tfp.experimental.linalg.LinearOperatorPSDKernel

A tf.linalg.LinearOperator representing a kernel covariance matrix.

tfp.experimental.linalg.LinearOperatorPSDKernel(
    kernel_fn,
    x1,
    x2=None,
    kernel_args=None,
    num_matmul_parts=None,
    is_non_singular=None,
    is_self_adjoint=None,
    is_positive_definite=None,
    is_square=None,
    name=None
)

Args
`kernel_fn`	A Python callable which takes `*kernel_args` and returns an instance of `tfp.math.psd_kernels.PositiveSemidefiniteKernel`. As a convenience, an instance may be passed instead of a function, but in this case gradients to kernel hyperparameters will not be available when using `num_matmul_parts`, and `kernel_args` must be `None`.
`x1`	A floating point `Tensor`, the row index points.
`x2`	Optional, a floating point `Tensor`, the column index points. If not provided, uses `x1`.
`kernel_args`	A tuple of arguments (which may themselves be `tf.nest` compatible structures) to be passed to `kernel_fn`. This argument identifies the set of tensors which will have gradients in a `num_matmul_parts`-chunked matmul/backprop.
`num_matmul_parts`	An optional Python `int` specifying the number of partitions into which the matrix should be broken when applying this linear operator. (An extra remainder partition is implied for uneven partitioning.) Because the use-case is avoiding a memory blowup, the partitioned matmul uses `parallel_iterations=1` and `back_prop=False`.
`is_non_singular`	Expect that this operator is non-singular.
`is_self_adjoint`	Expect that this operator is equal to its hermitian transpose. If `dtype` is real, this is equivalent to being symmetric.
`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
`is_square`	Expect that this operator acts like square [batch] matrices.
`name`	Optional name for related ops.

Attributes
`H`	Returns the adjoint of the current `LinearOperator`. Given `A` representing this `LinearOperator`, return `A*`. Note that calling `self.adjoint()` and `self.H` are equivalent.
`batch_shape`	`TensorShape` of batch dimensions of this `LinearOperator`. If this operator acts like the batch matrix `A` with `A.shape = [B1,...,Bb, M, N]`, then this returns `TensorShape([B1,...,Bb])`, equivalent to `A.shape[:-2]`
`domain_dimension`	Dimension (in the sense of vector spaces) of the domain of this operator. If this operator acts like the batch matrix `A` with `A.shape = [B1,...,Bb, M, N]`, then this returns `N`.
`dtype`	The `DType` of `Tensor`s handled by this `LinearOperator`.
`graph_parents`	List of graph dependencies of this `LinearOperator`. (deprecated) Deprecated: THIS FUNCTION IS DEPRECATED. It will be removed in a future version. Instructions for updating: Do not call `graph_parents`.
`is_non_singular`
`is_positive_definite`
`is_self_adjoint`
`is_square`	Return `True/False` depending on if this operator is square.
`kernel_args`
`kernel_fn`
`name`	Name prepended to all ops created by this `LinearOperator`.
`name_scope`	Returns a `tf.name_scope` instance for this class.
`non_trainable_variables`	Sequence of non-trainable variables owned by this module and its submodules. Note: this method uses reflection to find variables on the current instance and submodules. For performance reasons you may wish to cache the result of calling this method if you don't expect the return value to change.
`parameters`	Dictionary of parameters used to instantiate this `LinearOperator`.
`range_dimension`	Dimension (in the sense of vector spaces) of the range of this operator. If this operator acts like the batch matrix `A` with `A.shape = [B1,...,Bb, M, N]`, then this returns `M`.
`shape`	`TensorShape` of this `LinearOperator`. If this operator acts like the batch matrix `A` with `A.shape = [B1,...,Bb, M, N]`, then this returns `TensorShape([B1,...,Bb, M, N])`, equivalent to `A.shape`.
`submodules`	Sequence of all sub-modules. Submodules are modules which are properties of this module, or found as properties of modules which are properties of this module (and so on). `a = tf.Module()` `b = tf.Module()` `c = tf.Module()` `a.b = b` `b.c = c` `list(a.submodules) == [b, c]` `True` `list(b.submodules) == [c]` `True` `list(c.submodules) == []` `True`
`tensor_rank`	Rank (in the sense of tensors) of matrix corresponding to this operator. If this operator acts like the batch matrix `A` with `A.shape = [B1,...,Bb, M, N]`, then this returns `b + 2`.
`trainable_variables`	Sequence of trainable variables owned by this module and its submodules. Note: this method uses reflection to find variables on the current instance and submodules. For performance reasons you may wish to cache the result of calling this method if you don't expect the return value to change.
`variables`	Sequence of variables owned by this module and its submodules. Note: this method uses reflection to find variables on the current instance and submodules. For performance reasons you may wish to cache the result of calling this method if you don't expect the return value to change.
`x1`
`x2`

Methods

`add_to_tensor`

add_to_tensor(
    x, name='add_to_tensor'
)

Add matrix represented by this operator to x. Equivalent to A + x.

Args
`x`	`Tensor` with same `dtype` and shape broadcastable to `self.shape`.
`name`	A name to give this `Op`.

Returns
A `Tensor` with broadcast shape and same `dtype` as `self`.

`adjoint`

adjoint(
    name: str = 'adjoint'
) -> 'LinearOperator'

Returns the adjoint of the current LinearOperator.

Given A representing this LinearOperator, return A*. Note that calling self.adjoint() and self.H are equivalent.

Args
`name`	A name for this `Op`.

Returns
`LinearOperator` which represents the adjoint of this `LinearOperator`.

`assert_non_singular`

assert_non_singular(
    name='assert_non_singular'
)

Returns an Op that asserts this operator is non singular.

This operator is considered non-singular if

ConditionNumber < max{100, range_dimension, domain_dimension} * eps,
eps := np.finfo(self.dtype.as_numpy_dtype).eps

Args
`name`	A string name to prepend to created ops.

Returns
An `Assert` `Op`, that, when run, will raise an `InvalidArgumentError` if the operator is singular.

`assert_positive_definite`

assert_positive_definite(
    name='assert_positive_definite'
)

Returns an Op that asserts this operator is positive definite.

Here, positive definite means that 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.

Args
`name`	A name to give this `Op`.

Returns
An `Assert` `Op`, that, when run, will raise an `InvalidArgumentError` if the operator is not positive definite.

`assert_self_adjoint`

assert_self_adjoint(
    name='assert_self_adjoint'
)

Returns an Op that asserts this operator is self-adjoint.

Here we check that this operator is exactly equal to its hermitian transpose.

Args
`name`	A string name to prepend to created ops.

Returns
An `Assert` `Op`, that, when run, will raise an `InvalidArgumentError` if the operator is not self-adjoint.

`batch_shape_tensor`

batch_shape_tensor(
    name='batch_shape_tensor'
)

Shape of batch dimensions of this operator, determined at runtime.

If this operator acts like the batch matrix A with A.shape = [B1,...,Bb, M, N], then this returns a Tensor holding [B1,...,Bb].

Args
`name`	A name for this `Op`.

Returns
`int32` `Tensor`

`cholesky`

cholesky(
    name: str = 'cholesky'
) -> 'LinearOperator'

Returns a Cholesky factor as a LinearOperator.

Given A representing this LinearOperator, if A is positive definite self-adjoint, return L, where A = L L^T, i.e. the cholesky decomposition.

Args
`name`	A name for this `Op`.

Returns
`LinearOperator` which represents the lower triangular matrix in the Cholesky decomposition.

Raises
`ValueError`	When the `LinearOperator` is not hinted to be positive definite and self adjoint.

`col`

View source

col(
    index
)

Gets a column from the dense operator.

Args
`index`	The index (indices) of the column[s] to get, may be scalar or up to batch shape. Suggest int64 dtype if using with GPU.

Returns
`cols`	Column[s] of the matrix, with shape `(...batch_shape..., num_rows)`. Effectively the same as `operator.to_dense()[..., index]` for a scalar `index`, analogous to gather for non-scalar.

`cond`

cond(
    name='cond'
)

Returns the condition number of this linear operator.

Args
`name`	A name for this `Op`.

Returns
Shape `[B1,...,Bb]` `Tensor` of same `dtype` as `self`.

`determinant`

determinant(
    name='det'
)

Determinant for every batch member.

Args
`name`	A name for this `Op`.

Returns
`Tensor` with shape `self.batch_shape` and same `dtype` as `self`.

Raises
`NotImplementedError`	If `self.is_square` is `False`.

`diag_part`

diag_part(
    name='diag_part'
)

Efficiently get the [batch] diagonal part of this operator.

If this operator has shape [B1,...,Bb, M, N], this returns a Tensor diagonal, of shape [B1,...,Bb, min(M, N)], where diagonal[b1,...,bb, i] = self.to_dense()[b1,...,bb, i, i].

my_operator = LinearOperatorDiag([1., 2.])

# Efficiently get the diagonal
my_operator.diag_part()
==> [1., 2.]

# Equivalent, but inefficient method
tf.linalg.diag_part(my_operator.to_dense())
==> [1., 2.]

Args
`name`	A name for this `Op`.

Returns
`diag_part`	A `Tensor` of same `dtype` as self.

`domain_dimension_tensor`

domain_dimension_tensor(
    name='domain_dimension_tensor'
)

Dimension (in the sense of vector spaces) of the domain of this operator.

Determined at runtime.

If this operator acts like the batch matrix A with A.shape = [B1,...,Bb, M, N], then this returns N.

Args
`name`	A name for this `Op`.

Returns
`int32` `Tensor`

`eigvals`

eigvals(
    name='eigvals'
)

Returns the eigenvalues of this linear operator.

If the operator is marked as self-adjoint (via is_self_adjoint) this computation can be more efficient.

Args
`name`	A name for this `Op`.

Returns
Shape `[B1,...,Bb, N]` `Tensor` of same `dtype` as `self`.

`inverse`

inverse(
    name: str = 'inverse'
) -> 'LinearOperator'

Returns the Inverse of this LinearOperator.

Given A representing this LinearOperator, return a LinearOperator representing A^-1.

Args
`name`	A name scope to use for ops added by this method.

Returns
`LinearOperator` representing inverse of this matrix.

Raises
`ValueError`	When the `LinearOperator` is not hinted to be `non_singular`.

`log_abs_determinant`

log_abs_determinant(
    name='log_abs_det'
)

Log absolute value of determinant for every batch member.

Args
`name`	A name for this `Op`.

Returns
`Tensor` with shape `self.batch_shape` and same `dtype` as `self`.

Raises
`NotImplementedError`	If `self.is_square` is `False`.

`matmul`

matmul(
    x, adjoint=False, adjoint_arg=False, name='matmul'
)

Transform [batch] matrix x with left multiplication: x --> Ax.

# Make an operator acting like batch matrix A.  Assume A.shape = [..., M, N]
operator = LinearOperator(...)
operator.shape = [..., M, N]

X = ... # shape [..., N, R], batch matrix, R > 0.

Y = operator.matmul(X)
Y.shape
==> [..., M, R]

Y[..., :, r] = sum_j A[..., :, j] X[j, r]

Args
`x`	`LinearOperator` or `Tensor` with compatible shape and same `dtype` as `self`. See class docstring for definition of compatibility.
`adjoint`	Python `bool`. If `True`, left multiply by the adjoint: `A^H x`.
`adjoint_arg`	Python `bool`. If `True`, compute `A x^H` where `x^H` is the hermitian transpose (transposition and complex conjugation).
`name`	A name for this `Op`.

Returns
A `LinearOperator` or `Tensor` with shape `[..., M, R]` and same `dtype` as `self`.

`matvec`

matvec(
    x, adjoint=False, name='matvec'
)

Transform [batch] vector x with left multiplication: x --> Ax.

# Make an operator acting like batch matrix A.  Assume A.shape = [..., M, N]
operator = LinearOperator(...)

X = ... # shape [..., N], batch vector

Y = operator.matvec(X)
Y.shape
==> [..., M]

Y[..., :] = sum_j A[..., :, j] X[..., j]

Args
`x`	`Tensor` with compatible shape and same `dtype` as `self`. `x` is treated as a [batch] vector meaning for every set of leading dimensions, the last dimension defines a vector. See class docstring for definition of compatibility.
`adjoint`	Python `bool`. If `True`, left multiply by the adjoint: `A^H x`.
`name`	A name for this `Op`.

Returns
A `Tensor` with shape `[..., M]` and same `dtype` as `self`.

`range_dimension_tensor`

range_dimension_tensor(
    name='range_dimension_tensor'
)

Dimension (in the sense of vector spaces) of the range of this operator.

Determined at runtime.

If this operator acts like the batch matrix A with A.shape = [B1,...,Bb, M, N], then this returns M.

Args
`name`	A name for this `Op`.

Returns
`int32` `Tensor`

`row`

View source

row(
    index
)

Gets a row from the dense operator.

Args
`index`	The index (indices) of the row[s] to get, may be scalar or up to batch shape. Suggest int64 dtype if using with GPU.

Returns
`rows`	Row[s] of the matrix, with shape `(...batch_shape..., num_cols)`. Effectively the same as `operator.to_dense()[..., index, :]` for a scalar `index`, analogous to gather for non-scalar.

`shape_tensor`

shape_tensor(
    name='shape_tensor'
)

Shape of this LinearOperator, determined at runtime.

If this operator acts like the batch matrix A with A.shape = [B1,...,Bb, M, N], then this returns a Tensor holding [B1,...,Bb, M, N], equivalent to tf.shape(A).

Args
`name`	A name for this `Op`.

Returns
`int32` `Tensor`

`solve`

solve(
    rhs, adjoint=False, adjoint_arg=False, name='solve'
)

Solve (exact or approx) R (batch) systems of equations: A X = rhs.

The returned Tensor will be close to an exact solution if A is well conditioned. Otherwise closeness will vary. See class docstring for details.

Examples:

# Make an operator acting like batch matrix A.  Assume A.shape = [..., M, N]
operator = LinearOperator(...)
operator.shape = [..., M, N]

# Solve R > 0 linear systems for every member of the batch.
RHS = ... # shape [..., M, R]

X = operator.solve(RHS)
# X[..., :, r] is the solution to the r'th linear system
# sum_j A[..., :, j] X[..., j, r] = RHS[..., :, r]

operator.matmul(X)
==> RHS

Args
`rhs`	`Tensor` with same `dtype` as this operator and compatible shape. `rhs` is treated like a [batch] matrix meaning for every set of leading dimensions, the last two dimensions defines a matrix. See class docstring for definition of compatibility.
`adjoint`	Python `bool`. If `True`, solve the system involving the adjoint of this `LinearOperator`: `A^H X = rhs`.
`adjoint_arg`	Python `bool`. If `True`, solve `A X = rhs^H` where `rhs^H` is the hermitian transpose (transposition and complex conjugation).
`name`	A name scope to use for ops added by this method.

Returns
`Tensor` with shape `[...,N, R]` and same `dtype` as `rhs`.

Raises
`NotImplementedError`	If `self.is_non_singular` or `is_square` is False.

`solvevec`

solvevec(
    rhs, adjoint=False, name='solve'
)

Solve single equation with best effort: A X = rhs.

The returned Tensor will be close to an exact solution if A is well conditioned. Otherwise closeness will vary. See class docstring for details.

Examples:

# Make an operator acting like batch matrix A.  Assume A.shape = [..., M, N]
operator = LinearOperator(...)
operator.shape = [..., M, N]

# Solve one linear system for every member of the batch.
RHS = ... # shape [..., M]

X = operator.solvevec(RHS)
# X is the solution to the linear system
# sum_j A[..., :, j] X[..., j] = RHS[..., :]

operator.matvec(X)
==> RHS

Args
`rhs`	`Tensor` with same `dtype` as this operator. `rhs` is treated like a [batch] vector meaning for every set of leading dimensions, the last dimension defines a vector. See class docstring for definition of compatibility regarding batch dimensions.
`adjoint`	Python `bool`. If `True`, solve the system involving the adjoint of this `LinearOperator`: `A^H X = rhs`.
`name`	A name scope to use for ops added by this method.

Returns
`Tensor` with shape `[...,N]` and same `dtype` as `rhs`.

Raises
`NotImplementedError`	If `self.is_non_singular` or `is_square` is False.

`tensor_rank_tensor`

tensor_rank_tensor(
    name='tensor_rank_tensor'
)

Rank (in the sense of tensors) of matrix corresponding to this operator.

If this operator acts like the batch matrix A with A.shape = [B1,...,Bb, M, N], then this returns b + 2.

Args
`name`	A name for this `Op`.

Returns
`int32` `Tensor`, determined at runtime.

`to_dense`

to_dense(
    name='to_dense'
)

Return a dense (batch) matrix representing this operator.

`trace`

trace(
    name='trace'
)

Trace of the linear operator, equal to sum of self.diag_part().

If the operator is square, this is also the sum of the eigenvalues.

Args
`name`	A name for this `Op`.

Returns
Shape `[B1,...,Bb]` `Tensor` of same `dtype` as `self`.

`with_name_scope`

@classmethod
with_name_scope(
    method
)

Decorator to automatically enter the module name scope.

class MyModule(tf.Module):
  @tf.Module.with_name_scope
  def __call__(self, x):
    if not hasattr(self, 'w'):
      self.w = tf.Variable(tf.random.normal([x.shape[1], 3]))
    return tf.matmul(x, self.w)

Using the above module would produce tf.Variables and tf.Tensors whose names included the module name:

mod = MyModule()
mod(tf.ones([1, 2]))
<tf.Tensor: shape=(1, 3), dtype=float32, numpy=..., dtype=float32)>
mod.w
<tf.Variable 'my_module/Variable:0' shape=(2, 3) dtype=float32,
numpy=..., dtype=float32)>

Args
`method`	The method to wrap.

Returns
The original method wrapped such that it enters the module's name scope.

`getitem`

__getitem__(
    slices
)

`matmul`

__matmul__(
    other
)

tfp.experimental.linalg.LinearOperatorPSDKernel

Args

Attributes

Methods

add_to_tensor

adjoint

assert_non_singular

assert_positive_definite

assert_self_adjoint

batch_shape_tensor

cholesky

col

cond

determinant

diag_part

domain_dimension_tensor

eigvals

inverse

log_abs_determinant

matmul

matvec

range_dimension_tensor

row

shape_tensor

solve

Examples:

solvevec

Examples:

tensor_rank_tensor

to_dense

trace

with_name_scope

__getitem__

__matmul__

`add_to_tensor`

`adjoint`

`assert_non_singular`

`assert_positive_definite`

`assert_self_adjoint`

`batch_shape_tensor`

`cholesky`

`col`

`cond`

`determinant`

`diag_part`

`domain_dimension_tensor`

`eigvals`

`inverse`

`log_abs_determinant`

`matmul`

`matvec`

`range_dimension_tensor`

`row`

`shape_tensor`

`solve`

`solvevec`

`tensor_rank_tensor`

`to_dense`

`trace`

`with_name_scope`

`getitem`

`matmul`