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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
{
template<typename eT>
class DoubleShiftQR
{
private:
uword n; // Dimension of the matrix
Mat<eT> mat_H; // A copy of the matrix to be factorised
eT shift_s; // Shift constant
eT shift_t; // Shift constant
Mat<eT> ref_u; // Householder reflectors
Col<unsigned short> ref_nr; // How many rows does each reflector affects
// 3 - A general reflector
// 2 - A Givens rotation
// 1 - An identity transformation
const eT prec; // Approximately zero
const eT eps_rel;
const eT eps_abs;
bool computed; // Whether matrix has been factorised
inline void compute_reflector(const eT& x1, const eT& x2, const eT& x3, uword ind);
arma_inline void compute_reflector(const eT* x, uword ind);
// Update the block X = H(il:iu, il:iu)
inline void update_block(uword il, uword iu);
// P = I - 2 * u * u' = P'
// PX = X - 2 * u * (u'X)
inline void apply_PX(Mat<eT>& X, uword oi, uword oj, uword nrow, uword ncol, uword u_ind);
// x is a pointer to a vector
// Px = x - 2 * dot(x, u) * u
inline void apply_PX(eT* x, uword u_ind);
// XP = X - 2 * (X * u) * u'
inline void apply_XP(Mat<eT>& X, uword oi, uword oj, uword nrow, uword ncol, uword u_ind);
public:
inline DoubleShiftQR(uword size);
inline DoubleShiftQR(const Mat<eT>& mat_obj, eT s, eT t);
inline void compute(const Mat<eT>& mat_obj, eT s, eT t);
inline Mat<eT> matrix_QtHQ();
inline void apply_QtY(Col<eT>& y);
inline void apply_YQ(Mat<eT>& Y);
};
} // namespace newarp
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