solve_op.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 "Eigen/Core"
#include "Eigen/LU"
#include "paddle/fluid/framework/eigen.h"
#include "paddle/fluid/framework/op_registry.h"
#include "paddle/fluid/framework/operator.h"
#include "paddle/fluid/framework/tensor_util.h"
#include "paddle/fluid/operators/eigen/eigen_function.h"
#include "paddle/fluid/operators/math/blas.h"
#include "paddle/fluid/operators/math/math_function.h"
#include "paddle/fluid/operators/math/matrix_solve.h"
#include "paddle/fluid/operators/reduce_ops/reduce_sum_op.h"
#include "paddle/fluid/operators/squeeze_op.h"
#if defined(__NVCC__) || defined(__HIPCC__)
#include "paddle/fluid/operators/reduce_ops/cub_reduce.h"
#endif

#define MAX_RANK_SUPPORTED 6

namespace paddle {
namespace operators {

using Tensor = framework::Tensor;
using framework::To32BitIndex;

constexpr int kMULMKLDNNINT8 = 1;

struct IdentityFunctor {
  HOSTDEVICE explicit inline IdentityFunctor() {}

  template <typename U>
  HOSTDEVICE inline U operator()(const U& x) const {
    return x;
  }
};

template <typename DeviceContext, typename T>
void ReduceSumForSolve(const Tensor* input, Tensor* output,
                       const std::vector<int>& reduce_dims, bool keep_dim,
                       const paddle::framework::ExecutionContext& ctx) {
#if defined(__NVCC__) || defined(__HIPCC__)
  auto stream = ctx.cuda_device_context().stream();
  TensorReduce<T, T, cub::Sum, IdentityFunctor>(*input, output, reduce_dims,
                                                static_cast<T>(0), cub::Sum(),
                                                IdentityFunctor(), stream);
#else
  ReduceKernelFunctor<DeviceContext, T, ops::SumFunctor>(
      input, output, reduce_dims, keep_dim, false, ctx)
      .template apply<T>();
#endif
}

// check the input other is vector_case or not
static inline bool is_vector_rhs(const Tensor& input, const Tensor& other) {
  auto x_dim = input.dims();
  auto y_dim = other.dims();
  auto x_dim_size = x_dim.size();
  auto y_dim_size = y_dim.size();
  std::vector<int64_t> x_dims_vec = paddle::framework::vectorize(x_dim);
  std::vector<int64_t> y_dims_vec = paddle::framework::vectorize(y_dim);

  std::vector<int64_t>::const_iterator f = x_dims_vec.begin();
  std::vector<int64_t>::const_iterator l = x_dims_vec.end() - 1;
  std::vector<int64_t> x_dims_vec_cut(f, l);  // input.shape[:-1]

  std::vector<int64_t> expected_batched_rhs_shape(x_dims_vec_cut);
  bool vector_case =
      y_dim_size == 1 || (x_dim_size - 1 == y_dim_size &&
                          y_dims_vec == (expected_batched_rhs_shape));

  return vector_case;
}

// unsqueeze operation helper
static framework::DDim GetOutputShapeUnsqueeze(
    const std::vector<int> unsqz_dims, const framework::DDim& in_dims) {
  int output_size = in_dims.size() + static_cast<int>(unsqz_dims.size());
  int cur_output_size = in_dims.size();
  std::vector<int64_t> output_shape(output_size, 0);

  // Validity Check: rank range.
  PADDLE_ENFORCE_LE(output_size, 6,
                    platform::errors::InvalidArgument(
                        "The output "
                        "tensor's rank should be less than 6."));

  for (int axis : unsqz_dims) {
    int cur = axis < 0 ? axis + cur_output_size + 1 : axis;
    // Vaildity Check: the axis bound
    PADDLE_ENFORCE_GE(cur, 0, platform::errors::InvalidArgument(
                                  "The insert dimension value should "
                                  "not be less than 0"));
    PADDLE_ENFORCE_LE(cur, cur_output_size,
                      platform::errors::InvalidArgument(
                          "The insert dimension value shoule not be larger "
                          "than the dimension size of input tensor"));
    // Move old axis, and insert new axis
    for (int i = cur_output_size; i >= cur; --i) {
      if (output_shape[i] == 1) {
        // Move axis
        output_shape[i + 1] = 1;
        output_shape[i] = 0;
      }
    }
    output_shape[cur] = 1;
    // Add the output size.
    cur_output_size++;
  }

  // Make output shape
  for (int in_idx = 0, out_idx = 0; out_idx < output_size; ++out_idx) {
    if (output_shape[out_idx] == 0) {
      output_shape[out_idx] = in_dims[in_idx++];
    }
  }

  return framework::make_ddim(output_shape);
}

// operation like squeeze(-1)
static void to_squeeze(const framework::ExecutionContext& context,
                       const framework::Tensor& in, framework::Tensor* out) {
  auto x_dims = in.dims();
  std::vector<int> sqz_dims = {-1};
  auto out_dims = GetOutputShape(sqz_dims, x_dims, true);
  out->mutable_data(context.GetPlace(), in.type());
  framework::TensorCopy(
      in, context.GetPlace(),
      context.template device_context<platform::DeviceContext>(), out);
  out->Resize(out_dims);
}

// vector_case, need to operate like unsqueeze(-1)
static void to_unsqueeze(const framework::ExecutionContext& context,
                         const framework::Tensor& in, framework::Tensor* out) {
  auto x_dims = in.dims();
  std::vector<int> unsqz_dims = {-1};
  framework::DDim out_dims = out->dims();
  out_dims = GetOutputShapeUnsqueeze(unsqz_dims, x_dims);
  framework::TensorCopy(
      in, context.GetPlace(),
      context.template device_context<platform::DeviceContext>(), out);
  out->Resize(out_dims);
}

template <typename Container>
Container infer_size_impl(std::vector<int64_t> a, std::vector<int64_t> b) {
  size_t dimsA = a.size();
  size_t dimsB = b.size();
  size_t ndim = dimsA > dimsB ? dimsA : dimsB;
  Container expandedSizes(ndim);

  for (ptrdiff_t i = (ptrdiff_t)ndim - 1; i >= 0; --i) {
    ptrdiff_t offset = ndim - 1 - i;
    ptrdiff_t dimA = dimsA - 1 - offset;
    ptrdiff_t dimB = dimsB - 1 - offset;
    int64_t sizeA = (dimA >= 0) ? a[dimA] : 1;
    int64_t sizeB = (dimB >= 0) ? b[dimB] : 1;

    PADDLE_ENFORCE_EQ(
        (sizeA == sizeB || sizeA == 1 || sizeB == 1), true,
        platform::errors::PreconditionNotMet(
            "The size of tensor a (%d) must match the size of tensor b "
            "(%d) at non-singleton dimension %d.",
            sizeA, sizeB, i));

    expandedSizes[i] = sizeA == 1 ? sizeB : sizeA;
  }
  return expandedSizes;
}

// infer size for broadcast operation
static std::vector<int64_t> infer_size(std::vector<int64_t> a,
                                       std::vector<int64_t> b) {
  return infer_size_impl<std::vector<int64_t>>(a, b);
}

// broadcast the batch dimensions of arg1 and arg2.
static inline std::tuple<std::vector<int64_t>, std::vector<int64_t>>
_broadcast_batch_dims(const Tensor& arg1, const Tensor& arg2) {
  std::vector<int64_t> arg1_dims_vec =
      paddle::framework::vectorize(arg1.dims());
  std::vector<int64_t> arg2_dims_vec =
      paddle::framework::vectorize(arg2.dims());

  std::vector<int64_t>::const_iterator f1 = arg1_dims_vec.begin();
  std::vector<int64_t>::const_iterator l1 = arg1_dims_vec.end() - 2;
  std::vector<int64_t> arg1_dims_vec_cut(f1, l1);

  std::vector<int64_t>::const_iterator f2 = arg2_dims_vec.begin();
  std::vector<int64_t>::const_iterator l2 = arg2_dims_vec.end() - 2;
  std::vector<int64_t> arg2_dims_vec_cut(f2, l2);

  std::vector<int64_t> expand_batch_portion =
      infer_size(arg1_dims_vec_cut, arg2_dims_vec_cut);

  std::vector<int64_t> arg1_expand_size({expand_batch_portion});
  arg1_expand_size.insert(
      arg1_expand_size.end(),
      {arg1_dims_vec[static_cast<int>(arg1_dims_vec.size()) - 2],
       arg1_dims_vec[static_cast<int>(arg1_dims_vec.size()) - 1]});

  std::vector<int64_t> arg2_expand_size({expand_batch_portion});
  arg2_expand_size.insert(
      arg2_expand_size.end(),
      {arg2_dims_vec[static_cast<int>(arg2_dims_vec.size()) - 2],
       arg2_dims_vec[static_cast<int>(arg2_dims_vec.size()) - 1]});

  return std::make_tuple(arg1_expand_size, arg2_expand_size);
}

template <int Rank, typename T, typename DeviceContext>
void expand_impl(const DeviceContext& context, const Tensor& in, Tensor* out,
                 const std::vector<int64_t>& expand_shape) {
  auto vec_in_dims = framework::vectorize<int>(in.dims());
  auto diff = expand_shape.size() - vec_in_dims.size();
  vec_in_dims.insert(vec_in_dims.begin(), diff, 1);
  std::vector<int> repeat_times(vec_in_dims.size());

  for (size_t i = 0; i < vec_in_dims.size(); ++i) {
    PADDLE_ENFORCE_NE(
        expand_shape[i], 0,
        platform::errors::InvalidArgument("The expanded size cannot be zero."));
    if (i < diff) {
      PADDLE_ENFORCE_GT(
          expand_shape[i], 0,
          platform::errors::InvalidArgument(
              "The expanded size (%d) for non-existing dimensions must be "
              "positive for expand operation.",
              expand_shape[i]));
      repeat_times[i] = expand_shape[i];
    } else if (expand_shape[i] > 0) {
      if (vec_in_dims[i] != 1) {
        PADDLE_ENFORCE_EQ(
            vec_in_dims[i], expand_shape[i],
            platform::errors::InvalidArgument(
                "The value (%d) of the non-singleton dimension does not match"
                " the corresponding value (%d) in shape for expand operation.",
                vec_in_dims[i], expand_shape[i]));
        repeat_times[i] = 1;
      } else {
        repeat_times[i] = expand_shape[i];
      }
    } else {
      PADDLE_ENFORCE_EQ(
          expand_shape[i], -1,
          platform::errors::InvalidArgument(
              "When the value in shape is negative for expand_v2 op, "
              "only -1 is supported, but the value received is %d.",
              expand_shape[i]));
      repeat_times[i] = 1;
    }
  }

  Eigen::DSizes<Eigen::DenseIndex, Rank> bcast_dims;
  for (size_t i = 0; i < repeat_times.size(); ++i) {
    bcast_dims[i] = repeat_times[i];
  }

  framework::DDim new_in_dims = framework::make_ddim(vec_in_dims);
  framework::DDim out_dims(new_in_dims);
  for (size_t i = 0; i < repeat_times.size(); ++i) {
    out_dims[i] *= repeat_times[i];
  }

  out->Resize(out_dims);
  out->mutable_data<T>(context.GetPlace());
  auto x = EigenTensor<T, Rank>::From(in, new_in_dims);
  auto y = EigenTensor<T, Rank>::From(*out, out_dims);
  auto& place = *context.eigen_device();
  // use 32-bit index to speed up
  bool use_32bit_index = y.size() < Eigen::NumTraits<int>::highest();
  if (use_32bit_index) {
    EigenBroadcast<std::decay_t<decltype(place)>, T, Rank>::Eval(
        place, To32BitIndex(y), To32BitIndex(x), bcast_dims);
  } else {
    EigenBroadcast<std::decay_t<decltype(place)>, T, Rank>::Eval(place, y, x,
                                                                 bcast_dims);
  }
}

template <typename T, typename DeviceContext>
void TensorExpand(const DeviceContext& context, const Tensor& in, Tensor* out,
                  const std::vector<int64_t>& expand_shape) {
  // necessary check before expand operation
  PADDLE_ENFORCE_GE(expand_shape.size(), in.dims().size(),
                    platform::errors::InvalidArgument(
                        "The size of 'expand_shape' (%d) should >= the input "
                        "Tensor's rank (%d).",
                        expand_shape.size(), in.dims().size()));
  PADDLE_ENFORCE_LE(expand_shape.size(), MAX_RANK_SUPPORTED,
                    platform::errors::InvalidArgument(
                        "The size of 'expand_shape' (%d) should be <= %d",
                        expand_shape.size(), MAX_RANK_SUPPORTED));
  switch (expand_shape.size()) {
    case 1:
      expand_impl<1, T, DeviceContext>(context, in, out, expand_shape);
      break;
    case 2:
      expand_impl<2, T, DeviceContext>(context, in, out, expand_shape);
      break;
    case 3:
      expand_impl<3, T, DeviceContext>(context, in, out, expand_shape);
      break;
    case 4:
      expand_impl<4, T, DeviceContext>(context, in, out, expand_shape);
      break;
    case 5:
      expand_impl<5, T, DeviceContext>(context, in, out, expand_shape);
      break;
    case 6:
      expand_impl<6, T, DeviceContext>(context, in, out, expand_shape);
      break;
  }
}

template <typename DeviceContext, typename T>
static void linalg_solve(const framework::ExecutionContext& context,
                         const framework::Tensor* x, const framework::Tensor* y,
                         framework::Tensor* out) {
  out->mutable_data<T>(context.GetPlace());

  auto& dev_ctx = context.template device_context<DeviceContext>();
  math::MatrixSolveFunctor<DeviceContext, T> mat_solve;

  // input y can be vector or matrix
  // but need to be unsqueezed if y is a vector
  bool is_vector = false;
  is_vector = is_vector_rhs(*x, *y);

  Tensor tmp_y;
  if (is_vector) {
    tmp_y.mutable_data(context.GetPlace(), y->type());
    to_unsqueeze(context, *y, &tmp_y);
  } else {
    tmp_y.Resize(y->dims());
    tmp_y.mutable_data(context.GetPlace(), y->type());
    framework::TensorCopy(
        *y, context.GetPlace(),
        context.template device_context<platform::DeviceContext>(), &tmp_y);
  }

  Tensor tmp_x;
  tmp_x.Resize(x->dims());
  tmp_x.mutable_data(context.GetPlace(), x->type());
  framework::TensorCopy(
      *x, context.GetPlace(),
      context.template device_context<platform::DeviceContext>(), &tmp_x);

  std::vector<int64_t> x_broadcast_dims;
  std::vector<int64_t> y_broadcast_dims;
  std::tie(x_broadcast_dims, y_broadcast_dims) =
      _broadcast_batch_dims(tmp_x, tmp_y);

  Tensor tmp_x_bc;
  TensorExpand<T, DeviceContext>(dev_ctx, tmp_x, &tmp_x_bc, x_broadcast_dims);

  Tensor tmp_y_bc;
  TensorExpand<T, DeviceContext>(dev_ctx, tmp_y, &tmp_y_bc, y_broadcast_dims);

  auto x_dim = x->dims();
  auto y_dim = y->dims();
  auto x_dim_size = x_dim.size();
  auto y_dim_size = y_dim.size();

  if (is_vector) {                 // vector case
    out->Resize(tmp_y_bc.dims());  // out.unsqueeze(-1)
    mat_solve(dev_ctx, tmp_x_bc, tmp_y_bc, out);

    Tensor out_tmp;
    out_tmp.Resize(out->dims());
    out_tmp = *out;
    to_squeeze(context, out_tmp, out);  // out.squeeze(-1)
  } else {
    PADDLE_ENFORCE_EQ(
        x_dim[x_dim_size - 1], y_dim[y_dim_size - 2],
        platform::errors::InvalidArgument(
            "Matrix X1 with dimension greater than 2 and any matrix Y1,"
            "the matrix X1's width must be equal with matrix Y1's "
            "height. But received X's shape = [%s], X1's shape = [%s], X1's "
            "width = %s; Y's shape = [%s], Y1's shape = [%s], Y1's height = "
            "%s.",
            x_dim, x_dim, x_dim[x_dim_size - 1], y_dim, y_dim,
            y_dim[y_dim_size - 2]));
    mat_solve(dev_ctx, tmp_x_bc, tmp_y_bc, out);
  }
}

// for TransposeNormal
static std::vector<int> getNewAxis(const int b_rank) {
  std::vector<int> axis_1 = {0};
  std::vector<int> axis_2 = {1, 0};
  std::vector<int> axis_3 = {0, 2, 1};
  std::vector<int> axis_4 = {0, 1, 3, 2};
  std::vector<int> axis_5 = {0, 1, 2, 4, 3};
  std::vector<int> axis_6 = {0, 1, 2, 3, 5, 4};
  std::vector<int> axis_7 = {0, 1, 2, 3, 4, 6, 5};
  std::vector<int> axis_8 = {0, 1, 2, 3, 4, 5, 7, 6};
  std::vector<int> axis_9 = {0, 1, 2, 3, 4, 5, 6, 8, 7};
  switch (b_rank) {
    case 1:
      return axis_1;
      break;
    case 2:
      return axis_2;
      break;
    case 3:
      return axis_3;
      break;
    case 4:
      return axis_4;
      break;
    case 5:
      return axis_5;
      break;
    case 6:
      return axis_6;
      break;
    case 7:
      return axis_7;
      break;
    case 8:
      return axis_8;
      break;
    default:
      return axis_9;
  }
}

// for Resize
static std::vector<int64_t> getNewDimsVec(const DDim& b_dims) {
  std::vector<int64_t> b_dims_vec = paddle::framework::vectorize(b_dims);
  int size = b_dims_vec.size();
  if (size >= 2) {
    // swap the last 2 elements in b_dims_vec
    int64_t temp = b_dims_vec[size - 1];
    b_dims_vec[size - 1] = b_dims_vec[size - 2];
    b_dims_vec[size - 2] = temp;
    return b_dims_vec;
  }
  PADDLE_ENFORCE_NE(
      b_dims_vec.empty(), true,
      platform::errors::PreconditionNotMet(
          "The size of tensor b must not be %d after getting new dims", 0));
  // if b_dims_vec.size() == 1, just retun original vec
  return b_dims_vec;
}

template <typename DeviceContext, typename T>
class SolveKernel : public framework::OpKernel<T> {
 public:
  void Compute(const framework::ExecutionContext& context) const override {
    const auto* x = context.Input<framework::Tensor>("X");
    const auto* y = context.Input<framework::Tensor>("Y");
    Tensor* out = context.Output<framework::Tensor>("Out");
    linalg_solve<DeviceContext, T>(context, x, y, out);
  }
};

template <typename DeviceContext, typename T>
class SolveGradKernel : public framework::OpKernel<T> {
 public:
  void Compute(const framework::ExecutionContext& ctx) const override {
    auto* input = ctx.Input<framework::Tensor>("X");
    auto* y = ctx.Input<framework::Tensor>("Y");
    auto* dout = ctx.Input<framework::Tensor>(framework::GradVarName("Out"));

    // reuse the linalg.solve forward output
    auto* out = ctx.Input<framework::Tensor>("Out");

    auto* dx = ctx.Output<Tensor>(framework::GradVarName("X"));
    auto* dy = ctx.Output<Tensor>(framework::GradVarName("Y"));

    bool is_vector = false;
    is_vector = is_vector_rhs(*input, *y);

    Tensor tmp_y;
    if (is_vector) {
      tmp_y.mutable_data(ctx.GetPlace(), y->type());
      to_unsqueeze(ctx, *y, &tmp_y);
    } else {
      tmp_y.Resize(y->dims());
      tmp_y.mutable_data(ctx.GetPlace(), y->type());
      framework::TensorCopy(
          *y, ctx.GetPlace(),
          ctx.template device_context<platform::DeviceContext>(), &tmp_y);
    }

    Tensor tmp_x;
    tmp_x.Resize(input->dims());
    tmp_x.mutable_data(ctx.GetPlace(), input->type());
    framework::TensorCopy(
        *input, ctx.GetPlace(),
        ctx.template device_context<platform::DeviceContext>(), &tmp_x);

    std::vector<int64_t> x_broadcast_dims;
    std::vector<int64_t> y_broadcast_dims;
    std::tie(x_broadcast_dims, y_broadcast_dims) =
        _broadcast_batch_dims(tmp_x, tmp_y);

    // tmp_dx
    Tensor tmp_dx;
    tmp_dx.Resize(framework::make_ddim(x_broadcast_dims));
    tmp_dx.mutable_data<T>(ctx.GetPlace());

    // tmp_dy
    Tensor tmp_dy;
    tmp_dy.Resize(framework::make_ddim(y_broadcast_dims));
    tmp_dy.mutable_data<T>(ctx.GetPlace());

    Tensor tmp_input(input->type());
    const auto& new_dims_vec = getNewDimsVec(input->dims());
    tmp_input.Resize(framework::make_ddim(new_dims_vec));
    tmp_input.mutable_data<T>(ctx.GetPlace());
    math::TransposeNormal<DeviceContext, T> trans;
    std::vector<int> new_axis = getNewAxis(input->dims().size());
    auto& dev_ctx = ctx.template device_context<DeviceContext>();
    trans(dev_ctx, *input, &tmp_input, new_axis);

    if (dy) {
      dy->mutable_data<T>(ctx.GetPlace());
      // reuse linalg_solve forward logics to get tmp_dy
      linalg_solve<DeviceContext, T>(ctx, &tmp_input, dout, &tmp_dy);
    }

    if (dx) {
      dx->mutable_data<T>(ctx.GetPlace());
      // to get dx
      auto blas = math::GetBlas<DeviceContext, T>(ctx);
      if (input->dims().size() == 2 && y->dims().size() == 2) {
        auto mat_dim_a1 = math::CreateMatrixDescriptor(tmp_dy.dims(), 0, false);
        auto mat_dim_b1 = math::CreateMatrixDescriptor(out->dims(), 0, true);
        blas.MatMul(tmp_dy, mat_dim_a1, *out, mat_dim_b1, T(-1), &tmp_dx, T(0));
      } else if (is_vector_rhs(*input, *y)) {
        Tensor tmp_dy_;
        tmp_dy_.mutable_data(ctx.GetPlace(), y->type());
        to_unsqueeze(ctx, tmp_dy, &tmp_dy_);

        Tensor tmp_out_;
        tmp_out_.mutable_data(ctx.GetPlace(), out->type());
        to_unsqueeze(ctx, *out, &tmp_out_);

        auto mat_dim_a1 =
            math::CreateMatrixDescriptor(tmp_dy_.dims(), 0, false);
        auto mat_dim_b1 =
            math::CreateMatrixDescriptor(tmp_out_.dims(), 0, true);
        blas.MatMul(tmp_dy_, mat_dim_a1, tmp_out_, mat_dim_b1, T(-1), &tmp_dx,
                    T(0));
      } else {
        auto mat_dim_a1 = math::CreateMatrixDescriptor(tmp_dy.dims(), 0, false);
        auto mat_dim_b1 = math::CreateMatrixDescriptor(out->dims(), 0, true);
        blas.MatMul(tmp_dy, mat_dim_a1, *out, mat_dim_b1, T(-1), &tmp_dx, T(0));
      }
    }

    if (y->dims() != tmp_dy.dims()) {
      Tensor dy_help;
      dy_help.Resize(tmp_dy.dims());
      dy_help.mutable_data(ctx.GetPlace(), tmp_dy.type());
      framework::TensorCopy(
          tmp_dy, ctx.GetPlace(),
          ctx.template device_context<platform::DeviceContext>(), &dy_help);

      // get dims
      std::vector<std::int64_t> x_dims = vectorize(input->dims());
      std::vector<std::int64_t> y_dims = vectorize(y->dims());
      std::vector<std::int64_t> dout_dims = vectorize(dout->dims());

      if (is_vector_rhs(*input, *y)) {
        dout_dims.push_back(1);
      }

      int y_ndim = y_dims.size();
      int ndim = dout_dims.size();

      const std::vector<std::int64_t> dy_help_dims = vectorize(dy_help.dims());
      std::vector<std::int64_t> dy_broadcast_dims(ndim);

      std::fill(dy_broadcast_dims.data(),
                dy_broadcast_dims.data() + ndim - y_ndim, 1);
      std::copy(y_dims.data(), y_dims.data() + y_ndim,
                dy_broadcast_dims.data() + ndim - y_ndim);

      std::vector<int> dy_reduce_dims;
      for (int idx = 0; idx <= ndim - 3; idx++) {
        if (dy_help_dims[idx] != 1 && dy_broadcast_dims[idx] == 1) {
          dy_reduce_dims.push_back(idx);
        }
      }
      // reduce sum to get grad by ReduceSum
      if (dy) {
        if (dy_reduce_dims.empty()) {
          *dy = std::move(dy_help);
        } else {
          bool keep_dim = true;
          if (dy_help.dims().size() != dy->dims().size()) {
            keep_dim = false;
          }
          ReduceSumForSolve<DeviceContext, T>(&dy_help, dy, dy_reduce_dims,
                                              keep_dim, ctx);
        }
        dy->Resize(y->dims());
      }
    } else {
      framework::TensorCopy(
          tmp_dy, ctx.GetPlace(),
          ctx.template device_context<platform::DeviceContext>(), dy);
    }

    if (input->dims() != tmp_dx.dims()) {
      Tensor dx_help;
      dx_help.Resize(tmp_dx.dims());
      dx_help.mutable_data(ctx.GetPlace(), tmp_dx.type());
      framework::TensorCopy(
          tmp_dx, ctx.GetPlace(),
          ctx.template device_context<platform::DeviceContext>(), &dx_help);

      // get dims
      std::vector<std::int64_t> x_dims = vectorize(input->dims());
      std::vector<std::int64_t> y_dims = vectorize(y->dims());

      int x_ndim = x_dims.size();
      int ndim = x_broadcast_dims.size();

      const std::vector<std::int64_t> dx_help_dims = vectorize(dx_help.dims());
      std::vector<std::int64_t> dx_broadcast_dims(ndim);

      std::fill(dx_broadcast_dims.data(),
                dx_broadcast_dims.data() + ndim - x_ndim, 1);
      std::copy(x_dims.data(), x_dims.data() + x_ndim,
                dx_broadcast_dims.data() + ndim - x_ndim);

      std::vector<int> dx_reduce_dims;
      for (int idx = 0; idx <= ndim - 3; idx++) {
        if (dx_help_dims[idx] != 1 && dx_broadcast_dims[idx] == 1) {
          dx_reduce_dims.push_back(idx);
        }
      }
      // reduce sum to get grad by ReduceSum
      if (dx) {
        dx->mutable_data<T>(ctx.GetPlace());
        if (dx_reduce_dims.empty()) {
          *dx = std::move(dx_help);
        } else {
          bool keep_dim = true;
          if (dx_help.dims().size() != dx->dims().size()) {
            keep_dim = false;
          }
          ReduceSumForSolve<DeviceContext, T>(&dx_help, dx, dx_reduce_dims,
                                              keep_dim, ctx);
        }
        dx->Resize(input->dims());
      }
    } else {
      framework::TensorCopy(
          tmp_dx, ctx.GetPlace(),
          ctx.template device_context<platform::DeviceContext>(), dx);
    }
  }
};
}  // namespace operators
}  // namespace paddle