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Anton Kamalov
2025-12-06 16:01:44 +03:00
parent 5d3506215c
commit e613b4f004
23 changed files with 14518 additions and 1 deletions
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GCS/qp_eq.cpp Normal file
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/***************************************************************************
* Copyright (c) 2011 Konstantinos Poulios <logari81@gmail.com> *
* *
* This file is part of the FreeCAD CAx development system. *
* *
* This library is free software; you can redistribute it and/or *
* modify it under the terms of the GNU Library General Public *
* License as published by the Free Software Foundation; either *
* version 2 of the License, or (at your option) any later version. *
* *
* This library is distributed in the hope that it will be useful, *
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
* GNU Library General Public License for more details. *
* *
* You should have received a copy of the GNU Library General Public *
* License along with this library; see the file COPYING.LIB. If not, *
* write to the Free Software Foundation, Inc., 59 Temple Place, *
* Suite 330, Boston, MA 02111-1307, USA *
* *
***************************************************************************/
#ifdef _MSC_VER
#pragma warning(disable : 4244)
#endif
#include <Eigen/QR>
#include <iostream>
using namespace Eigen;
// minimizes ( 0.5 * x^T * H * x + g^T * x ) under the condition ( A*x + c = 0 )
// it returns the solution in x, the row-space of A in Y, and the null space of A in Z
int qp_eq(MatrixXd& H, VectorXd& g, MatrixXd& A, VectorXd& c, VectorXd& x, MatrixXd& Y, MatrixXd& Z)
{
FullPivHouseholderQR<MatrixXd> qrAT(A.transpose());
MatrixXd Q = qrAT.matrixQ();
size_t params_num = qrAT.rows();
size_t constr_num = qrAT.cols();
size_t rank = qrAT.rank();
if (rank != constr_num || constr_num > params_num) {
return -1;
}
// A^T = Q*R*P^T = Q1*R1*P^T
// Q = [Q1,Q2], R=[R1;0]
// Y = Q1 * inv(R^T) * P^T
// Z = Q2
Y = qrAT.matrixQR()
.topRows(constr_num)
.triangularView<Upper>()
.transpose()
.solve<OnTheRight>(Q.leftCols(rank))
* qrAT.colsPermutation().transpose();
if (params_num == rank) {
x = -Y * c;
}
else {
Z = Q.rightCols(params_num - rank);
MatrixXd ZTHZ = Z.transpose() * H * Z;
VectorXd rhs = Z.transpose() * (H * Y * c - g);
VectorXd y = ZTHZ.colPivHouseholderQr().solve(rhs);
x = -Y * c + Z * y;
}
return 0;
}