arcadiaphy commented on a change in pull request #15007: Add matrix determinant
operator in linalg
URL: https://github.com/apache/incubator-mxnet/pull/15007#discussion_r287312933
##########
File path: src/operator/tensor/la_op.cc
##########
@@ -939,5 +939,153 @@ NNVM_REGISTER_OP(_backward_linalg_inverse)
.set_attr<nnvm::TIsBackward>("TIsBackward", true)
.set_attr<FCompute>("FCompute<cpu>", LaOpBackward<cpu, 2, 2, 2, 1,
inverse_backward>);
+NNVM_REGISTER_OP(_linalg_det)
+.add_alias("linalg_det")
+.describe(R"code(Compute the determinant of a matrix.
+Input is a tensor *A* of dimension *n >= 2*.
+
+If *n=2*, *A* is a square matrix. We compute:
+
+ *out* = *det(A)*
+
+If *n>2*, *det* is performed separately on the trailing two dimensions
+for all inputs (batch mode).
+
+.. note:: The operator supports float32 and float64 data types only.
+
+Examples::
+
+ Single matrix inversion
+ A = [[1., 4.], [2., 3.]]
+ det(A) = [-5.]
+
+ Batch matrix inversion
+ A = [[[1., 4.], [2., 3.]],
+ [[2., 3.], [1., 4.]]]
+ det(A) = [-5., 5.]
+)code" ADD_FILELINE)
+.set_num_inputs(1)
+.set_num_outputs(3)
+.set_attr<nnvm::FListInputNames>("FListInputNames", [](const NodeAttrs& attrs)
+ { return std::vector<std::string>{"A"}; })
+.set_attr<nnvm::FNumVisibleOutputs>("FNumVisibleOutputs", [](const NodeAttrs&
attrs) {
+ return 1; })
+.set_attr<mxnet::FInferShape>("FInferShape", DetShape<1>)
+.set_attr<nnvm::FInferType>("FInferType", DetType<1>)
+.set_attr<FResourceRequest>("FResourceRequest", [](const NodeAttrs& attrs)
+ { return std::vector<ResourceRequest>{ResourceRequest::kTempSpace}; })
+.set_attr<FCompute>("FCompute<cpu>", LaOpDetForward<cpu, 1, det>)
+.set_attr<nnvm::FGradient>("FGradient",
ReduceDetGrad<1>{"_backward_linalg_det"})
+.add_argument("A", "NDArray-or-Symbol", "Tensor of square matrix");
+
+NNVM_REGISTER_OP(_backward_linalg_det)
+.set_num_inputs(4)
+.set_num_outputs(1)
+.set_attr<FResourceRequest>("FResourceRequest", [](const NodeAttrs& attrs)
+ { return std::vector<ResourceRequest>{ResourceRequest::kTempSpace}; })
+.set_attr<nnvm::TIsBackward>("TIsBackward", true)
+.set_attr<FCompute>("FCompute<cpu>", LaOpDetBackward<cpu, 1, det_backward>);
+
+NNVM_REGISTER_OP(_linalg_logdet)
+.add_alias("linalg_logdet")
+.describe(R"code(Compute the log determinant of a matrix.
+Input is a tensor *A* of dimension *n >= 2*.
+
+If *n=2*, *A* is a square matrix. We compute:
+
+ *out* = *log(det(A))*
+
+If *n>2*, *logdet* is performed separately on the trailing two dimensions
+for all inputs (batch mode).
+
+.. note:: The operator supports float32 and float64 data types only.
+
+Examples::
+
+ Single matrix inversion
+ A = [[2., 3.], [1., 4.]]
+ logdet(A) = [1.609438]
+
+ Batch matrix inversion
+ A = [[[2., 3.], [1., 4.]],
+ [[1., 2.], [2., 4.]],
+ [[1., 2.], [4., 3.]]]
+ logdet(A) = [1.609438, -inf, nan]
+)code" ADD_FILELINE)
+.set_num_inputs(1)
+.set_num_outputs(3)
+.set_attr<nnvm::FListInputNames>("FListInputNames", [](const NodeAttrs& attrs)
+ { return std::vector<std::string>{"A"}; })
+.set_attr<nnvm::FNumVisibleOutputs>("FNumVisibleOutputs", [](const NodeAttrs&
attrs) {
+ return 1; })
+.set_attr<mxnet::FInferShape>("FInferShape", DetShape<1>)
+.set_attr<nnvm::FInferType>("FInferType", DetType<1>)
+.set_attr<FResourceRequest>("FResourceRequest", [](const NodeAttrs& attrs)
+ { return std::vector<ResourceRequest>{ResourceRequest::kTempSpace}; })
+.set_attr<FCompute>("FCompute<cpu>", LaOpDetForward<cpu, 1, logdet>)
+.set_attr<nnvm::FGradient>("FGradient",
ReduceDetGrad<1>{"_backward_linalg_logdet"})
+.add_argument("A", "NDArray-or-Symbol", "Tensor of square matrix");
+
+NNVM_REGISTER_OP(_backward_linalg_logdet)
+.set_num_inputs(4)
+.set_num_outputs(1)
+.set_attr<FResourceRequest>("FResourceRequest", [](const NodeAttrs& attrs)
+ { return std::vector<ResourceRequest>{ResourceRequest::kTempSpace}; })
+.set_attr<nnvm::TIsBackward>("TIsBackward", true)
+.set_attr<FCompute>("FCompute<cpu>", LaOpDetBackward<cpu, 1, logdet_backward>);
+
+NNVM_REGISTER_OP(_linalg_slogdet)
+.add_alias("linalg_slogdet")
+.describe(R"code(Compute the sign and log of the determinant of a matrix.
+Input is a tensor *A* of dimension *n >= 2*.
+
+If *n=2*, *A* is a square matrix. We compute:
+
+ *sign* = *sign(det(A))*
+ *logabsdet* = *log(abs(det(A)))*
+
+If *n>2*, *slogdet* is performed separately on the trailing two dimensions
+for all inputs (batch mode).
+
+.. note:: The operator supports float32 and float64 data types only.
+.. note:: The gradient is not properly defined on sign, so the gradient of
+ it is not backwarded.
+
+Examples::
+
+ Single matrix inversion
+ A = [[2., 3.], [1., 4.]]
+ sign, logabsdet = slogdet(A)
+ sign = [1.]
+ logabsdet = [1.609438]
+
+ Batch matrix inversion
+ A = [[[2., 3.], [1., 4.]],
+ [[1., 2.], [2., 4.]],
+ [[1., 2.], [4., 3.]]]
+ sign, logabsdet = slogdet(A)
+ sign = [1., 0., -1.]
+ logabsdet = [1.609438, -inf, 1.609438]
+)code" ADD_FILELINE)
+.set_num_inputs(1)
+.set_num_outputs(4)
+.set_attr<nnvm::FListInputNames>("FListInputNames", [](const NodeAttrs& attrs)
+ { return std::vector<std::string>{"A"}; })
+.set_attr<nnvm::FNumVisibleOutputs>("FNumVisibleOutputs", [](const NodeAttrs&
attrs) {
+ return 2; })
+.set_attr<mxnet::FInferShape>("FInferShape", DetShape<2>)
+.set_attr<nnvm::FInferType>("FInferType", DetType<2>)
Review comment:
If canonical type inference is used, then pivot tensor has different sizes
for float and double. I need to calculate how much DType space is enough to
hold pivot integers like what's done in workspace estimate. I think just use
int is more clear and simple here.
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