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// Copyright (c) 2018, ETH Zurich and UNC Chapel Hill.
// All rights reserved.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are met:
//
// * Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
//
// * Redistributions in binary form must reproduce the above copyright
// notice, this list of conditions and the following disclaimer in the
// documentation and/or other materials provided with the distribution.
//
// * Neither the name of ETH Zurich and UNC Chapel Hill nor the names of
// its contributors may be used to endorse or promote products derived
// from this software without specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDERS OR CONTRIBUTORS BE
// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
// POSSIBILITY OF SUCH DAMAGE.
//
// Author: Johannes L. Schoenberger (jsch at inf.ethz.ch)
#ifndef COLMAP_SRC_UTIL_MATRIX_H_
#define COLMAP_SRC_UTIL_MATRIX_H_
#include <Eigen/Core>
#include <Eigen/Dense>
#include <Eigen/QR>
namespace colmap {
// Check if the given floating point array contains a NaN value.
template <typename Derived>
inline bool IsNaN(const Eigen::MatrixBase<Derived>& x);
// Check if the given floating point array contains infinity.
template <typename Derived>
inline bool IsInf(const Eigen::MatrixBase<Derived>& x);
// Perform RQ decomposition on matrix. The RQ decomposition transforms a matrix
// A into the product of an upper triangular matrix R (also known as
// right-triangular) and an orthogonal matrix Q.
template <typename MatrixType>
void DecomposeMatrixRQ(const MatrixType& A, MatrixType* R, MatrixType* Q);
////////////////////////////////////////////////////////////////////////////////
// Implementation
////////////////////////////////////////////////////////////////////////////////
template <typename Derived>
bool IsNaN(const Eigen::MatrixBase<Derived>& x) {
return !(x.array() == x.array()).all();
}
template <typename Derived>
bool IsInf(const Eigen::MatrixBase<Derived>& x) {
return !((x - x).array() == (x - x).array()).all();
}
template <typename MatrixType>
void DecomposeMatrixRQ(const MatrixType& A, MatrixType* R, MatrixType* Q) {
const MatrixType A_flipud_transpose =
A.transpose().rowwise().reverse().eval();
const Eigen::HouseholderQR<MatrixType> QR(A_flipud_transpose);
const MatrixType& Q0 = QR.householderQ();
const MatrixType& R0 = QR.matrixQR();
*R = R0.transpose().colwise().reverse().eval();
*R = R->rowwise().reverse().eval();
for (int i = 0; i < R->rows(); ++i) {
for (int j = 0; j < R->cols() && (R->cols() - j) > (R->rows() - i); ++j) {
(*R)(i, j) = 0;
}
}
*Q = Q0.transpose().colwise().reverse().eval();
// Make the decomposition unique by requiring that det(Q) > 0.
if (Q->determinant() < 0) {
Q->row(1) *= -1.0;
R->col(1) *= -1.0;
}
}
} // namespace colmap
#endif // COLMAP_SRC_UTIL_MATRIX_H_
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