def _solvevec(self, rhs, adjoint=False): """Default implementation of _solvevec.""" rhs_mat = array_ops.expand_dims(rhs, axis=-1) solution_mat = self.solve(rhs_mat, adjoint=adjoint) return array_ops.squeeze(solution_mat, axis=-1)
def solvevec(self, 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:
```python
# Make an operator acting like batch matrix A. Assume tensor_shape.TensorShape(A.shape) = [..., M, N]
operator = LinearOperator(...)
tensor_shape.TensorShape(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, or list of `Tensor`s
(for blockwise operators). `Tensor`s are treated as [batch] vectors,
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.
"""
with self._name_scope(name): # pylint: disable=not-callable
block_dimensions = (self._block_domain_dimensions() if adjoint
else self._block_range_dimensions())
if linear_operator_util.arg_is_blockwise(block_dimensions, rhs, -1):
for i, block in enumerate(rhs):
if not isinstance(block, linear_operator.LinearOperator):
block = ops.convert_to_tensor(block)
# self._check_input_dtype(block)
block_dimensions[i].assert_is_compatible_with(tensor_shape.TensorShape(block.shape)[-1])
rhs[i] = block
rhs_mat = [array_ops.expand_dims(block, axis=-1) for block in rhs]
solution_mat = self.solve(rhs_mat, adjoint=adjoint)
return [array_ops.squeeze(x, axis=-1) for x in solution_mat]
rhs = ops.convert_to_tensor(rhs, name="rhs")
# self._check_input_dtype(rhs)
op_dimension = (self.domain_dimension if adjoint
else self.range_dimension)
op_dimension.assert_is_compatible_with(tensor_shape.TensorShape(rhs.shape)[-1])
rhs_mat = array_ops.expand_dims(rhs, axis=-1)
solution_mat = self.solve(rhs_mat, adjoint=adjoint)
return array_ops.squeeze(solution_mat, axis=-1)
def _matvec(self, x, adjoint=False): x_mat = array_ops.expand_dims(x, axis=-1) y_mat = self.matmul(x_mat, adjoint=adjoint) return array_ops.squeeze(y_mat, axis=-1)