

``mx.symbol.linalg_slogdet``
========================================================

Description
----------------------

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. 
.. note:: No gradient is backwarded when A is non-invertible. Please see           the docs of operator det for detail.


**Example**::

	 
	 Single matrix signed log determinant
	 A = [[2., 3.], [1., 4.]]
	 sign, logabsdet = slogdet(A)
	 sign = [1.]
	 logabsdet = [1.609438]
	 
	 Batch matrix signed log determinant
	 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]
	 
	 
Usage
----------

.. code:: r

	mx.symbol.linalg_slogdet(...)

Arguments
------------------

+----------------------------------------+------------------------------------------------------------+
| Argument                               | Description                                                |
+========================================+============================================================+
| ``A``                                  | NDArray-or-Symbol.                                         |
|                                        |                                                            |
|                                        | Tensor of square matrix                                    |
+----------------------------------------+------------------------------------------------------------+
| ``name``                               | string, optional.                                          |
|                                        |                                                            |
|                                        | Name of the resulting symbol.                              |
+----------------------------------------+------------------------------------------------------------+

Value
----------

``out`` The result mx.symbol


Link to Source Code: http://github.com/apache/incubator-mxnet/blob/1.6.0/src/operator/tensor/la_op.cc#L1031