// See docs in ../ops/linalg_ops.cc.
// TODO(konstantinos): Enable complex inputs. This will require additional tests
//                     and OP_REQUIRES.

#include <cmath>

#include "tensorflow/core/framework/kernel_def_builder.h"
#include "tensorflow/core/framework/op_kernel.h"
#include "tensorflow/core/kernels/linalg_ops_common.h"
#include "tensorflow/core/lib/core/errors.h"
#include "tensorflow/core/platform/logging.h"
#include "tensorflow/core/platform/port.h"
#include "tensorflow/core/public/tensor_shape.h"
#include "third_party/eigen3/Eigen/Cholesky"

namespace tensorflow {

template <class Scalar, bool SupportsBatchOperationT>
class CholeskyOp : public LinearAlgebraOp<Scalar, SupportsBatchOperationT> {
 public:
  explicit CholeskyOp(OpKernelConstruction* context)
      : LinearAlgebraOp<Scalar, SupportsBatchOperationT>(context) {}

  TensorShape GetOutputMatrixShape(
      const TensorShape& input_matrix_shape) override {
    return input_matrix_shape;
  }

  int64 GetCostPerUnit(const TensorShape& input_matrix_shape) override {
    const int64 rows = input_matrix_shape.dim_size(0);
    if (rows > (1LL << 20)) {
      // A big number to cap the cost in case overflow.
      return kint32max;
    } else {
      return rows * rows * rows;
    }
  }

  using typename LinearAlgebraOp<Scalar, SupportsBatchOperationT>::MatrixMap;
  using
      typename LinearAlgebraOp<Scalar, SupportsBatchOperationT>::ConstMatrixMap;

  void ComputeMatrix(OpKernelContext* context, const ConstMatrixMap& input,
                     MatrixMap* output) override {
    OP_REQUIRES(context, input.rows() == input.cols(),
                errors::InvalidArgument("Input matrix must be square."));
    if (input.rows() == 0) {
      // If X is an empty matrix (0 rows, 0 col), X * X' == X.
      // Therefore, we return X.
      return;
    }
    // Perform the actual LL^T Cholesky decomposition. This will only use
    // the lower triangular part of data_in by default. The upper triangular
    // part of the matrix will not be read.
    Eigen::LLT<Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic,
                             Eigen::RowMajor>> llt_decomposition(input);

    // Output the lower triangular in a dense form.
    *output = llt_decomposition.matrixL();

    OP_REQUIRES(context, llt_decomposition.info() == Eigen::Success,
                errors::InvalidArgument("LLT decomposition was not successful. "
                                        "The input might not be valid."));
  }
};

REGISTER_LINALG_OP("Cholesky", (CholeskyOp<float, false>), float);
REGISTER_LINALG_OP("Cholesky", (CholeskyOp<double, false>), double);
REGISTER_LINALG_OP("BatchCholesky", (CholeskyOp<float, true>), float);
REGISTER_LINALG_OP("BatchCholesky", (CholeskyOp<double, true>), double);
}  // namespace tensorflow