matrix_solve.h

/* Copyright (c) 2021 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. */

#pragma once

#include <string>
#include "Eigen/Core"
#include "Eigen/LU"
#include "paddle/fluid/framework/tensor.h"
#include "paddle/fluid/platform/device_context.h"

namespace paddle {
namespace operators {
namespace math {

template <typename DeviceContext, typename T>
void compute_solve_eigen(const DeviceContext& context,
                         const framework::Tensor& a, const framework::Tensor& b,
                         framework::Tensor* out) {
  using Matrix =
      Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor>;
  using EigenMatrixMap = Eigen::Map<Matrix>;
  using ConstEigenMatrixMap = Eigen::Map<const Matrix>;
  // prepare for a
  const auto& a_mat_dims = a.dims();
  const int a_rank = a_mat_dims.size();
  int n = a_mat_dims[a_rank - 1];
  int a_batch_size = a_rank > 2 ? a.numel() / (n * n) : 1;

  // prepare for b
  const auto& b_mat_dims = b.dims();
  const int b_rank = b_mat_dims.size();
  int b_h = n;
  int b_w = b_mat_dims[b_rank - 1];
  int b_batch_size = b_rank > 2 ? b.numel() / (b_h * b_w) : 1;

  const T* a_ptr = a.data<T>();
  const T* b_ptr = b.data<T>();
  out->Resize(b_mat_dims);  // make sure the out dims is right

  T* out_ptr = out->mutable_data<T>(context.GetPlace());
  if (a_batch_size == b_batch_size) {
    for (int i = 0; i < a_batch_size; ++i) {
      ConstEigenMatrixMap a_mat(a_ptr + i * n * n, n, n);
      ConstEigenMatrixMap b_mat(b_ptr + i * b_h * b_w, b_h, b_w);
      EigenMatrixMap out_mat(out_ptr + i * b_h * b_w, b_h, b_w);
      Eigen::PartialPivLU<Matrix> lu;
      lu.compute(a_mat);
      const T min_abs_pivot = lu.matrixLU().diagonal().cwiseAbs().minCoeff();
      PADDLE_ENFORCE_GT(
          min_abs_pivot, static_cast<T>(0),
          platform::errors::InvalidArgument("Input is not invertible."));
      out_mat.noalias() = lu.solve(b_mat);
    }
  } else {
    PADDLE_ENFORCE_EQ(a_batch_size, b_batch_size,
                      platform::errors::InvalidArgument(
                          "All input tensors must have the same rank."));
  }
}

// only used for complex input
template <typename T>
void SolveLinearSystem(T* matrix_data, T* rhs_data, T* out_data, int order,
                       int rhs_cols, int batch) {
  using Treal = typename Eigen::NumTraits<T>::Real;

  // cast paddle::complex into std::complex
  std::complex<Treal>* matrix_data_ =
      reinterpret_cast<std::complex<Treal>*>(matrix_data);
  std::complex<Treal>* rhs_data_ =
      reinterpret_cast<std::complex<Treal>*>(rhs_data);
  std::complex<Treal>* out_data_ =
      reinterpret_cast<std::complex<Treal>*>(out_data);

  using Matrix = Eigen::Matrix<std::complex<Treal>, Eigen::Dynamic,
                               Eigen::Dynamic, Eigen::RowMajor>;
  using InputMatrixMap = Eigen::Map<Matrix>;
  using OutputMatrixMap = Eigen::Map<Matrix>;

  for (int i = 0; i < batch; ++i) {
    auto input_matrix =
        InputMatrixMap(matrix_data_ + i * order * order, order, order);
    auto input_rhs =
        InputMatrixMap(rhs_data_ + i * order * rhs_cols, order, rhs_cols);
    auto output =
        OutputMatrixMap(out_data_ + i * order * rhs_cols, order, rhs_cols);

    Eigen::PartialPivLU<Matrix> lu_decomposition(order);
    lu_decomposition.compute(input_matrix);

    const Treal min_abs_piv =
        lu_decomposition.matrixLU().diagonal().cwiseAbs().minCoeff();
    PADDLE_ENFORCE_GT(min_abs_piv, Treal(0),
                      platform::errors::InvalidArgument(
                          "Something's wrong with SolveLinearSystem. "));

    output = lu_decomposition.solve(input_rhs);
  }
}

template <typename DeviceContext, typename T>
class MatrixSolveFunctor {
 public:
  void operator()(const DeviceContext& context, const framework::Tensor& a,
                  const framework::Tensor& b, framework::Tensor* out);
};

}  // namespace math
}  // namespace operators
}  // namespace paddle