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