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/* Copyright 2015 The TensorFlow 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.
==============================================================================*/
// See docs in ../ops/linalg_ops.cc.
#include "third_party/eigen3/Eigen/Core"
#include "third_party/eigen3/Eigen/LU"
#include "tensorflow/core/framework/kernel_def_builder.h"
#include "tensorflow/core/framework/op_kernel.h"
#include "tensorflow/core/framework/tensor_shape.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/macros.h"
#include "tensorflow/core/platform/types.h"
namespace tensorflow {
template <class Scalar>
class MatrixSolveOp : public LinearAlgebraOp<Scalar> {
public:
typedef LinearAlgebraOp<Scalar> Base;
explicit MatrixSolveOp(OpKernelConstruction* context) : Base(context) {
OP_REQUIRES_OK(context, context->GetAttr("adjoint", &adjoint_));
}
using TensorShapes = typename Base::TensorShapes;
using Matrix = typename Base::Matrix;
using MatrixMaps = typename Base::MatrixMaps;
using ConstMatrixMap = typename Base::ConstMatrixMap;
using ConstMatrixMaps = typename Base::ConstMatrixMaps;
void ValidateInputMatrixShapes(
OpKernelContext* context,
const TensorShapes& input_matrix_shapes) const final {
Base::ValidateSquareSolver(context, input_matrix_shapes);
}
TensorShapes GetOutputMatrixShapes(
const TensorShapes& input_matrix_shapes) const final {
return TensorShapes({TensorShape({input_matrix_shapes[0].dim_size(1),
input_matrix_shapes[1].dim_size(1)})});
}
int64 GetCostPerUnit(const TensorShapes& input_matrix_shapes) const final {
double rows = static_cast<double>(input_matrix_shapes[0].dim_size(0));
double num_rhss = static_cast<double>(input_matrix_shapes[1].dim_size(1));
double cost = rows * rows * (rows + num_rhss);
return cost >= static_cast<double>(kint64max) ? kint64max
: static_cast<int64>(cost);
}
void ComputeMatrix(OpKernelContext* context, const ConstMatrixMaps& inputs,
MatrixMaps* outputs) final {
const ConstMatrixMap& matrix = inputs[0];
const ConstMatrixMap& rhs = inputs[1];
if (matrix.rows() == 0 || rhs.cols() == 0) {
// To be consistent with the MatrixInverse op, we define the solution for
// an empty set of equation as the empty matrix.
return;
}
Eigen::PartialPivLU<Matrix> lu_decomposition(matrix.rows());
if (adjoint_) {
// TODO(rmlarsen): For Eigen 3.2, this creates a temporary copy.
// Make sure to backport: https://bitbucket.org/eigen/eigen/commits/ \
// bd2219a74c96dfe3f6bc2c23588749e36d2d8173
lu_decomposition.compute(matrix.adjoint());
} else {
lu_decomposition.compute(matrix);
}
// PartialPivLU cannot give strong guarantees on invertibility,
// but we can at least guard against exact zero pivots. This can occur as
// a result of basic user mistakes such providing integer valued
// matrices that are exactly singular, or due to underflow if this
// code is run with denormals being flushed to zero.
using RealScalar = typename Base::RealScalar;
const RealScalar min_abs_pivot =
lu_decomposition.matrixLU().diagonal().cwiseAbs().minCoeff();
OP_REQUIRES(context, min_abs_pivot > RealScalar(0),
errors::InvalidArgument("Input matrix is not invertible."));
// TODO(rmlarsen): Add check based on condition number estimation.
// The necessary changes to Eigen are in
// https://bitbucket.org/eigen/eigen/pull-requests/174/ \
// add-matrix-condition-number-estimation/diff
outputs->at(0) = lu_decomposition.solve(rhs);
}
private:
bool adjoint_;
TF_DISALLOW_COPY_AND_ASSIGN(MatrixSolveOp);
};
REGISTER_LINALG_OP("MatrixSolve", (MatrixSolveOp<float>), float);
REGISTER_LINALG_OP("MatrixSolve", (MatrixSolveOp<double>), double);
REGISTER_LINALG_OP("MatrixSolve", (MatrixSolveOp<complex64>), complex64);
REGISTER_LINALG_OP("MatrixSolve", (MatrixSolveOp<complex128>), complex128);
REGISTER_LINALG_OP("BatchMatrixSolve", (MatrixSolveOp<float>), float);
REGISTER_LINALG_OP("BatchMatrixSolve", (MatrixSolveOp<double>), double);
REGISTER_LINALG_OP("BatchMatrixSolve", (MatrixSolveOp<complex64>), complex64);
REGISTER_LINALG_OP("BatchMatrixSolve", (MatrixSolveOp<complex128>), complex128);
} // namespace tensorflow
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