def broadcast_all(*values):
r"""
Given a list of values (possibly containing numbers), returns a list where each
value is broadcasted based on the following rules:
- `torch.*Tensor` instances are broadcasted as per :ref:`_broadcasting-semantics`.
- numbers.Number instances (scalars) are upcast to tensors having
the same size and type as the first tensor passed to `values`. If all the
values are scalars, then they are upcasted to scalar Tensors.
Args:
values (list of `numbers.Number`, `torch.*Tensor` or objects implementing __torch_function__)
Raises:
ValueError: if any of the values is not a `numbers.Number` instance,
a `torch.*Tensor` instance, or an instance implementing __torch_function__
"""
if not all(is_tensor_like(v) or isinstance(v, Number) for v in values):
raise ValueError(
'Input arguments must all be instances of numbers.Number, '
'torch.Tensor or objects implementing __torch_function__.')
if not all(is_tensor_like(v) for v in values):
options: Dict[str, Any] = dict(dtype=torch.get_default_dtype())
for value in values:
if isinstance(value, torch.Tensor):
options = dict(dtype=value.dtype, device=value.device)
break
new_values = [
v if is_tensor_like(v) else torch.tensor(v, **options)
for v in values
]
return torch.broadcast_tensors(*new_values)
return torch.broadcast_tensors(*values)
def iter_tensors(x, only_requiring_grad=False):
if is_tensor_like(x):
if x.requires_grad or not only_requiring_grad:
yield x
elif isinstance(x, container_abcs.Iterable) and not isinstance(x, str):
for elem in x:
for result in iter_tensors(elem, only_requiring_grad):
yield result
def iter_tensors(x: Union[torch.Tensor, Iterable[torch.Tensor]], only_requiring_grad: bool = False) -> Iterable[torch.Tensor]:
if is_tensor_like(x):
# mypy doesn't narrow type of `x` to torch.Tensor
if x.requires_grad or not only_requiring_grad: # type: ignore
yield x # type: ignore
elif isinstance(x, container_abcs.Iterable) and not isinstance(x, str):
for elem in x:
for result in iter_tensors(elem, only_requiring_grad):
yield result
def make_jacobian(input, num_out):
if is_tensor_like(input):
if not input.is_floating_point() and not input.is_complex():
return None
if not input.requires_grad:
return None
return input.new_zeros((input.nelement(), num_out), dtype=input.dtype, layout=torch.strided)
elif isinstance(input, container_abcs.Iterable) and not isinstance(input, str):
jacobians = list(filter(
lambda x: x is not None, (make_jacobian(elem, num_out) for elem in input)))
if not jacobians:
return None
return type(input)(jacobians) # type: ignore
else:
return None
def _get_numerical_jacobian(fn,
inputs,
outputs=None,
target=None,
eps=1e-3,
grad_out=1.0) -> List[Tuple[torch.Tensor, ...]]:
"""Computes the numerical jacobian for a given fn and inputs. Returns M * N jacobians
where M is the number of input tensors that require grad, and N is the number of output
float/complex tensors.
Args:
fn: the function to compute the jacobian for
inputs: inputs to `fn`
outputs: provide precomputed outputs to avoid one extra invocation of fn
target: the Tensors wrt whom Jacobians are calculated (default=`inputs`)
eps: the magnitude of the perturbation during finite differencing (default=`1e-3`)
grad_out: grad output value used to calculate gradients.
Returns:
A list of M N-tuples of tensors
Note that `target` may not even be part of `input` to `fn`, so please be
**very careful** in this to not clone `target`.
"""
jacobians: List[Tuple[torch.Tensor, ...]] = []
if outputs is None:
outputs = _as_tuple(fn(*_as_tuple(inputs)))
if target is None:
target = inputs
inp_indices = [
i for i, a in enumerate(target)
if is_tensor_like(a) and a.requires_grad
]
for i, (inp,
inp_idx) in enumerate(zip(iter_tensors(target, True),
inp_indices)):
jacobians += [
get_numerical_jacobian_wrt_specific_input(fn, inp, inp_idx, inputs,
outputs, eps, grad_out)
]
return jacobians
def check_inputs(fail_test, tupled_inputs, check_sparse_nnz) -> bool:
if not check_sparse_nnz and any(
t.is_sparse for t in tupled_inputs if isinstance(t, torch.Tensor)):
return fail_test(
'gradcheck expects all tensor inputs are dense when check_sparse_nnz is set to False.'
)
# Make sure that gradients are saved for at least one input
any_input_requiring_grad = False
for idx, inp in enumerate(tupled_inputs):
if is_tensor_like(inp) and inp.requires_grad:
if not (inp.dtype == torch.float64
or inp.dtype == torch.complex128):
warnings.warn(
f'Input #{idx} requires gradient and '
'is not a double precision floating point or complex. '
'This check will likely fail if all the inputs are '
'not of double precision floating point or complex. ')
content = inp._values() if inp.is_sparse else inp
# TODO: To cover more problematic cases, replace stride = 0 check with
# "any overlap in memory" once we have a proper function to check it.
if content.layout is not torch._mkldnn: # type: ignore
if not all(
st > 0 or sz <= 1
for st, sz in zip(content.stride(), content.size())):
raise RuntimeError(
f'The {idx}th input has a dimension with stride 0. gradcheck only '
'supports inputs that are non-overlapping to be able to '
'compute the numerical gradients correctly. You should call '
'.contiguous on the input before passing it to gradcheck.'
)
any_input_requiring_grad = True
inp.retain_grad()
if not any_input_requiring_grad:
raise ValueError(
'gradcheck expects at least one input tensor to require gradient, '
'but none of the them have requires_grad=True.')
return True
def gradcheck(
func: Callable[
..., Union[_TensorOrTensors]], # See Note [VarArg of Tensors]
inputs: _TensorOrTensors,
eps: float = 1e-6,
atol: float = 1e-5,
rtol: float = 1e-3,
raise_exception: bool = True,
check_sparse_nnz: bool = False,
nondet_tol: float = 0.0,
check_undefined_grad: bool = True,
check_grad_dtypes: bool = False) -> bool:
r"""Check gradients computed via small finite differences against analytical
gradients w.r.t. tensors in :attr:`inputs` that are of floating point or complex type
and with ``requires_grad=True``.
The check between numerical and analytical gradients uses :func:`~torch.allclose`.
For complex functions, no notion of Jacobian exists. Gradcheck verifies if the numerical and
analytical values of Wirtinger and Conjugate Wirtinger derivative are consistent. The gradient
computation is done under the assumption that the overall function has a real valued output.
For functions with complex output, gradcheck compares the numerical and analytical gradients
for two values of :attr:`grad_output`: 1 and 1j. For more details, check out
:ref:`complex_autograd-doc`.
.. note::
The default values are designed for :attr:`input` of double precision.
This check will likely fail if :attr:`input` is of less precision, e.g.,
``FloatTensor``.
.. warning::
If any checked tensor in :attr:`input` has overlapping memory, i.e.,
different indices pointing to the same memory address (e.g., from
:func:`torch.expand`), this check will likely fail because the numerical
gradients computed by point perturbation at such indices will change
values at all other indices that share the same memory address.
Args:
func (function): a Python function that takes Tensor inputs and returns
a Tensor or a tuple of Tensors
inputs (tuple of Tensor or Tensor): inputs to the function
eps (float, optional): perturbation for finite differences
atol (float, optional): absolute tolerance
rtol (float, optional): relative tolerance
raise_exception (bool, optional): indicating whether to raise an exception if
the check fails. The exception gives more information about the
exact nature of the failure. This is helpful when debugging gradchecks.
check_sparse_nnz (bool, optional): if True, gradcheck allows for SparseTensor input,
and for any SparseTensor at input, gradcheck will perform check at nnz positions only.
nondet_tol (float, optional): tolerance for non-determinism. When running
identical inputs through the differentiation, the results must either match
exactly (default, 0.0) or be within this tolerance.
check_undefined_grad (bool, options): if True, check if undefined output grads
are supported and treated as zeros, for ``Tensor`` outputs.
Returns:
True if all differences satisfy allclose condition
"""
def fail_test(msg):
if raise_exception:
raise RuntimeError(msg)
return False
tupled_inputs = _as_tuple(inputs)
if not check_sparse_nnz and any(
t.is_sparse for t in tupled_inputs if isinstance(t, torch.Tensor)):
return fail_test(
'gradcheck expects all tensor inputs are dense when check_sparse_nnz is set to False.'
)
# Make sure that gradients are saved for at least one input
any_input_requiring_grad = False
for idx, inp in enumerate(tupled_inputs):
if is_tensor_like(inp) and inp.requires_grad:
if not (inp.dtype == torch.float64
or inp.dtype == torch.complex128):
warnings.warn(
'The {}th input requires gradient and '
'is not a double precision floating point or complex. '
'This check will likely fail if all the inputs are '
'not of double precision floating point or complex. ')
content = inp._values() if inp.is_sparse else inp
# TODO: To cover more problematic cases, replace stride = 0 check with
# "any overlap in memory" once we have a proper function to check it.
if content.layout is not torch._mkldnn: # type: ignore
if not all(
st > 0 or sz <= 1
for st, sz in zip(content.stride(), content.size())):
raise RuntimeError(
'The {}th input has a dimension with stride 0. gradcheck only '
'supports inputs that are non-overlapping to be able to '
'compute the numerical gradients correctly. You should call '
'.contiguous on the input before passing it to gradcheck.'
)
any_input_requiring_grad = True
inp.retain_grad()
if not any_input_requiring_grad:
raise ValueError(
'gradcheck expects at least one input tensor to require gradient, '
'but none of the them have requires_grad=True.')
func_out = func(*tupled_inputs)
output = _differentiable_outputs(func_out)
if not output:
for i, o in enumerate(func_out):
def fn(input):
return _as_tuple(func(*input))[i]
numerical = get_numerical_jacobian(fn, tupled_inputs, eps=eps)
for n in numerical:
if torch.ne(n, 0).sum() > 0:
return fail_test(
'Numerical gradient for function expected to be zero')
return True
for i, o in enumerate(output):
if not o.requires_grad:
continue
def fn(input):
return _as_tuple(func(*input))[i]
analytical, reentrant, correct_grad_sizes, correct_grad_types = get_analytical_jacobian(
tupled_inputs, o, nondet_tol=nondet_tol)
numerical = get_numerical_jacobian(fn, tupled_inputs, eps=eps)
out_is_complex = o.is_complex()
if out_is_complex:
# analytical vjp with grad_out = 1.0j
analytical_with_imag_grad_out, reentrant_with_imag_grad_out, \
correct_grad_sizes_with_imag_grad_out, correct_grad_types_with_imag_grad_out \
= get_analytical_jacobian(tupled_inputs, o, nondet_tol=nondet_tol, grad_out=1j)
numerical_with_imag_grad_out = get_numerical_jacobian(
fn, tupled_inputs, eps=eps, grad_out=1j)
if not correct_grad_types and check_grad_dtypes:
return fail_test('Gradient has dtype mismatch')
if out_is_complex and not correct_grad_types_with_imag_grad_out and check_grad_dtypes:
return fail_test(
'Gradient (calculated using complex valued grad output) has dtype mismatch'
)
if not correct_grad_sizes:
return fail_test('Analytical gradient has incorrect size')
if out_is_complex and not correct_grad_sizes_with_imag_grad_out:
return fail_test(
'Analytical gradient (calculated using complex valued grad output) has incorrect size'
)
def checkIfNumericalAnalyticAreClose(a, n, j, error_str=''):
if not torch.allclose(a, n, rtol, atol):
return fail_test(
error_str +
'Jacobian mismatch for output %d with respect to input %d,\n'
'numerical:%s\nanalytical:%s\n' % (i, j, n, a))
inp_tensors = iter_tensors(tupled_inputs, True)
for j, (a, n, inp) in enumerate(zip(analytical, numerical,
inp_tensors)):
if a.numel() != 0 or n.numel() != 0:
if o.is_complex():
# C -> C, R -> C
a_with_imag_grad_out = analytical_with_imag_grad_out[j]
n_with_imag_grad_out = numerical_with_imag_grad_out[j]
checkIfNumericalAnalyticAreClose(
a_with_imag_grad_out, n_with_imag_grad_out, j,
"Gradients failed to compare equal for grad output = 1j. "
)
if inp.is_complex():
# C -> R, C -> C
checkIfNumericalAnalyticAreClose(
a, n, j,
"Gradients failed to compare equal for grad output = 1. "
)
else:
# R -> R, R -> C
checkIfNumericalAnalyticAreClose(a, n, j)
def not_reentrant_error(error_str=''):
error_msg = "Backward" + error_str + " is not reentrant, i.e., running backward with same \
input and grad_output multiple times gives different values, \
although analytical gradient matches numerical gradient. \
The tolerance for nondeterminism was {}.".format(
nondet_tol)
return fail_test(error_msg)
if not reentrant:
return not_reentrant_error()
if out_is_complex and not reentrant_with_imag_grad_out:
return not_reentrant_error(
' (calculated using complex valued grad output)')
# check if the backward multiplies by grad_output
output = _differentiable_outputs(func(*tupled_inputs))
if any([o.requires_grad for o in output]):
diff_input_list: List[torch.Tensor] = list(
iter_tensors(tupled_inputs, True))
if not diff_input_list:
raise RuntimeError("no Tensors requiring grad found in input")
grads_input = torch.autograd.grad(
output,
diff_input_list, [
torch.zeros_like(o,
memory_format=torch.legacy_contiguous_format)
for o in output
],
allow_unused=True)
for gi, di in zip(grads_input, diff_input_list):
if gi is None:
continue
if isinstance(gi, torch.Tensor) and gi.layout != torch.strided:
if gi.layout != di.layout:
return fail_test('grad is incorrect layout (' +
str(gi.layout) + ' is not ' +
str(di.layout) + ')')
if gi.layout == torch.sparse_coo:
if gi.sparse_dim() != di.sparse_dim():
return fail_test(
'grad is sparse tensor, but has incorrect sparse_dim'
)
if gi.dense_dim() != di.dense_dim():
return fail_test(
'grad is sparse tensor, but has incorrect dense_dim'
)
gi = gi.to_dense()
di = di.to_dense()
if not gi.eq(0).all():
return fail_test('backward not multiplied by grad_output')
if gi.dtype != di.dtype or gi.device != di.device or gi.is_sparse != di.is_sparse:
return fail_test("grad is incorrect type")
if gi.size() != di.size():
return fail_test('grad is incorrect size')
if check_undefined_grad:
def warn_bc_breaking():
warnings.warn((
'Backwards compatibility: New undefined gradient support checking '
'feature is enabled by default, but it may break existing callers '
'of this function. If this is true for you, you can call this '
'function with "check_undefined_grad=False" to disable the feature'
))
def check_undefined_grad_support(output_to_check):
grads_output = [
torch.zeros_like(
o, memory_format=torch.legacy_contiguous_format)
for o in output_to_check
]
try:
grads_input = torch.autograd.grad(output_to_check,
diff_input_list,
grads_output,
allow_unused=True)
except RuntimeError:
warn_bc_breaking()
return fail_test((
'Expected backward function to handle undefined output grads. '
'Please look at "Notes about undefined output gradients" in '
'"tools/autograd/derivatives.yaml"'))
for gi, i in zip(grads_input, diff_input_list):
if (gi is not None) and (not gi.eq(0).all()):
warn_bc_breaking()
return fail_test((
'Expected all input grads to be undefined or zero when all output grads are undefined '
'or zero. Please look at "Notes about undefined output gradients" in '
'"tools/autograd/derivatives.yaml"'))
return True
# All backward functions must work properly if all output grads are undefined
outputs_to_check = [[
torch._C._functions.UndefinedGrad()(o)
for o in _differentiable_outputs(func(*tupled_inputs))
# This check filters out Tensor-likes that aren't instances of Tensor.
if isinstance(o, torch.Tensor)
]]
# If there are multiple output grads, we should be able to undef one at a time without error
if len(outputs_to_check[0]) > 1:
for undef_grad_idx in range(len(output)):
output_to_check = _differentiable_outputs(
func(*tupled_inputs))
outputs_to_check.append([
torch._C._functions.UndefinedGrad()(o)
if idx == undef_grad_idx else o
for idx, o in enumerate(output_to_check)
])
for output_to_check in outputs_to_check:
if not check_undefined_grad_support(output_to_check):
return False
return True
def wrapped_fn():
inp = tuple(
prepped_input(a, x if i ==
input_idx else None) if is_tensor_like(a) else a
for i, a in enumerate(_as_tuple(inputs)))
return tuple(a.clone() for a in _as_tuple(fn(*inp)))
def is_float_or_complex_tensor(obj):
return is_tensor_like(obj) and (obj.is_floating_point()
or obj.is_complex())
