gesvd.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 "../layout/policies.hpp"
#include "../macros.hpp"
#include "../mem/address_space.hpp"
#include "../mem/policies.hpp"
#include "../traits.hpp"
 
#ifndef NDA_HAVE_DEVICE
#include "../device.hpp"
#endif // NDA_HAVE_DEVICE
 
#include <algorithm>
#include <cmath>
#include <complex>
#include <concepts>
#include <utility>
 
namespace nda::lapack {

  template <MemoryMatrix A, MemoryVector S, MemoryMatrix U, MemoryMatrix VT>
    requires(have_same_value_type_v<A, U, VT> and mem::have_compatible_addr_space<A, S, U, VT> and is_blas_lapack_v<get_value_t<A>>
             and std::same_as<double, get_value_t<S>>)
  int gesvd(A &&a, S &&s, U &&u, VT &&vt) { // NOLINT (temporary views are allowed here)
    static_assert(has_C_layout<A> == has_C_layout<U> and has_C_layout<A> == has_C_layout<VT>,
                  "Error in nda::lapack::gesvd: Matrix layouts have to be the same");
 
    // check the dimensions of the 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});
    resize_or_check_if_view(u, {m, m});
    resize_or_check_if_view(vt, {n, n});
 
    // cusolverDn?gesvd only supports matrices with m >= n
    if constexpr (mem::have_device_compatible_addr_space<A, S, U, VT>) {
      if constexpr (has_C_layout<A>) {
        EXPECTS(n >= m);
      } else {
        EXPECTS(m >= n);
      }
    }
 
    // arrays/views must be LAPACK compatible
    EXPECTS(a.indexmap().min_stride() == 1);
    EXPECTS(s.indexmap().min_stride() == 1);
    EXPECTS(u.indexmap().min_stride() == 1);
    EXPECTS(vt.indexmap().min_stride() == 1);
 
    // call host/device implementation depending on address space of input arrays/views
    auto gesvd_call = []<typename... Ts>(Ts &&...args) {
      if constexpr (mem::have_device_compatible_addr_space<A, S, U, VT>) {
#if defined(NDA_HAVE_DEVICE)
        lapack::device::gesvd(std::forward<Ts>(args)...);
#else
        compile_error_no_gpu();
#endif
      } else {
        lapack::f77::gesvd(std::forward<Ts>(args)...);
      }
    };
 
    // first call to get the optimal buffer size
    using value_type = get_value_t<A>;
    value_type tmp_lwork{};
    auto rwork = array<double, 1, C_layout, heap<mem::get_addr_space<A>>>(5 * k);
    int info   = 0;
    if constexpr (has_C_layout<A>) {
      gesvd_call('A', 'A', n, m, a.data(), get_ld(a), s.data(), vt.data(), get_ld(vt), u.data(), get_ld(u), &tmp_lwork, -1, rwork.data(), info);
    } else {
      gesvd_call('A', 'A', m, n, a.data(), get_ld(a), s.data(), u.data(), get_ld(u), vt.data(), get_ld(vt), &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, C_layout, heap<mem::get_addr_space<A>>> work(lwork);
    if constexpr (has_C_layout<A>) {
      gesvd_call('A', 'A', n, m, a.data(), get_ld(a), s.data(), vt.data(), get_ld(vt), u.data(), get_ld(u), work.data(), lwork, rwork.data(), info);
    } else {
      gesvd_call('A', 'A', m, n, a.data(), get_ld(a), s.data(), u.data(), get_ld(u), vt.data(), get_ld(vt), work.data(), lwork, rwork.data(), info);
    }
 
    return info;
  }
 
} // namespace nda::lapack