Squashed 'third_party/eigen/' content from commit 61d72f6
Change-Id: Iccc90fa0b55ab44037f018046d2fcffd90d9d025
git-subtree-dir: third_party/eigen
git-subtree-split: 61d72f6383cfa842868c53e30e087b0258177257
diff --git a/test/qr_colpivoting.cpp b/test/qr_colpivoting.cpp
new file mode 100644
index 0000000..eb3feac
--- /dev/null
+++ b/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));
+}