180 lines
5.9 KiB
C
180 lines
5.9 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) 2014 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_MIN_QUAD_WITH_FIXED_H
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#define IGL_MIN_QUAD_WITH_FIXED_H
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#include "igl_inline.h"
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#define EIGEN_YES_I_KNOW_SPARSE_MODULE_IS_NOT_STABLE_YET
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#include <Eigen/Core>
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#include <Eigen/Dense>
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#include <Eigen/Sparse>
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// Bug in unsupported/Eigen/SparseExtra needs iostream first
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#include <iostream>
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#include <unsupported/Eigen/SparseExtra>
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namespace igl
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{
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template <typename T>
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struct min_quad_with_fixed_data;
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// Known Bugs: rows of Aeq **should probably** be linearly independent.
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// During precomputation, the rows of a Aeq are checked via QR. But in case
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// they're not then resulting probably will no longer be sparse: it will be
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// slow.
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//
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// MIN_QUAD_WITH_FIXED Minimize a quadratic energy of the form
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//
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// trace( 0.5*Z'*A*Z + Z'*B + constant )
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//
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// subject to
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//
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// Z(known,:) = Y, and
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// Aeq*Z = Beq
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//
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// Templates:
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// T should be a eigen matrix primitive type like int or double
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// Inputs:
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// A n by n matrix of quadratic coefficients
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// known list of indices to known rows in Z
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// Y list of fixed values corresponding to known rows in Z
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// Aeq m by n list of linear equality constraint coefficients
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// pd flag specifying whether A(unknown,unknown) is positive definite
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// Outputs:
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// data factorization struct with all necessary information to solve
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// using min_quad_with_fixed_solve
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// Returns true on success, false on error
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//
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// Benchmark: For a harmonic solve on a mesh with 325K facets, matlab 2.2
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// secs, igl/min_quad_with_fixed.h 7.1 secs
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//
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template <typename T, typename Derivedknown>
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IGL_INLINE bool min_quad_with_fixed_precompute(
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const Eigen::SparseMatrix<T>& A,
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const Eigen::MatrixBase<Derivedknown> & known,
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const Eigen::SparseMatrix<T>& Aeq,
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const bool pd,
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min_quad_with_fixed_data<T> & data
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);
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// Solves a system previously factored using min_quad_with_fixed_precompute
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//
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// Template:
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// T type of sparse matrix (e.g. double)
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// DerivedY type of Y (e.g. derived from VectorXd or MatrixXd)
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// DerivedZ type of Z (e.g. derived from VectorXd or MatrixXd)
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// Inputs:
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// data factorization struct with all necessary precomputation to solve
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// B n by k column of linear coefficients
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// Y b by k list of constant fixed values
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// Beq m by k list of linear equality constraint constant values
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// Outputs:
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// Z n by k solution
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// sol #unknowns+#lagrange by k solution to linear system
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// Returns true on success, false on error
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template <
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typename T,
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typename DerivedB,
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typename DerivedY,
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typename DerivedBeq,
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typename DerivedZ,
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typename Derivedsol>
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IGL_INLINE bool min_quad_with_fixed_solve(
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const min_quad_with_fixed_data<T> & data,
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const Eigen::MatrixBase<DerivedB> & B,
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const Eigen::MatrixBase<DerivedY> & Y,
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const Eigen::MatrixBase<DerivedBeq> & Beq,
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Eigen::PlainObjectBase<DerivedZ> & Z,
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Eigen::PlainObjectBase<Derivedsol> & sol);
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// Wrapper without sol
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template <
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typename T,
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typename DerivedB,
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typename DerivedY,
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typename DerivedBeq,
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typename DerivedZ>
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IGL_INLINE bool min_quad_with_fixed_solve(
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const min_quad_with_fixed_data<T> & data,
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const Eigen::MatrixBase<DerivedB> & B,
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const Eigen::MatrixBase<DerivedY> & Y,
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const Eigen::MatrixBase<DerivedBeq> & Beq,
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Eigen::PlainObjectBase<DerivedZ> & Z);
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template <
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typename T,
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typename Derivedknown,
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typename DerivedB,
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typename DerivedY,
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typename DerivedBeq,
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typename DerivedZ>
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IGL_INLINE bool min_quad_with_fixed(
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const Eigen::SparseMatrix<T>& A,
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const Eigen::MatrixBase<DerivedB> & B,
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const Eigen::MatrixBase<Derivedknown> & known,
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const Eigen::MatrixBase<DerivedY> & Y,
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const Eigen::SparseMatrix<T>& Aeq,
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const Eigen::MatrixBase<DerivedBeq> & Beq,
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const bool pd,
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Eigen::PlainObjectBase<DerivedZ> & Z);
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}
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template <typename T>
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struct igl::min_quad_with_fixed_data
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{
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// Size of original system: number of unknowns + number of knowns
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int n;
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// Whether A(unknown,unknown) is positive definite
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bool Auu_pd;
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// Whether A(unknown,unknown) is symmetric
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bool Auu_sym;
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// Indices of known variables
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Eigen::VectorXi known;
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// Indices of unknown variables
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Eigen::VectorXi unknown;
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// Indices of lagrange variables
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Eigen::VectorXi lagrange;
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// Indices of unknown variable followed by Indices of lagrange variables
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Eigen::VectorXi unknown_lagrange;
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// Matrix multiplied against Y when constructing right hand side
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Eigen::SparseMatrix<T> preY;
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enum SolverType
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{
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LLT = 0,
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LDLT = 1,
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LU = 2,
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QR_LLT = 3,
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NUM_SOLVER_TYPES = 4
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} solver_type;
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// Solvers
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Eigen::SimplicialLLT <Eigen::SparseMatrix<T > > llt;
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Eigen::SimplicialLDLT<Eigen::SparseMatrix<T > > ldlt;
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Eigen::SparseLU<Eigen::SparseMatrix<T, Eigen::ColMajor>, Eigen::COLAMDOrdering<int> > lu;
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// QR factorization
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// Are rows of Aeq linearly independent?
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bool Aeq_li;
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// Columns of Aeq corresponding to unknowns
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int neq;
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Eigen::SparseQR<Eigen::SparseMatrix<T>, Eigen::COLAMDOrdering<int> > AeqTQR;
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Eigen::SparseMatrix<T> Aeqk;
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Eigen::SparseMatrix<T> Aequ;
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Eigen::SparseMatrix<T> Auu;
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Eigen::SparseMatrix<T> AeqTQ1;
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Eigen::SparseMatrix<T> AeqTQ1T;
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Eigen::SparseMatrix<T> AeqTQ2;
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Eigen::SparseMatrix<T> AeqTQ2T;
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Eigen::SparseMatrix<T> AeqTR1;
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Eigen::SparseMatrix<T> AeqTR1T;
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Eigen::SparseMatrix<T> AeqTE;
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Eigen::SparseMatrix<T> AeqTET;
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// Debug
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Eigen::SparseMatrix<T> NA;
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Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic> NB;
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};
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#ifndef IGL_STATIC_LIBRARY
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# include "min_quad_with_fixed.cpp"
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#endif
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#endif
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