1c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// This file is part of Eigen, a lightweight C++ template library 2c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// for linear algebra. 3c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// 4c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com> 5c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// 6c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// This Source Code Form is subject to the terms of the Mozilla 7c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// Public License v. 2.0. If a copy of the MPL was not distributed 8c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. 9c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 10c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#include "main.h" 11c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#include <Eigen/QR> 12c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 13c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename Derived1, typename Derived2> 14c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathbool areNotApprox(const MatrixBase<Derived1>& m1, const MatrixBase<Derived2>& m2, typename Derived1::RealScalar epsilon = NumTraits<typename Derived1::RealScalar>::dummy_precision()) 15c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 16c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath return !((m1-m2).cwiseAbs2().maxCoeff() < epsilon * epsilon 17c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * (std::max)(m1.cwiseAbs2().maxCoeff(), m2.cwiseAbs2().maxCoeff())); 18c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 19c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 20c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename MatrixType> void product(const MatrixType& m) 21c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 22c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /* this test covers the following files: 23c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Identity.h Product.h 24c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath */ 25c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef typename MatrixType::Index Index; 26c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef typename MatrixType::Scalar Scalar; 27c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> RowVectorType; 28c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> ColVectorType; 29c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> RowSquareMatrixType; 30c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, MatrixType::ColsAtCompileTime> ColSquareMatrixType; 31c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime, 32c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MatrixType::Flags&RowMajorBit?ColMajor:RowMajor> OtherMajorMatrixType; 33c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 34c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Index rows = m.rows(); 35c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Index cols = m.cols(); 36c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 37c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // this test relies a lot on Random.h, and there's not much more that we can do 38c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // to test it, hence I consider that we will have tested Random.h 39c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MatrixType m1 = MatrixType::Random(rows, cols), 40c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m2 = MatrixType::Random(rows, cols), 41c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m3(rows, cols); 42c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath RowSquareMatrixType 43c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath identity = RowSquareMatrixType::Identity(rows, rows), 44c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath square = RowSquareMatrixType::Random(rows, rows), 45c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath res = RowSquareMatrixType::Random(rows, rows); 46c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath ColSquareMatrixType 47c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath square2 = ColSquareMatrixType::Random(cols, cols), 48c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath res2 = ColSquareMatrixType::Random(cols, cols); 49c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath RowVectorType v1 = RowVectorType::Random(rows); 50c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath ColVectorType vc2 = ColVectorType::Random(cols), vcres(cols); 51c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath OtherMajorMatrixType tm1 = m1; 52c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 53c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Scalar s1 = internal::random<Scalar>(); 54c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 55c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Index r = internal::random<Index>(0, rows-1), 56c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath c = internal::random<Index>(0, cols-1), 57c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath c2 = internal::random<Index>(0, cols-1); 58c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 59c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // begin testing Product.h: only associativity for now 60c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // (we use Transpose.h but this doesn't count as a test for it) 61c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX((m1*m1.transpose())*m2, m1*(m1.transpose()*m2)); 62c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m3 = m1; 63c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m3 *= m1.transpose() * m2; 64c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(m3, m1 * (m1.transpose()*m2)); 65c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(m3, m1 * (m1.transpose()*m2)); 66c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 67c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // continue testing Product.h: distributivity 68c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(square*(m1 + m2), square*m1+square*m2); 69c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(square*(m1 - m2), square*m1-square*m2); 70c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 71c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // continue testing Product.h: compatibility with ScalarMultiple.h 72c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(s1*(square*m1), (s1*square)*m1); 73c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(s1*(square*m1), square*(m1*s1)); 74c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 75c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // test Product.h together with Identity.h 76c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(v1, identity*v1); 77c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(v1.transpose(), v1.transpose() * identity); 78c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // again, test operator() to check const-qualification 79c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(MatrixType::Identity(rows, cols)(r,c), static_cast<Scalar>(r==c)); 80c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 81c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if (rows!=cols) 82c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_RAISES_ASSERT(m3 = m1*m1); 83c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 84c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // test the previous tests were not screwed up because operator* returns 0 85c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // (we use the more accurate default epsilon) 86c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if (!NumTraits<Scalar>::IsInteger && (std::min)(rows,cols)>1) 87c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 88c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY(areNotApprox(m1.transpose()*m2,m2.transpose()*m1)); 89c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 90c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 91c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // test optimized operator+= path 92c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath res = square; 93c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath res.noalias() += m1 * m2.transpose(); 94c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(res, square + m1 * m2.transpose()); 95c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if (!NumTraits<Scalar>::IsInteger && (std::min)(rows,cols)>1) 96c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 97c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY(areNotApprox(res,square + m2 * m1.transpose())); 98c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 99c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath vcres = vc2; 100c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath vcres.noalias() += m1.transpose() * v1; 101c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(vcres, vc2 + m1.transpose() * v1); 102c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 103c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // test optimized operator-= path 104c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath res = square; 105c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath res.noalias() -= m1 * m2.transpose(); 106c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(res, square - (m1 * m2.transpose())); 107c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if (!NumTraits<Scalar>::IsInteger && (std::min)(rows,cols)>1) 108c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 109c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY(areNotApprox(res,square - m2 * m1.transpose())); 110c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 111c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath vcres = vc2; 112c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath vcres.noalias() -= m1.transpose() * v1; 113c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(vcres, vc2 - m1.transpose() * v1); 114c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 115c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath tm1 = m1; 116c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(tm1.transpose() * v1, m1.transpose() * v1); 117c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(v1.transpose() * tm1, v1.transpose() * m1); 118c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 119c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // test submatrix and matrix/vector product 120c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath for (int i=0; i<rows; ++i) 121c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath res.row(i) = m1.row(i) * m2.transpose(); 122c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(res, m1 * m2.transpose()); 123c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // the other way round: 124c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath for (int i=0; i<rows; ++i) 125c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath res.col(i) = m1 * m2.transpose().col(i); 126c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(res, m1 * m2.transpose()); 127c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 128c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath res2 = square2; 129c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath res2.noalias() += m1.transpose() * m2; 130c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(res2, square2 + m1.transpose() * m2); 131c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if (!NumTraits<Scalar>::IsInteger && (std::min)(rows,cols)>1) 132c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 133c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY(areNotApprox(res2,square2 + m2.transpose() * m1)); 134c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 135c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 136c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(res.col(r).noalias() = square.adjoint() * square.col(r), (square.adjoint() * square.col(r)).eval()); 137c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(res.col(r).noalias() = square * square.col(r), (square * square.col(r)).eval()); 138c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 139c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // inner product 140c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Scalar x = square2.row(c) * square2.col(c2); 141c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(x, square2.row(c).transpose().cwiseProduct(square2.col(c2)).sum()); 142615d816d068b4d0f5e8df601930b5f160bf7eda1Tim Murray 143615d816d068b4d0f5e8df601930b5f160bf7eda1Tim Murray // outer product 144615d816d068b4d0f5e8df601930b5f160bf7eda1Tim Murray VERIFY_IS_APPROX(m1.col(c) * m1.row(r), m1.block(0,c,rows,1) * m1.block(r,0,1,cols)); 145615d816d068b4d0f5e8df601930b5f160bf7eda1Tim Murray VERIFY_IS_APPROX(m1.row(r).transpose() * m1.col(c).transpose(), m1.block(r,0,1,cols).transpose() * m1.block(0,c,rows,1).transpose()); 146615d816d068b4d0f5e8df601930b5f160bf7eda1Tim Murray VERIFY_IS_APPROX(m1.block(0,c,rows,1) * m1.row(r), m1.block(0,c,rows,1) * m1.block(r,0,1,cols)); 147615d816d068b4d0f5e8df601930b5f160bf7eda1Tim Murray VERIFY_IS_APPROX(m1.col(c) * m1.block(r,0,1,cols), m1.block(0,c,rows,1) * m1.block(r,0,1,cols)); 148615d816d068b4d0f5e8df601930b5f160bf7eda1Tim Murray VERIFY_IS_APPROX(m1.leftCols(1) * m1.row(r), m1.block(0,0,rows,1) * m1.block(r,0,1,cols)); 149615d816d068b4d0f5e8df601930b5f160bf7eda1Tim Murray VERIFY_IS_APPROX(m1.col(c) * m1.topRows(1), m1.block(0,c,rows,1) * m1.block(0,0,1,cols)); 150c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 151