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/householder.cpp b/test/householder.cpp
new file mode 100644
index 0000000..c5f6b5e
--- /dev/null
+++ b/test/householder.cpp
@@ -0,0 +1,138 @@
+// 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::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(numext::imag(m1(0,0)), numext::real(m1(0,0)));
+ VERIFY_IS_APPROX(numext::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(numext::imag(m3(0,0)), numext::real(m3(0,0)));
+ VERIFY_IS_APPROX(numext::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
+
+ SquareMatrixType hseq_mat = hseq;
+ SquareMatrixType hseq_mat_conj = hseq.conjugate();
+ SquareMatrixType hseq_mat_adj = hseq.adjoint();
+ SquareMatrixType hseq_mat_trans = hseq.transpose();
+ SquareMatrixType m6 = SquareMatrixType::Random(rows, rows);
+ VERIFY_IS_APPROX(hseq_mat.adjoint(), hseq_mat_adj);
+ VERIFY_IS_APPROX(hseq_mat.conjugate(), hseq_mat_conj);
+ VERIFY_IS_APPROX(hseq_mat.transpose(), hseq_mat_trans);
+ VERIFY_IS_APPROX(hseq_mat * m6, hseq_mat * m6);
+ VERIFY_IS_APPROX(hseq_mat.adjoint() * m6, hseq_mat_adj * m6);
+ VERIFY_IS_APPROX(hseq_mat.conjugate() * m6, hseq_mat_conj * m6);
+ VERIFY_IS_APPROX(hseq_mat.transpose() * m6, hseq_mat_trans * m6);
+ VERIFY_IS_APPROX(m6 * hseq_mat, m6 * hseq_mat);
+ VERIFY_IS_APPROX(m6 * hseq_mat.adjoint(), m6 * hseq_mat_adj);
+ VERIFY_IS_APPROX(m6 * hseq_mat.conjugate(), m6 * hseq_mat_conj);
+ VERIFY_IS_APPROX(m6 * hseq_mat.transpose(), m6 * hseq_mat_trans);
+
+ // 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>()) );
+ }
+}