd::Zero(neq);
// constrained floating base dynamics
// H_float*qdd - J_float'*lambda - Dbar_float*beta = -C_float
Aeq.topLeftCorner(6,nq) = pdata->H_float;
beq.topRows(6) = -pdata->C_float;
if (nc>0) {
Aeq.block(0,nq,6,nc*nd) = -D_float;
}
if (nc > 0) {
// relative acceleration constraint
Aeq.block(6,0,neps,nq) = Jp;
Aeq.block(6,nq,neps,nf) = MatrixXd::Zero(neps,nf); // note: obvious sparsity here
Aeq.block(6,nq+nf,neps,neps) = MatrixXd::Identity(neps,neps); // note: obvious sparsity here
beq.segment(6,neps) = (-Jpdot -params->Kp_accel*Jp)*qd;
}
// add in body spatial equality constraints
// VectorXd body_vdot;
MatrixXd orig = MatrixXd::Zero(4,1);
orig(3,0) = 1;
int equality_ind = 6+neps;
MatrixXd Jb(6,nq);
MatrixXd Jbdot(6,nq);
for (int i=0; i<desired_body_accelerations.size(); i++) {
if (desired_body_accelerations[i].weight < 0) { // negative implies constraint
if (!inSupport(active_supports,desired_body_accelerations[i].body_id0)) {
pdata->r->forwardJac(desired_body_accelerations[i].body_id0,orig,1,Jb);
pdata->r->forwardJacDot(desired_body_accelerations[i].body_id0,orig,1,Jbdot);
for (int j=0; j<6; j++) {
if (!std::isnan(desired_body_accelerations[i].body_vdot(j))) {
Aeq.block(equality_ind,0,1,nq) = Jb.row(j);
beq[equality_ind++] = -Jbdot.row(j)*qd + desired_body_accelerations[i].body_vdot(j);
}
}
}
}
}
if (qp_input->whole_body_data.num_constrained_dofs>0) {
// add joint acceleration constraints
for (int i=0; i<qp_input->whole_body_data.num_constrained_dofs; i++) {
Aeq(equality_ind,(int)condof[i]-1) = 1;
beq[equality_ind++] = pid_out.qddot_des[(int)condof[i]-1];
}
}
int n_ineq = 2*nu+2*6*desired_body_accelerations.size();
MatrixXd Ain = MatrixXd::Zero(n_ineq,nparams); // note: obvious sparsity here
VectorXd bin = VectorXd::Zero(n_ineq);
// linear input saturation constraints
// u=B_act'*(H_act*qdd + C_act - Jz_act'*z - Dbar_act*beta)
// using transpose instead of inverse because B is orthogonal
Ain.topLeftCorner(nu,nq) = pdata->B_act.transpose()*pdata->H_act;
Ain.block(0,nq,nu,nc*nd) = -pdata->B_act.transpose()*D_act;
bin.head(nu) = -pdata->B_act.transpose()*pdata->C_act + pdata->umax;
Ain.block(nu,0,nu,nparams) = -1*Ain.block(0,0,nu,nparams);
bin.segment(nu,nu) = pdata->B_act.transpose()*pdata->C_act - pdata->umin;
int constraint_start_index = 2*nu;
for (int i=0; i<desired_body_accelerations.size(); i++) {
pdata->r->forwardJac(desired_body_accelerations[i].body_id0,orig,1,Jb);
pdata->r->forwardJacDot(desired_body_accelerations[i].body_id0,orig,1,Jbdot);
Ain.block(constraint_start_index,0,6,pdata->r->num_positions) = Jb;
bin.segment(constraint_start_index,6) = -Jbdot*qd + desired_body_accelerations[i].accel_bounds.max;
constraint_start_index += 6;
Ain.block(constraint_start_index,0,6,pdata->r->num_positions) = -Jb;
bin.segment(constraint_start_index,6) = Jbdot*qd - desired_body_accelerations[i].accel_bounds.min;
constraint_start_index += 6;
}
for (int i=0; i<n_ineq; i++) {
// remove inf constraints---needed by gurobi
if (std::isinf(double(bin(i)))) {
Ain.row(i) = 0*Ain.row(i);
bin(i)=0;
}
}
GRBmodel * model = nullptr;
int info=-1;
// set obj,lb,up
VectorXd lb(nparams), ub(nparams);
lb.head(nq) = pdata->qdd_lb;
ub.head(nq) = pdata->qdd_ub;
lb.segment(nq,nf) = VectorXd::Zero(nf);
ub.segment(nq,nf) = 1e3*VectorXd::Ones(nf);
lb.tail(neps) = -params->slack_limit*VectorXd::Ones(neps);
ub.tail(neps) = params->slack_limit*VectorXd::Ones(neps);
VectorXd alpha(nparams);
MatrixXd Qnfdiag(nf,1), Qneps(neps,1);
vector<MatrixXd*> QBlkDiag( nc>0 ? 3 : 1 ); // nq, nf, neps // this one is for gurobi
VectorXd w = (params->whole_body.w_qdd.array() + REG).matrix();
#ifdef USE_MATRIX_INVERSION_LEMMA
double max_body_accel_weight = -numeric_limits<double>::infinity();
for (int i=0; i < desired_body_accelerations.size(); i++) {
max_body_accel_weight = max(max_body_accel_weight, desired_body_accelerations[i].weight);
}
bool include_body_accel_cost_terms = desired_body_accelerations.size() > 0 && max_body_accel_weight > 1e-10;
if (pdata->use_fast_qp > 0 && !include_angular_momentum && !include_body_accel_cost_terms)
{
// TODO: update to include angular momentum, body accel objectives.
// We want Hqp inverse, which I can compute efficiently using the
// matrix inversion lemma (see wikipedia):
// inv(A + U'CV) = inv(A) - inv(A)*U* inv([ inv(C)+ V*inv(A)*U ]) V inv(A)
if (nc>0) {
MatrixXd Wi = ((1/(params->whole_body.w_qdd.array() + REG)).matrix()).asDiagonal();
if (R_DQyD_ls.trace()>1e-15) { // R_DQyD_ls is not zero
pdata->Hqp = Wi - Wi*Jcom.transpose()*(R_DQyD_ls.inverse() + Jcom*Wi*Jcom.transpose()).inverse()*Jcom*Wi;
}
}
else {
pdata->Hqp = MatrixXd::Constant(nq,1,1/(1+REG));
}
#ifdef TEST_FAST_QP
if (nc>0) {
MatrixXd Hqp_test(nq,nq);
MatrixXd W = w.asDiagonal();
Hqp_test = (Jcom.transpose()*R_DQyD_ls*Jcom + W).inverse();
if (((Hqp_test-pdata->Hqp).array().abs()).maxCoeff() > 1e-6) {
mexErrMsgTxt("Q submatrix inverse from matrix inversion lemma does not match direct Q inverse.");
}
}
#endif
Qnfdiag = MatrixXd::Constant(nf,1,1/REG);
Qneps = MatrixXd::Constant(neps,1,1/(.001+REG));
QBlkDiag[0] = &pdata->Hqp;
if (nc>0) {
QBlkDiag[1] = &Qnfdiag;
QBlkDiag[2] = &Qneps; // quadratic slack var cost, Q(nparams-neps:end,nparams-neps:end)=eye(neps)
}
MatrixXd Ain_lb_ub(n_ineq+2*nparams,nparams);
VectorXd bin_lb_ub(n_ineq+2*nparams);
Ain_lb_ub << Ain, // note: obvious sparsity here
-MatrixXd::Identity(nparams,nparams),
MatrixXd::Identity(nparams,nparams);
bin_lb_ub << bin, -lb, ub;
info = fastQPThatTakesQinv(QBlkDiag, f, Aeq, beq, Ain_lb_ub, bin_lb_ub, pdata->state.active, alpha);
//if (info<0) mexPrintf("fastQP info = %d. Calling gurobi.\n", info);
}
else {
#endif
if (nc>0) {
pdata->Hqp = Jcom.transpose()*R_DQyD_ls*Jcom;
if (include_angular_momentum) {
pdata->Hqp += pdata->Ak.transpose()*params->W_kdot*pdata->Ak;
}
pdata->Hqp += params->whole_body.w_qdd.asDiagonal();
pdata->Hqp += REG*MatrixXd::Identity(nq,nq);
} else {
pdata->Hqp = (1+REG)*MatrixXd::Identity(nq,nq);
}
// add in body spatial acceleration cost terms
for (int i=0; i<desired_body_accelerations.size(); i++) {
if (desired_body_accelerations[i].weight > 0) {
if (!inSupport(active_supports,desired_body_accelerations[i].body_id0)) {
pdata->r->forwardJac(desired_body_accelerations[i].body_id0,orig,1,Jb);
pdata->r->forwardJacDot(desired_body_accelerations[i].body_id0,orig,1,Jbdot);
for (int j=0; j<6; j++) {
if (!std::isnan(desired_body_accelerations[i].body_vdot[j])) {
pdata->Hqp += desired_body_accelerations[i].weight*(Jb.row(j)).transpose()*Jb.row(j);
f.head(nq) += desired_body_accelerations[i].weight*(qd.transpose()*Jbdot.row(j).transpose() - desired_body_accelerations[i].body_vdot[j])*Jb.row(j).transpose();
}
}
}
}
}
Qnfdiag = MatrixXd::Constant(nf,1,params->w_grf+REG);
Qneps = MatrixXd::Constant(neps,1,params->w_slack+REG);
QBlkDiag[0] = &pdata->Hqp;
if (nc>0) {
QBlkDiag[1] = &Qnfdiag;
QBlkDiag[2] = &Qneps; // quadratic slack var cost, Q(nparams-neps:end,nparams-neps:end)=eye(neps)
}
MatrixXd Ain_lb_ub(n_ineq+2*nparams,nparams);
VectorXd bin_lb_ub(n_ineq+2*nparams);
Ain_lb_ub << Ain, // note: obvious sparsity here
-MatrixXd::Identity(nparams,nparams),
MatrixXd::Identity(nparams,nparams);
bin_lb_ub << bin, -lb, ub;
if (pdata->use_fast_qp > 0)
{ // set up and call fastqp
info = fastQP(QBlkDiag, f, Aeq, beq, Ain_lb_ub, bin_lb_ub, pdata->state.active, alpha);
//if (info<0) mexPrintf("fastQP info=%d... calling Gurobi.\n", info);
}
else {
// use gurobi active set
model = gurobiActiveSetQP(pdata->env,QBlkDiag,f,Aeq,beq,Ain,bin,lb,ub,pdata->state.vbasis,pdata->state.vbasis_len,pdata->state.cbasis,pdata->state.cbasis_len,alpha);
CGE(GRBgetintattr(model,"NumVars",&(pdata->state.vbasis_len)), pdata->env);
CGE(GRBgetintattr(model,"NumConstrs",&(pdata->state.cbasis_len)), pdata->env);
info=66;
//info = -1;
}
if (info<0) {
model = gurobiQP(pdata->env,QBlkDiag,f,Aeq,beq,Ain,bin,lb,ub,pdata->state.active,alpha);
int status; CGE(GRBgetintattr(model, "Status", &status), pdata->env);
//if (status!=2) mexPrintf("Gurobi reports non-optimal status = %d\n", status);
}
#ifdef USE_MATRIX_INVERSION_LEMMA
}
#endif
//----------------------------------------------------------------------
// Solve for inputs ----------------------------------------------------
qp_output->qdd = alpha.head(nq);
VectorXd beta = alpha.segment(nq,nc*nd);
// use transpose because B_act is orthogonal
qp_output->u = pdata->B_act.transpose()*(pdata->H_act*qp_output->qdd + pdata->C_act - D_act*beta);
//y = pdata->B_act.jacobiSvd(ComputeThinU|ComputeThinV).solve(pdata->H_act*qdd + pdata->C_act - Jz_act.transpose()*lambda - D_act*beta);
bool foot_contact[2];
foot_contact[0] = b_contact_force(pdata->rpc.body_ids.r_foot) == 1;
foot_contact[1] = b_contact_force(pdata->rpc.body_ids.l_foot) == 1;
qp_output->qd_ref = velocityReference(pdata, t, q, qd, qp_output->qdd, foot_contact, &(params->vref_integrator), &(pdata->rpc));
// Remember t for next time around
pdata->state.t_prev = t;
// If a debug pointer was passed in, fill it with useful data
if (debug) {
debug->active_supports.resize(active_supports.size());
for (int i=0; i < active_supports.size(); i++) {
debug->active_supports[i] = active_supports[i];
}
debug->nc = nc;
debug->normals = normals;
debug->B = B;
debug->alpha = alpha;
debug->f = f;
debug->Aeq = Aeq;
debug->beq = beq;
debug->Ain_lb_ub = Ain_lb_ub;
debug->bin_lb_ub = bin_lb_ub;
debug->Qnfdiag = Qnfdiag;
debug->Qneps = Qneps;
debug->x_bar = x_bar;
debug->S = S;
debug->s1 = s1;
debug->s1dot = s1dot;
debug->s2dot = qp_input->zmp_data.s2dot;
debug->A_ls = A_ls;
debug->B_ls = B_ls;
debug->Jcom = Jcom;
debug->Jcomdot = Jcomdot;
debug->beta = beta;
}
// if we used gurobi, clean up
if (model) {
GRBfreemodel(model);
}
// GRBfreeenv(env);
return info;
}
void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[])
{
int error;
if (nrhs<1) mexErrMsgTxt("usage: ptr = QPControllermex(0,control_obj,robot_obj,...); alpha=QPControllermex(ptr,...,...)");
if (nlhs<1) mexErrMsgTxt("take at least one output... please.");
struct QPControllerData* pdata;
mxArray* pm;
double* pr;
int i,j;
if (mxGetScalar(prhs[0])==0) { // then construct the data object and return
pdata = new struct QPControllerData;
// get control object properties
const mxArray* pobj = prhs[1];
pm = myGetProperty(pobj,"slack_limit");
pdata->slack_limit = mxGetScalar(pm);
pm = myGetProperty(pobj,"W_kdot");
assert(mxGetM(pm)==3); assert(mxGetN(pm)==3);
pdata->W_kdot.resize(mxGetM(pm),mxGetN(pm));
memcpy(pdata->W_kdot.data(),mxGetPr(pm),sizeof(double)*mxGetM(pm)*mxGetN(pm));
pm= myGetProperty(pobj,"w_grf");
pdata->w_grf = mxGetScalar(pm);
pm= myGetProperty(pobj,"w_slack");
pdata->w_slack = mxGetScalar(pm);
pm = myGetProperty(pobj,"Kp_ang");
pdata->Kp_ang = mxGetScalar(pm);
pm = myGetProperty(pobj,"Kp_accel");
pdata->Kp_accel = mxGetScalar(pm);
pm= myGetProperty(pobj,"n_body_accel_inputs");
pdata->n_body_accel_inputs = (int) mxGetScalar(pm);
pm= myGetProperty(pobj,"n_body_accel_bounds");
pdata->n_body_accel_bounds = (int) mxGetScalar(pm);
mxArray* body_accel_bounds = myGetProperty(pobj,"body_accel_bounds");
Vector6d vecbound;
for (int i=0; i<pdata->n_body_accel_bounds; i++) {
pdata->accel_bound_body_idx.push_back((int) mxGetScalar(mxGetField(body_accel_bounds,i,"body_idx"))-1);
pm = mxGetField(body_accel_bounds,i,"min_acceleration");
assert(mxGetM(pm)==6); assert(mxGetN(pm)==1);
memcpy(vecbound.data(),mxGetPr(pm),sizeof(double)*6);
pdata->min_body_acceleration.push_back(vecbound);
pm = mxGetField(body_accel_bounds,i,"max_acceleration");
assert(mxGetM(pm)==6); assert(mxGetN(pm)==1);
memcpy(vecbound.data(),mxGetPr(pm),sizeof(double)*6);
pdata->max_body_acceleration.push_back(vecbound);
}
pm = myGetProperty(pobj,"body_accel_input_weights");
pdata->body_accel_input_weights.resize(pdata->n_body_accel_inputs);
memcpy(pdata->body_accel_input_weights.data(),mxGetPr(pm),sizeof(double)*pdata->n_body_accel_inputs);
pdata->n_body_accel_eq_constraints = 0;
for (int i=0; i<pdata->n_body_accel_inputs; i++) {
if (pdata->body_accel_input_weights(i) < 0)
pdata->n_body_accel_eq_constraints++;
}
// get robot mex model ptr
if (!mxIsNumeric(prhs[2]) || mxGetNumberOfElements(prhs[2])!=1)
mexErrMsgIdAndTxt("Drake:QPControllermex:BadInputs","the third argument should be the robot mex ptr");
memcpy(&(pdata->r),mxGetData(prhs[2]),sizeof(pdata->r));
pdata->B.resize(mxGetM(prhs[3]),mxGetN(prhs[3]));
memcpy(pdata->B.data(),mxGetPr(prhs[3]),sizeof(double)*mxGetM(prhs[3])*mxGetN(prhs[3]));
int nq = pdata->r->num_dof, nu = pdata->B.cols();
pm = myGetProperty(pobj,"w_qdd");
pdata->w_qdd.resize(nq);
memcpy(pdata->w_qdd.data(),mxGetPr(pm),sizeof(double)*nq);
pdata->umin.resize(nu);
pdata->umax.resize(nu);
memcpy(pdata->umin.data(),mxGetPr(prhs[4]),sizeof(double)*nu);
memcpy(pdata->umax.data(),mxGetPr(prhs[5]),sizeof(double)*nu);
pdata->B_act.resize(nu,nu);
pdata->B_act = pdata->B.bottomRows(nu);
// get the map ptr back from matlab
if (!mxIsNumeric(prhs[6]) || mxGetNumberOfElements(prhs[6])!=1)
mexErrMsgIdAndTxt("Drake:QPControllermex:BadInputs","the seventh argument should be the map ptr");
memcpy(&pdata->map_ptr,mxGetPr(prhs[6]),sizeof(pdata->map_ptr));
// pdata->map_ptr = NULL;
if (!pdata->map_ptr)
mexWarnMsgTxt("Map ptr is NULL. Assuming flat terrain at z=0");
// create gurobi environment
error = GRBloadenv(&(pdata->env),NULL);
// set solver params (http://www.gurobi.com/documentation/5.5/reference-manual/node798#sec:Parameters)
mxArray* psolveropts = myGetProperty(pobj,"gurobi_options");
int method = (int) mxGetScalar(myGetField(psolveropts,"method"));
CGE ( GRBsetintparam(pdata->env,"outputflag",0), pdata->env );
CGE ( GRBsetintparam(pdata->env,"method",method), pdata->env );
// CGE ( GRBsetintparam(pdata->env,"method",method), pdata->env );
CGE ( GRBsetintparam(pdata->env,"presolve",0), pdata->env );
if (method==2) {
CGE ( GRBsetintparam(pdata->env,"bariterlimit",20), pdata->env );
CGE ( GRBsetintparam(pdata->env,"barhomogeneous",0), pdata->env );
CGE ( GRBsetdblparam(pdata->env,"barconvtol",0.0005), pdata->env );
}
mxClassID cid;
if (sizeof(pdata)==4) cid = mxUINT32_CLASS;
else if (sizeof(pdata)==8) cid = mxUINT64_CLASS;
else mexErrMsgIdAndTxt("Drake:constructModelmex:PointerSize","Are you on a 32-bit machine or 64-bit machine??");
plhs[0] = mxCreateNumericMatrix(1,1,cid,mxREAL);
memcpy(mxGetData(plhs[0]),&pdata,sizeof(pdata));
// preallocate some memory
pdata->H.resize(nq,nq);
pdata->H_float.resize(6,nq);
pdata->H_act.resize(nu,nq);
pdata->C.resize(nq);
pdata->C_float.resize(6);
pdata->C_act.resize(nu);
pdata->J.resize(3,nq);
pdata->Jdot.resize(3,nq);
pdata->J_xy.resize(2,nq);
pdata->Jdot_xy.resize(2,nq);
pdata->Hqp.resize(nq,nq);
pdata->fqp.resize(nq);
pdata->Ag.resize(6,nq);
pdata->Agdot.resize(6,nq);
pdata->Ak.resize(3,nq);
pdata->Akdot.resize(3,nq);
pdata->vbasis_len = 0;
pdata->cbasis_len = 0;
pdata->vbasis = NULL;
pdata->cbasis = NULL;
return;
}
// first get the ptr back from matlab
if (!mxIsNumeric(prhs[0]) || mxGetNumberOfElements(prhs[0])!=1)
mexErrMsgIdAndTxt("Drake:QPControllermex:BadInputs","the first argument should be the ptr");
memcpy(&pdata,mxGetData(prhs[0]),sizeof(pdata));
// for (i=0; i<pdata->r->num_bodies; i++)
// mexPrintf("body %d (%s) has %d contact points\n", i, pdata->r->bodies[i].linkname.c_str(), pdata->r->bodies[i].contact_pts.cols());
int nu = pdata->B.cols(), nq = pdata->r->num_dof;
const int dim = 3, // 3D
nd = 2*m_surface_tangents; // for friction cone approx, hard coded for now
assert(nu+6 == nq);
int narg=1;
int use_fast_qp = (int) mxGetScalar(prhs[narg++]);
Map< VectorXd > qddot_des(mxGetPr(prhs[narg++]),nq);
double *q = mxGetPr(prhs[narg++]);
double *qd = &q[nq];
vector<VectorXd,aligned_allocator<VectorXd>> body_accel_inputs;
for (int i=0; i<pdata->n_body_accel_inputs; i++) {
assert(mxGetM(prhs[narg])==7); assert(mxGetN(prhs[narg])==1);
VectorXd v = VectorXd::Zero(7,1);
memcpy(v.data(),mxGetPr(prhs[narg++]),sizeof(double)*7);
body_accel_inputs.push_back(v);
}
int num_condof;
VectorXd condof;
if (!mxIsEmpty(prhs[narg])) {
assert(mxGetN(prhs[narg])==1);
num_condof=mxGetM(prhs[narg]);
condof = VectorXd::Zero(num_condof);
memcpy(condof.data(),mxGetPr(prhs[narg++]),sizeof(double)*num_condof);
}
else {
num_condof=0;
narg++; // skip over empty vector
}
int desired_support_argid = narg++;
Map<MatrixXd> A_ls(mxGetPr(prhs[narg]),mxGetM(prhs[narg]),mxGetN(prhs[narg])); narg++;
Map<MatrixXd> B_ls(mxGetPr(prhs[narg]),mxGetM(prhs[narg]),mxGetN(prhs[narg])); narg++;
Map<MatrixXd> Qy (mxGetPr(prhs[narg]),mxGetM(prhs[narg]),mxGetN(prhs[narg])); narg++;
Map<MatrixXd> R_ls(mxGetPr(prhs[narg]),mxGetM(prhs[narg]),mxGetN(prhs[narg])); narg++;
Map<MatrixXd> C_ls(mxGetPr(prhs[narg]),mxGetM(prhs[narg]),mxGetN(prhs[narg])); narg++;
Map<MatrixXd> D_ls(mxGetPr(prhs[narg]),mxGetM(prhs[narg]),mxGetN(prhs[narg])); narg++;
Map<MatrixXd> S (mxGetPr(prhs[narg]),mxGetM(prhs[narg]),mxGetN(prhs[narg])); narg++;
Map<VectorXd> s1(mxGetPr(prhs[narg]),mxGetM(prhs[narg])); narg++;
Map<VectorXd> s1dot(mxGetPr(prhs[narg]),mxGetM(prhs[narg])); narg++;
double s2dot = mxGetScalar(prhs[narg++]);
Map<VectorXd> x0(mxGetPr(prhs[narg]),mxGetM(prhs[narg])); narg++;
Map<VectorXd> u0(mxGetPr(prhs[narg]),mxGetM(prhs[narg])); narg++;
Map<VectorXd> y0(mxGetPr(prhs[narg]),mxGetM(prhs[narg])); narg++;
Map<VectorXd> qdd_lb(mxGetPr(prhs[narg]),mxGetM(prhs[narg])); narg++;
Map<VectorXd> qdd_ub(mxGetPr(prhs[narg]),mxGetM(prhs[narg])); narg++;
memcpy(pdata->w_qdd.data(),mxGetPr(prhs[narg++]),sizeof(double)*nq);
double mu = mxGetScalar(prhs[narg++]);
double terrain_height = mxGetScalar(prhs[narg++]); // nonzero if we're using DRCFlatTerrainMap
MatrixXd R_DQyD_ls = R_ls + D_ls.transpose()*Qy*D_ls;
pdata->r->doKinematics(q,false,qd);
//---------------------------------------------------------------------
// Compute active support from desired supports -----------------------
vector<SupportStateElement> active_supports;
set<int> contact_bodies; // redundant, clean up later
int num_active_contact_pts=0;
if (!mxIsEmpty(prhs[desired_support_argid])) {
VectorXd phi;
mxArray* mxBodies = myGetField(prhs[desired_support_argid],"bodies");
if (!mxBodies) mexErrMsgTxt("couldn't get bodies");
double* pBodies = mxGetPr(mxBodies);
mxArray* mxContactPts = myGetField(prhs[desired_support_argid],"contact_pts");
if (!mxContactPts) mexErrMsgTxt("couldn't get contact points");
mxArray* mxContactSurfaces = myGetField(prhs[desired_support_argid],"contact_surfaces");
if (!mxContactSurfaces) mexErrMsgTxt("couldn't get contact surfaces");
double* pContactSurfaces = mxGetPr(mxContactSurfaces);
for (i=0; i<mxGetNumberOfElements(mxBodies);i++) {
mxArray* mxBodyContactPts = mxGetCell(mxContactPts,i);
int nc = mxGetNumberOfElements(mxBodyContactPts);
if (nc<1) continue;
SupportStateElement se;
se.body_idx = (int) pBodies[i]-1;
pr = mxGetPr(mxBodyContactPts);
for (j=0; j<nc; j++) {
se.contact_pt_inds.insert((int)pr[j]-1);
}
se.contact_surface = (int) pContactSurfaces[i]-1;
active_supports.push_back(se);
num_active_contact_pts += nc;
contact_bodies.insert((int)se.body_idx);
}
}
pdata->r->HandC(q,qd,(MatrixXd*)NULL,pdata->H,pdata->C,(MatrixXd*)NULL,(MatrixXd*)NULL,(MatrixXd*)NULL);
pdata->H_float = pdata->H.topRows(6);
pdata->H_act = pdata->H.bottomRows(nu);
pdata->C_float = pdata->C.head(6);
pdata->C_act = pdata->C.tail(nu);
bool include_angular_momentum = (pdata->W_kdot.array().maxCoeff() > 1e-10);
if (include_angular_momentum) {
pdata->r->getCMM(q,qd,pdata->Ag,pdata->Agdot);
pdata->Ak = pdata->Ag.topRows(3);
pdata->Akdot = pdata->Agdot.topRows(3);
}
Vector3d xcom;
// consider making all J's into row-major
pdata->r->getCOM(xcom);
pdata->r->getCOMJac(pdata->J);
pdata->r->getCOMJacDot(pdata->Jdot);
pdata->J_xy = pdata->J.topRows(2);
pdata->Jdot_xy = pdata->Jdot.topRows(2);
MatrixXd Jcom,Jcomdot;
if (x0.size()==6) {
Jcom = pdata->J;
Jcomdot = pdata->Jdot;
}
else {
Jcom = pdata->J_xy;
Jcomdot = pdata->Jdot_xy;
}
Map<VectorXd> qdvec(qd,nq);
MatrixXd B,JB,Jp,Jpdot,normals;
int nc = contactConstraintsBV(pdata->r,num_active_contact_pts,mu,active_supports,pdata->map_ptr,B,JB,Jp,Jpdot,normals,terrain_height);
int neps = nc*dim;
VectorXd x_bar,xlimp;
MatrixXd D_float(6,JB.cols()), D_act(nu,JB.cols());
if (nc>0) {
if (x0.size()==6) {
// x,y,z com
xlimp.resize(6);
xlimp.topRows(3) = xcom;
xlimp.bottomRows(3) = Jcom*qdvec;
}
else {
xlimp.resize(4);
xlimp.topRows(2) = xcom.topRows(2);
xlimp.bottomRows(2) = Jcom*qdvec;
}
x_bar = xlimp-x0;
D_float = JB.topRows(6);
D_act = JB.bottomRows(nu);
}
int nf = nc*nd; // number of contact force variables
int nparams = nq+nf+neps;
Vector3d kdot_des;
if (include_angular_momentum) {
VectorXd k = pdata->Ak*qdvec;
kdot_des = -pdata->Kp_ang*k; // TODO: parameterize
}
//----------------------------------------------------------------------
// QP cost function ----------------------------------------------------
//
// min: ybar*Qy*ybar + ubar*R*ubar + (2*S*xbar + s1)*(A*x + B*u) +
// w_qdd*quad(qddot_ref - qdd) + w_eps*quad(epsilon) +
// w_grf*quad(beta) + quad(kdot_des - (A*qdd + Adot*qd))
VectorXd f(nparams);
{
if (nc > 0) {
// NOTE: moved Hqp calcs below, because I compute the inverse directly for FastQP (and sparse Hqp for gurobi)
VectorXd tmp = C_ls*xlimp;
VectorXd tmp1 = Jcomdot*qdvec;
MatrixXd tmp2 = R_DQyD_ls*Jcom;
pdata->fqp = tmp.transpose()*Qy*D_ls*Jcom;
pdata->fqp += tmp1.transpose()*tmp2;
pdata->fqp += (S*x_bar + 0.5*s1).transpose()*B_ls*Jcom;
pdata->fqp -= u0.transpose()*tmp2;
pdata->fqp -= y0.transpose()*Qy*D_ls*Jcom;
pdata->fqp -= (pdata->w_qdd.array()*qddot_des.array()).matrix().transpose();
if (include_angular_momentum) {
pdata->fqp += qdvec.transpose()*pdata->Akdot.transpose()*pdata->W_kdot*pdata->Ak;
pdata->fqp -= kdot_des.transpose()*pdata->W_kdot*pdata->Ak;
}
f.head(nq) = pdata->fqp.transpose();
} else {
f.head(nq) = -qddot_des;
}
}
f.tail(nf+neps) = VectorXd::Zero(nf+neps);
int neq = 6+neps+6*pdata->n_body_accel_eq_constraints+num_condof;
MatrixXd Aeq = MatrixXd::Zero(neq,nparams);
VectorXd beq = VectorXd::Zero(neq);
// constrained floating base dynamics
// H_float*qdd - J_float'*lambda - Dbar_float*beta = -C_float
Aeq.topLeftCorner(6,nq) = pdata->H_float;
beq.topRows(6) = -pdata->C_float;
if (nc>0) {
Aeq.block(0,nq,6,nc*nd) = -D_float;
}
if (nc > 0) {
// relative acceleration constraint
Aeq.block(6,0,neps,nq) = Jp;
Aeq.block(6,nq,neps,nf) = MatrixXd::Zero(neps,nf); // note: obvious sparsity here
Aeq.block(6,nq+nf,neps,neps) = MatrixXd::Identity(neps,neps); // note: obvious sparsity here
beq.segment(6,neps) = (-Jpdot -pdata->Kp_accel*Jp)*qdvec;
}
// add in body spatial equality constraints
VectorXd body_vdot;
MatrixXd orig = MatrixXd::Zero(4,1);
orig(3,0) = 1;
int body_idx;
int equality_ind = 6+neps;
MatrixXd Jb(6,nq);
MatrixXd Jbdot(6,nq);
for (int i=0; i<pdata->n_body_accel_inputs; i++) {
if (pdata->body_accel_input_weights(i) < 0) {
// negative implies constraint
body_vdot = body_accel_inputs[i].bottomRows(6);
body_idx = (int)(body_accel_inputs[i][0])-1;
if (!inSupport(active_supports,body_idx)) {
pdata->r->forwardJac(body_idx,orig,1,Jb);
pdata->r->forwardJacDot(body_idx,orig,1,Jbdot);
for (int j=0; j<6; j++) {
if (!std::isnan(body_vdot[j])) {
Aeq.block(equality_ind,0,1,nq) = Jb.row(j);
beq[equality_ind++] = -Jbdot.row(j)*qdvec + body_vdot[j];
}
}
}
}
}
if (num_condof>0) {
// add joint acceleration constraints
for (int i=0; i<num_condof; i++) {
Aeq(equality_ind,(int)condof[i]-1) = 1;
beq[equality_ind++] = qddot_des[(int)condof[i]-1];
}
}
int n_ineq = 2*nu+2*6*pdata->n_body_accel_bounds;
MatrixXd Ain = MatrixXd::Zero(n_ineq,nparams); // note: obvious sparsity here
VectorXd bin = VectorXd::Zero(n_ineq);
// linear input saturation constraints
// u=B_act'*(H_act*qdd + C_act - Jz_act'*z - Dbar_act*beta)
// using transpose instead of inverse because B is orthogonal
Ain.topLeftCorner(nu,nq) = pdata->B_act.transpose()*pdata->H_act;
Ain.block(0,nq,nu,nc*nd) = -pdata->B_act.transpose()*D_act;
bin.head(nu) = -pdata->B_act.transpose()*pdata->C_act + pdata->umax;
Ain.block(nu,0,nu,nparams) = -1*Ain.block(0,0,nu,nparams);
bin.segment(nu,nu) = pdata->B_act.transpose()*pdata->C_act - pdata->umin;
int body_index;
int constraint_start_index = 2*nu;
for (int i=0; i<pdata->n_body_accel_bounds; i++) {
body_index = pdata->accel_bound_body_idx[i];
pdata->r->forwardJac(body_index,orig,1,Jb);
pdata->r->forwardJacDot(body_index,orig,1,Jbdot);
Ain.block(constraint_start_index,0,6,pdata->r->num_dof) = Jb;
bin.segment(constraint_start_index,6) = -Jbdot*qdvec + pdata->max_body_acceleration[i];
constraint_start_index += 6;
Ain.block(constraint_start_index,0,6,pdata->r->num_dof) = -Jb;
bin.segment(constraint_start_index,6) = Jbdot*qdvec - pdata->min_body_acceleration[i];
constraint_start_index += 6;
}
for (int i=0; i<n_ineq; i++) {
// remove inf constraints---needed by gurobi
if (std::isinf(double(bin(i)))) {
Ain.row(i) = 0*Ain.row(i);
bin(i)=0;
}
}
GRBmodel * model = NULL;
int info=-1;
// set obj,lb,up
VectorXd lb(nparams), ub(nparams);
lb.head(nq) = qdd_lb;
ub.head(nq) = qdd_ub;
lb.segment(nq,nf) = VectorXd::Zero(nf);
ub.segment(nq,nf) = 1e3*VectorXd::Ones(nf);
lb.tail(neps) = -pdata->slack_limit*VectorXd::Ones(neps);
ub.tail(neps) = pdata->slack_limit*VectorXd::Ones(neps);
VectorXd alpha(nparams);
MatrixXd Qnfdiag(nf,1), Qneps(neps,1);
vector<MatrixXd*> QBlkDiag( nc>0 ? 3 : 1 ); // nq, nf, neps // this one is for gurobi
VectorXd w = (pdata->w_qdd.array() + REG).matrix();
#ifdef USE_MATRIX_INVERSION_LEMMA
bool include_body_accel_cost_terms = pdata->n_body_accel_inputs > 0 && pdata->body_accel_input_weights.array().maxCoeff() > 1e-10;
if (use_fast_qp > 0 && !include_angular_momentum && !include_body_accel_cost_terms)
{
// TODO: update to include angular momentum, body accel objectives.
// We want Hqp inverse, which I can compute efficiently using the
// matrix inversion lemma (see wikipedia):
// inv(A + U'CV) = inv(A) - inv(A)*U* inv([ inv(C)+ V*inv(A)*U ]) V inv(A)
if (nc>0) {
MatrixXd Wi = ((1/(pdata->w_qdd.array() + REG)).matrix()).asDiagonal();
if (R_DQyD_ls.trace()>1e-15) { // R_DQyD_ls is not zero
pdata->Hqp = Wi - Wi*Jcom.transpose()*(R_DQyD_ls.inverse() + Jcom*Wi*Jcom.transpose()).inverse()*Jcom*Wi;
}
}
else {
pdata->Hqp = MatrixXd::Constant(nq,1,1/(1+REG));
}
#ifdef TEST_FAST_QP
if (nc>0) {
MatrixXd Hqp_test(nq,nq);
MatrixXd W = w.asDiagonal();
Hqp_test = (Jcom.transpose()*R_DQyD_ls*Jcom + W).inverse();
if (((Hqp_test-pdata->Hqp).array().abs()).maxCoeff() > 1e-6) {
mexErrMsgTxt("Q submatrix inverse from matrix inversion lemma does not match direct Q inverse.");
}
}
#endif
Qnfdiag = MatrixXd::Constant(nf,1,1/REG);
Qneps = MatrixXd::Constant(neps,1,1/(.001+REG));
QBlkDiag[0] = &pdata->Hqp;
if (nc>0) {
QBlkDiag[1] = &Qnfdiag;
QBlkDiag[2] = &Qneps; // quadratic slack var cost, Q(nparams-neps:end,nparams-neps:end)=eye(neps)
}
MatrixXd Ain_lb_ub(n_ineq+2*nparams,nparams);
VectorXd bin_lb_ub(n_ineq+2*nparams);
Ain_lb_ub << Ain, // note: obvious sparsity here
-MatrixXd::Identity(nparams,nparams),
MatrixXd::Identity(nparams,nparams);
bin_lb_ub << bin, -lb, ub;
info = fastQPThatTakesQinv(QBlkDiag, f, Aeq, beq, Ain_lb_ub, bin_lb_ub, pdata->active, alpha);
//if (info<0) mexPrintf("fastQP info = %d. Calling gurobi.\n", info);
}
else {
#endif
if (nc>0) {
pdata->Hqp = Jcom.transpose()*R_DQyD_ls*Jcom;
if (include_angular_momentum) {
pdata->Hqp += pdata->Ak.transpose()*pdata->W_kdot*pdata->Ak;
}
pdata->Hqp += pdata->w_qdd.asDiagonal();
pdata->Hqp += REG*MatrixXd::Identity(nq,nq);
} else {
pdata->Hqp = (1+REG)*MatrixXd::Identity(nq,nq);
}
// add in body spatial acceleration cost terms
double w_i;
for (int i=0; i<pdata->n_body_accel_inputs; i++) {
w_i=pdata->body_accel_input_weights(i);
if (w_i > 0) {
body_vdot = body_accel_inputs[i].bottomRows(6);
body_idx = (int)(body_accel_inputs[i][0])-1;
if (!inSupport(active_supports,body_idx)) {
pdata->r->forwardJac(body_idx,orig,1,Jb);
pdata->r->forwardJacDot(body_idx,orig,1,Jbdot);
for (int j=0; j<6; j++) {
if (!std::isnan(body_vdot[j])) {
pdata->Hqp += w_i*(Jb.row(j)).transpose()*Jb.row(j);
f.head(nq) += w_i*(qdvec.transpose()*Jbdot.row(j).transpose() - body_vdot[j])*Jb.row(j).transpose();
}
}
}
}
}
Qnfdiag = MatrixXd::Constant(nf,1,pdata->w_grf+REG);
Qneps = MatrixXd::Constant(neps,1,pdata->w_slack+REG);
QBlkDiag[0] = &pdata->Hqp;
if (nc>0) {
QBlkDiag[1] = &Qnfdiag;
QBlkDiag[2] = &Qneps; // quadratic slack var cost, Q(nparams-neps:end,nparams-neps:end)=eye(neps)
}
MatrixXd Ain_lb_ub(n_ineq+2*nparams,nparams);
VectorXd bin_lb_ub(n_ineq+2*nparams);
Ain_lb_ub << Ain, // note: obvious sparsity here
-MatrixXd::Identity(nparams,nparams),
MatrixXd::Identity(nparams,nparams);
bin_lb_ub << bin, -lb, ub;
if (use_fast_qp > 0)
{ // set up and call fastqp
info = fastQP(QBlkDiag, f, Aeq, beq, Ain_lb_ub, bin_lb_ub, pdata->active, alpha);
//if (info<0) mexPrintf("fastQP info=%d... calling Gurobi.\n", info);
}
else {
// use gurobi active set
model = gurobiActiveSetQP(pdata->env,QBlkDiag,f,Aeq,beq,Ain,bin,lb,ub,pdata->vbasis,pdata->vbasis_len,pdata->cbasis,pdata->cbasis_len,alpha);
CGE(GRBgetintattr(model,"NumVars",&pdata->vbasis_len), pdata->env);
CGE(GRBgetintattr(model,"NumConstrs",&pdata->cbasis_len), pdata->env);
info=66;
//info = -1;
}
if (info<0) {
model = gurobiQP(pdata->env,QBlkDiag,f,Aeq,beq,Ain,bin,lb,ub,pdata->active,alpha);
int status; CGE(GRBgetintattr(model, "Status", &status), pdata->env);
//if (status!=2) mexPrintf("Gurobi reports non-optimal status = %d\n", status);
}
#ifdef USE_MATRIX_INVERSION_LEMMA
}
#endif
//----------------------------------------------------------------------
// Solve for inputs ----------------------------------------------------
VectorXd y(nu);
VectorXd qdd = alpha.head(nq);
VectorXd beta = alpha.segment(nq,nc*nd);
// use transpose because B_act is orthogonal
y = pdata->B_act.transpose()*(pdata->H_act*qdd + pdata->C_act - D_act*beta);
//y = pdata->B_act.jacobiSvd(ComputeThinU|ComputeThinV).solve(pdata->H_act*qdd + pdata->C_act - Jz_act.transpose()*lambda - D_act*beta);
if (nlhs>0) {
plhs[0] = eigenToMatlab(y);
}
if (nlhs>1) {
plhs[1] = eigenToMatlab(qdd);
}
if (nlhs>2) {
plhs[2] = mxCreateNumericMatrix(1,1,mxINT32_CLASS,mxREAL);
memcpy(mxGetData(plhs[2]),&info,sizeof(int));
}
if (nlhs>3) {
plhs[3] = mxCreateDoubleMatrix(1,active_supports.size(),mxREAL);
pr = mxGetPr(plhs[3]);
int i=0;
for (vector<SupportStateElement>::iterator iter = active_supports.begin(); iter!=active_supports.end(); iter++) {
pr[i++] = (double) (iter->body_idx + 1);
}
}
if (nlhs>4) {
plhs[4] = eigenToMatlab(alpha);
}
if (nlhs>5) {
plhs[5] = eigenToMatlab(pdata->Hqp);
}
if (nlhs>6) {
plhs[6] = eigenToMatlab(f);
}
if (nlhs>7) {
plhs[7] = eigenToMatlab(Aeq);
}
if (nlhs>8) {
plhs[8] = eigenToMatlab(beq);
}
if (nlhs>9) {
plhs[9] = eigenToMatlab(Ain_lb_ub);
}
if (nlhs>10) {
plhs[10] = eigenToMatlab(bin_lb_ub);
}
if (nlhs>11) {
plhs[11] = eigenToMatlab(Qnfdiag);
}
if (nlhs>12) {
plhs[12] = eigenToMatlab(Qneps);
}
if (nlhs>13) {
double Vdot;
if (nc>0)
// note: Sdot is 0 for ZMP/double integrator dynamics, so we omit that term here
Vdot = ((2*x_bar.transpose()*S + s1.transpose())*(A_ls*x_bar + B_ls*(Jcomdot*qdvec + Jcom*qdd)) + s1dot.transpose()*x_bar)(0) + s2dot;
else
Vdot = 0;
plhs[13] = mxCreateDoubleScalar(Vdot);
}
if (nlhs>14) {
RigidBodyManipulator* r = pdata->r;
VectorXd individual_cops = individualSupportCOPs(r, active_supports, normals, B, beta);
plhs[14] = eigenToMatlab(individual_cops);
}
if (model) {
GRBfreemodel(model);
}
// GRBfreeenv(env);
}
CFeatures* CJade::apply(CFeatures* features)
{
ASSERT(features);
SG_REF(features);
SGMatrix<float64_t> X = ((CDenseFeatures<float64_t>*)features)->get_feature_matrix();
int n = X.num_rows;
int T = X.num_cols;
int m = n;
Map<MatrixXd> EX(X.matrix,n,T);
// Mean center X
VectorXd mean = (EX.rowwise().sum() / (float64_t)T);
MatrixXd SPX = EX.colwise() - mean;
MatrixXd cov = (SPX * SPX.transpose()) / (float64_t)T;
#ifdef DEBUG_JADE
std::cout << "cov" << std::endl;
std::cout << cov << std::endl;
#endif
// Whitening & Projection onto signal subspace
SelfAdjointEigenSolver<MatrixXd> eig;
eig.compute(cov);
#ifdef DEBUG_JADE
std::cout << "eigenvectors" << std::endl;
std::cout << eig.eigenvectors() << std::endl;
std::cout << "eigenvalues" << std::endl;
std::cout << eig.eigenvalues().asDiagonal() << std::endl;
#endif
// Scaling
VectorXd scales = eig.eigenvalues().cwiseSqrt();
MatrixXd B = scales.cwiseInverse().asDiagonal() * eig.eigenvectors().transpose();
#ifdef DEBUG_JADE
std::cout << "whitener" << std::endl;
std::cout << B << std::endl;
#endif
// Sphering
SPX = B * SPX;
// Estimation of the cumulant matrices
int dimsymm = (m * ( m + 1)) / 2; // Dim. of the space of real symm matrices
int nbcm = dimsymm; // number of cumulant matrices
m_cumulant_matrix = SGMatrix<float64_t>(m,m*nbcm); // Storage for cumulant matrices
Map<MatrixXd> CM(m_cumulant_matrix.matrix,m,m*nbcm);
MatrixXd R(m,m); R.setIdentity();
MatrixXd Qij = MatrixXd::Zero(m,m); // Temp for a cum. matrix
VectorXd Xim = VectorXd::Zero(m); // Temp
VectorXd Xjm = VectorXd::Zero(m); // Temp
VectorXd Xijm = VectorXd::Zero(m); // Temp
int Range = 0;
for (int im = 0; im < m; im++)
{
Xim = SPX.row(im);
Xijm = Xim.cwiseProduct(Xim);
Qij = SPX.cwiseProduct(Xijm.replicate(1,m).transpose()) * SPX.transpose() / (float)T - R - 2*R.col(im)*R.col(im).transpose();
CM.block(0,Range,m,m) = Qij;
Range = Range + m;
for (int jm = 0; jm < im; jm++)
{
Xjm = SPX.row(jm);
Xijm = Xim.cwiseProduct(Xjm);
Qij = SPX.cwiseProduct(Xijm.replicate(1,m).transpose()) * SPX.transpose() / (float)T - R.col(im)*R.col(jm).transpose() - R.col(jm)*R.col(im).transpose();
CM.block(0,Range,m,m) = sqrt(2)*Qij;
Range = Range + m;
}
}
#ifdef DEBUG_JADE
std::cout << "cumulatant matrices" << std::endl;
std::cout << CM << std::endl;
#endif
// Stack cumulant matrix into ND Array
index_t * M_dims = SG_MALLOC(index_t, 3);
M_dims[0] = m;
M_dims[1] = m;
M_dims[2] = nbcm;
SGNDArray< float64_t > M(M_dims, 3);
for (int i = 0; i < nbcm; i++)
{
Map<MatrixXd> EM(M.get_matrix(i),m,m);
EM = CM.block(0,i*m,m,m);
}
// Diagonalize
SGMatrix<float64_t> Q = CJADiagOrth::diagonalize(M, m_mixing_matrix, tol, max_iter);
Map<MatrixXd> EQ(Q.matrix,m,m);
EQ = -1 * EQ.inverse();
#ifdef DEBUG_JADE
std::cout << "diagonalizer" << std::endl;
std::cout << EQ << std::endl;
#endif
// Separating matrix
SGMatrix<float64_t> sep_matrix = SGMatrix<float64_t>(m,m);
Map<MatrixXd> C(sep_matrix.matrix,m,m);
C = EQ.transpose() * B;
// Sort
VectorXd A = (B.inverse()*EQ).cwiseAbs2().colwise().sum();
bool swap = false;
do
{
swap = false;
for (int j = 1; j < n; j++)
{
if ( A(j) < A(j-1) )
{
std::swap(A(j),A(j-1));
C.col(j).swap(C.col(j-1));
swap = true;
}
}
} while(swap);
for (int j = 0; j < m/2; j++)
C.row(j).swap( C.row(m-1-j) );
// Fix Signs
VectorXd signs = VectorXd::Zero(m);
for (int i = 0; i < m; i++)
{
if( C(i,0) < 0 )
signs(i) = -1;
else
signs(i) = 1;
}
C = signs.asDiagonal() * C;
#ifdef DEBUG_JADE
std::cout << "un mixing matrix" << std::endl;
std::cout << C << std::endl;
#endif
// Unmix
EX = C * EX;
m_mixing_matrix = SGMatrix<float64_t>(m,m);
Map<MatrixXd> Emixing_matrix(m_mixing_matrix.matrix,m,m);
Emixing_matrix = C.inverse();
return features;
}
/** create a matrix with designed eigenvalues.
* A V = V E
*/
inline MatrixXd matE(const VectorXd &e){
int n = e.size();
MatrixXd V(MatrixXd::Random(n, n));
return V * e.asDiagonal() * V.inverse();
}
void RandomPCA::pca(MatrixXd &X, int method, bool transpose,
unsigned int ndim, unsigned int nextra, unsigned int maxiter, double tol,
long seed, int kernel, double sigma, bool rbf_center,
unsigned int rbf_sample, bool save_kernel, bool do_orth, bool do_loadings)
{
unsigned int N;
if(kernel != KERNEL_LINEAR)
{
transpose = false;
verbose && std::cout << timestamp()
<< " Kernel not linear, can't transpose" << std::endl;
}
verbose && std::cout << timestamp() << " Transpose: "
<< (transpose ? "yes" : "no") << std::endl;
if(transpose)
{
if(stand_method != STANDARDIZE_NONE)
X_meansd = standardize_transpose(X, stand_method, verbose);
N = X.cols();
}
else
{
if(stand_method != STANDARDIZE_NONE)
X_meansd = standardize(X, stand_method, verbose);
N = X.rows();
}
unsigned int total_dim = ndim + nextra;
MatrixXd R = make_gaussian(X.cols(), total_dim, seed);
MatrixXd Y = X * R;
verbose && std::cout << timestamp() << " dim(Y): " << dim(Y) << std::endl;
normalize(Y);
MatrixXd Yn;
verbose && std::cout << timestamp() << " dim(X): " << dim(X) << std::endl;
MatrixXd K;
if(kernel == KERNEL_RBF)
{
if(sigma == 0)
{
unsigned int med_samples = fminl(rbf_sample, N);
double med = median_dist(X, med_samples, seed, verbose);
sigma = sqrt(med);
}
verbose && std::cout << timestamp() << " Using RBF kernel with sigma="
<< sigma << std::endl;
K.noalias() = rbf_kernel(X, sigma, rbf_center, verbose);
}
else
{
verbose && std::cout << timestamp() << " Using linear kernel" << std::endl;
K.noalias() = X * X.transpose() / (N - 1);
}
//trace = K.diagonal().array().sum() / (N - 1);
trace = K.diagonal().array().sum();
verbose && std::cout << timestamp() << " Trace(K): " << trace
<< " (N: " << N << ")" << std::endl;
verbose && std::cout << timestamp() << " dim(K): " << dim(K) << std::endl;
if(save_kernel)
{
verbose && std::cout << timestamp() << " saving K" << std::endl;
save_text("kernel.txt", K);
}
for(unsigned int iter = 0 ; iter < maxiter ; iter++)
{
verbose && std::cout << timestamp() << " iter " << iter;
Yn.noalias() = K * Y;
if(do_orth)
{
verbose && std::cout << " (orthogonalising)";
ColPivHouseholderQR<MatrixXd> qr(Yn);
MatrixXd I = MatrixXd::Identity(Yn.rows(), Yn.cols());
Yn = qr.householderQ() * I;
Yn.conservativeResize(NoChange, Yn.cols());
}
else
normalize(Yn);
double diff = (Y - Yn).array().square().sum() / Y.size();
verbose && std::cout << " " << diff << std::endl;
Y.noalias() = Yn;
if(diff < tol)
break;
}
verbose && std::cout << timestamp() << " QR begin" << std::endl;
ColPivHouseholderQR<MatrixXd> qr(Y);
MatrixXd Q = MatrixXd::Identity(Y.rows(), Y.cols());
Q = qr.householderQ() * Q;
Q.conservativeResize(NoChange, Y.cols());
verbose && std::cout << timestamp() << " dim(Q): " << dim(Q) << std::endl;
verbose && std::cout << timestamp() << " QR done" << std::endl;
MatrixXd B = Q.transpose() * X;
verbose && std::cout << timestamp() << " dim(B): " << dim(B) << std::endl;
MatrixXd Et;
pca_small(B, method, Et, d, verbose);
verbose && std::cout << timestamp() << " dim(Et): " << dim(Et) << std::endl;
d = d.array() / (N - 1);
if(transpose)
{
V.noalias() = Q * Et;
// We divide P by sqrt(N - 1) since X has not been divided
// by it (but B has)
P.noalias() = X.transpose() * V;
VectorXd s = 1 / (d.array().sqrt() * sqrt(N - 1));
MatrixXd Dinv = s.asDiagonal();
U = P * Dinv;
}
else
{
// P = U D = X V
U.noalias() = Q * Et;
P.noalias() = U * d.asDiagonal();
if(do_loadings)
{
VectorXd s = 1 / (d.array().sqrt() * sqrt(N - 1));
MatrixXd Dinv = s.asDiagonal();
V = X.transpose() * U * Dinv;
}
}
P.conservativeResize(NoChange, ndim);
U.conservativeResize(NoChange, ndim);
V.conservativeResize(NoChange, ndim);
d.conservativeResize(ndim);
pve = d.array() / trace;
}
//#define IGL_LINPROG_VERBOSE
IGL_INLINE bool igl::linprog(
const Eigen::VectorXd & c,
const Eigen::MatrixXd & _A,
const Eigen::VectorXd & b,
const int k,
Eigen::VectorXd & x)
{
// This is a very literal translation of
// http://www.mathworks.com/matlabcentral/fileexchange/2166-introduction-to-linear-algebra/content/strang/linprog.m
using namespace Eigen;
using namespace std;
bool success = true;
// number of constraints
const int m = _A.rows();
// number of original variables
const int n = _A.cols();
// number of iterations
int it = 0;
// maximum number of iterations
//const int MAXIT = 10*m;
const int MAXIT = 100*m;
// residual tolerance
const double tol = 1e-10;
const auto & sign = [](const Eigen::VectorXd & B) -> Eigen::VectorXd
{
Eigen::VectorXd Bsign(B.size());
for(int i = 0;i<B.size();i++)
{
Bsign(i) = B(i)>0?1:(B(i)<0?-1:0);
}
return Bsign;
};
// initial (inverse) basis matrix
VectorXd Dv = sign(sign(b).array()+0.5);
Dv.head(k).setConstant(1.);
MatrixXd D = Dv.asDiagonal();
// Incorporate slack variables
MatrixXd A(_A.rows(),_A.cols()+D.cols());
A<<_A,D;
// Initial basis
VectorXi B = igl::colon<int>(n,n+m-1);
// non-basis, may turn out that vector<> would be better here
VectorXi N = igl::colon<int>(0,n-1);
int j;
double bmin = b.minCoeff(&j);
int phase;
VectorXd xb;
VectorXd s;
VectorXi J;
if(k>0 && bmin<0)
{
phase = 1;
xb = VectorXd::Ones(m);
// super cost
s.resize(n+m+1);
s<<VectorXd::Zero(n+k),VectorXd::Ones(m-k+1);
N.resize(n+1);
N<<igl::colon<int>(0,n-1),B(j);
J.resize(B.size()-1);
// [0 1 2 3 4]
// ^
// [0 1]
// [3 4]
J.head(j) = B.head(j);
J.tail(B.size()-j-1) = B.tail(B.size()-j-1);
B(j) = n+m;
MatrixXd AJ;
igl::slice(A,J,2,AJ);
const VectorXd a = b - AJ.rowwise().sum();
{
MatrixXd old_A = A;
A.resize(A.rows(),A.cols()+a.cols());
A<<old_A,a;
}
D.col(j) = -a/a(j);
D(j,j) = 1./a(j);
}else if(k==m)
{
phase = 2;
xb = b;
s.resize(c.size()+m);
// cost function
s<<c,VectorXd::Zero(m);
}else //k = 0 or bmin >=0
{
phase = 1;
xb = b.array().abs();
s.resize(n+m);
// super cost
s<<VectorXd::Zero(n+k),VectorXd::Ones(m-k);
}
while(phase<3)
{
double df = -1;
int t = std::numeric_limits<int>::max();
// Lagrange mutipliers fro Ax=b
VectorXd yb = D.transpose() * igl::slice(s,B);
while(true)
{
if(MAXIT>0 && it>=MAXIT)
{
#ifdef IGL_LINPROG_VERBOSE
cerr<<"linprog: warning! maximum iterations without convergence."<<endl;
#endif
success = false;
break;
}
// no freedom for minimization
if(N.size() == 0)
{
break;
}
// reduced costs
VectorXd sN = igl::slice(s,N);
MatrixXd AN = igl::slice(A,N,2);
VectorXd r = sN - AN.transpose() * yb;
int q;
// determine new basic variable
double rmin = r.minCoeff(&q);
// optimal! infinity norm
if(rmin>=-tol*(sN.array().abs().maxCoeff()+1))
{
break;
}
// increment iteration count
it++;
// apply Bland's rule to avoid cycling
if(df>=0)
{
if(MAXIT == -1)
{
#ifdef IGL_LINPROG_VERBOSE
cerr<<"linprog: warning! degenerate vertex"<<endl;
#endif
success = false;
}
igl::find((r.array()<0).eval(),J);
double Nq = igl::slice(N,J).minCoeff();
// again seems like q is assumed to be a scalar though matlab code
// could produce a vector for multiple matches
(N.array()==Nq).cast<int>().maxCoeff(&q);
}
VectorXd d = D*A.col(N(q));
VectorXi I;
igl::find((d.array()>tol).eval(),I);
if(I.size() == 0)
{
#ifdef IGL_LINPROG_VERBOSE
cerr<<"linprog: warning! solution is unbounded"<<endl;
#endif
// This seems dubious:
it=-it;
success = false;
break;
}
VectorXd xbd = igl::slice(xb,I).array()/igl::slice(d,I).array();
// new use of r
int p;
{
double r;
r = xbd.minCoeff(&p);
p = I(p);
// apply Bland's rule to avoid cycling
if(df>=0)
{
igl::find((xbd.array()==r).eval(),J);
double Bp = igl::slice(B,igl::slice(I,J)).minCoeff();
// idiotic way of finding index in B of Bp
// code down the line seems to assume p is a scalar though the matlab
// code could find a vector of matches)
(B.array()==Bp).cast<int>().maxCoeff(&p);
}
// update x
xb -= r*d;
xb(p) = r;
// change in f
df = r*rmin;
}
// row vector
RowVectorXd v = D.row(p)/d(p);
yb += v.transpose() * (s(N(q)) - d.transpose()*igl::slice(s,B));
d(p)-=1;
// update inverse basis matrix
D = D - d*v;
t = B(p);
B(p) = N(q);
if(t>(n+k-1))
{
// remove qth entry from N
VectorXi old_N = N;
N.resize(N.size()-1);
N.head(q) = old_N.head(q);
N.head(q) = old_N.head(q);
N.tail(old_N.size()-q-1) = old_N.tail(old_N.size()-q-1);
}else
{
N(q) = t;
}
}
// iterative refinement
xb = (xb+D*(b-igl::slice(A,B,2)*xb)).eval();
// must be due to rounding
VectorXi I;
igl::find((xb.array()<0).eval(),I);
if(I.size()>0)
{
// so correct
VectorXd Z = VectorXd::Zero(I.size(),1);
igl::slice_into(Z,I,xb);
}
// B, xb,n,m,res=A(:,B)*xb-b
if(phase == 2 || it<0)
{
break;
}
if(xb.transpose()*igl::slice(s,B) > tol)
{
it = -it;
#ifdef IGL_LINPROG_VERBOSE
cerr<<"linprog: warning, no feasible solution"<<endl;
#endif
success = false;
break;
}
// re-initialize for Phase 2
phase = phase+1;
s*=1e6*c.array().abs().maxCoeff();
s.head(n) = c;
}
x.resize(std::max(B.maxCoeff()+1,n));
igl::slice_into(xb,B,x);
x = x.head(n).eval();
return success;
}