NaiveConvolutionTranspose2d.cpp

#include <ATen/ATen.h>
#include <ATen/NativeFunctions.h>
#include <ATen/TensorUtils.h>

#include <ATen/native/CPUBlas.h>
#include <ATen/native/im2col.h>

namespace at {
namespace native {

template<typename scalar_t>
bool gemv(char trans, int64_t m, int64_t n, scalar_t alpha, scalar_t *a, int64_t lda, scalar_t *x, int64_t incx, scalar_t beta, scalar_t *y, int64_t incy);

namespace {

static inline void slow_conv_transpose2d_shape_check(
    const Tensor& input,
    const Tensor& grad_output,
    const Tensor& weight,
    const Tensor& bias,
    int kernel_height,
    int kernel_width,
    int stride_height,
    int stride_width,
    int pad_height,
    int pad_width,
    int output_padding_height,
    int output_padding_width,
    int dilation_height,
    int dilation_width,
    bool weight_nullable) {
  TORCH_CHECK(
      kernel_width > 0 && kernel_height > 0,
      "kernel size should be greater than zero, but got kernel_height: ",
      kernel_height,
      " kernel_width: ",
      kernel_width);
  TORCH_CHECK(
      stride_width > 0 && stride_height > 0,
      "stride should be greater than zero, but got stride_height: ",
      stride_height,
      " stride_width: ",
      stride_width);
  TORCH_CHECK(
      dilation_width > 0 && dilation_height > 0,
      "dilation should be greater than zero, but got dilation_height: ",
      dilation_height,
      ", dilation_width: ",
      dilation_width);
  TORCH_CHECK(
      (output_padding_width < stride_width ||
       output_padding_width < dilation_width) &&
          (output_padding_height < stride_height ||
           output_padding_height < dilation_height),
      "output padding must be smaller than either stride or dilation, but got output_padding_height: ",
      output_padding_height,
      " output_padding_width: ",
      output_padding_width,
      " stride_height: ",
      stride_height,
      " stride_width: ",
      stride_width,
      " dilation_height: ",
      dilation_height,
      " dilation_width: ",
      dilation_width);

  if (weight.defined()) {
    TORCH_CHECK(
        weight.numel() != 0 && (weight.dim() == 2 || weight.dim() == 4),
        "non-empty 2D or 4D weight tensor expected, but got: ",
        weight.sizes());
    if (bias.defined()) {
      check_dim_size(bias, 1, 0, weight.size(1));
    }
  } else if (!weight_nullable) {
    AT_ERROR("weight tensor is expected to be non-nullable");
  }

  int ndim = input.dim();
  int dimf = 0;
  int dimh = 1;
  int dimw = 2;

  if (ndim == 4) {
    dimf++;
    dimh++;
    dimw++;
  }

  TORCH_CHECK(
      input.numel() != 0 && (ndim == 3 || ndim == 4),
      "non-empty 3D or 4D input tensor expected but got a tensor with size ",
      input.sizes());

  int64_t input_height = input.size(dimh);
  int64_t input_width = input.size(dimw);
  int64_t output_height = (input_height - 1) * stride_height - 2 * pad_height +
      (dilation_height * (kernel_height - 1) + 1) + output_padding_height;
  int64_t output_width = (input_width - 1) * stride_width - 2 * pad_width +
      (dilation_width * (kernel_width - 1) + 1) + output_padding_width;

  if (output_width < 1 || output_height < 1) {
    AT_ERROR(
        "Given input size per channel: (",
        input_height,
        " x ",
        input_width,
        "). "
        "Calculated output size per channel: (",
        output_height,
        " x ",
        output_width,
        "). Output size is too small");
  }

  if (weight.defined()) {
    int64_t n_input_plane = weight.size(0);
    check_dim_size(input, ndim, dimf, n_input_plane);
  }

  if (grad_output.defined()) {
    if (weight.defined()) {
      int64_t n_output_plane = weight.size(1);
      check_dim_size(grad_output, ndim, dimf, n_output_plane);
    } else if (bias.defined()) {
      int64_t n_output_plane = bias.size(0);
      check_dim_size(grad_output, ndim, dimf, n_output_plane);
    }
    check_dim_size(grad_output, ndim, dimh, output_height);
    check_dim_size(grad_output, ndim, dimw, output_width);
  }
}

void slow_conv_transpose2d_out_cpu_template(
    Tensor& output,
    const Tensor& input_,
    const Tensor& weight_,
    IntArrayRef kernel_size,
    const Tensor& bias_,
    IntArrayRef stride,
    IntArrayRef padding,
    IntArrayRef output_padding,
    IntArrayRef dilation,
    Tensor& columns_,
    Tensor& ones_) {
  TORCH_CHECK(
      kernel_size.size() == 2,
      "It is expected kernel_size equals to 2, but got size ",
      kernel_size.size());

  TORCH_CHECK(
      dilation.size() == 2,
      "It is expected dilation equals to 2, but got size ",
      dilation.size());

  TORCH_CHECK(
      padding.size() == 2,
      "It is expected padding equals to 2, but got size ",
      padding.size());

  TORCH_CHECK(
      stride.size() == 2,
      "It is expected stride equals to 2, but got size ",
      stride.size());

  TORCH_CHECK(
      output_padding.size() == 2,
      "It is expected stride equals to 2, but got size ",
      output_padding.size());

  Tensor columns = columns_;
  Tensor ones = ones_;

  int64_t kernel_height = kernel_size[0];
  int64_t kernel_width = kernel_size[1];
  int64_t dilation_height = dilation[0];
  int64_t dilation_width = dilation[1];
  int64_t pad_height = padding[0];
  int64_t pad_width = padding[1];
  int64_t stride_height = stride[0];
  int64_t stride_width = stride[1];
  int64_t output_padding_height = output_padding[0];
  int64_t output_padding_width = output_padding[1];

  slow_conv_transpose2d_shape_check(
      input_,
      Tensor(),
      weight_,
      bias_,
      kernel_height,
      kernel_width,
      stride_height,
      stride_width,
      pad_height,
      pad_width,
      output_padding_height,
      output_padding_width,
      dilation_height,
      dilation_width,
      false);

  int n_input_plane = weight_.size(0);
  int n_output_plane = weight_.size(1);

  Tensor input = input_.contiguous();
  Tensor weight = weight_.contiguous();

  TORCH_CHECK(columns.is_contiguous(), "columns needs to be contiguous");

  Tensor bias = Tensor();

  if (bias_.defined()) {
    bias = bias_.contiguous();
    TORCH_CHECK(ones.is_contiguous(), "ones needs to be contiguous");
  }

  bool is_batch = false;
  if (input.dim() == 3) {
    // Force batch
    is_batch = true;
    input.resize_({1, input.size(0), input.size(1), input.size(2)});
  }

  int64_t input_height = input.size(2);
  int64_t input_width = input.size(3);
  int64_t output_height = (input_height - 1) * stride_height - 2 * pad_height +
      (dilation_height * (kernel_height - 1) + 1) + output_padding_height;
  int64_t output_width = (input_width - 1) * stride_width - 2 * pad_width +
      (dilation_width * (kernel_width - 1) + 1) + output_padding_width;

  // Batch size + input planes
  int64_t batch_size = input.size(0);

  // Resize output
  output.resize_({batch_size, n_output_plane, output_height, output_width});

  // Resize temporary columns
  columns.resize_({n_output_plane * kernel_width * kernel_height,
                   input_height * input_width});
  columns.zero_();

  // Define a buffer of ones, for bias accumulation
  // Note: this buffer can be shared with other modules, it only ever gets
  // increased, and always contains ones.
  if (ones.dim() != 2 ||
      ones.size(0) * ones.size(1) < output_height * output_width) {
    // Resize plane and fill with ones...
    ones.resize_({output_height, output_width});
    ones.fill_(1);
  }

  AT_DISPATCH_FLOATING_TYPES_AND(at::ScalarType::Long,
      input.scalar_type(), "slow_conv_transpose2d_out_cpu", [&] {
        // For each elt in batch, do:
        for (int elt = 0; elt < batch_size; elt++) {
          // Helpers
          Tensor input_n;
          Tensor output_n;

          // Matrix mulitply per output:
          input_n = input.select(0, elt);
          output_n = output.select(0, elt);

          // M,N,K are dims of matrix A and B
          // (see http://docs.nvidia.com/cuda/cublas/#cublas-lt-t-gt-gemm)
          int64_t m = weight.size(1) * weight.size(2) * weight.size(3);
          int64_t n = columns.size(1);
          int64_t k = weight.size(0);

          // Do GEMM (note: this is a bit confusing because gemm assumes
          // column-major matrices)
          cpublas::gemm(
              cpublas::NoTranspose,
              cpublas::Transpose,
              n,
              m,
              k,
              1,
              input_n.data_ptr<scalar_t>(),
              n,
              weight.data_ptr<scalar_t>(),
              m,
              0,
              columns.data_ptr<scalar_t>(),
              n);

          // Unpack columns back into input:
          col2im<scalar_t>(
              columns.data_ptr<scalar_t>(),
              n_output_plane,
              output_height,
              output_width,
              input_height,
              input_width,
              kernel_height,
              kernel_width,
              pad_height,
              pad_width,
              stride_height,
              stride_width,
              dilation_height,
              dilation_width,
              output_n.data_ptr<scalar_t>());

          // Do Bias after:
          // M,N,K are dims of matrix A and B
          // (see http://docs.nvidia.com/cuda/cublas/#cublas-lt-t-gt-gemm)
          int64_t m_ = n_output_plane;
          int64_t n_ = output_height * output_width;
          int64_t k_ = 1;

          // Do GEMM (note: this is a bit confusing because gemm assumes
          // column-major matrices)
          if (bias_.defined()) {
            cpublas::gemm(
                cpublas::Transpose,
                cpublas::NoTranspose,
                n_,
                m_,
                k_,
                1,
                ones.data_ptr<scalar_t>(),
                k_,
                bias.data_ptr<scalar_t>(),
                k_,
                1,
                output_n.data_ptr<scalar_t>(),
                n_);
          }
        }

        // Resize output
        if (is_batch) {
          output.resize_({n_output_plane, output_height, output_width});
          input.resize_({n_input_plane, input_height, input_width});
        }
      });
}

static void slow_conv_transpose2d_backward_out_cpu_template(
    const Tensor& input_,
    const Tensor& grad_output_,
    Tensor& grad_input,
    const Tensor& weight_,
    const Tensor& grad_columns_,
    IntArrayRef kernel_size,
    IntArrayRef stride,
    IntArrayRef padding,
    IntArrayRef output_padding,
    IntArrayRef dilation) {
  TORCH_CHECK(
      kernel_size.size() == 2,
      "It is expected kernel_size equals to 2, but got size ",
      kernel_size.size());

  TORCH_CHECK(
      dilation.size() == 2,
      "It is expected dilation equals to 2, but got size ",
      dilation.size());

  TORCH_CHECK(
      padding.size() == 2,
      "It is expected padding equals to 2, but got size ",
      padding.size());

  TORCH_CHECK(
      stride.size() == 2,
      "It is expected stride equals to 2, but got size ",
      stride.size());

  TORCH_CHECK(
      output_padding.size() == 2,
      "It is expected stride equals to 2, but got size ",
      output_padding.size());

  int64_t kernel_height = kernel_size[0];
  int64_t kernel_width = kernel_size[1];
  int64_t dilation_height = dilation[0];
  int64_t dilation_width = dilation[1];
  int64_t pad_height = padding[0];
  int64_t pad_width = padding[1];
  int64_t stride_height = stride[0];
  int64_t stride_width = stride[1];
  int64_t output_padding_height = output_padding[0];
  int64_t output_padding_width = output_padding[1];

  int64_t n_input_plane = weight_.size(0);
  int64_t n_output_plane = weight_.size(1);

  Tensor grad_columns = grad_columns_;

  slow_conv_transpose2d_shape_check(
      input_,
      grad_output_,
      weight_,
      Tensor(),
      kernel_height,
      kernel_width,
      stride_height,
      stride_width,
      pad_height,
      pad_width,
      output_padding_height,
      output_padding_width,
      dilation_height,
      dilation_width,
      false);

  Tensor input = input_.contiguous();
  Tensor grad_output = grad_output_.contiguous();
  Tensor weight = weight_.contiguous();

  TORCH_CHECK(
      grad_columns.is_contiguous(), "grad_columns needs to be contiguous");

  bool is_batch = false;
  if (input.dim() == 3) {
    // Force batch
    is_batch = true;
    input.resize_({1, input.size(0), input.size(1), input.size(2)});
    grad_output.resize_(
        {1, grad_output.size(0), grad_output.size(1), grad_output.size(2)});
  }

  int64_t input_width = input.size(3);
  int64_t input_height = input.size(2);
  int64_t output_height = (input_height - 1) * stride_height - 2 * pad_height +
      (dilation_height * (kernel_height - 1) + 1) + output_padding_height;
  int64_t output_width = (input_width - 1) * stride_width - 2 * pad_width +
      (dilation_width * (kernel_width - 1) + 1) + output_padding_width;

  // Batch size + input planes
  int64_t batch_size = input.size(0);

  // Resize output
  grad_input.resize_({batch_size, n_input_plane, input_height, input_width});
  grad_input.zero_();

  // Resize temporary columns
  grad_columns.resize_({n_output_plane * kernel_width * kernel_height,
                        input_height * input_width});

  AT_DISPATCH_FLOATING_TYPES(
      grad_output.scalar_type(), "slow_conv_transpose2d_backward_out_cpu", [&] {
        // Helpers
        Tensor grad_input_n = Tensor();
        Tensor grad_output_n = Tensor();

        // For each elt in batch, do:
        for (int elt = 0; elt < batch_size; elt++) {
          // Matrix mulitply per sample:
          grad_input_n = grad_input.select(0, elt);
          grad_output_n = grad_output.select(0, elt);

          // Extract columns:
          im2col<scalar_t>(
              grad_output_n.data_ptr<scalar_t>(),
              n_output_plane,
              output_height,
              output_width,
              input_height,
              input_width,
              kernel_height,
              kernel_width,
              pad_height,
              pad_width,
              stride_height,
              stride_width,
              dilation_height,
              dilation_width,
              grad_columns.data_ptr<scalar_t>());

          // M,N,K are dims of matrix A and B
          // (see http://docs.nvidia.com/cuda/cublas/#cublas-lt-t-gt-gemm)
          int64_t m = weight.size(0);
          int64_t n = grad_columns.size(1);
          int64_t k = weight.size(1) * weight.size(2) * weight.size(3);

          // Do GEMM (note: this is a bit confusing because gemm assumes
          // column-major matrices)
          cpublas::gemm(
              cpublas::NoTranspose,
              cpublas::NoTranspose,
              n,
              m,
              k,
              1,
              grad_columns.data_ptr<scalar_t>(),
              n,
              weight.data_ptr<scalar_t>(),
              k,
              0,
              grad_input_n.data_ptr<scalar_t>(),
              n);
        }

        // Resize output
        if (is_batch) {
          grad_output.resize_({n_output_plane, output_height, output_width});
          input.resize_({n_input_plane, input_height, input_width});
          grad_input.resize_({n_input_plane, input_height, input_width});
        }
      });
}

void slow_conv_transpose2d_acc_grad_parameters_cpu(
    const Tensor& input_,
    const Tensor& grad_output_,
    Tensor& grad_weight,
    Tensor& grad_bias,
    const Tensor& columns_,
    const Tensor& ones_,
    IntArrayRef kernel_size,
    IntArrayRef stride,
    IntArrayRef padding,
    IntArrayRef output_padding,
    IntArrayRef dilation,
    int scale_) {
  TORCH_CHECK(
      kernel_size.size() == 2,
      "It is expected kernel_size equals to 2, but got size ",
      kernel_size.size());

  TORCH_CHECK(
      dilation.size() == 2,
      "It is expected dilation equals to 2, but got size ",
      dilation.size());

  TORCH_CHECK(
      padding.size() == 2,
      "It is expected padding equals to 2, but got size ",
      padding.size());

  TORCH_CHECK(
      stride.size() == 2,
      "It is expected stride equals to 2, but got size ",
      stride.size());

  TORCH_CHECK(
      output_padding.size() == 2,
      "It is expected stride equals to 2, but got size ",
      output_padding.size());

  int64_t kernel_height = kernel_size[0];
  int64_t kernel_width = kernel_size[1];
  int64_t dilation_height = dilation[0];
  int64_t dilation_width = dilation[1];
  int64_t pad_height = padding[0];
  int64_t pad_width = padding[1];
  int64_t stride_height = stride[0];
  int64_t stride_width = stride[1];
  int64_t output_padding_height = output_padding[0];
  int64_t output_padding_width = output_padding[1];

  Tensor columns = columns_;
  Tensor ones = ones_;

  slow_conv_transpose2d_shape_check(
      input_,
      grad_output_,
      grad_weight,
      grad_bias,
      kernel_height,
      kernel_width,
      stride_height,
      stride_width,
      pad_height,
      pad_width,
      output_padding_height,
      output_padding_width,
      dilation_height,
      dilation_width,
      true);

  int64_t n_output_plane;
  if (grad_weight.defined()) {
    n_output_plane = grad_weight.size(1);
  } else if (grad_bias.defined()) {
    n_output_plane = grad_bias.size(0);
  } else {
    return;
  }

  Tensor input = input_.contiguous();
  Tensor grad_output = grad_output_.contiguous();

  if (grad_weight.defined()) {
    TORCH_CHECK(
        grad_weight.is_contiguous(), "grad_weight needs to be contiguous");
  }
  TORCH_CHECK(columns.is_contiguous(), "columns needs to be contiguous");
  if (grad_bias.defined()) {
    TORCH_CHECK(grad_bias.is_contiguous(), "grad_bias needs to be contiguous");
    TORCH_CHECK(ones.is_contiguous(), "ones needs to be contiguous");
  }

  bool is_batch = false;
  if (input.dim() == 3) {
    // Force batch
    is_batch = true;
    input.resize_({1, input.size(0), input.size(1), input.size(2)});
    grad_output.resize_(
        {1, grad_output.size(0), grad_output.size(1), grad_output.size(2)});
  }

  int64_t input_width = input.size(3);
  int64_t input_height = input.size(2);
  int64_t output_height = (input_height - 1) * stride_height - 2 * pad_height +
      (dilation_height * (kernel_height - 1) + 1) + output_padding_height;
  int64_t output_width = (input_width - 1) * stride_width - 2 * pad_width +
      (dilation_width * (kernel_width - 1) + 1) + output_padding_width;

  // Batch size + input planes
  int64_t batch_size = input.size(0);

  // Define a buffer of ones, for bias accumulation
  if (ones.dim() != 2 ||
      ones.size(0) * ones.size(1) < output_height * output_width) {
    // Resize plane and fill with ones...
    ones.resize_({output_height, output_width});
    ones.fill_(1);
  }

  // Resize temporary columns
  columns.resize_({n_output_plane * kernel_width * kernel_height,
                   input_height * input_width});

  AT_DISPATCH_FLOATING_TYPES(
      input.scalar_type(), "slow_conv_transpose2d_acc_grad_parameters_cpu", [&] {
        // Helpers
        Tensor input_n = Tensor();
        Tensor grad_output_n = Tensor();

        scalar_t scale = static_cast<scalar_t>(scale_);

        // For each elt in batch, do:
        for (int elt = 0; elt < batch_size; elt++) {
          // Matrix mulitply per output:
          grad_output_n = grad_output.select(0, elt);

          // Do Weight:
          if (grad_weight.defined()) {
            // Matrix mulitply per output:
            input_n = input.select(0, elt);

            // Extract columns:
            im2col<scalar_t>(
                grad_output_n.data_ptr<scalar_t>(),
                n_output_plane,
                output_height,
                output_width,
                input_height,
                input_width,
                kernel_height,
                kernel_width,
                pad_height,
                pad_width,
                stride_height,
                stride_width,
                dilation_height,
                dilation_width,
                columns.data_ptr<scalar_t>());

            // M,N,K are dims of matrix A and B
            // (see http://docs.nvidia.com/cuda/cublas/#cublas-lt-t-gt-gemm)
            int64_t n = columns.size(0); // n_output_plane * kh * kw
            int64_t m = input_n.size(0); // n_input_plane
            int64_t k = columns.size(1); // input_height * input_width

            // Do GEMM (note: this is a bit confusing because gemm assumes
            // column-major matrices)
            cpublas::gemm(
                cpublas::Transpose,
                cpublas::NoTranspose,
                n,
                m,
                k,
                scale,
                columns.data_ptr<scalar_t>(),
                k,
                input_n.data_ptr<scalar_t>(),
                k,
                1,
                grad_weight.data_ptr<scalar_t>(),
                n);
          }

          // Do Bias:
          if (grad_bias.defined()) {
            // M,N,K are dims of matrix A and B
            // (see http://docs.nvidia.com/cuda/cublas/#cublas-lt-t-gt-gemm)
            int64_t m_ = n_output_plane;
            int64_t k_ = output_height * output_width;

            // Do GEMV (note: this is a bit confusing because gemv assumes
            // column-major matrices)
            native::gemv<scalar_t>(
                't',
                k_,
                m_,
                scale,
                grad_output_n.data_ptr<scalar_t>(),
                k_,
                ones.data_ptr<scalar_t>(),
                1,
                1,
                grad_bias.data_ptr<scalar_t>(),
                1);
          }
        }

        // Resize
        if (is_batch) {
          grad_output.resize_({n_output_plane, output_height, output_width});
          input.resize_({input.size(1), input_height, input_width});
        }
      });
}

} // namespace

Tensor& slow_conv_transpose2d_out_cpu(
    Tensor& output,
    const Tensor& input,
    const Tensor& weight,
    IntArrayRef kernel_size,
    const Tensor& bias,
    IntArrayRef stride,
    IntArrayRef padding,
    IntArrayRef output_padding,
    IntArrayRef dilation) {
  Tensor columns = at::empty_like(input, LEGACY_CONTIGUOUS_MEMORY_FORMAT);
  Tensor ones = at::empty_like(input, LEGACY_CONTIGUOUS_MEMORY_FORMAT);

  slow_conv_transpose2d_out_cpu_template(
      output,
      input,
      weight,
      kernel_size,
      bias,
      stride,
      padding,
      output_padding,
      dilation,
      columns,
      ones);

  return output;
}

Tensor slow_conv_transpose2d_cpu(
    const Tensor& input,
    const Tensor& weight,
    IntArrayRef kernel_size,
    const Tensor& bias,
    IntArrayRef stride,
    IntArrayRef padding,
    IntArrayRef output_padding,
    IntArrayRef dilation) {
  Tensor output = at::empty_like(input, LEGACY_CONTIGUOUS_MEMORY_FORMAT);
  Tensor columns = at::empty_like(input, LEGACY_CONTIGUOUS_MEMORY_FORMAT);
  Tensor ones = at::empty_like(input, LEGACY_CONTIGUOUS_MEMORY_FORMAT);

  slow_conv_transpose2d_out_cpu_template(
      output,
      input,
      weight,
      kernel_size,
      bias,
      stride,
      padding,
      output_padding,
      dilation,
      columns,
      ones);

  return output;
}

std::tuple<Tensor&, Tensor&, Tensor&> slow_conv_transpose2d_backward_out_cpu(
    Tensor& grad_input,
    Tensor& grad_weight,
    Tensor& grad_bias,
    const Tensor& grad_output,
    const Tensor& input,
    const Tensor& weight,
    IntArrayRef kernel_size,
    IntArrayRef stride,
    IntArrayRef padding,
    IntArrayRef output_padding,
    IntArrayRef dilation,
    const Tensor& columns,
    const Tensor& ones) {
  if (grad_input.defined()) {
    slow_conv_transpose2d_backward_out_cpu_template(
        input,
        grad_output,
        grad_input,
        weight,
        columns,
        kernel_size,
        stride,
        padding,
        output_padding,
        dilation);
  }

  if (grad_weight.defined()) {
    grad_weight.resize_(weight.sizes());
    grad_weight.zero_();
  }

  if (grad_bias.defined()) {
    grad_bias.resize_({weight.size(1)});
    grad_bias.zero_();
  }

  if (grad_weight.defined() || grad_bias.defined()) {
    slow_conv_transpose2d_acc_grad_parameters_cpu(
        input,
        grad_output,
        grad_weight,
        grad_bias,
        columns,
        ones,
        kernel_size,
        stride,
        padding,
        output_padding,
        dilation,
        1);
  }

  return std::tuple<Tensor&, Tensor&, Tensor&>(
      grad_input, grad_weight, grad_bias);
}

std::tuple<Tensor, Tensor, Tensor> slow_conv_transpose2d_backward_cpu(
    const Tensor& grad_output,
    const Tensor& input,
    const Tensor& weight,
    IntArrayRef kernel_size,
    IntArrayRef stride,
    IntArrayRef padding,
    IntArrayRef output_padding,
    IntArrayRef dilation,
    const Tensor& columns,
    const Tensor& ones,
    std::array<bool, 3> output_mask) {
  Tensor grad_input;
  Tensor grad_weight;
  Tensor grad_bias;

  if (output_mask[0]) {
    grad_input = at::empty({0}, grad_output.options());
  } else {
    grad_input = Tensor();
  }

  if (output_mask[1]) {
    grad_weight = at::empty({0}, grad_output.options());
  } else {
    grad_weight = Tensor();
  }

  if (output_mask[2]) {
    grad_bias = at::empty({0}, grad_output.options());
  } else {
    grad_bias = Tensor();
  }

  if (grad_input.defined()) {
    slow_conv_transpose2d_backward_out_cpu_template(
        input,
        grad_output,
        grad_input,
        weight,
        columns,
        kernel_size,
        stride,
        padding,
        output_padding,
        dilation);
  }

  if (grad_weight.defined()) {
    grad_weight.resize_(weight.sizes());
    grad_weight.zero_();
  }

  if (grad_bias.defined()) {
    grad_bias.resize_({weight.size(1)});
    grad_bias.zero_();
  }

  if (grad_weight.defined() || grad_bias.defined()) {
    slow_conv_transpose2d_acc_grad_parameters_cpu(
        input,
        grad_output,
        grad_weight,
        grad_bias,
        columns,
        ones,
        kernel_size,
        stride,
        padding,
        output_padding,
        dilation,
        1);
  }

  return std::tuple<Tensor, Tensor, Tensor>(grad_input, grad_weight, grad_bias);
}

} // namespace native
} // namespace at