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97 lines
3 KiB
C++
97 lines
3 KiB
C++
// 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 "min_quad_dense.h"
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#include <Eigen/Core>
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#include <Eigen/LU>
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#include "EPS.h"
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#include <cstdio>
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template <typename T>
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IGL_INLINE void igl::min_quad_dense_precompute(
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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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typedef Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> Mat;
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// This threshold seems to matter a lot but I'm not sure how to
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// set it
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const T treshold = igl::FLOAT_EPS;
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//const T treshold = igl::DOUBLE_EPS;
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const int n = A.rows();
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assert(A.cols() == n);
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const int m = Aeq.rows();
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assert(Aeq.cols() == n);
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// Lagrange multipliers method:
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Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> LM(n + m, n + m);
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LM.block(0, 0, n, n) = A;
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LM.block(0, n, n, m) = Aeq.transpose();
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LM.block(n, 0, m, n) = Aeq;
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LM.block(n, n, m, m).setZero();
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Mat LMpinv;
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if(use_lu_decomposition)
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{
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// if LM is close to singular, use at your own risk :)
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LMpinv = LM.inverse();
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}else
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{
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// use SVD
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typedef Eigen::Matrix<T, Eigen::Dynamic, 1> Vec;
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Vec singValues;
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Eigen::JacobiSVD<Mat> svd;
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svd.compute(LM, Eigen::ComputeFullU | Eigen::ComputeFullV );
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const Mat& u = svd.matrixU();
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const Mat& v = svd.matrixV();
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const Vec& singVals = svd.singularValues();
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Vec pi_singVals(n + m);
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int zeroed = 0;
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for (int i=0; i<n + m; i++)
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{
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T sv = singVals(i, 0);
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assert(sv >= 0);
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// printf("sv: %lg ? %lg\n",(double) sv,(double)treshold);
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if (sv > treshold) pi_singVals(i, 0) = T(1) / sv;
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else
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{
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pi_singVals(i, 0) = T(0);
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zeroed++;
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}
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}
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printf("min_quad_dense_precompute: %i singular values zeroed (threshold = %e)\n", zeroed, treshold);
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Eigen::DiagonalMatrix<T, Eigen::Dynamic> pi_diag(pi_singVals);
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LMpinv = v * pi_diag * u.transpose();
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}
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S = LMpinv.block(0, 0, n, n + m);
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//// debug:
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//mlinit(&g_pEngine);
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//
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//mlsetmatrix(&g_pEngine, "A", A);
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//mlsetmatrix(&g_pEngine, "Aeq", Aeq);
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//mlsetmatrix(&g_pEngine, "LM", LM);
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//mlsetmatrix(&g_pEngine, "u", u);
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//mlsetmatrix(&g_pEngine, "v", v);
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//MatrixXd svMat = singVals;
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//mlsetmatrix(&g_pEngine, "singVals", svMat);
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//mlsetmatrix(&g_pEngine, "LMpinv", LMpinv);
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//mlsetmatrix(&g_pEngine, "S", S);
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//int hu = 1;
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}
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#ifdef IGL_STATIC_LIBRARY
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// Explicit template instantiation
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template void igl::min_quad_dense_precompute<double>(Eigen::Matrix<double, -1, -1, 0, -1, -1> const&, Eigen::Matrix<double, -1, -1, 0, -1, -1> const&, bool, Eigen::Matrix<double, -1, -1, 0, -1, -1>&);
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#endif
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