Source code for pennylane.math.utils
# 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.
"""Utility functions"""
import warnings
import autoray as ar
import numpy as _np
# pylint: disable=import-outside-toplevel
from autograd.numpy.numpy_boxes import ArrayBox
from autoray import numpy as np
from . import single_dispatch # pylint:disable=unused-import
[docs]def allequal(tensor1, tensor2, **kwargs):
"""Returns True if two tensors are element-wise equal along a given axis.
This function is equivalent to calling ``np.all(tensor1 == tensor2, **kwargs)``,
but allows for ``tensor1`` and ``tensor2`` to differ in type.
Args:
tensor1 (tensor_like): tensor to compare
tensor2 (tensor_like): tensor to compare
**kwargs: Accepts any keyword argument that is accepted by ``np.all``,
such as ``axis``, ``out``, and ``keepdims``. See the `NumPy documentation
<https://numpy.org/doc/stable/reference/generated/numpy.all.html>`__ for
more details.
Returns:
ndarray, bool: If ``axis=None``, a logical AND reduction is applied to all elements
and a boolean will be returned, indicating if all elements evaluate to ``True``. Otherwise,
a boolean NumPy array will be returned.
**Example**
>>> a = torch.tensor([1, 2])
>>> b = np.array([1, 2])
>>> allequal(a, b)
True
"""
t1 = ar.to_numpy(tensor1)
t2 = ar.to_numpy(tensor2)
return np.all(t1 == t2, **kwargs)
[docs]def allclose(a, b, rtol=1e-05, atol=1e-08, **kwargs):
"""Wrapper around np.allclose, allowing tensors ``a`` and ``b``
to differ in type"""
try:
# Some frameworks may provide their own allclose implementation.
# Try and use it if available.
res = np.allclose(a, b, rtol=rtol, atol=atol, **kwargs)
except (TypeError, AttributeError, ImportError, RuntimeError):
# Otherwise, convert the input to NumPy arrays.
#
# TODO: replace this with a bespoke, framework agnostic
# low-level implementation to avoid the NumPy conversion:
#
# np.abs(a - b) <= atol + rtol * np.abs(b)
#
t1 = ar.to_numpy(a)
t2 = ar.to_numpy(b)
res = np.allclose(t1, t2, rtol=rtol, atol=atol, **kwargs)
return res
allclose.__doc__ = _np.allclose.__doc__
[docs]def cast(tensor, dtype):
"""Casts the given tensor to a new type.
Args:
tensor (tensor_like): tensor to cast
dtype (str, np.dtype): Any supported NumPy dtype representation; this can be
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: a tensor with the same shape and values as ``tensor`` and the
same dtype as ``dtype``
**Example**
We can use NumPy dtype specifiers:
>>> x = torch.tensor([1, 2])
>>> cast(x, np.float64)
tensor([1., 2.], dtype=torch.float64)
We can also use strings:
>>> x = tf.Variable([1, 2])
>>> cast(x, "complex128")
<tf.Tensor: shape=(2,), dtype=complex128, numpy=array([1.+0.j, 2.+0.j])>
"""
if isinstance(tensor, (list, tuple, int, float, complex)):
tensor = np.asarray(tensor)
if not isinstance(dtype, str):
try:
dtype = np.dtype(dtype).name
except (AttributeError, TypeError, ImportError):
dtype = getattr(dtype, "name", dtype)
return ar.astype(tensor, ar.to_backend_dtype(dtype, like=ar.infer_backend(tensor)))
[docs]def cast_like(tensor1, tensor2):
"""Casts a tensor to the same dtype as another.
Args:
tensor1 (tensor_like): tensor to cast
tensor2 (tensor_like): tensor with corresponding dtype to cast to
Returns:
tensor_like: a tensor with the same shape and values as ``tensor1`` and the
same dtype as ``tensor2``
**Example**
>>> x = torch.tensor([1, 2])
>>> y = torch.tensor([3., 4.])
>>> cast_like(x, y)
tensor([1., 2.])
"""
if isinstance(tensor2, tuple) and len(tensor2) > 0:
tensor2 = tensor2[0]
if isinstance(tensor2, ArrayBox):
dtype = ar.to_numpy(tensor2._value).dtype.type # pylint: disable=protected-access
elif not is_abstract(tensor2):
dtype = ar.to_numpy(tensor2).dtype.type
else:
dtype = tensor2.dtype
return cast(tensor1, dtype)
[docs]def convert_like(tensor1, tensor2):
"""Convert a tensor to the same type as another.
Args:
tensor1 (tensor_like): tensor to convert
tensor2 (tensor_like): tensor with corresponding type to convert to
Returns:
tensor_like: a tensor with the same shape, values, and dtype as ``tensor1`` and the
same type as ``tensor2``.
**Example**
>>> x = np.array([1, 2])
>>> y = tf.Variable([3, 4])
>>> convert_like(x, y)
<tf.Tensor: shape=(2,), dtype=int64, numpy=array([1, 2])>
"""
interface = get_interface(tensor2)
if interface == "torch":
dev = tensor2.device
return np.asarray(tensor1, device=dev, like=interface)
return np.asarray(tensor1, like=interface)
[docs]def get_interface(*values):
"""Determines the correct framework to dispatch to given a tensor-like object or a
sequence of tensor-like objects.
Args:
*values (tensor_like): variable length argument list with single tensor-like objects
Returns:
str: the name of the interface
To determine the framework to dispatch to, the following rules
are applied:
* Tensors that are incompatible (such as Torch, TensorFlow and Jax tensors)
cannot both be present.
* Autograd tensors *may* be present alongside Torch, TensorFlow and Jax tensors,
but Torch, TensorFlow and Jax take precendence; the autograd arrays will
be treated as non-differentiable NumPy arrays. A warning will be raised
suggesting that vanilla NumPy be used instead.
* Vanilla NumPy arrays and SciPy sparse matrices can be used alongside other tensor objects;
they will always be treated as non-differentiable constants.
.. warning::
``get_interface`` defaults to ``"numpy"`` whenever Python built-in objects are passed.
I.e. a list or tuple of ``torch`` tensors will be identified as ``"numpy"``:
>>> get_interface([torch.tensor([1]), torch.tensor([1])])
"numpy"
The correct usage in that case is to unpack the arguments ``get_interface(*[torch.tensor([1]), torch.tensor([1])])``.
"""
if len(values) == 1:
return _get_interface_of_single_tensor(values[0])
interfaces = {_get_interface_of_single_tensor(v) for v in values}
if len(interfaces - {"numpy", "scipy", "autograd"}) > 1:
# contains multiple non-autograd interfaces
raise ValueError("Tensors contain mixed types; cannot determine dispatch library")
non_numpy_scipy_interfaces = set(interfaces) - {"numpy", "scipy"}
if len(non_numpy_scipy_interfaces) > 1:
# contains autograd and another interface
warnings.warn(
f"Contains tensors of types {non_numpy_scipy_interfaces}; dispatch will prioritize "
"TensorFlow, PyTorch, and Jax over Autograd. Consider replacing Autograd with vanilla NumPy.",
UserWarning,
)
if "tensorflow" in interfaces:
return "tensorflow"
if "torch" in interfaces:
return "torch"
if "jax" in interfaces:
return "jax"
if "autograd" in interfaces:
return "autograd"
return "numpy"
def _get_interface_of_single_tensor(tensor):
"""Returns the name of the package that any array/tensor manipulations
will dispatch to. The returned strings correspond to those used for PennyLane
:doc:`interfaces </introduction/interfaces>`.
Args:
tensor (tensor_like): tensor input
Returns:
str: name of the interface
**Example**
>>> x = torch.tensor([1., 2.])
>>> get_interface(x)
'torch'
>>> from pennylane import numpy as np
>>> x = np.array([4, 5], requires_grad=True)
>>> get_interface(x)
'autograd'
"""
namespace = tensor.__class__.__module__.split(".")[0]
if namespace in ("pennylane", "autograd"):
return "autograd"
res = ar.infer_backend(tensor)
if res == "builtins":
return "numpy"
return res
[docs]def get_deep_interface(value):
"""
Given a deep data structure with interface-specific scalars at the bottom, return their
interface name.
Args:
value (list, tuple): A deep list-of-lists, tuple-of-tuples, or combination with
interface-specific data hidden within it
Returns:
str: The name of the interface deep within the value
**Example**
>>> x = [[jax.numpy.array(1), jax.numpy.array(2)], [jax.numpy.array(3), jax.numpy.array(4)]]
>>> get_deep_interface(x)
'jax'
This can be especially useful when converting to the appropriate interface:
>>> qml.math.asarray(x, like=qml.math.get_deep_interface(x))
Array([[1, 2],
[3, 4]], dtype=int64)
"""
itr = value
while isinstance(itr, (list, tuple)):
if len(itr) == 0:
return "builtins"
itr = itr[0]
return ar.infer_backend(itr)
[docs]def is_abstract(tensor, like=None):
"""Returns True if the tensor is considered abstract.
Abstract arrays have no internal value, and are used primarily when
tracing Python functions, for example, in order to perform just-in-time
(JIT) compilation.
Abstract tensors most commonly occur within a function that has been
decorated using ``@tf.function`` or ``@jax.jit``.
.. note::
Currently Autograd tensors and Torch tensors will always return ``False``.
This is because:
- Autograd does not provide JIT compilation, and
- ``@torch.jit.script`` is not currently compatible with QNodes.
Args:
tensor (tensor_like): input tensor
like (str): The name of the interface. Will be determined automatically
if not provided.
Returns:
bool: whether the tensor is abstract or not
**Example**
Consider the following JAX function:
.. code-block:: python
import jax
from jax import numpy as jnp
def function(x):
print("Value:", x)
print("Abstract:", qml.math.is_abstract(x))
return jnp.sum(x ** 2)
When we execute it, we see that the tensor is not abstract; it has known value:
>>> x = jnp.array([0.5, 0.1])
>>> function(x)
Value: [0.5, 0.1]
Abstract: False
Array(0.26, dtype=float32)
However, if we use the ``@jax.jit`` decorator, the tensor will now be abstract:
>>> x = jnp.array([0.5, 0.1])
>>> jax.jit(function)(x)
Value: Traced<ShapedArray(float32[2])>with<DynamicJaxprTrace(level=0/1)>
Abstract: True
Array(0.26, dtype=float32)
Note that JAX uses an abstract *shaped* array, so although we won't be able to
include conditionals within our function that depend on the value of the tensor,
we *can* include conditionals that depend on the shape of the tensor.
Similarly, consider the following TensorFlow function:
.. code-block:: python
import tensorflow as tf
def function(x):
print("Value:", x)
print("Abstract:", qml.math.is_abstract(x))
return tf.reduce_sum(x ** 2)
>>> x = tf.Variable([0.5, 0.1])
>>> function(x)
Value: <tf.Variable 'Variable:0' shape=(2,) dtype=float32, numpy=array([0.5, 0.1], dtype=float32)>
Abstract: False
<tf.Tensor: shape=(), dtype=float32, numpy=0.26>
If we apply the ``@tf.function`` decorator, the tensor will now be abstract:
>>> tf.function(function)(x)
Value: <tf.Variable 'Variable:0' shape=(2,) dtype=float32>
Abstract: True
<tf.Tensor: shape=(), dtype=float32, numpy=0.26>
"""
interface = like or get_interface(tensor)
if interface == "jax":
import jax
from jax.interpreters.partial_eval import DynamicJaxprTracer
if isinstance(
tensor,
(
jax.interpreters.ad.JVPTracer,
jax.interpreters.batching.BatchTracer,
jax.interpreters.partial_eval.JaxprTracer,
),
):
# Tracer objects will be used when computing gradients or applying transforms.
# If the value of the tracer is known, it will contain a ConcreteArray.
# Otherwise, it will be abstract.
return not isinstance(tensor.aval, jax.core.ConcreteArray)
return isinstance(tensor, DynamicJaxprTracer)
if interface == "tensorflow":
import tensorflow as tf
from tensorflow.python.framework.ops import EagerTensor
return not isinstance(tf.convert_to_tensor(tensor), EagerTensor)
# Autograd does not have a JIT
# QNodes do not currently support TorchScript:
# NotSupportedError: Compiled functions can't take variable number of arguments or
# use keyword-only arguments with defaults.
return False
def import_should_record_backprop(): # pragma: no cover
"""Return should_record_backprop or an equivalent function from TensorFlow."""
import tensorflow.python as tfpy
if hasattr(tfpy.eager.tape, "should_record_backprop"):
from tensorflow.python.eager.tape import should_record_backprop
elif hasattr(tfpy.eager.tape, "should_record"):
from tensorflow.python.eager.tape import should_record as should_record_backprop
elif hasattr(tfpy.eager.record, "should_record_backprop"):
from tensorflow.python.eager.record import should_record_backprop
else:
raise ImportError("Cannot import should_record_backprop from TensorFlow.")
return should_record_backprop
[docs]def requires_grad(tensor, interface=None):
"""Returns True if the tensor is considered trainable.
.. warning::
The implementation depends on the contained tensor type, and
may be context dependent.
For example, Torch tensors and PennyLane tensors track trainability
as a property of the tensor itself. TensorFlow, on the other hand,
only tracks trainability if being watched by a gradient tape.
Args:
tensor (tensor_like): input tensor
interface (str): The name of the interface. Will be determined automatically
if not provided.
**Example**
Calling this function on a PennyLane NumPy array:
>>> x = np.array([1., 5.], requires_grad=True)
>>> requires_grad(x)
True
>>> x.requires_grad = False
>>> requires_grad(x)
False
PyTorch has similar behaviour.
With TensorFlow, the output is dependent on whether the tensor
is currently being watched by a gradient tape:
>>> x = tf.Variable([0.6, 0.1])
>>> requires_grad(x)
False
>>> with tf.GradientTape() as tape:
... print(requires_grad(x))
True
While TensorFlow constants are by default not trainable, they can be
manually watched by the gradient tape:
>>> x = tf.constant([0.6, 0.1])
>>> with tf.GradientTape() as tape:
... print(requires_grad(x))
False
>>> with tf.GradientTape() as tape:
... tape.watch([x])
... print(requires_grad(x))
True
"""
interface = interface or get_interface(tensor)
if interface == "tensorflow":
import tensorflow as tf
should_record_backprop = import_should_record_backprop()
return should_record_backprop([tf.convert_to_tensor(tensor)])
if interface == "autograd":
if isinstance(tensor, ArrayBox):
return True
return getattr(tensor, "requires_grad", False)
if interface == "torch":
return getattr(tensor, "requires_grad", False)
if interface in {"numpy", "scipy"}:
return False
if interface == "jax":
import jax
return isinstance(tensor, jax.core.Tracer)
raise ValueError(f"Argument {tensor} is an unknown object")
[docs]def in_backprop(tensor, interface=None):
"""Returns True if the tensor is considered to be in a backpropagation environment, it works for Autograd,
TensorFlow and Jax. It is not only checking the differentiability of the tensor like :func:`~.requires_grad`, but
rather checking if the gradient is actually calculated.
Args:
tensor (tensor_like): input tensor
interface (str): The name of the interface. Will be determined automatically
if not provided.
**Example**
>>> x = tf.Variable([0.6, 0.1])
>>> requires_grad(x)
False
>>> with tf.GradientTape() as tape:
... print(requires_grad(x))
True
.. seealso:: :func:`~.requires_grad`
"""
interface = interface or get_interface(tensor)
if interface == "tensorflow":
import tensorflow as tf
should_record_backprop = import_should_record_backprop()
return should_record_backprop([tf.convert_to_tensor(tensor)])
if interface == "autograd":
return isinstance(tensor, ArrayBox)
if interface == "jax":
import jax
return isinstance(tensor, jax.core.Tracer)
if interface in {"numpy", "scipy"}:
return False
raise ValueError(f"Cannot determine if {tensor} is in backpropagation.")
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