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// SPDX-License-Identifier: Apache-2.0
//
// Copyright 2008-2016 Conrad Sanderson (http://conradsanderson.id.au)
// Copyright 2008-2016 National ICT Australia (NICTA)
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
// ------------------------------------------------------------------------
namespace newarp
{
//! Perform the QR decomposition of an upper Hessenberg matrix.
template<typename eT>
class UpperHessenbergQR
{
protected:
uword n;
Mat<eT> mat_T;
// Gi = [ cos[i] sin[i]]
// [-sin[i] cos[i]]
// Q = G1 * G2 * ... * G_{n-1}
Col<eT> rot_cos;
Col<eT> rot_sin;
bool computed;
public:
//! Default constructor. Computation can
//! be performed later by calling the compute() method.
inline UpperHessenbergQR();
//! Constructor to create an object that performs and stores the
//! QR decomposition of an upper Hessenberg matrix `mat_obj`.
inline UpperHessenbergQR(const Mat<eT>& mat_obj);
//! Conduct the QR factorisation of an upper Hessenberg matrix.
virtual void compute(const Mat<eT>& mat_obj);
//! Return the \f$RQ\f$ matrix, the multiplication of \f$R\f$ and \f$Q\f$,
//! which is an upper Hessenberg matrix.
virtual Mat<eT> matrix_RQ();
//! Apply the \f$Q\f$ matrix to another matrix \f$Y\f$.
inline void apply_YQ(Mat<eT>& Y);
};
//! Perform the QR decomposition of a tridiagonal matrix, a special
//! case of upper Hessenberg matrices.
template<typename eT>
class TridiagQR : public UpperHessenbergQR<eT>
{
public:
//! Default constructor. Computation can
//! be performed later by calling the compute() method.
inline TridiagQR();
//! Constructor to create an object that performs and stores the
//! QR decomposition of a tridiagonal matrix `mat_obj`.
inline TridiagQR(const Mat<eT>& mat_obj);
//! Conduct the QR factorisation of a tridiagonal matrix.
inline void compute(const Mat<eT>& mat_obj);
//! Return the \f$RQ\f$ matrix, the multiplication of \f$R\f$ and \f$Q\f$,
//! which is a tridiagonal matrix.
inline Mat<eT> matrix_RQ();
};
} // namespace newarp
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