tfp.experimental.linalg.LinearOperatorUnitary

Encapsulates a Unitary Linear Operator.

tfp.experimental.linalg.LinearOperatorUnitary(
    matrix,
    is_non_singular=None,
    is_self_adjoint=None,
    is_positive_definite=None,
    is_square=None,
    name='LinearOperatorUnitary'
)

Args
matrix	Shape [B1,...,Bb, N, N] Tensor with b >= 0 N >= 0. The orthogonal matrix.
is_non_singular	Expect that this operator is non-singular.
is_self_adjoint	Expect that this operator is equal to its hermitian transpose. If diag.dtype is real, this is auto-set to True.
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	A name for this LinearOperator.

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 Tensors 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.
matrix
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.

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.

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.

Note: This currently only supports self-adjoint operators.

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

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 &#x27;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
)