gerq2.hpp

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//
// Copyright (c) 2021-2023, University of Colorado Denver. All rights reserved.
//
// This file is part of <T>LAPACK.
// <T>LAPACK is free software: you can redistribute it and/or modify it under
// the terms of the BSD 3-Clause license. See the accompanying LICENSE file.
 
#ifndef TLAPACK_GERQ2_HH
#define TLAPACK_GERQ2_HH
 
#include "tlapack/base/utils.hpp"
#include "tlapack/lapack/larf.hpp"
#include "tlapack/lapack/larfg.hpp"
 
namespace tlapack {
 
template <class T, TLAPACK_SMATRIX matrix_t, TLAPACK_VECTOR vector_t>
constexpr WorkInfo gerq2_worksize(const matrix_t& A, const vector_t& tau)
{
    using idx_t = size_type<matrix_t>;
    using range = pair<idx_t, idx_t>;
 
    // constants
    const idx_t m = nrows(A);
 
    if (m > 1) {
        auto&& C = rows(A, range{1, m});
        return larf_worksize<T>(RIGHT_SIDE, BACKWARD, ROWWISE_STORAGE,
                                row(A, 0), tau[0], C);
    }
 
    return WorkInfo(0);
}
 
template <TLAPACK_SMATRIX matrix_t,
          TLAPACK_VECTOR vector_t,
          TLAPACK_WORKSPACE work_t>
int gerq2_work(matrix_t& A, vector_t& tau, work_t& work)
{
    using idx_t = size_type<matrix_t>;
    using range = pair<idx_t, idx_t>;
 
    // constants
    const idx_t m = nrows(A);
    const idx_t n = ncols(A);
    const idx_t k = min(m, n);
 
    // check arguments
    tlapack_check_false((idx_t)size(tau) < k);
 
    // quick return
    if (n <= 0) return 0;
 
    for (idx_t i2 = 0; i2 < k; ++i2) {
        idx_t i = k - 1 - i2;
 
        // Define v := A[m-1-i2,0:n-i2]
        auto v = slice(A, m - 1 - i2, range{0, n - i2});
 
        // Generate the (i+1)-th elementary Householder reflection on v
        larfg(BACKWARD, ROWWISE_STORAGE, v, tau[i]);
 
        // Apply the reflector to the rest of the matrix
        if (m > i2 + 1) {
            auto C = slice(A, range{0, m - 1 - i2}, range{0, n - i2});
            larf_work(RIGHT_SIDE, BACKWARD, ROWWISE_STORAGE, v, tau[i], C,
                      work);
        }
    }
 
    return 0;
}
 
template <TLAPACK_SMATRIX matrix_t, TLAPACK_VECTOR vector_t>
int gerq2(matrix_t& A, vector_t& tau)
{
    using idx_t = size_type<matrix_t>;
    using T = type_t<matrix_t>;
 
    // functor
    Create<matrix_t> new_matrix;
 
    // constants
    const idx_t n = ncols(A);
 
    // quick return
    if (n <= 0) return 0;
 
    // Allocates workspace
    WorkInfo workinfo = gerq2_worksize<T>(A, tau);
    std::vector<T> work_;
    auto work = new_matrix(work_, workinfo.m, workinfo.n);
 
    return gerq2_work(A, tau, work);
}
 
}  // namespace tlapack
 
#endif  // TLAPACK_GERQ2_HH