gelss.hpp

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// Copyright (c) 2020--present, The Simons Foundation
// This file is part of TRIQS/nda and is licensed under the Apache License, Version 2.0.
// SPDX-License-Identifier: Apache-2.0
// See LICENSE in the root of this distribution for details.

 
#pragma once
 
#include "./interface/cxx_interface.hpp"
#include "../basic_array.hpp"
#include "../basic_functions.hpp"
#include "../concepts.hpp"
#include "../declarations.hpp"
#include "../macros.hpp"
#include "../mem/address_space.hpp"
#include "../traits.hpp"
 
#include <algorithm>
#include <cmath>
#include <complex>
#include <type_traits>
 
namespace nda::lapack {

  template <MemoryMatrix A, MemoryArray B, MemoryVector S>
    requires(have_same_value_type_v<A, B> and mem::have_host_compatible_addr_space<A, B, S> and is_blas_lapack_v<get_value_t<A>>)
  int gelss(A &&a, B &&b, S &&s, double rcond, int &rank) { // NOLINT (temporary views are allowed here)
    static_assert(std::is_same_v<get_value_t<S>, double>, "Error in nda::lapack::gelss: Singular value array must have elements of type double");
    static_assert(has_F_layout<A> and has_F_layout<B>, "Error in nda::lapack::gelss: Matrices/arrays must have Fortran layout");
    static_assert(get_rank<B> == 1 || get_rank<B> == 2, "Error in nda::lapack::gelss: Right hand side must have rank 1 or 2");
 
    // check the dimensions of the input/output arrays/views and resize if necessary
    auto const [m, n] = a.shape();
    auto const k      = std::min(m, n);
    resize_or_check_if_view(s, {k});
    EXPECTS(b.extent(0) == m);
 
    // arrays/views must be LAPACK compatible
    EXPECTS(a.indexmap().min_stride() == 1);
    EXPECTS(b.indexmap().min_stride() == 1);
    EXPECTS(s.indexmap().min_stride() == 1);
 
    // first call to get the optimal buffer size
    using value_type = get_value_t<A>;
    value_type tmp_lwork{};
    auto rwork = array<double, 1>(5 * k);
    int info   = 0;
    int nrhs   = (get_rank<B> == 2 ? b.extent(1) : 1);
    f77::gelss(m, n, nrhs, a.data(), get_ld(a), b.data(), get_ld(b), s.data(), rcond, rank, &tmp_lwork, -1, rwork.data(), info);
    int lwork = static_cast<int>(std::ceil(std::real(tmp_lwork)));
 
    // allocate work buffer and perform actual library call
    array<value_type, 1> work(lwork);
    f77::gelss(m, n, nrhs, a.data(), get_ld(a), b.data(), get_ld(b), s.data(), rcond, rank, work.data(), lwork, rwork.data(), info);
 
    return info;
  }
 
} // namespace nda::lapack