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      1 // This file is part of Eigen, a lightweight C++ template library
      2 // for linear algebra.
      3 //
      4 // Copyright (C) 2012 Alexey Korepanov <kaikaikai (at) yandex.ru>
      5 //
      6 // This Source Code Form is subject to the terms of the Mozilla
      7 // Public License v. 2.0. If a copy of the MPL was not distributed
      8 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
      9 
     10 #define EIGEN_RUNTIME_NO_MALLOC
     11 #include "main.h"
     12 #include <limits>
     13 #include <Eigen/Eigenvalues>
     14 
     15 template<typename MatrixType> void real_qz(const MatrixType& m)
     16 {
     17   /* this test covers the following files:
     18      RealQZ.h
     19   */
     20   using std::abs;
     21   typedef typename MatrixType::Index Index;
     22   typedef typename MatrixType::Scalar Scalar;
     23 
     24   Index dim = m.cols();
     25 
     26   MatrixType A = MatrixType::Random(dim,dim),
     27              B = MatrixType::Random(dim,dim);
     28 
     29 
     30   // Regression test for bug 985: Randomly set rows or columns to zero
     31   Index k=internal::random<Index>(0, dim-1);
     32   switch(internal::random<int>(0,10)) {
     33   case 0:
     34     A.row(k).setZero(); break;
     35   case 1:
     36     A.col(k).setZero(); break;
     37   case 2:
     38     B.row(k).setZero(); break;
     39   case 3:
     40     B.col(k).setZero(); break;
     41   default:
     42     break;
     43   }
     44 
     45   RealQZ<MatrixType> qz(dim);
     46   // TODO enable full-prealocation of required memory, this probably requires an in-place mode for HessenbergDecomposition
     47   //Eigen::internal::set_is_malloc_allowed(false);
     48   qz.compute(A,B);
     49   //Eigen::internal::set_is_malloc_allowed(true);
     50 
     51   VERIFY_IS_EQUAL(qz.info(), Success);
     52   // check for zeros
     53   bool all_zeros = true;
     54   for (Index i=0; i<A.cols(); i++)
     55     for (Index j=0; j<i; j++) {
     56       if (abs(qz.matrixT()(i,j))!=Scalar(0.0))
     57       {
     58         std::cerr << "Error: T(" << i << "," << j << ") = " << qz.matrixT()(i,j) << std::endl;
     59         all_zeros = false;
     60       }
     61       if (j<i-1 && abs(qz.matrixS()(i,j))!=Scalar(0.0))
     62       {
     63         std::cerr << "Error: S(" << i << "," << j << ") = " << qz.matrixS()(i,j) << std::endl;
     64         all_zeros = false;
     65       }
     66       if (j==i-1 && j>0 && abs(qz.matrixS()(i,j))!=Scalar(0.0) && abs(qz.matrixS()(i-1,j-1))!=Scalar(0.0))
     67       {
     68         std::cerr << "Error: S(" << i << "," << j << ") = " << qz.matrixS()(i,j)  << " && S(" << i-1 << "," << j-1 << ") = " << qz.matrixS()(i-1,j-1) << std::endl;
     69         all_zeros = false;
     70       }
     71     }
     72   VERIFY_IS_EQUAL(all_zeros, true);
     73   VERIFY_IS_APPROX(qz.matrixQ()*qz.matrixS()*qz.matrixZ(), A);
     74   VERIFY_IS_APPROX(qz.matrixQ()*qz.matrixT()*qz.matrixZ(), B);
     75   VERIFY_IS_APPROX(qz.matrixQ()*qz.matrixQ().adjoint(), MatrixType::Identity(dim,dim));
     76   VERIFY_IS_APPROX(qz.matrixZ()*qz.matrixZ().adjoint(), MatrixType::Identity(dim,dim));
     77 }
     78 
     79 void test_real_qz()
     80 {
     81   int s = 0;
     82   for(int i = 0; i < g_repeat; i++) {
     83     CALL_SUBTEST_1( real_qz(Matrix4f()) );
     84     s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
     85     CALL_SUBTEST_2( real_qz(MatrixXd(s,s)) );
     86 
     87     // some trivial but implementation-wise tricky cases
     88     CALL_SUBTEST_2( real_qz(MatrixXd(1,1)) );
     89     CALL_SUBTEST_2( real_qz(MatrixXd(2,2)) );
     90     CALL_SUBTEST_3( real_qz(Matrix<double,1,1>()) );
     91     CALL_SUBTEST_4( real_qz(Matrix2d()) );
     92   }
     93 
     94   TEST_SET_BUT_UNUSED_VARIABLE(s)
     95 }
     96