# LostTech.TensorFlow : API Documentation

Type LinearOperatorDiag

Namespace tensorflow.linalg

Parent LinearOperator

Interfaces ILinearOperatorDiag

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

This operator acts like a [batch] diagonal 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.

`LinearOperatorDiag` is initialized with a (batch) vector. #### 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

Suppose `operator` is a `LinearOperatorDiag` of shape `[N, N]`, and `x.shape = [N, R]`. Then

* `operator.matmul(x)` involves `N * R` multiplications. * `operator.solve(x)` involves `N` divisions and `N * R` multiplications. * `operator.determinant()` involves a size `N` `reduce_prod`.

If instead `operator` and `x` have shape `[B1,...,Bb, N, N]` and `[B1,...,Bb, N, R]`, every operation increases in complexity by `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 diagonal linear operator.
diag = [1., -1.]
operator = LinearOperatorDiag(diag)  operator.to_dense()
==> [[1.,  0.]
[0., -1.]]  operator.shape
==> [2, 2]  operator.log_abs_determinant()
==> scalar Tensor  x =... Shape [2, 4] Tensor
operator.matmul(x)
==> Shape [2, 4] Tensor  # Create a [2, 3] batch of 4 x 4 linear operators.
diag = tf.random.normal(shape=[2, 3, 4])
operator = LinearOperatorDiag(diag)  # Create a shape [2, 1, 4, 2] vector.  Note that this shape is compatible
# since the batch dimensions, [2, 1], are broadcast to
# operator.batch_shape = [2, 3].
y = tf.random.normal(shape=[2, 1, 4, 2])
x = operator.solve(y)
==> operator.matmul(x) = y ```