geqr2.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_GEQR2_HH
#define TLAPACK_GEQR2_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 geqr2_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 n = ncols(A);
 
    if (n > 1) {
        auto&& C = cols(A, range{1, n});
        return larf_worksize<T>(LEFT_SIDE, FORWARD, COLUMNWISE_STORAGE,
                                col(A, 0), tau[0], C);
    }
 
    return WorkInfo(0);
}
 
template <TLAPACK_SMATRIX matrix_t,
          TLAPACK_VECTOR vector_t,
          TLAPACK_WORKSPACE work_t>
int geqr2_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 = std::min<idx_t>(m, n - 1);
 
    // check arguments
    tlapack_check_false((idx_t)size(tau) < min(m, n));
 
    // quick return
    if (n <= 0 || m <= 0) return 0;
 
    for (idx_t i = 0; i < k; ++i) {
        // Define v := A[i:m,i]
        auto v = slice(A, range{i, m}, i);
 
        // Generate the (i+1)-th elementary Householder reflection on v
        larfg(FORWARD, COLUMNWISE_STORAGE, v, tau[i]);
 
        // Define C := A[i:m,i+1:n]
        auto C = slice(A, range{i, m}, range{i + 1, n});
 
        // C := ( I - conj(tau_i) v v^H ) C
        larf_work(LEFT_SIDE, FORWARD, COLUMNWISE_STORAGE, v, conj(tau[i]), C,
                  work);
    }
    if (n - 1 < m) {
        // Define v := A[n-1:m,n-1]
        auto v = slice(A, range{n - 1, m}, n - 1);
        // Generate the n-th elementary Householder reflection on v
        larfg(FORWARD, COLUMNWISE_STORAGE, v, tau[n - 1]);
    }
 
    return 0;
}
 
template <TLAPACK_SMATRIX matrix_t, TLAPACK_VECTOR vector_t>
int geqr2(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 m = nrows(A);
    const idx_t n = ncols(A);
 
    // quick return
    if (n <= 0 || m <= 0) return 0;
 
    // Allocates workspace
    WorkInfo workinfo = geqr2_worksize<T>(A, tau);
    std::vector<T> work_;
    auto work = new_matrix(work_, workinfo.m, workinfo.n);
 
    return geqr2_work(A, tau, work);
}
 
}  // namespace tlapack
 
#endif  // TLAPACK_GEQR2_HH