# 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

# 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"""
# pylint: disable=import-outside-toplevel
from autograd.numpy.numpy_boxes import ArrayBox
import autoray as ar
from autoray import numpy as np
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)):
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 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(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)
"""
namespace = tensor.__class__.__module__.split(".")

if namespace in ("pennylane", "autograd"):

res = ar.infer_backend(tensor)

if res == "builtins":
return "numpy"

return res

[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
DeviceArray(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)>with<DynamicJaxprTrace(level=0/1)>
Abstract: True
DeviceArray(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.ad.JVPTracer, jax.interpreters.batching.BatchTracer)):
# 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

"""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)
True
>>> x.requires_grad = False
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])
False
>>> with tf.GradientTape() as tape:
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:
False
>>> with tf.GradientTape() as tape:
...     tape.watch([x])
True
"""
interface = interface or get_interface(tensor)

if interface == "tensorflow":
import tensorflow as tf

try:
from tensorflow.python.eager.tape import should_record_backprop
except ImportError:  # pragma: no cover
from tensorflow.python.eager.tape import (
should_record as 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 == "numpy":
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])
False
>>> with tf.GradientTape() as tape:
True

.. seealso:: :func:~.requires_grad
"""
interface = interface or get_interface(tensor)

if interface == "tensorflow":
import tensorflow as tf

try:
from tensorflow.python.eager.tape import should_record_backprop
except ImportError:  # pragma: no cover
from tensorflow.python.eager.tape import (
should_record as 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 == "numpy":
return False

raise ValueError(f"Cannot determine if {tensor} is in backpropagation.")


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