From 44861dcbfeee041223c4aac1ee075e92fa4daa01 Mon Sep 17 00:00:00 2001
From: Stanislaw Halik <sthalik@misaki.pl>
Date: Sun, 18 Sep 2016 12:42:15 +0200
Subject: update

---
 eigen/test/qr_colpivoting.cpp | 150 ++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 150 insertions(+)
 create mode 100644 eigen/test/qr_colpivoting.cpp

(limited to 'eigen/test/qr_colpivoting.cpp')

diff --git a/eigen/test/qr_colpivoting.cpp b/eigen/test/qr_colpivoting.cpp
new file mode 100644
index 0000000..eb3feac
--- /dev/null
+++ b/eigen/test/qr_colpivoting.cpp
@@ -0,0 +1,150 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2009 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 qr()
+{
+  typedef typename MatrixType::Index Index;
+
+  Index rows = internal::random<Index>(2,EIGEN_TEST_MAX_SIZE), cols = internal::random<Index>(2,EIGEN_TEST_MAX_SIZE), cols2 = internal::random<Index>(2,EIGEN_TEST_MAX_SIZE);
+  Index rank = internal::random<Index>(1, (std::min)(rows, cols)-1);
+
+  typedef typename MatrixType::Scalar Scalar;
+  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> MatrixQType;
+  MatrixType m1;
+  createRandomPIMatrixOfRank(rank,rows,cols,m1);
+  ColPivHouseholderQR<MatrixType> qr(m1);
+  VERIFY(rank == qr.rank());
+  VERIFY(cols - qr.rank() == qr.dimensionOfKernel());
+  VERIFY(!qr.isInjective());
+  VERIFY(!qr.isInvertible());
+  VERIFY(!qr.isSurjective());
+
+  MatrixQType q = qr.householderQ();
+  VERIFY_IS_UNITARY(q);
+
+  MatrixType r = qr.matrixQR().template triangularView<Upper>();
+  MatrixType c = q * r * qr.colsPermutation().inverse();
+  VERIFY_IS_APPROX(m1, c);
+
+  MatrixType m2 = MatrixType::Random(cols,cols2);
+  MatrixType m3 = m1*m2;
+  m2 = MatrixType::Random(cols,cols2);
+  m2 = qr.solve(m3);
+  VERIFY_IS_APPROX(m3, m1*m2);
+}
+
+template<typename MatrixType, int Cols2> void qr_fixedsize()
+{
+  enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime };
+  typedef typename MatrixType::Scalar Scalar;
+  int rank = internal::random<int>(1, (std::min)(int(Rows), int(Cols))-1);
+  Matrix<Scalar,Rows,Cols> m1;
+  createRandomPIMatrixOfRank(rank,Rows,Cols,m1);
+  ColPivHouseholderQR<Matrix<Scalar,Rows,Cols> > qr(m1);
+  VERIFY(rank == qr.rank());
+  VERIFY(Cols - qr.rank() == qr.dimensionOfKernel());
+  VERIFY(qr.isInjective() == (rank == Rows));
+  VERIFY(qr.isSurjective() == (rank == Cols));
+  VERIFY(qr.isInvertible() == (qr.isInjective() && qr.isSurjective()));
+
+  Matrix<Scalar,Rows,Cols> r = qr.matrixQR().template triangularView<Upper>();
+  Matrix<Scalar,Rows,Cols> c = qr.householderQ() * r * qr.colsPermutation().inverse();
+  VERIFY_IS_APPROX(m1, c);
+
+  Matrix<Scalar,Cols,Cols2> m2 = Matrix<Scalar,Cols,Cols2>::Random(Cols,Cols2);
+  Matrix<Scalar,Rows,Cols2> m3 = m1*m2;
+  m2 = Matrix<Scalar,Cols,Cols2>::Random(Cols,Cols2);
+  m2 = qr.solve(m3);
+  VERIFY_IS_APPROX(m3, m1*m2);
+}
+
+template<typename MatrixType> void qr_invertible()
+{
+  using std::log;
+  using std::abs;
+  typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
+  typedef typename MatrixType::Scalar Scalar;
+
+  int size = internal::random<int>(10,50);
+
+  MatrixType m1(size, size), m2(size, size), m3(size, size);
+  m1 = MatrixType::Random(size,size);
+
+  if (internal::is_same<RealScalar,float>::value)
+  {
+    // let's build a matrix more stable to inverse
+    MatrixType a = MatrixType::Random(size,size*2);
+    m1 += a * a.adjoint();
+  }
+
+  ColPivHouseholderQR<MatrixType> qr(m1);
+  m3 = MatrixType::Random(size,size);
+  m2 = qr.solve(m3);
+  //VERIFY_IS_APPROX(m3, m1*m2);
+
+  // now construct a matrix with prescribed determinant
+  m1.setZero();
+  for(int i = 0; i < size; i++) m1(i,i) = internal::random<Scalar>();
+  RealScalar absdet = abs(m1.diagonal().prod());
+  m3 = qr.householderQ(); // get a unitary
+  m1 = m3 * m1 * m3;
+  qr.compute(m1);
+  VERIFY_IS_APPROX(absdet, qr.absDeterminant());
+  VERIFY_IS_APPROX(log(absdet), qr.logAbsDeterminant());
+}
+
+template<typename MatrixType> void qr_verify_assert()
+{
+  MatrixType tmp;
+
+  ColPivHouseholderQR<MatrixType> qr;
+  VERIFY_RAISES_ASSERT(qr.matrixQR())
+  VERIFY_RAISES_ASSERT(qr.solve(tmp))
+  VERIFY_RAISES_ASSERT(qr.householderQ())
+  VERIFY_RAISES_ASSERT(qr.dimensionOfKernel())
+  VERIFY_RAISES_ASSERT(qr.isInjective())
+  VERIFY_RAISES_ASSERT(qr.isSurjective())
+  VERIFY_RAISES_ASSERT(qr.isInvertible())
+  VERIFY_RAISES_ASSERT(qr.inverse())
+  VERIFY_RAISES_ASSERT(qr.absDeterminant())
+  VERIFY_RAISES_ASSERT(qr.logAbsDeterminant())
+}
+
+void test_qr_colpivoting()
+{
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST_1( qr<MatrixXf>() );
+    CALL_SUBTEST_2( qr<MatrixXd>() );
+    CALL_SUBTEST_3( qr<MatrixXcd>() );
+    CALL_SUBTEST_4(( qr_fixedsize<Matrix<float,3,5>, 4 >() ));
+    CALL_SUBTEST_5(( qr_fixedsize<Matrix<double,6,2>, 3 >() ));
+    CALL_SUBTEST_5(( qr_fixedsize<Matrix<double,1,1>, 1 >() ));
+  }
+
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST_1( qr_invertible<MatrixXf>() );
+    CALL_SUBTEST_2( qr_invertible<MatrixXd>() );
+    CALL_SUBTEST_6( qr_invertible<MatrixXcf>() );
+    CALL_SUBTEST_3( qr_invertible<MatrixXcd>() );
+  }
+
+  CALL_SUBTEST_7(qr_verify_assert<Matrix3f>());
+  CALL_SUBTEST_8(qr_verify_assert<Matrix3d>());
+  CALL_SUBTEST_1(qr_verify_assert<MatrixXf>());
+  CALL_SUBTEST_2(qr_verify_assert<MatrixXd>());
+  CALL_SUBTEST_6(qr_verify_assert<MatrixXcf>());
+  CALL_SUBTEST_3(qr_verify_assert<MatrixXcd>());
+
+  // Test problem size constructors
+  CALL_SUBTEST_9(ColPivHouseholderQR<MatrixXf>(10, 20));
+}
-- 
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