paddlepaddle--paddle/paddle/phi/kernels/cpu/qr_kernel.cc

// Copyright (c) 2022 PaddlePaddle Authors. All Rights Reserved.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//     http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.

#include "paddle/phi/kernels/qr_kernel.h"

#include <Eigen/Dense>

#include "paddle/phi/backends/cpu/cpu_context.h"
#include "paddle/phi/core/kernel_registry.h"
#include "paddle/phi/kernels/diagonal_kernel.h"
#include "paddle/phi/kernels/fill_diagonal_tensor_kernel.h"
#include "paddle/phi/kernels/funcs/complex_functors.h"
#include "paddle/phi/kernels/funcs/math_function.h"
#include "paddle/phi/kernels/funcs/parse_qr_mode.h"

namespace phi {

template <class T, class Context>
static DenseTensor Fill(const Context& dev_ctx,
                        std::vector<int64_t> shape,
                        T fill_value) {
  DenseTensor ret;
  ret.Resize(shape);
  dev_ctx.template Alloc<T>(&ret);
  funcs::SetConstant<Context, T>()(dev_ctx, &ret, fill_value);
  return ret;
}

template <class T, class Context>
static DenseTensor identity_matrix(const Context& dev_ctx, common::DDim shape) {
  DenseTensor M = Fill<T, Context>(dev_ctx, vectorize<int64_t>(shape), T(0));
  size_t rank = M.dims().size();
  int64_t M_diag_len = std::min(M.dims()[rank - 1], M.dims()[rank - 2]);
  std::vector<int64_t> M_diag_shape;
  for (size_t i = 0; i < rank - 2; ++i) {
    M_diag_shape.push_back(M.dims()[i]);
  }
  M_diag_shape.push_back(M_diag_len);
  DenseTensor M_diag = Fill<T, Context>(
      dev_ctx, vectorize<int64_t>(make_ddim(M_diag_shape)), T(1));
  M = FillDiagonalTensor<T, Context>(dev_ctx, M, M_diag, 0, rank - 2, rank - 1);
  return M;
}

template <typename T, typename Context>
struct QrFunctor {
  void operator()(const Context& dev_ctx,
                  const DenseTensor& x,
                  bool compute_q,
                  bool reduced_mode,
                  DenseTensor* q,
                  DenseTensor* r) {
    auto x_dims = x.dims();
    int x_rank = x_dims.size();
    int m = static_cast<int>(x_dims[x_rank - 2]);
    int n = static_cast<int>(x_dims[x_rank - 1]);
    int min_mn = std::min(m, n);
    int k = reduced_mode ? min_mn : m;
    int64_t batch_size = static_cast<int64_t>(x.numel() / (m * n));
    int64_t x_stride = static_cast<int64_t>(m) * n;
    int64_t q_stride = static_cast<int64_t>(m) * k;
    int64_t r_stride = static_cast<int64_t>(k) * n;
    auto* x_data = x.data<dtype::Real<T>>();
    T* q_data = nullptr;
    if (compute_q) {
      q_data = dev_ctx.template Alloc<dtype::Real<T>>(
          q, batch_size * m * k * sizeof(dtype::Real<T>));
    }
    auto* r_data = dev_ctx.template Alloc<dtype::Real<T>>(
        r, batch_size * k * n * sizeof(dtype::Real<T>));

    // Implement QR by calling Eigen
    for (int i = 0; i < batch_size; ++i) {
      const T* x_matrix_ptr = x_data + i * x_stride;
      T* r_matrix_ptr = r_data + i * r_stride;
      using EigenDynamicMatrix =
          Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor>;
      auto x_matrix = Eigen::Map<const EigenDynamicMatrix>(x_matrix_ptr, m, n);
      Eigen::HouseholderQR<EigenDynamicMatrix> qr(x_matrix);
      if (reduced_mode) {
        auto qr_top_matrix = qr.matrixQR().block(0, 0, min_mn, n);
        auto r_matrix_view =
            qr_top_matrix.template triangularView<Eigen::Upper>();
        auto r_matrix = EigenDynamicMatrix(r_matrix_view);
        memcpy(r_matrix_ptr, r_matrix.data(), r_matrix.size() * sizeof(T));
      } else {
        auto r_matrix_view =
            qr.matrixQR().template triangularView<Eigen::Upper>();
        auto r_matrix = EigenDynamicMatrix(r_matrix_view);
        memcpy(r_matrix_ptr, r_matrix.data(), r_matrix.size() * sizeof(T));
      }

      if (compute_q) {
        T* q_matrix_ptr = q_data + i * q_stride;
        if (reduced_mode) {
          auto q_matrix =
              qr.householderQ() * EigenDynamicMatrix::Identity(m, min_mn);
          q_matrix.transposeInPlace();
          memcpy(q_matrix_ptr, q_matrix.data(), q_matrix.size() * sizeof(T));
        } else {
          auto q_matrix =
              qr.householderQ() * EigenDynamicMatrix::Identity(m, m);
          q_matrix.transposeInPlace();
          memcpy(q_matrix_ptr, q_matrix.data(), q_matrix.size() * sizeof(T));
        }
      }
    }
  }
};

template <typename T, typename Context>
struct QrFunctor<dtype::complex<T>, Context> {
  void operator()(const Context& dev_ctx,
                  const DenseTensor& x,
                  bool compute_q,
                  bool reduced_mode,
                  DenseTensor* q,
                  DenseTensor* r) {
    auto x_dims = x.dims();
    int x_rank = x_dims.size();
    int m = static_cast<int>(x_dims[x_rank - 2]);
    int n = static_cast<int>(x_dims[x_rank - 1]);
    int min_mn = std::min(m, n);
    int k = reduced_mode ? min_mn : m;
    int batch_size = static_cast<int>(x.numel() / (m * n));
    int64_t x_stride = static_cast<int64_t>(m) * n;
    int64_t q_stride = static_cast<int64_t>(m) * k;
    int64_t r_stride = static_cast<int64_t>(k) * n;
    auto* x_data = x.data<dtype::complex<T>>();
    dtype::complex<T>* q_data = nullptr;
    if (compute_q) {
      q_data = dev_ctx.template Alloc<dtype::complex<T>>(
          q, batch_size * m * k * sizeof(dtype::complex<T>));
    }
    auto* r_data = dev_ctx.template Alloc<dtype::complex<T>>(
        r, batch_size * k * n * sizeof(dtype::complex<T>));

    // Implement QR by calling Eigen
    for (int i = 0; i < batch_size; ++i) {
      const dtype::complex<T>* x_matrix_ptr = x_data + i * x_stride;
      dtype::complex<T>* r_matrix_ptr = r_data + i * r_stride;
      using EigenDynamicMatrix = Eigen::Matrix<std::complex<T>,
                                               Eigen::Dynamic,
                                               Eigen::Dynamic,
                                               Eigen::RowMajor>;
      auto x_matrix = Eigen::Map<const EigenDynamicMatrix>(
          reinterpret_cast<const std::complex<T>*>(x_matrix_ptr), m, n);
      Eigen::HouseholderQR<EigenDynamicMatrix> qr(x_matrix);
      if (reduced_mode) {
        auto qr_top_matrix = qr.matrixQR().block(0, 0, min_mn, n);
        auto r_matrix_view =
            qr_top_matrix.template triangularView<Eigen::Upper>();
        auto r_matrix = EigenDynamicMatrix(r_matrix_view);
        memcpy(r_matrix_ptr,
               r_matrix.data(),
               r_matrix.size() * sizeof(dtype::complex<T>));
      } else {
        auto r_matrix_view =
            qr.matrixQR().template triangularView<Eigen::Upper>();
        auto r_matrix = EigenDynamicMatrix(r_matrix_view);
        memcpy(r_matrix_ptr,
               r_matrix.data(),
               r_matrix.size() * sizeof(dtype::complex<T>));
      }

      if (compute_q) {
        dtype::complex<T>* q_matrix_ptr = q_data + i * q_stride;
        if (reduced_mode) {
          auto q_matrix =
              qr.householderQ() * EigenDynamicMatrix::Identity(m, min_mn);
          q_matrix.transposeInPlace();
          memcpy(q_matrix_ptr,
                 q_matrix.data(),
                 q_matrix.size() * sizeof(dtype::complex<T>));
        } else {
          auto q_matrix =
              qr.householderQ() * EigenDynamicMatrix::Identity(m, m);
          q_matrix.transposeInPlace();
          memcpy(q_matrix_ptr,
                 q_matrix.data(),
                 q_matrix.size() * sizeof(dtype::complex<T>));
        }
      }
    }
  }
};

template <typename T, typename Context>
void QrKernel(const Context& dev_ctx,
              const DenseTensor& x,
              const std::string& mode,
              DenseTensor* q,
              DenseTensor* r) {
  bool compute_q = false;
  bool reduced_mode = false;
  std::tie(compute_q, reduced_mode) = funcs::ParseQrMode(mode);
  if (x.numel() == 0) {
    if (q->numel() == 0) {
      q->Resize(q->dims());
    } else {
      *q = identity_matrix<T, Context>(dev_ctx, q->dims());
    }
    r->Resize(r->dims());
    dev_ctx.template Alloc<T>(q);
    dev_ctx.template Alloc<T>(r);
    return;
  }
  QrFunctor<T, Context>()(dev_ctx, x, compute_q, reduced_mode, q, r);
}

}  // namespace phi

PD_REGISTER_KERNEL(qr,
                   CPU,
                   ALL_LAYOUT,
                   phi::QrKernel,
                   float,
                   double,
                   phi::complex64,
                   phi::complex128) {}