cart-elc

Source code for CART-ELC
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sparseqr.cpp (4587B)

      1 // This file is part of Eigen, a lightweight C++ template library
      2 // for linear algebra.
      3 //
      4 // Copyright (C) 2012 Desire Nuentsa Wakam <desire.nuentsa_wakam@inria.fr>
      5 // Copyright (C) 2014 Gael Guennebaud <gael.guennebaud@inria.fr>
      6 //
      7 // This Source Code Form is subject to the terms of the Mozilla
      8 // Public License v. 2.0. If a copy of the MPL was not distributed
      9 #include "sparse.h"
     10 #include <Eigen/SparseQR>
     11 
     12 template<typename MatrixType,typename DenseMat>
     13 int generate_sparse_rectangular_problem(MatrixType& A, DenseMat& dA, int maxRows = 300, int maxCols = 150)
     14 {
     15   eigen_assert(maxRows >= maxCols);
     16   typedef typename MatrixType::Scalar Scalar;
     17   int rows = internal::random<int>(1,maxRows);
     18   int cols = internal::random<int>(1,maxCols);
     19   double density = (std::max)(8./(rows*cols), 0.01);
     20   
     21   A.resize(rows,cols);
     22   dA.resize(rows,cols);
     23   initSparse<Scalar>(density, dA, A,ForceNonZeroDiag);
     24   A.makeCompressed();
     25   int nop = internal::random<int>(0, internal::random<double>(0,1) > 0.5 ? cols/2 : 0);
     26   for(int k=0; k<nop; ++k)
     27   {
     28     int j0 = internal::random<int>(0,cols-1);
     29     int j1 = internal::random<int>(0,cols-1);
     30     Scalar s = internal::random<Scalar>();
     31     A.col(j0)  = s * A.col(j1);
     32     dA.col(j0) = s * dA.col(j1);
     33   }
     34   
     35 //   if(rows<cols) {
     36 //     A.conservativeResize(cols,cols);
     37 //     dA.conservativeResize(cols,cols);
     38 //     dA.bottomRows(cols-rows).setZero();
     39 //   }
     40   
     41   return rows;
     42 }
     43 
     44 template<typename Scalar> void test_sparseqr_scalar()
     45 {
     46   typedef typename NumTraits<Scalar>::Real RealScalar;
     47   typedef SparseMatrix<Scalar,ColMajor> MatrixType; 
     48   typedef Matrix<Scalar,Dynamic,Dynamic> DenseMat;
     49   typedef Matrix<Scalar,Dynamic,1> DenseVector;
     50   MatrixType A;
     51   DenseMat dA;
     52   DenseVector refX,x,b; 
     53   SparseQR<MatrixType, COLAMDOrdering<int> > solver; 
     54   generate_sparse_rectangular_problem(A,dA);
     55   
     56   b = dA * DenseVector::Random(A.cols());
     57   solver.compute(A);
     58 
     59   // Q should be MxM
     60   VERIFY_IS_EQUAL(solver.matrixQ().rows(), A.rows());
     61   VERIFY_IS_EQUAL(solver.matrixQ().cols(), A.rows());
     62 
     63   // R should be MxN
     64   VERIFY_IS_EQUAL(solver.matrixR().rows(), A.rows());
     65   VERIFY_IS_EQUAL(solver.matrixR().cols(), A.cols());
     66 
     67   // Q and R can be multiplied
     68   DenseMat recoveredA = solver.matrixQ()
     69                       * DenseMat(solver.matrixR().template triangularView<Upper>())
     70                       * solver.colsPermutation().transpose();
     71   VERIFY_IS_EQUAL(recoveredA.rows(), A.rows());
     72   VERIFY_IS_EQUAL(recoveredA.cols(), A.cols());
     73 
     74   // and in the full rank case the original matrix is recovered
     75   if (solver.rank() == A.cols())
     76   {
     77       VERIFY_IS_APPROX(A, recoveredA);
     78   }
     79 
     80   if(internal::random<float>(0,1)>0.5f)
     81     solver.factorize(A);  // this checks that calling analyzePattern is not needed if the pattern do not change.
     82   if (solver.info() != Success)
     83   {
     84     std::cerr << "sparse QR factorization failed\n";
     85     exit(0);
     86     return;
     87   }
     88   x = solver.solve(b);
     89   if (solver.info() != Success)
     90   {
     91     std::cerr << "sparse QR factorization failed\n";
     92     exit(0);
     93     return;
     94   }
     95 
     96   // Compare with a dense QR solver
     97   ColPivHouseholderQR<DenseMat> dqr(dA);
     98   refX = dqr.solve(b);
     99   
    100   bool rank_deficient = A.cols()>A.rows() || dqr.rank()<A.cols();
    101   if(rank_deficient)
    102   {
    103     // rank deficient problem -> we might have to increase the threshold
    104     // to get a correct solution.
    105     RealScalar th = RealScalar(20)*dA.colwise().norm().maxCoeff()*(A.rows()+A.cols()) * NumTraits<RealScalar>::epsilon();
    106     for(Index k=0; (k<16) && !test_isApprox(A*x,b); ++k)
    107     {
    108       th *= RealScalar(10);
    109       solver.setPivotThreshold(th);
    110       solver.compute(A);
    111       x = solver.solve(b);
    112     }
    113   }
    114 
    115   VERIFY_IS_APPROX(A * x, b);
    116   
    117   // For rank deficient problem, the estimated rank might
    118   // be slightly off, so let's only raise a warning in such cases.
    119   if(rank_deficient) ++g_test_level;
    120   VERIFY_IS_EQUAL(solver.rank(), dqr.rank());
    121   if(rank_deficient) --g_test_level;
    122 
    123   if(solver.rank()==A.cols()) // full rank
    124     VERIFY_IS_APPROX(x, refX);
    125 //   else
    126 //     VERIFY((dA * refX - b).norm() * 2 > (A * x - b).norm() );
    127 
    128   // Compute explicitly the matrix Q
    129   MatrixType Q, QtQ, idM;
    130   Q = solver.matrixQ();
    131   //Check  ||Q' * Q - I ||
    132   QtQ = Q * Q.adjoint();
    133   idM.resize(Q.rows(), Q.rows()); idM.setIdentity();
    134   VERIFY(idM.isApprox(QtQ));
    135   
    136   // Q to dense
    137   DenseMat dQ;
    138   dQ = solver.matrixQ();
    139   VERIFY_IS_APPROX(Q, dQ);
    140 }
    141 EIGEN_DECLARE_TEST(sparseqr)
    142 {
    143   for(int i=0; i<g_repeat; ++i)
    144   {
    145     CALL_SUBTEST_1(test_sparseqr_scalar<double>());
    146     CALL_SUBTEST_2(test_sparseqr_scalar<std::complex<double> >());
    147   }
    148 }
    149