371 lines
12 KiB
C++
371 lines
12 KiB
C++
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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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#include "active_set.h"
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#include "min_quad_with_fixed.h"
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#include "slice.h"
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#include "slice_into.h"
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#include "cat.h"
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//#include "matlab_format.h"
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#include <iostream>
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#include <limits>
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#include <algorithm>
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template <
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typename AT,
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typename DerivedB,
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typename Derivedknown,
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typename DerivedY,
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typename AeqT,
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typename DerivedBeq,
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typename AieqT,
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typename DerivedBieq,
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typename Derivedlx,
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typename Derivedux,
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typename DerivedZ
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>
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IGL_INLINE igl::SolverStatus igl::active_set(
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const Eigen::SparseMatrix<AT>& A,
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const Eigen::PlainObjectBase<DerivedB> & B,
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const Eigen::PlainObjectBase<Derivedknown> & known,
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const Eigen::PlainObjectBase<DerivedY> & Y,
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const Eigen::SparseMatrix<AeqT>& Aeq,
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const Eigen::PlainObjectBase<DerivedBeq> & Beq,
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const Eigen::SparseMatrix<AieqT>& Aieq,
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const Eigen::PlainObjectBase<DerivedBieq> & Bieq,
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const Eigen::PlainObjectBase<Derivedlx> & p_lx,
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const Eigen::PlainObjectBase<Derivedux> & p_ux,
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const igl::active_set_params & params,
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Eigen::PlainObjectBase<DerivedZ> & Z
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)
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{
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//#define ACTIVE_SET_CPP_DEBUG
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#if defined(ACTIVE_SET_CPP_DEBUG) && !defined(_MSC_VER)
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# warning "ACTIVE_SET_CPP_DEBUG"
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#endif
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using namespace Eigen;
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using namespace std;
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SolverStatus ret = SOLVER_STATUS_ERROR;
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const int n = A.rows();
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assert(n == A.cols() && "A must be square");
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// Discard const qualifiers
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//if(B.size() == 0)
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//{
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// B = DerivedB::Zero(n,1);
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//}
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assert(n == B.rows() && "B.rows() must match A.rows()");
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assert(B.cols() == 1 && "B must be a column vector");
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assert(Y.cols() == 1 && "Y must be a column vector");
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assert((Aeq.size() == 0 && Beq.size() == 0) || Aeq.cols() == n);
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assert((Aeq.size() == 0 && Beq.size() == 0) || Aeq.rows() == Beq.rows());
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assert((Aeq.size() == 0 && Beq.size() == 0) || Beq.cols() == 1);
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assert((Aieq.size() == 0 && Bieq.size() == 0) || Aieq.cols() == n);
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assert((Aieq.size() == 0 && Bieq.size() == 0) || Aieq.rows() == Bieq.rows());
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assert((Aieq.size() == 0 && Bieq.size() == 0) || Bieq.cols() == 1);
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Eigen::Matrix<typename Derivedlx::Scalar,Eigen::Dynamic,1> lx;
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Eigen::Matrix<typename Derivedux::Scalar,Eigen::Dynamic,1> ux;
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if(p_lx.size() == 0)
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{
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lx = Derivedlx::Constant(
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n,1,-numeric_limits<typename Derivedlx::Scalar>::max());
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}else
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{
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lx = p_lx;
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}
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if(p_ux.size() == 0)
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{
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ux = Derivedux::Constant(
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n,1,numeric_limits<typename Derivedux::Scalar>::max());
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}else
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{
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ux = p_ux;
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}
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assert(lx.rows() == n && "lx must have n rows");
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assert(ux.rows() == n && "ux must have n rows");
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assert(ux.cols() == 1 && "lx must be a column vector");
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assert(lx.cols() == 1 && "ux must be a column vector");
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assert((ux.array()-lx.array()).minCoeff() > 0 && "ux(i) must be > lx(i)");
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if(Z.size() != 0)
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{
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// Initial guess should have correct size
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assert(Z.rows() == n && "Z must have n rows");
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assert(Z.cols() == 1 && "Z must be a column vector");
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}
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assert(known.cols() == 1 && "known must be a column vector");
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// Number of knowns
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const int nk = known.size();
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// Initialize active sets
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typedef int BOOL;
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#define TRUE 1
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#define FALSE 0
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Matrix<BOOL,Dynamic,1> as_lx = Matrix<BOOL,Dynamic,1>::Constant(n,1,FALSE);
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Matrix<BOOL,Dynamic,1> as_ux = Matrix<BOOL,Dynamic,1>::Constant(n,1,FALSE);
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Matrix<BOOL,Dynamic,1> as_ieq = Matrix<BOOL,Dynamic,1>::Constant(Aieq.rows(),1,FALSE);
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// Keep track of previous Z for comparison
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DerivedZ old_Z;
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old_Z = DerivedZ::Constant(
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n,1,numeric_limits<typename DerivedZ::Scalar>::max());
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int iter = 0;
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while(true)
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{
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#ifdef ACTIVE_SET_CPP_DEBUG
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cout<<"Iteration: "<<iter<<":"<<endl;
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cout<<" pre"<<endl;
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#endif
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// FIND BREACHES OF CONSTRAINTS
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int new_as_lx = 0;
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int new_as_ux = 0;
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int new_as_ieq = 0;
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if(Z.size() > 0)
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{
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for(int z = 0;z < n;z++)
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{
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if(Z(z) < lx(z))
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{
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new_as_lx += (as_lx(z)?0:1);
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//new_as_lx++;
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as_lx(z) = TRUE;
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}
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if(Z(z) > ux(z))
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{
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new_as_ux += (as_ux(z)?0:1);
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//new_as_ux++;
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as_ux(z) = TRUE;
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}
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}
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if(Aieq.rows() > 0)
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{
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DerivedZ AieqZ;
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AieqZ = Aieq*Z;
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for(int a = 0;a<Aieq.rows();a++)
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{
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if(AieqZ(a) > Bieq(a))
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{
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new_as_ieq += (as_ieq(a)?0:1);
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as_ieq(a) = TRUE;
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}
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}
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}
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#ifdef ACTIVE_SET_CPP_DEBUG
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cout<<" new_as_lx: "<<new_as_lx<<endl;
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cout<<" new_as_ux: "<<new_as_ux<<endl;
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#endif
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const double diff = (Z-old_Z).squaredNorm();
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#ifdef ACTIVE_SET_CPP_DEBUG
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cout<<"diff: "<<diff<<endl;
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#endif
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if(diff < params.solution_diff_threshold)
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{
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ret = SOLVER_STATUS_CONVERGED;
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break;
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}
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old_Z = Z;
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}
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const int as_lx_count = std::count(as_lx.data(),as_lx.data()+n,TRUE);
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const int as_ux_count = std::count(as_ux.data(),as_ux.data()+n,TRUE);
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const int as_ieq_count =
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std::count(as_ieq.data(),as_ieq.data()+as_ieq.size(),TRUE);
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#ifndef NDEBUG
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{
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int count = 0;
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for(int a = 0;a<as_ieq.size();a++)
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{
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if(as_ieq(a))
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{
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assert(as_ieq(a) == TRUE);
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count++;
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}
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}
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assert(as_ieq_count == count);
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}
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#endif
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// PREPARE FIXED VALUES
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Derivedknown known_i;
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known_i.resize(nk + as_lx_count + as_ux_count,1);
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DerivedY Y_i;
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Y_i.resize(nk + as_lx_count + as_ux_count,1);
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{
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known_i.block(0,0,known.rows(),known.cols()) = known;
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Y_i.block(0,0,Y.rows(),Y.cols()) = Y;
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int k = nk;
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// Then all lx
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for(int z = 0;z < n;z++)
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{
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if(as_lx(z))
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{
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known_i(k) = z;
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Y_i(k) = lx(z);
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k++;
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}
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}
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// Finally all ux
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for(int z = 0;z < n;z++)
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{
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if(as_ux(z))
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{
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known_i(k) = z;
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Y_i(k) = ux(z);
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k++;
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}
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}
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assert(k==Y_i.size());
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assert(k==known_i.size());
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}
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//cout<<matlab_format((known_i.array()+1).eval(),"known_i")<<endl;
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// PREPARE EQUALITY CONSTRAINTS
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VectorXi as_ieq_list(as_ieq_count,1);
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// Gather active constraints and resp. rhss
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DerivedBeq Beq_i;
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Beq_i.resize(Beq.rows()+as_ieq_count,1);
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Beq_i.head(Beq.rows()) = Beq;
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{
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int k =0;
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for(int a=0;a<as_ieq.size();a++)
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{
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if(as_ieq(a))
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{
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assert(k<as_ieq_list.size());
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as_ieq_list(k)=a;
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Beq_i(Beq.rows()+k,0) = Bieq(k,0);
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k++;
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}
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}
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assert(k == as_ieq_count);
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}
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// extract active constraint rows
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SparseMatrix<AeqT> Aeq_i,Aieq_i;
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slice(Aieq,as_ieq_list,1,Aieq_i);
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// Append to equality constraints
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cat(1,Aeq,Aieq_i,Aeq_i);
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min_quad_with_fixed_data<AT> data;
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#ifndef NDEBUG
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{
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// NO DUPES!
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Matrix<BOOL,Dynamic,1> fixed = Matrix<BOOL,Dynamic,1>::Constant(n,1,FALSE);
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for(int k = 0;k<known_i.size();k++)
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{
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assert(!fixed[known_i(k)]);
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fixed[known_i(k)] = TRUE;
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}
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}
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#endif
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DerivedZ sol;
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if(known_i.size() == A.rows())
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{
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// Everything's fixed?
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#ifdef ACTIVE_SET_CPP_DEBUG
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cout<<" everything's fixed."<<endl;
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#endif
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Z.resize(A.rows(),Y_i.cols());
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slice_into(Y_i,known_i,1,Z);
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sol.resize(0,Y_i.cols());
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assert(Aeq_i.rows() == 0 && "All fixed but linearly constrained");
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}else
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{
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#ifdef ACTIVE_SET_CPP_DEBUG
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cout<<" min_quad_with_fixed_precompute"<<endl;
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#endif
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if(!min_quad_with_fixed_precompute(A,known_i,Aeq_i,params.Auu_pd,data))
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{
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cerr<<"Error: min_quad_with_fixed precomputation failed."<<endl;
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if(iter > 0 && Aeq_i.rows() > Aeq.rows())
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{
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cerr<<" *Are you sure rows of [Aeq;Aieq] are linearly independent?*"<<
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endl;
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}
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ret = SOLVER_STATUS_ERROR;
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break;
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}
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#ifdef ACTIVE_SET_CPP_DEBUG
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cout<<" min_quad_with_fixed_solve"<<endl;
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#endif
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if(!min_quad_with_fixed_solve(data,B,Y_i,Beq_i,Z,sol))
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{
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cerr<<"Error: min_quad_with_fixed solve failed."<<endl;
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ret = SOLVER_STATUS_ERROR;
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break;
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}
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//cout<<matlab_format((Aeq*Z-Beq).eval(),"cr")<<endl;
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//cout<<matlab_format(Z,"Z")<<endl;
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#ifdef ACTIVE_SET_CPP_DEBUG
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cout<<" post"<<endl;
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#endif
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// Computing Lagrange multipliers needs to be adjusted slightly if A is not symmetric
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assert(data.Auu_sym);
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}
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// Compute Lagrange multiplier values for known_i
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SparseMatrix<AT> Ak;
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// Slow
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slice(A,known_i,1,Ak);
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DerivedB Bk;
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slice(B,known_i,Bk);
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MatrixXd Lambda_known_i = -(0.5*Ak*Z + 0.5*Bk);
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// reverse the lambda values for lx
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Lambda_known_i.block(nk,0,as_lx_count,1) =
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(-1*Lambda_known_i.block(nk,0,as_lx_count,1)).eval();
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// Extract Lagrange multipliers for Aieq_i (always at back of sol)
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VectorXd Lambda_Aieq_i(Aieq_i.rows(),1);
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for(int l = 0;l<Aieq_i.rows();l++)
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{
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Lambda_Aieq_i(Aieq_i.rows()-1-l) = sol(sol.rows()-1-l);
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}
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// Remove from active set
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for(int l = 0;l<as_lx_count;l++)
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{
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if(Lambda_known_i(nk + l) < params.inactive_threshold)
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{
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as_lx(known_i(nk + l)) = FALSE;
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}
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}
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for(int u = 0;u<as_ux_count;u++)
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{
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if(Lambda_known_i(nk + as_lx_count + u) <
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params.inactive_threshold)
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{
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as_ux(known_i(nk + as_lx_count + u)) = FALSE;
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}
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}
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for(int a = 0;a<as_ieq_count;a++)
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{
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if(Lambda_Aieq_i(a) < params.inactive_threshold)
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{
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as_ieq(as_ieq_list(a)) = FALSE;
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}
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}
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iter++;
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//cout<<iter<<endl;
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if(params.max_iter>0 && iter>=params.max_iter)
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{
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ret = SOLVER_STATUS_MAX_ITER;
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break;
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||
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}
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|
|
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||
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}
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||
|
|
|
||
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return ret;
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||
|
|
}
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||
|
|
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||
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||
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#ifdef IGL_STATIC_LIBRARY
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// Explicit template instantiation
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template igl::SolverStatus igl::active_set<double, Eigen::Matrix<double, -1, 1, 0, -1, 1>, Eigen::Matrix<int, -1, 1, 0, -1, 1>, Eigen::Matrix<double, -1, 1, 0, -1, 1>, double, Eigen::Matrix<double, -1, 1, 0, -1, 1>, double, Eigen::Matrix<double, -1, 1, 0, -1, 1>, Eigen::Matrix<double, -1, 1, 0, -1, 1>, Eigen::Matrix<double, -1, 1, 0, -1, 1>, Eigen::Matrix<double, -1, 1, 0, -1, 1> >(Eigen::SparseMatrix<double, 0, int> const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 1, 0, -1, 1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 1, 0, -1, 1> > const&, Eigen::SparseMatrix<double, 0, int> const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 1, 0, -1, 1> > const&, Eigen::SparseMatrix<double, 0, int> const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 1, 0, -1, 1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 1, 0, -1, 1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 1, 0, -1, 1> > const&, igl::active_set_params const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 1, 0, -1, 1> >&);
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|
template igl::SolverStatus igl::active_set<double, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, double, Eigen::Matrix<double, -1, 1, 0, -1, 1>, double, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1> >(Eigen::SparseMatrix<double, 0, int> const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::SparseMatrix<double, 0, int> const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 1, 0, -1, 1> > const&, Eigen::SparseMatrix<double, 0, int> const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, igl::active_set_params const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&);
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#endif
|