Source code for pennylane.math.multi_dispatch
# Copyright 2018-2021 Xanadu Quantum Technologies Inc.
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
# http://www.apache.org/licenses/LICENSE-2.0
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""Multiple dispatch functions"""
# pylint: disable=import-outside-toplevel,too-many-return-statements
import functools
from collections.abc import Sequence
import autoray as ar
import numpy as onp
from autograd.numpy.numpy_boxes import ArrayBox
from autoray import numpy as np
from numpy import ndarray
from . import single_dispatch # pylint:disable=unused-import
from .utils import cast, cast_like, get_interface, requires_grad
# pylint:disable=redefined-outer-name
[docs]def array(*args, like=None, **kwargs):
"""Creates an array or tensor object of the target framework.
If the PyTorch interface is specified, this method preserves the Torch device used.
If the JAX interface is specified, this method uses JAX numpy arrays, which do not cause issues with jit tracers.
Returns:
tensor_like: the tensor_like object of the framework
"""
res = np.array(*args, like=like, **kwargs)
if like is not None and get_interface(like) == "torch":
res = res.to(device=like.device)
return res
[docs]def eye(*args, like=None, **kwargs):
"""Creates an identity array or tensor object of the target framework.
This method preserves the Torch device used.
Returns:
tensor_like: the tensor_like object of the framework
"""
res = np.eye(*args, like=like, **kwargs)
if like is not None and get_interface(like) == "torch":
res = res.to(device=like.device)
return res
[docs]def multi_dispatch(argnum=None, tensor_list=None):
r"""Decorater to dispatch arguments handled by the interface.
This helps simplify definitions of new functions inside PennyLane. We can
decorate the function, indicating the arguments that are tensors handled
by the interface:
>>> @qml.math.multi_dispatch(argnum=[0, 1])
... def some_function(tensor1, tensor2, option, like):
... # the interface string is stored in `like`.
... ...
Args:
argnum (list[int]): A list of integers indicating the indices
to dispatch (i.e., the arguments that are tensors handled by an interface).
If ``None``, dispatch over all arguments.
tensor_lists (list[int]): a list of integers indicating which indices
in ``argnum`` are expected to be lists of tensors. If an argument
marked as tensor list is not a ``tuple`` or ``list``, it is treated
as if it was not marked as tensor list. If ``None``, this option is ignored.
Returns:
func: A wrapped version of the function, which will automatically attempt
to dispatch to the correct autodifferentiation framework for the requested
arguments. Note that the ``like`` argument will be optional, but can be provided
if an explicit override is needed.
.. seealso:: :func:`pennylane.math.multi_dispatch._multi_dispatch`
.. note::
This decorator makes the interface argument "like" optional as it utilizes
the utility function `_multi_dispatch` to automatically detect the appropriate
interface based on the tensor types.
**Examples**
We can redefine external functions to be suitable for PennyLane. Here, we
redefine Autoray's ``stack`` function.
>>> stack = multi_dispatch(argnum=0, tensor_list=0)(autoray.numpy.stack)
We can also use the ``multi_dispatch`` decorator to dispatch
arguments of more more elaborate custom functions. Here is an example
of a ``custom_function`` that
computes :math:`c \\sum_i (v_i)^T v_i`, where :math:`v_i` are vectors in ``values`` and
:math:`c` is a fixed ``coefficient``. Note how ``argnum=0`` only points to the first argument ``values``,
how ``tensor_list=0`` indicates that said first argument is a list of vectors, and that ``coefficient`` is not
dispatched.
>>> @math.multi_dispatch(argnum=0, tensor_list=0)
>>> def custom_function(values, like, coefficient=10):
>>> # values is a list of vectors
>>> # like can force the interface (optional)
>>> if like == "tensorflow":
>>> # add interface-specific handling if necessary
>>> return coefficient * np.sum([math.dot(v,v) for v in values])
We can then run
>>> values = [np.array([1, 2, 3]) for _ in range(5)]
>>> custom_function(values)
700
"""
def decorator(fn):
@functools.wraps(fn)
def wrapper(*args, **kwargs):
argnums = argnum if argnum is not None else list(range(len(args)))
tensor_lists = tensor_list if tensor_list is not None else []
if not isinstance(argnums, Sequence):
argnums = [argnums]
if not isinstance(tensor_lists, Sequence):
tensor_lists = [tensor_lists]
dispatch_args = []
for a in argnums:
# Only use extend if the marked argument really
# is a (native) python Sequence
if a in tensor_lists and isinstance(args[a], (list, tuple)):
dispatch_args.extend(args[a])
else:
dispatch_args.append(args[a])
interface = kwargs.pop("like", None)
interface = interface or get_interface(*dispatch_args)
kwargs["like"] = interface
return fn(*args, **kwargs)
return wrapper
return decorator
@multi_dispatch(argnum=[0, 1])
def kron(*args, like=None, **kwargs):
"""The kronecker/tensor product of args."""
if like == "scipy":
return onp.kron(*args, **kwargs) # Dispatch scipy kron to numpy backed specifically.
return ar.numpy.kron(*args, like=like, **kwargs)
[docs]@multi_dispatch(argnum=[0], tensor_list=[0])
def block_diag(values, like=None):
"""Combine a sequence of 2D tensors to form a block diagonal tensor.
Args:
values (Sequence[tensor_like]): Sequence of 2D arrays/tensors to form
the block diagonal tensor.
Returns:
tensor_like: the block diagonal tensor
**Example**
>>> t = [
... np.array([[1, 2], [3, 4]]),
... torch.tensor([[1, 2, 3], [-1, -6, -3]]),
... torch.tensor(5)
... ]
>>> qml.math.block_diag(t)
tensor([[ 1, 2, 0, 0, 0, 0],
[ 3, 4, 0, 0, 0, 0],
[ 0, 0, 1, 2, 3, 0],
[ 0, 0, -1, -6, -3, 0],
[ 0, 0, 0, 0, 0, 5]])
"""
values = np.coerce(values, like=like)
return np.block_diag(values, like=like)
[docs]@multi_dispatch(argnum=[0], tensor_list=[0])
def concatenate(values, axis=0, like=None):
"""Concatenate a sequence of tensors along the specified axis.
.. warning::
Tensors that are incompatible (such as Torch and TensorFlow tensors)
cannot both be present.
Args:
values (Sequence[tensor_like]): Sequence of tensor-like objects to
concatenate. The objects must have the same shape, except in the dimension corresponding
to axis (the first, by default).
axis (int): The axis along which the input tensors are concatenated. If axis is None,
tensors are flattened before use. Default is 0.
Returns:
tensor_like: The concatenated tensor.
**Example**
>>> x = tf.constant([0.6, 0.1, 0.6])
>>> y = tf.Variable([0.1, 0.2, 0.3])
>>> z = np.array([5., 8., 101.])
>>> concatenate([x, y, z])
<tf.Tensor: shape=(3, 3), dtype=float32, numpy=
array([6.00e-01, 1.00e-01, 6.00e-01, 1.00e-01, 2.00e-01, 3.00e-01, 5.00e+00, 8.00e+00, 1.01e+02], dtype=float32)>
"""
if like == "torch":
import torch
device = (
"cuda"
if any(t.device.type == "cuda" for t in values if isinstance(t, torch.Tensor))
else "cpu"
)
if axis is None:
# flatten and then concatenate zero'th dimension
# to reproduce numpy's behaviour
values = [
np.flatten(torch.as_tensor(t, device=torch.device(device))) # pragma: no cover
for t in values
]
axis = 0
else:
values = [
torch.as_tensor(t, device=torch.device(device)) for t in values # pragma: no cover
]
if like == "tensorflow" and axis is None:
# flatten and then concatenate zero'th dimension
# to reproduce numpy's behaviour
values = [np.flatten(np.array(t)) for t in values]
axis = 0
return np.concatenate(values, axis=axis, like=like)
[docs]@multi_dispatch(argnum=[0], tensor_list=[0])
def diag(values, k=0, like=None):
"""Construct a diagonal tensor from a list of scalars.
Args:
values (tensor_like or Sequence[scalar]): sequence of numeric values that
make up the diagonal
k (int): The diagonal in question. ``k=0`` corresponds to the main diagonal.
Use ``k>0`` for diagonals above the main diagonal, and ``k<0`` for
diagonals below the main diagonal.
Returns:
tensor_like: the 2D diagonal tensor
**Example**
>>> x = [1., 2., tf.Variable(3.)]
>>> qml.math.diag(x)
<tf.Tensor: shape=(3, 3), dtype=float32, numpy=
array([[1., 0., 0.],
[0., 2., 0.],
[0., 0., 3.]], dtype=float32)>
>>> y = tf.Variable([0.65, 0.2, 0.1])
>>> qml.math.diag(y, k=-1)
<tf.Tensor: shape=(4, 4), dtype=float32, numpy=
array([[0. , 0. , 0. , 0. ],
[0.65, 0. , 0. , 0. ],
[0. , 0.2 , 0. , 0. ],
[0. , 0. , 0.1 , 0. ]], dtype=float32)>
>>> z = torch.tensor([0.1, 0.2])
>>> qml.math.diag(z, k=1)
tensor([[0.0000, 0.1000, 0.0000],
[0.0000, 0.0000, 0.2000],
[0.0000, 0.0000, 0.0000]])
"""
if isinstance(values, (list, tuple)):
values = np.stack(np.coerce(values, like=like), like=like)
return np.diag(values, k=k, like=like)
@multi_dispatch(argnum=[0, 1])
def matmul(tensor1, tensor2, like=None):
"""Returns the matrix product of two tensors."""
if like == "torch":
if get_interface(tensor1) != "torch":
tensor1 = ar.numpy.asarray(tensor1, like="torch")
if get_interface(tensor2) != "torch":
tensor2 = ar.numpy.asarray(tensor2, like="torch")
tensor2 = cast_like(tensor2, tensor1) # pylint: disable=arguments-out-of-order
return ar.numpy.matmul(tensor1, tensor2, like=like)
[docs]@multi_dispatch(argnum=[0, 1])
def dot(tensor1, tensor2, like=None):
"""Returns the matrix or dot product of two tensors.
* If both tensors are 0-dimensional, elementwise multiplication
is performed and a 0-dimensional scalar returned.
* If both tensors are 1-dimensional, the dot product is returned.
* If the first array is 2-dimensional and the second array 1-dimensional,
the matrix-vector product is returned.
* If both tensors are 2-dimensional, the matrix product is returned.
* Finally, if the the first array is N-dimensional and the second array
M-dimensional, a sum product over the last dimension of the first array,
and the second-to-last dimension of the second array is returned.
Args:
tensor1 (tensor_like): input tensor
tensor2 (tensor_like): input tensor
Returns:
tensor_like: the matrix or dot product of two tensors
"""
x, y = np.coerce([tensor1, tensor2], like=like)
if like == "torch":
if x.ndim == 0 and y.ndim == 0:
return x * y
if x.ndim <= 2 and y.ndim <= 2:
return x @ y
return np.tensordot(x, y, axes=[[-1], [-2]], like=like)
if like in {"tensorflow", "autograd"}:
shape_y = len(np.shape(y))
shape_x = len(np.shape(x))
if shape_x == 0 and shape_y == 0:
return x * y
if shape_y == 1:
return np.tensordot(x, y, axes=[[-1], [0]], like=like)
if shape_x == 2 and shape_y == 2:
return x @ y
return np.tensordot(x, y, axes=[[-1], [-2]], like=like)
return np.dot(x, y, like=like)
[docs]@multi_dispatch(argnum=[0, 1])
def tensordot(tensor1, tensor2, axes=None, like=None):
"""Returns the tensor product of two tensors.
In general ``axes`` specifies either the set of axes for both
tensors that are contracted (with the first/second entry of ``axes``
giving all axis indices for the first/second tensor) or --- if it is
an integer --- the number of last/first axes of the first/second
tensor to contract over.
There are some non-obvious special cases:
* If both tensors are 0-dimensional, ``axes`` must be 0.
and a 0-dimensional scalar is returned containing the simple product.
* If both tensors are 1-dimensional and ``axes=0``, the outer product
is returned.
* Products between a non-0-dimensional and a 0-dimensional tensor are not
supported in all interfaces.
Args:
tensor1 (tensor_like): input tensor
tensor2 (tensor_like): input tensor
axes (int or list[list[int]]): Axes to contract over, see detail description.
Returns:
tensor_like: the tensor product of the two input tensors
"""
tensor1, tensor2 = np.coerce([tensor1, tensor2], like=like)
return np.tensordot(tensor1, tensor2, axes=axes, like=like)
[docs]@multi_dispatch(argnum=[0], tensor_list=[0])
def get_trainable_indices(values, like=None):
"""Returns a set containing the trainable indices of a sequence of
values.
Args:
values (Iterable[tensor_like]): Sequence of tensor-like objects to inspect
Returns:
set[int]: Set containing the indices of the trainable tensor-like objects
within the input sequence.
**Example**
>>> def cost_fn(params):
... print("Trainable:", qml.math.get_trainable_indices(params))
... return np.sum(np.sin(params[0] * params[1]))
>>> values = [np.array([0.1, 0.2], requires_grad=True),
... np.array([0.5, 0.2], requires_grad=False)]
>>> cost_fn(values)
Trainable: {0}
tensor(0.0899685, requires_grad=True)
"""
trainable_params = set()
for idx, p in enumerate(values):
if requires_grad(p, interface=like):
trainable_params.add(idx)
return trainable_params
[docs]def ones_like(tensor, dtype=None):
"""Returns a tensor of all ones with the same shape and dtype
as the input tensor.
Args:
tensor (tensor_like): input tensor
dtype (str, np.dtype, None): The desired output datatype of the array. If not provided, the dtype of
``tensor`` is used. This argument can be any supported NumPy dtype representation, including
a string (``"float64"``), a ``np.dtype`` object (``np.dtype("float64")``), or
a dtype class (``np.float64``). If ``tensor`` is not a NumPy array, the
**equivalent** dtype in the dispatched framework is used.
Returns:
tensor_like: an all-ones tensor with the same shape and
size as ``tensor``
**Example**
>>> x = torch.tensor([1., 2.])
>>> ones_like(x)
tensor([1, 1])
>>> y = tf.Variable([[0], [5]])
>>> ones_like(y, dtype=np.complex128)
<tf.Tensor: shape=(2, 1), dtype=complex128, numpy=
array([[1.+0.j],
[1.+0.j]])>
"""
if dtype is not None:
return cast(np.ones_like(tensor), dtype)
return np.ones_like(tensor)
[docs]@multi_dispatch(argnum=[0], tensor_list=[0])
def stack(values, axis=0, like=None):
"""Stack a sequence of tensors along the specified axis.
.. warning::
Tensors that are incompatible (such as Torch and TensorFlow tensors)
cannot both be present.
Args:
values (Sequence[tensor_like]): Sequence of tensor-like objects to
stack. Each object in the sequence must have the same size in the given axis.
axis (int): The axis along which the input tensors are stacked. ``axis=0`` corresponds
to vertical stacking.
Returns:
tensor_like: The stacked array. The stacked array will have one additional dimension
compared to the unstacked tensors.
**Example**
>>> x = tf.constant([0.6, 0.1, 0.6])
>>> y = tf.Variable([0.1, 0.2, 0.3])
>>> z = np.array([5., 8., 101.])
>>> stack([x, y, z])
<tf.Tensor: shape=(3, 3), dtype=float32, numpy=
array([[6.00e-01, 1.00e-01, 6.00e-01],
[1.00e-01, 2.00e-01, 3.00e-01],
[5.00e+00, 8.00e+00, 1.01e+02]], dtype=float32)>
"""
values = np.coerce(values, like=like)
return np.stack(values, axis=axis, like=like)
[docs]def einsum(indices, *operands, like=None, optimize=None):
"""Evaluates the Einstein summation convention on the operands.
Args:
indices (str): Specifies the subscripts for summation as comma separated list of
subscript labels. An implicit (classical Einstein summation) calculation is
performed unless the explicit indicator ‘->’ is included as well as subscript
labels of the precise output form.
*operands (tuple[tensor_like]): The tensors for the operation.
Returns:
tensor_like: The calculation based on the Einstein summation convention.
**Examples**
>>> a = np.arange(25).reshape(5,5)
>>> b = np.arange(5)
>>> c = np.arange(6).reshape(2,3)
Trace of a matrix:
>>> qml.math.einsum('ii', a)
60
Extract the diagonal (requires explicit form):
>>> qml.math.einsum('ii->i', a)
array([ 0, 6, 12, 18, 24])
Sum over an axis (requires explicit form):
>>> qml.math.einsum('ij->i', a)
array([ 10, 35, 60, 85, 110])
Compute a matrix transpose, or reorder any number of axes:
>>> np.einsum('ij->ji', c)
array([[0, 3],
[1, 4],
[2, 5]])
Matrix vector multiplication:
>>> np.einsum('ij,j', a, b)
array([ 30, 80, 130, 180, 230])
"""
if like is None:
like = get_interface(*operands)
operands = np.coerce(operands, like=like)
if optimize is None or like == "torch":
# torch einsum doesn't support the optimize keyword argument
return np.einsum(indices, *operands, like=like)
if like == "tensorflow":
# Unpacking and casting necessary for higher order derivatives,
# and avoiding implicit fp32 down-conversions.
op1, op2 = operands
op1 = array(op1, like=op1[0], dtype=op1[0].dtype)
op2 = array(op2, like=op2[0], dtype=op2[0].dtype)
return np.einsum(indices, op1, op2, like=like)
return np.einsum(indices, *operands, like=like, optimize=optimize)
[docs]def where(condition, x=None, y=None):
"""Returns elements chosen from x or y depending on a boolean tensor condition,
or the indices of entries satisfying the condition.
The input tensors ``condition``, ``x``, and ``y`` must all be broadcastable to the same shape.
Args:
condition (tensor_like[bool]): A boolean tensor. Where ``True`` , elements from
``x`` will be chosen, otherwise ``y``. If ``x`` and ``y`` are ``None`` the
indices where ``condition==True`` holds will be returned.
x (tensor_like): values from which to choose if the condition evaluates to ``True``
y (tensor_like): values from which to choose if the condition evaluates to ``False``
Returns:
tensor_like or tuple[tensor_like]: If ``x is None`` and ``y is None``, a tensor
or tuple of tensors with the indices where ``condition`` is ``True`` .
Else, a tensor with elements from ``x`` where the ``condition`` is ``True``,
and ``y`` otherwise. In this case, the output tensor has the same shape as
the input tensors.
**Example with three arguments**
>>> a = torch.tensor([0.6, 0.23, 0.7, 1.5, 1.7], requires_grad=True)
>>> b = torch.tensor([-1., -2., -3., -4., -5.], requires_grad=True)
>>> math.where(a < 1, a, b)
tensor([ 0.6000, 0.2300, 0.7000, -4.0000, -5.0000], grad_fn=<SWhereBackward>)
.. warning::
The output format for ``x=None`` and ``y=None`` follows the respective
interface and differs between TensorFlow and all other interfaces:
For TensorFlow, the output is a tensor with shape
``(num_true, len(condition.shape))`` where ``num_true`` is the number
of entries in ``condition`` that are ``True`` .
The entry at position ``(i, j)`` is the ``j`` th entry of the ``i`` th
index.
For all other interfaces, the output is a tuple of tensor-like objects,
with the ``j`` th object indicating the ``j`` th entries of all indices.
Also see the examples below.
**Example with single argument**
For Torch, Autograd, JAX and NumPy, the output formatting is as follows:
>>> a = [[0.6, 0.23, 1.7],[1.5, 0.7, -0.2]]
>>> math.where(torch.tensor(a) < 1)
(tensor([0, 0, 1, 1]), tensor([0, 1, 1, 2]))
This is not a single tensor-like object but corresponds to the shape
``(2, 4)`` . For TensorFlow, on the other hand:
>>> math.where(tf.constant(a) < 1)
tf.Tensor(
[[0 0]
[0 1]
[1 1]
[1 2]], shape=(4, 2), dtype=int64)
As we can see, the dimensions are swapped and the output is a single Tensor.
Note that the number of dimensions of the output does *not* depend on the input
shape, it is always two-dimensional.
"""
if x is None and y is None:
interface = get_interface(condition)
res = np.where(condition, like=interface)
if interface == "tensorflow":
return np.transpose(np.stack(res))
return res
interface = get_interface(condition, x, y)
res = np.where(condition, x, y, like=interface)
return res
[docs]@multi_dispatch(argnum=[0, 1])
def frobenius_inner_product(A, B, normalize=False, like=None):
r"""Frobenius inner product between two matrices.
.. math::
\langle A, B \rangle_F = \sum_{i,j=1}^n A_{ij} B_{ij} = \operatorname{tr} (A^T B)
The Frobenius inner product is equivalent to the Hilbert-Schmidt inner product for
matrices with real-valued entries.
Args:
A (tensor_like[float]): First matrix, assumed to be a square array.
B (tensor_like[float]): Second matrix, assumed to be a square array.
normalize (bool): If True, divide the inner product by the Frobenius norms of A and B.
Returns:
float: Frobenius inner product of A and B
**Example**
>>> A = np.random.random((3,3))
>>> B = np.random.random((3,3))
>>> qml.math.frobenius_inner_product(A, B)
3.091948202943376
"""
A, B = np.coerce([A, B], like=like)
inner_product = np.sum(A * B)
if normalize:
norm = np.sqrt(np.sum(A * A) * np.sum(B * B))
inner_product = inner_product / norm
return inner_product
@multi_dispatch(argnum=[1])
def scatter(indices, array, new_dims, like=None):
"""Scatters an array into a tensor of shape new_dims according to indices.
This operation is similar to scatter_element_add, except that the tensor
is zero-initialized. Calling scatter(indices, array, new_dims) is identical
to calling scatter_element_add(np.zeros(new_dims), indices, array)
Args:
indices (tensor_like[int]): Indices to update
array (tensor_like[float]): Values to assign to the new tensor
new_dims (int or tuple[int]): The shape of the new tensor
like (str): Manually chosen interface to dispatch to.
Returns:
tensor_like[float]: The tensor with the values modified the given indices.
**Example**
>>> indices = np.array([4, 3, 1, 7])
>>> updates = np.array([9, 10, 11, 12])
>>> shape = 8
>>> qml.math.scatter(indices, updates, shape)
array([ 0, 11, 0, 10, 9, 0, 0, 12])
"""
return np.scatter(indices, array, new_dims, like=like)
[docs]@multi_dispatch(argnum=[0, 2])
def scatter_element_add(tensor, index, value, like=None):
"""In-place addition of a multidimensional value over various
indices of a tensor.
Args:
tensor (tensor_like[float]): Tensor to add the value to
index (tuple or list[tuple]): Indices to which to add the value
value (float or tensor_like[float]): Value to add to ``tensor``
like (str): Manually chosen interface to dispatch to.
Returns:
tensor_like[float]: The tensor with the value added at the given indices.
**Example**
>>> tensor = torch.tensor([[0.1, 0.2, 0.3], [0.4, 0.5, 0.6]])
>>> index = (1, 2)
>>> value = -3.1
>>> qml.math.scatter_element_add(tensor, index, value)
tensor([[ 0.1000, 0.2000, 0.3000],
[ 0.4000, 0.5000, -2.5000]])
If multiple indices are given, in the form of a list of tuples, the
``k`` th tuple is interpreted to contain the ``k`` th entry of all indices:
>>> indices = [(1, 0), (2, 1)] # This will modify the entries (1, 2) and (0, 1)
>>> values = torch.tensor([10, 20])
>>> qml.math.scatter_element_add(tensor, indices, values)
tensor([[ 0.1000, 20.2000, 0.3000],
[ 0.4000, 0.5000, 10.6000]])
"""
if len(np.shape(tensor)) == 0 and index == ():
return tensor + value
return np.scatter_element_add(tensor, index, value, like=like)
[docs]def unwrap(values, max_depth=None):
"""Unwrap a sequence of objects to NumPy arrays.
Note that tensors on GPUs will automatically be copied
to the CPU.
Args:
values (Sequence[tensor_like]): sequence of tensor-like objects to unwrap
max_depth (int): Positive integer indicating the depth of unwrapping to perform
for nested tensor-objects. This argument only applies when unwrapping
Autograd ``ArrayBox`` objects.
**Example**
>>> values = [np.array([0.1, 0.2]), torch.tensor(0.1, dtype=torch.float64), torch.tensor([0.5, 0.2])]
>>> math.unwrap(values)
[array([0.1, 0.2]), 0.1, array([0.5, 0.2], dtype=float32)]
This function will continue to work during backpropagation:
>>> def cost_fn(params):
... unwrapped_params = math.unwrap(params)
... print("Unwrapped:", [(i, type(i)) for i in unwrapped_params])
... return np.sum(np.sin(params))
>>> params = np.array([0.1, 0.2, 0.3])
>>> grad = autograd.grad(cost_fn)(params)
Unwrapped: [(0.1, <class 'float'>), (0.2, <class 'float'>), (0.3, <class 'float'>)]
>>> print(grad)
[0.99500417 0.98006658 0.95533649]
"""
def convert(val):
if isinstance(val, (tuple, list)):
return unwrap(val)
new_val = (
np.to_numpy(val, max_depth=max_depth) if isinstance(val, ArrayBox) else np.to_numpy(val)
)
return new_val.tolist() if isinstance(new_val, ndarray) and not new_val.shape else new_val
if isinstance(values, (tuple, list)):
return type(values)(convert(val) for val in values)
return (
np.to_numpy(values, max_depth=max_depth)
if isinstance(values, ArrayBox)
else np.to_numpy(values)
)
[docs]@multi_dispatch(argnum=[0, 1])
def add(*args, like=None, **kwargs):
"""Add arguments element-wise."""
if like == "scipy":
return onp.add(*args, **kwargs) # Dispatch scipy add to numpy backed specifically.
arg_interfaces = {get_interface(args[0]), get_interface(args[1])}
# case of one torch tensor and one vanilla numpy array
if like == "torch" and len(arg_interfaces) == 2:
# In autoray 0.6.5, np.add dispatches to torch instead of
# numpy if one parameter is a torch tensor and the other is
# a numpy array. torch.add raises an Exception if one of the
# arguments is a numpy array, so here we cast both arguments
# to be tensors.
dev = getattr(args[0], "device", None) or getattr(args[1], "device")
arg0 = np.asarray(args[0], device=dev, like=like)
arg1 = np.asarray(args[1], device=dev, like=like)
return np.add(arg0, arg1, *args[2:], **kwargs)
return np.add(*args, **kwargs, like=like)
[docs]@multi_dispatch()
def iscomplex(tensor, like=None):
"""Return True if the tensor has a non-zero complex component."""
if like == "tensorflow":
import tensorflow as tf
imag_tensor = tf.math.imag(tensor)
return tf.math.count_nonzero(imag_tensor) > 0
if like == "torch":
import torch
if torch.is_complex(tensor):
imag_tensor = torch.imag(tensor)
return torch.count_nonzero(imag_tensor) > 0
return False
return np.iscomplex(tensor)
@multi_dispatch()
def expm(tensor, like=None):
"""Compute the matrix exponential of an array :math:`e^{X}`.
..note::
This function is not differentiable with Autograd, as it
relies on the scipy implementation.
"""
if like == "torch":
return tensor.matrix_exp()
if like == "jax":
from jax.scipy.linalg import expm as jax_expm
return jax_expm(tensor)
if like == "tensorflow":
import tensorflow as tf
return tf.linalg.expm(tensor)
from scipy.linalg import expm as scipy_expm
return scipy_expm(tensor)
@multi_dispatch()
def norm(tensor, like=None, **kwargs):
"""Compute the norm of a tensor in each interface."""
if like == "jax":
from jax.numpy.linalg import norm
elif like == "tensorflow":
from tensorflow import norm
elif like == "torch":
from torch.linalg import norm
if "axis" in kwargs:
axis_val = kwargs.pop("axis")
kwargs["dim"] = axis_val
elif (
like == "autograd" and kwargs.get("ord", None) is None and kwargs.get("axis", None) is None
):
norm = _flat_autograd_norm
else:
from scipy.linalg import norm
return norm(tensor, **kwargs)
def _flat_autograd_norm(tensor, **kwargs): # pylint: disable=unused-argument
"""Helper function for computing the norm of an autograd tensor when the order or axes are not
specified. This is used for differentiability."""
x = np.ravel(tensor)
sq_norm = np.dot(x, np.conj(x))
return np.real(np.sqrt(sq_norm))
@multi_dispatch(argnum=[1])
def gammainc(m, t, like=None):
r"""Return the lower incomplete Gamma function.
The lower incomplete Gamma function is defined in scipy as
.. math::
\gamma(m, t) = \frac{1}{\Gamma(m)} \int_{0}^{t} x^{m-1} e^{-x} dx,
where :math:`\Gamma` denotes the Gamma function.
Args:
m (float): exponent of the incomplete Gamma function
t (array[float]): upper limit of the incomplete Gamma function
Returns:
(array[float]): value of the incomplete Gamma function
"""
if like == "jax":
from jax.scipy.special import gammainc
return gammainc(m, t)
if like == "autograd":
from autograd.scipy.special import gammainc
return gammainc(m, t)
import scipy
return scipy.special.gammainc(m, t)
[docs]@multi_dispatch()
def detach(tensor, like=None):
"""Detach a tensor from its trace and return just its numerical values.
Args:
tensor (tensor_like): Tensor to detach
like (str): Manually chosen interface to dispatch to.
Returns:
tensor_like: A tensor in the same interface as the input tensor but
with a stopped gradient.
"""
if like == "jax":
import jax
return jax.lax.stop_gradient(tensor)
if like == "torch":
return tensor.detach()
if like == "tensorflow":
import tensorflow as tf
return tf.stop_gradient(tensor)
if like == "autograd":
return np.to_numpy(tensor)
return tensor
def jax_argnums_to_tape_trainable(qnode, argnums, program, args, kwargs):
"""This functions gets the tape parameters from the QNode construction given some argnums (only for Jax).
The tape parameters are transformed to JVPTracer if they are from argnums. This function imitates the behavior
of Jax in order to mark trainable parameters.
Args:
qnode(qml.QNode): the quantum node.
argnums(int, list[int]): the parameters that we want to set as trainable (on the QNode level).
program(qml.transforms.core.TransformProgram): the transform program to be applied on the tape.
Return:
list[float, jax.JVPTracer]: List of parameters where the trainable one are `JVPTracer`.
"""
import jax
with jax.core.new_main(jax.interpreters.ad.JVPTrace) as main:
trace = jax.interpreters.ad.JVPTrace(main, 0)
args_jvp = [
(
jax.interpreters.ad.JVPTracer(trace, arg, jax.numpy.zeros(arg.shape))
if i in argnums
else arg
)
for i, arg in enumerate(args)
]
qnode.construct(args_jvp, kwargs)
tape = qnode.qtape
tapes, _ = program((tape,))
del trace
return tuple(tape.get_parameters(trainable_only=False) for tape in tapes)
@multi_dispatch(tensor_list=[1])
def set_index(array, idx, val, like=None):
"""Set the value at a specified index in an array.
Calls ``array[idx]=val`` and returns the updated array unless JAX.
Args:
array (tensor_like): array to be modified
idx (int, tuple): index to modify
val (int, float): value to set
Returns:
a new copy of the array with the specified index updated to ``val``.
Whether the original array is modified is interface-dependent.
.. note:: TensorFlow EagerTensor does not support item assignment
"""
if like == "jax":
from jax import numpy as jnp
# ensure array is jax array (interface may be jax because of idx or val and not array)
jax_array = jnp.array(array)
return jax_array.at[idx].set(val)
array[idx] = val
return array
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