Merged branch 'dev_native' into lm_sla_supports_auto

Added igl library files

src/igl/active_set.h

@@ -0,0 +1,111 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// 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_ACTIVE_SET_H
+#define IGL_ACTIVE_SET_H
+
+#include "igl_inline.h"
+#include "SolverStatus.h"
+#include <Eigen/Core>
+#include <Eigen/Sparse>
+
+namespace igl
+{
+  struct active_set_params;
+  // Known Bugs: rows of [Aeq;Aieq] **must** be linearly independent. Should be
+  // using QR decomposition otherwise:
+  //   http://www.okstate.edu/sas/v8/sashtml/ormp/chap5/sect32.htm
+  //
+  // ACTIVE_SET Minimize quadratic energy 
+  //
+  // 0.5*Z'*A*Z + Z'*B + C with constraints
+  //
+  // that Z(known) = Y, optionally also subject to the constraints Aeq*Z = Beq,
+  // and further optionally subject to the linear inequality constraints that
+  // Aieq*Z <= Bieq and constant inequality constraints lx <= x <= ux
+  //
+  // Inputs:
+  //   A  n by n matrix of quadratic coefficients
+  //   B  n by 1 column of linear coefficients
+  //   known  list of indices to known rows in Z
+  //   Y  list of fixed values corresponding to known rows in Z
+  //   Aeq  meq by n list of linear equality constraint coefficients
+  //   Beq  meq by 1 list of linear equality constraint constant values
+  //   Aieq  mieq by n list of linear inequality constraint coefficients
+  //   Bieq  mieq by 1 list of linear inequality constraint constant values
+  //   lx  n by 1 list of lower bounds [] implies -Inf
+  //   ux  n by 1 list of upper bounds [] implies Inf
+  //   params  struct of additional parameters (see below)
+  //   Z  if not empty, is taken to be an n by 1 list of initial guess values
+  //     (see output)
+  // Outputs:
+  //   Z  n by 1 list of solution values
+  // Returns true on success, false on error
+  //
+  // Benchmark: For a harmonic solve on a mesh with 325K facets, matlab 2.2
+  // secs, igl/min_quad_with_fixed.h 7.1 secs
+  //
+  template <
+    typename AT, 
+    typename DerivedB,
+    typename Derivedknown, 
+    typename DerivedY,
+    typename AeqT,
+    typename DerivedBeq,
+    typename AieqT,
+    typename DerivedBieq,
+    typename Derivedlx,
+    typename Derivedux,
+    typename DerivedZ
+    >
+  IGL_INLINE igl::SolverStatus active_set(
+    const Eigen::SparseMatrix<AT>& A,
+    const Eigen::PlainObjectBase<DerivedB> & B,
+    const Eigen::PlainObjectBase<Derivedknown> & known,
+    const Eigen::PlainObjectBase<DerivedY> & Y,
+    const Eigen::SparseMatrix<AeqT>& Aeq,
+    const Eigen::PlainObjectBase<DerivedBeq> & Beq,
+    const Eigen::SparseMatrix<AieqT>& Aieq,
+    const Eigen::PlainObjectBase<DerivedBieq> & Bieq,
+    const Eigen::PlainObjectBase<Derivedlx> & lx,
+    const Eigen::PlainObjectBase<Derivedux> & ux,
+    const igl::active_set_params & params,
+    Eigen::PlainObjectBase<DerivedZ> & Z
+    );
+};
+
+#include "EPS.h"
+struct igl::active_set_params
+{
+  // Input parameters for active_set:
+  //   Auu_pd  whether Auu is positive definite {false}
+  //   max_iter  Maximum number of iterations (0 = Infinity, {100})
+  //   inactive_threshold  Threshold on Lagrange multiplier values to determine
+  //     whether to keep constraints active {EPS}
+  //   constraint_threshold  Threshold on whether constraints are violated (0
+  //     is perfect) {EPS}
+  //   solution_diff_threshold  Threshold on the squared norm of the difference
+  //     between two consecutive solutions {EPS}
+  bool Auu_pd;
+  int max_iter;
+  double inactive_threshold;
+  double constraint_threshold;
+  double solution_diff_threshold;
+  active_set_params():
+    Auu_pd(false),
+    max_iter(100),
+    inactive_threshold(igl::DOUBLE_EPS),
+    constraint_threshold(igl::DOUBLE_EPS),
+    solution_diff_threshold(igl::DOUBLE_EPS)
+    {};
+};
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "active_set.cpp"
+#endif
+
+#endif