paddlepaddle--paddle/paddle/phi/kernels/impl/slogdeterminant_kernel_impl.h

// 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.

#pragma once

#include <algorithm>
#include <cmath>
#include <vector>

#include "glog/logging.h"

#include "paddle/phi/core/enforce.h"
#include "paddle/phi/core/tensor_utils.h"
#include "paddle/phi/kernels/full_kernel.h"
#include "paddle/phi/kernels/impl/determinant_kernel_impl.h"
#include "paddle/phi/kernels/slogdeterminant_kernel.h"

namespace phi {

// T is not complex
template <typename T>
T _sign(T val) {
  return static_cast<T>(T(0) < val) - (val < T(0));
}

// T is complex
template <typename T>
T _sign(T det, T modulus) {
  return det / modulus;
}

template <typename T, typename Context>
struct SlogDeterminantFunctor {
  void operator()(const Context& dev_ctx,
                  const DenseTensor& input,
                  int64_t rank,
                  int64_t batch_count,
                  DenseTensor* output) {
    std::vector<T> input_vec;
    std::vector<T> sign_vec;
    std::vector<T> log_vec;
    std::vector<T> output_vec;
    TensorToVector(input, dev_ctx, &input_vec);
    for (int64_t i = 0; i < batch_count; ++i) {  // maybe can be parallel
      auto begin_iter = input_vec.begin() + i * rank * rank;
      auto end_iter = input_vec.begin() + (i + 1) * rank * rank;
      std::vector<T> sub_vec(begin_iter,
                             end_iter);  // get every square matrix data
      typename detail::EigenMatrix<T>::MatrixType matrix(rank, rank);
      for (int64_t i = 0; i < rank; ++i) {
        for (int64_t j = 0; j < rank; ++j) {
          matrix(i, j) = sub_vec[rank * i + j];
        }
      }
      VLOG(2) << "det value: " << matrix.determinant();
      VLOG(2) << "matrix val: " << matrix;
      auto det_val = matrix.determinant();
      sign_vec.push_back(_sign(det_val));
      det_val >= 0
          ? log_vec.push_back(std::log(det_val))
          : log_vec.push_back(std::log(std::abs(
                det_val)));  // for computing log value of a negative value.
    }
    // merge sign_vec and log_vec as final output_vec
    output_vec.insert(output_vec.end(), sign_vec.begin(), sign_vec.end());
    output_vec.insert(output_vec.end(), log_vec.begin(), log_vec.end());
    TensorFromVector(output_vec, dev_ctx, output);
  }
};

template <typename T, typename Context>
struct SlogDeterminantFunctor<dtype::complex<T>, Context> {
  void operator()(const Context& dev_ctx,
                  const DenseTensor& input,
                  int64_t rank,
                  int64_t batch_count,
                  DenseTensor* output) {
    using MatrixType =
        Eigen::Matrix<std::complex<T>, Eigen::Dynamic, Eigen::Dynamic>;
    std::vector<dtype::complex<T>> input_vec;
    std::vector<dtype::complex<T>> sign_vec;
    std::vector<dtype::complex<T>> log_vec;
    std::vector<dtype::complex<T>> output_vec;
    TensorToVector(input, dev_ctx, &input_vec);
    for (int64_t i = 0; i < batch_count; ++i) {  // maybe can be parallel
      auto begin_iter = input_vec.begin() + i * rank * rank;
      auto end_iter = input_vec.begin() + (i + 1) * rank * rank;
      std::vector<dtype::complex<T>> sub_vec(
          begin_iter,
          end_iter);  // get every square matrix data
      MatrixType matrix(rank, rank);
      for (int64_t i = 0; i < rank; ++i) {
        for (int64_t j = 0; j < rank; ++j) {
          matrix(i, j) = static_cast<std::complex<T>>(sub_vec[rank * i + j]);
        }
      }
      VLOG(2) << "det value: " << matrix.determinant();
      VLOG(2) << "matrix val: " << matrix;
      std::complex<T> det_val = matrix.determinant();
      T abs_det_val = std::abs(det_val);
      sign_vec.push_back(static_cast<dtype::complex<T>>(
          _sign(det_val, static_cast<std::complex<T>>(abs_det_val))));
      log_vec.push_back(static_cast<dtype::complex<T>>(std::log(abs_det_val)));
    }
    // merge sign_vec and log_vec as final output_vec
    output_vec.insert(output_vec.end(), sign_vec.begin(), sign_vec.end());
    output_vec.insert(output_vec.end(), log_vec.begin(), log_vec.end());
    TensorFromVector(output_vec, dev_ctx, output);
  }
};

template <typename T, typename Context>
void SlogDeterminantKernel(const Context& dev_ctx,
                           const DenseTensor& x,
                           DenseTensor* out) {
  auto input_dim = vectorize(x.dims());
  auto input_dim_size = input_dim.size();

  // shape [*, M, M], check whether it contains 0 in '*'.
  if (input_dim.size() > 2) {
    bool size_0 = false;
    std::vector<int> tmp_dim_vec(input_dim.begin(), input_dim.end() - 2);
    for (size_t i = 0; i < tmp_dim_vec.size(); ++i) {
      if (tmp_dim_vec[i] == 0) {
        size_0 = true;
        break;
      }
    }
    if (size_0) {
      tmp_dim_vec.insert(tmp_dim_vec.begin(),
                         2);  // make the output dims as same as numpy
      out->Resize(tmp_dim_vec);
      dev_ctx.template Alloc<T>(out);
      return;
    }
  }

  auto batch_count = detail::GetBatchCount(x.dims());
  VLOG(2) << "input dim:" << x.dims();
  PADDLE_ENFORCE_GE(
      input_dim_size,
      2,
      errors::InvalidArgument("the input matrix dimension size should greater "
                              "than or equal to 2."));
  PADDLE_ENFORCE_EQ(
      input_dim[input_dim_size - 1],
      input_dim[input_dim_size - 2],
      errors::InvalidArgument("the input matrix should be square matrix."));
  auto rank = input_dim[input_dim_size - 1];  // square matrix length
  SlogDeterminantFunctor<T, Context>()(dev_ctx, x, rank, batch_count, out);
  std::vector<int> output_dim_vec(input_dim.begin(), input_dim.end() - 2);
  if (input_dim.size() == static_cast<size_t>(2)) {
    // when input is a two-dimension matrix, The det value is a number.
    output_dim_vec = {};
  }
  output_dim_vec.insert(output_dim_vec.begin(),
                        2);  // make the output dims as same as numpy
  auto output_dims = make_ddim(output_dim_vec);
  out->Resize(output_dims);
  VLOG(2) << "output dim:" << out->dims();
}

template <typename T, typename Context>
struct SlogDeterminantV2Functor {
  void operator()(const Context& dev_ctx,
                  const DenseTensor& input,
                  int64_t rank,
                  int64_t batch_count,
                  DenseTensor* sign,
                  DenseTensor* logdet) {
    if (input.numel() == 0) {
      dev_ctx.template Alloc<T>(sign);
      if (sign->numel() > 0) {
        Full<T, Context>(dev_ctx, sign->dims(), static_cast<T>(1), sign);
      }
      dev_ctx.template Alloc<T>(logdet);
      if (logdet->numel() > 0) {
        Full<T, Context>(
            dev_ctx, logdet->dims(), static_cast<dtype::complex<T>>(0), logdet);
      }
      return;
    }
    std::vector<T> input_vec;
    T* sign_data = dev_ctx.template Alloc<T>(sign);
    T* logdet_data = dev_ctx.template Alloc<T>(logdet);
    TensorToVector(input, dev_ctx, &input_vec);
    for (int64_t i = 0; i < batch_count; ++i) {  // maybe can be parallel
      auto begin_iter = input_vec.begin() + i * rank * rank;
      auto end_iter = input_vec.begin() + (i + 1) * rank * rank;
      std::vector<T> sub_vec(begin_iter,
                             end_iter);  // get every square matrix data
      typename detail::EigenMatrix<T>::MatrixType matrix(rank, rank);
      for (int64_t i = 0; i < rank; ++i) {
        for (int64_t j = 0; j < rank; ++j) {
          matrix(i, j) = sub_vec[rank * i + j];
        }
      }
      VLOG(2) << "det value: " << matrix.determinant();
      VLOG(2) << "matrix val: " << matrix;
      T det_val = matrix.determinant();
      sign_data[i] = _sign(det_val);
      det_val >= 0
          ? logdet_data[i] = std::log(det_val)
          : logdet_data[i] = std::log(std::abs(
                det_val));  // for computing log value of a negative value.
    }
  }
};

template <typename T, typename Context>
struct SlogDeterminantV2Functor<dtype::complex<T>, Context> {
  void operator()(const Context& dev_ctx,
                  const DenseTensor& input,
                  int64_t rank,
                  int64_t batch_count,
                  DenseTensor* sign,
                  DenseTensor* logdet) {
    if (input.numel() == 0) {
      dev_ctx.template Alloc<dtype::complex<T>>(sign);
      dev_ctx.template Alloc<dtype::complex<T>>(sign);
      if (sign->numel() > 0) {
        Full<dtype::complex<T>, Context>(
            dev_ctx, sign->dims(), static_cast<dtype::complex<T>>(1), sign);
      }
      dev_ctx.template Alloc<T>(logdet);
      if (logdet->numel() > 0) {
        Full<T, Context>(
            dev_ctx, logdet->dims(), static_cast<dtype::complex<T>>(0), logdet);
      }
      return;
    }
    using MatrixType =
        Eigen::Matrix<std::complex<T>, Eigen::Dynamic, Eigen::Dynamic>;
    using Complex_T = typename dtype::complex<T>;
    std::vector<Complex_T> input_vec;
    Complex_T* sign_data = dev_ctx.template Alloc<Complex_T>(sign);
    T* logdet_data = dev_ctx.template Alloc<T>(logdet);
    TensorToVector(input, dev_ctx, &input_vec);
    for (int64_t i = 0; i < batch_count; ++i) {  // maybe can be parallel
      auto begin_iter = input_vec.begin() + i * rank * rank;
      auto end_iter = input_vec.begin() + (i + 1) * rank * rank;
      std::vector<dtype::complex<T>> sub_vec(
          begin_iter,
          end_iter);  // get every square matrix data
      MatrixType matrix(rank, rank);
      for (int64_t i = 0; i < rank; ++i) {
        for (int64_t j = 0; j < rank; ++j) {
          matrix(i, j) = static_cast<std::complex<T>>(sub_vec[rank * i + j]);
        }
      }
      VLOG(2) << "det value: " << matrix.determinant();
      VLOG(2) << "matrix val: " << matrix;
      std::complex<T> det_val = matrix.determinant();
      T abs_det_val = std::abs(det_val);
      T epsilon = std::numeric_limits<T>::epsilon();

      if (abs_det_val <= epsilon) {
        sign_data[i] = Complex_T(0.0, 0.0);
        logdet_data[i] = -std::numeric_limits<T>::infinity();
      } else {
        sign_data[i] = static_cast<Complex_T>(
            _sign(det_val, static_cast<std::complex<T>>(abs_det_val)));
        logdet_data[i] = std::log(abs_det_val);
      }
    }
  }
};

template <typename T, typename Context>
void SlogDeterminantV2Kernel(const Context& dev_ctx,
                             const DenseTensor& x,
                             DenseTensor* sign,
                             DenseTensor* logdet) {
  auto input_dim = vectorize(x.dims());
  auto input_dim_size = input_dim.size();

  auto batch_count = detail::GetBatchCount(x.dims());
  VLOG(3) << "input dim:" << x.dims();
  PADDLE_ENFORCE_GE(
      input_dim_size,
      2,
      errors::InvalidArgument("the input matrix dimension size should greater "
                              "than or equal to 2."));
  PADDLE_ENFORCE_EQ(
      input_dim[input_dim_size - 1],
      input_dim[input_dim_size - 2],
      errors::InvalidArgument("the input matrix should be square matrix."));
  auto rank = input_dim[input_dim_size - 1];  // square matrix length
  SlogDeterminantV2Functor<T, Context>()(
      dev_ctx, x, rank, batch_count, sign, logdet);
  VLOG(3) << "sign dim:" << sign->dims();
}

}  // namespace phi