LostTech.TensorFlow : API Documentation

Type LinearOperatorIdentity

Namespace tensorflow.linalg

Parent BaseLinearOperatorIdentity

Interfaces ILinearOperatorIdentity

`LinearOperator` acting like a [batch] square identity matrix.

This operator acts like a [batch] identity matrix `A` with shape `[B1,...,Bb, N, N]` for some `b >= 0`. The first `b` indices index a batch member. For every batch index `(i1,...,ib)`, `A[i1,...,ib, : :]` is an `N x N` matrix. This matrix `A` is not materialized, but for purposes of broadcasting this shape will be relevant.

`LinearOperatorIdentity` is initialized with `num_rows`, and optionally `batch_shape`, and `dtype` arguments. If `batch_shape` is `None`, this operator efficiently passes through all arguments. If `batch_shape` is provided, broadcasting may occur, which will require making copies. ### Shape compatibility

This operator acts on [batch] matrix with compatible shape. `x` is a batch matrix with compatible shape for `matmul` and `solve` if

``` operator.shape = [B1,...,Bb] + [N, N], with b >= 0 x.shape = [C1,...,Cc] + [N, R], and [C1,...,Cc] broadcasts with [B1,...,Bb] to [D1,...,Dd] ```

### Performance

If `batch_shape` initialization arg is `None`:

* `operator.matmul(x)` is `O(1)` * `operator.solve(x)` is `O(1)` * `operator.determinant()` is `O(1)`

If `batch_shape` initialization arg is provided, and static checks cannot rule out the need to broadcast:

* `operator.matmul(x)` is `O(D1*...*Dd*N*R)` * `operator.solve(x)` is `O(D1*...*Dd*N*R)` * `operator.determinant()` is `O(B1*...*Bb)`

#### Matrix property hints

This `LinearOperator` is initialized with boolean flags of the form `is_X`, for `X = non_singular, self_adjoint, positive_definite, square`. These have the following meaning:

* If `is_X == True`, callers should expect the operator to have the property `X`. This is a promise that should be fulfilled, but is *not* a runtime assert. For example, finite floating point precision may result in these promises being violated. * If `is_X == False`, callers should expect the operator to not have `X`. * If `is_X == None` (the default), callers should have no expectation either way.
Show Example 
# Create a 2 x 2 identity matrix.
            operator = LinearOperatorIdentity(num_rows=2, dtype=tf.float32) 
 operator.to_dense()
==> [[1., 0.]
     [0., 1.]] 
 operator.shape
==> [2, 2] 
 operator.log_abs_determinant()
==> 0. 
 x =... Shape [2, 4] Tensor
operator.matmul(x)
==> Shape [2, 4] Tensor, same as x. 
 y = tf.random.normal(shape=[3, 2, 4])
# Note that y.shape is compatible with operator.shape because operator.shape
# is broadcast to [3, 2, 2].
# This broadcast does NOT require copying data, since we can infer that y
# will be passed through without changing shape.  We are always able to infer
# this if the operator has no batch_shape.
x = operator.solve(y)
==> Shape [3, 2, 4] Tensor, same as y. 
 # Create a 2-batch of 2x2 identity matrices
operator = LinearOperatorIdentity(num_rows=2, batch_shape=[2])
operator.to_dense()
==> [[[1., 0.]
      [0., 1.]],
     [[1., 0.]
      [0., 1.]]] 
 # Here, even though the operator has a batch shape, the input is the same as
# the output, so x can be passed through without a copy.  The operator is able
# to detect that no broadcast is necessary because both x and the operator
# have statically defined shape.
x =... Shape [2, 2, 3]
operator.matmul(x)
==> Shape [2, 2, 3] Tensor, same as x 
 # Here the operator and x have different batch_shape, and are broadcast.
# This requires a copy, since the output is different size than the input.
x =... Shape [1, 2, 3]
operator.matmul(x)
==> Shape [2, 2, 3] Tensor, equal to [x, x]

Methods

Properties

Public static methods

LinearOperatorIdentity NewDyn(object num_rows, object batch_shape, object dtype, ImplicitContainer<T> is_non_singular, ImplicitContainer<T> is_self_adjoint, ImplicitContainer<T> is_positive_definite, ImplicitContainer<T> is_square, ImplicitContainer<T> assert_proper_shapes, ImplicitContainer<T> name)

Initialize a `LinearOperatorIdentity`.

The `LinearOperatorIdentity` is initialized with arguments defining `dtype` and shape.

This operator is able to broadcast the leading (batch) dimensions, which sometimes requires copying data. If `batch_shape` is `None`, the operator can take arguments of any batch shape without copying. See examples.
Parameters
object num_rows
Scalar non-negative integer `Tensor`. Number of rows in the corresponding identity matrix.
object batch_shape
Optional `1-D` integer `Tensor`. The shape of the leading dimensions. If `None`, this operator has no leading dimensions.
object dtype
Data type of the matrix that this operator represents.
ImplicitContainer<T> is_non_singular
Expect that this operator is non-singular.
ImplicitContainer<T> is_self_adjoint
Expect that this operator is equal to its hermitian transpose.
ImplicitContainer<T> is_positive_definite
Expect that this operator is positive definite, meaning the quadratic form `x^H A x` has positive real part for all nonzero `x`. Note that we do not require the operator to be self-adjoint to be positive-definite. See: https://en.wikipedia.org/wiki/Positive-definite_matrix#Extension_for_non-symmetric_matrices
ImplicitContainer<T> is_square
Expect that this operator acts like square [batch] matrices.
ImplicitContainer<T> assert_proper_shapes
Python `bool`. If `False`, only perform static checks that initialization and method arguments have proper shape. If `True`, and static checks are inconclusive, add asserts to the graph.
ImplicitContainer<T> name
A name for this `LinearOperator`

Public properties

object batch_shape get;

object batch_shape_dyn get;

Dimension domain_dimension get;

object domain_dimension_dyn get;

object dtype get;

object dtype_dyn get;

IList<object> graph_parents get;

object graph_parents_dyn get;

Nullable<bool> is_non_singular get;

object is_non_singular_dyn get;

object is_positive_definite get;

object is_positive_definite_dyn get;

object is_self_adjoint get;

object is_self_adjoint_dyn get;

Nullable<bool> is_square get;

object is_square_dyn get;

object name get;

object name_dyn get;

object name_scope get;

object name_scope_dyn get;

object PythonObject get;

Dimension range_dimension get;

object range_dimension_dyn get;

TensorShape shape get;

object shape_dyn get;

ValueTuple<object> submodules get;

object submodules_dyn get;

Nullable<int> tensor_rank get;

object tensor_rank_dyn get;

object trainable_variables get;

object trainable_variables_dyn get;

object variables get;

object variables_dyn get;