1 files changed, 123 insertions, 0 deletions
diff --git a/test/householder.cpp b/test/householder.cpp
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+++ b/test/householder.cpp
@@ -0,0 +1,123 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <Eigen/QR>
+
+template<typename MatrixType> void householder(const MatrixType& m)
+{
+  typedef typename MatrixType::Index Index;
+  static bool even = true;
+  even = !even;
+  /* this test covers the following files:
+     Householder.h
+  */
+  Index rows = m.rows();
+  Index cols = m.cols();
+
+  typedef typename MatrixType::Scalar Scalar;
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
+  typedef Matrix<Scalar, internal::decrement_size<MatrixType::RowsAtCompileTime>::ret, 1> EssentialVectorType;
+  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType;
+  typedef Matrix<Scalar, Dynamic, MatrixType::ColsAtCompileTime> HBlockMatrixType;
+  typedef Matrix<Scalar, Dynamic, 1> HCoeffsVectorType;
+
+  typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, MatrixType::ColsAtCompileTime> RightSquareMatrixType;
+  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, Dynamic> VBlockMatrixType;
+  typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, MatrixType::RowsAtCompileTime> TMatrixType;
+  
+  Matrix<Scalar, EIGEN_SIZE_MAX(MatrixType::RowsAtCompileTime,MatrixType::ColsAtCompileTime), 1> _tmp((std::max)(rows,cols));
+  Scalar* tmp = &_tmp.coeffRef(0,0);
+
+  Scalar beta;
+  RealScalar alpha;
+  EssentialVectorType essential;
+
+  VectorType v1 = VectorType::Random(rows), v2;
+  v2 = v1;
+  v1.makeHouseholder(essential, beta, alpha);
+  v1.applyHouseholderOnTheLeft(essential,beta,tmp);
+  VERIFY_IS_APPROX(v1.norm(), v2.norm());
+  if(rows>=2) VERIFY_IS_MUCH_SMALLER_THAN(v1.tail(rows-1).norm(), v1.norm());
+  v1 = VectorType::Random(rows);
+  v2 = v1;
+  v1.applyHouseholderOnTheLeft(essential,beta,tmp);
+  VERIFY_IS_APPROX(v1.norm(), v2.norm());
+
+  MatrixType m1(rows, cols),
+             m2(rows, cols);
+
+  v1 = VectorType::Random(rows);
+  if(even) v1.tail(rows-1).setZero();
+  m1.colwise() = v1;
+  m2 = m1;
+  m1.col(0).makeHouseholder(essential, beta, alpha);
+  m1.applyHouseholderOnTheLeft(essential,beta,tmp);
+  VERIFY_IS_APPROX(m1.norm(), m2.norm());
+  if(rows>=2) VERIFY_IS_MUCH_SMALLER_THAN(m1.block(1,0,rows-1,cols).norm(), m1.norm());
+  VERIFY_IS_MUCH_SMALLER_THAN(internal::imag(m1(0,0)), internal::real(m1(0,0)));
+  VERIFY_IS_APPROX(internal::real(m1(0,0)), alpha);
+
+  v1 = VectorType::Random(rows);
+  if(even) v1.tail(rows-1).setZero();
+  SquareMatrixType m3(rows,rows), m4(rows,rows);
+  m3.rowwise() = v1.transpose();
+  m4 = m3;
+  m3.row(0).makeHouseholder(essential, beta, alpha);
+  m3.applyHouseholderOnTheRight(essential,beta,tmp);
+  VERIFY_IS_APPROX(m3.norm(), m4.norm());
+  if(rows>=2) VERIFY_IS_MUCH_SMALLER_THAN(m3.block(0,1,rows,rows-1).norm(), m3.norm());
+  VERIFY_IS_MUCH_SMALLER_THAN(internal::imag(m3(0,0)), internal::real(m3(0,0)));
+  VERIFY_IS_APPROX(internal::real(m3(0,0)), alpha);
+
+  // test householder sequence on the left with a shift
+
+  Index shift = internal::random<Index>(0, std::max<Index>(rows-2,0));
+  Index brows = rows - shift;
+  m1.setRandom(rows, cols);
+  HBlockMatrixType hbm = m1.block(shift,0,brows,cols);
+  HouseholderQR<HBlockMatrixType> qr(hbm);
+  m2 = m1;
+  m2.block(shift,0,brows,cols) = qr.matrixQR();
+  HCoeffsVectorType hc = qr.hCoeffs().conjugate();
+  HouseholderSequence<MatrixType, HCoeffsVectorType> hseq(m2, hc);
+  hseq.setLength(hc.size()).setShift(shift);
+  VERIFY(hseq.length() == hc.size());
+  VERIFY(hseq.shift() == shift);
+
+  MatrixType m5 = m2;
+  m5.block(shift,0,brows,cols).template triangularView<StrictlyLower>().setZero();
+  VERIFY_IS_APPROX(hseq * m5, m1); // test applying hseq directly
+  m3 = hseq;
+  VERIFY_IS_APPROX(m3 * m5, m1); // test evaluating hseq to a dense matrix, then applying
+
+  // test householder sequence on the right with a shift
+
+  TMatrixType tm2 = m2.transpose();
+  HouseholderSequence<TMatrixType, HCoeffsVectorType, OnTheRight> rhseq(tm2, hc);
+  rhseq.setLength(hc.size()).setShift(shift);
+  VERIFY_IS_APPROX(rhseq * m5, m1); // test applying rhseq directly
+  m3 = rhseq;
+  VERIFY_IS_APPROX(m3 * m5, m1); // test evaluating rhseq to a dense matrix, then applying
+}
+
+void test_householder()
+{
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST_1( householder(Matrix<double,2,2>()) );
+    CALL_SUBTEST_2( householder(Matrix<float,2,3>()) );
+    CALL_SUBTEST_3( householder(Matrix<double,3,5>()) );
+    CALL_SUBTEST_4( householder(Matrix<float,4,4>()) );
+    CALL_SUBTEST_5( householder(MatrixXd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+    CALL_SUBTEST_6( householder(MatrixXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+    CALL_SUBTEST_7( householder(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+    CALL_SUBTEST_8( householder(Matrix<double,1,1>()) );
+  }
+}