gelq2.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_GELQ2_HH
#define TLAPACK_GELQ2_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 gelq2_worksize(const matrix_t& A, const vector_t& tauw)
{
    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, FORWARD, ROWWISE_STORAGE, row(A, 0),
                                tauw[0], C);
    }
    return WorkInfo(0);
}
 
template <TLAPACK_SMATRIX matrix_t,
          TLAPACK_VECTOR vector_t,
          TLAPACK_WORKSPACE work_t>
int gelq2_work(matrix_t& A, vector_t& tauw, 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(tauw) < k);
 
    for (idx_t j = 0; j < k; ++j) {
        // Define w := A(j,j:n)
        auto w = slice(A, j, range(j, n));
 
        // Generate elementary reflector H(j) to annihilate A(j,j+1:n)
        larfg(FORWARD, ROWWISE_STORAGE, w, tauw[j]);
 
        // If either condition is satisfied, Q11 will not be empty
        if (j < k - 1 || k < m) {
            // Apply H(j) to A(j+1:m,j:n) from the right
            auto Q11 = slice(A, range(j + 1, m), range(j, n));
            larf_work(RIGHT_SIDE, FORWARD, ROWWISE_STORAGE, w, tauw[j], Q11,
                      work);
        }
    }
 
    return 0;
}
 
template <TLAPACK_SMATRIX matrix_t, TLAPACK_VECTOR vector_t>
int gelq2(matrix_t& A, vector_t& tauw)
{
    using T = type_t<matrix_t>;
 
    // functor
    Create<matrix_t> new_matrix;
 
    // Allocates workspace
    WorkInfo workinfo = gelq2_worksize<T>(A, tauw);
    std::vector<T> work_;
    auto work = new_matrix(work_, workinfo.m, workinfo.n);
 
    return gelq2_work(A, tauw, work);
}
}  // namespace tlapack
 
#endif  // TLAPACK_GELQ2_HH