// This file is part of libigl, a simple c++ geometry processing library. // // Copyright (C) 2013 Alec Jacobson // // This Source Code Form is subject to the terms of the Mozilla Public License // v. 2.0. If a copy of the MPL was not distributed with this file, You can // obtain one at http://mozilla.org/MPL/2.0/. #ifndef IGL_KKT_INVERSE_H #define IGL_KKT_INVERSE_H #include "igl_inline.h" #include //// debug //#include //Engine *g_pEngine; namespace igl { /// Constructs the inverse of the KKT matrix of a convex, linear equality /// constrained quadratic minimization problem. /// /// Systems of the form: /// /// / A Aeqᵀ \ / x \ = / b \ /// \ Aeq 0 / \ λ / \ beq / /// \_____.______/\__.__/ \___.___/ /// M z c /// /// Arise, for example, when solve convex, linear equality constrained /// quadratic minimization problems: /// /// min ½ xᵀ A x - xᵀb subject to Aeq x = beq /// /// This function constructs a matrix S such that x = S c solves the system /// above. That is: /// /// S = [In 0] M⁻¹ /// /// so that /// /// x = S c /// /// @tparam T should be a eigen matrix primitive type like float or double /// @param[in] A n by n matrix of quadratic coefficients /// @param[in] B n by 1 column of linear coefficients /// @param[in] Aeq m by n list of linear equality constraint coefficients /// @param[in] Beq m by 1 list of linear equality constraint constant values /// @param[in] use_lu_decomposition use lu rather than SVD /// @param[out] S n by (n + m) "solve" matrix, such that S*[B', Beq'] is a solution /// @return true on success, false on error template IGL_INLINE void kkt_inverse( const Eigen::Matrix& A, const Eigen::Matrix& Aeq, const bool use_lu_decomposition, Eigen::Matrix& S); } #ifndef IGL_STATIC_LIBRARY # include "kkt_inverse.cpp" #endif #endif