def mtp_hessian_grad_and_value(fun, x):
"""
Makes a function that returns MTP, Jacobian and value of a function.
For a scalar-valued function `fun` the matrix-Tressian-product (MTP) is
here defined as a function of a matrix `m` corresponding to
mtp(m) = sum(m[:, :] * t[:, :, :], axis=(-1, -2))
where `t` is the 'Tressian' of `f = fun(x)` wrt `x` i.e. the 3D array of
third-order partial derivatives of the scalar-valued function such that
t[i, j, k] = ∂³f / (∂x[i] ∂x[j] ∂x[k])
Assumes that the function `fun` broadcasts along the first dimension of the
input being differentiated with respect to such that a batch of outputs can
be computed concurrently for a batch of inputs.
"""
mtp, (hessian, grad,
val) = make_vjp(lambda x: atuple(hessian_grad_and_value(fun)(x)), x)
return (
lambda m: mtp((m, vspace(grad).zeros(), vspace(val).zeros())),
hessian,
grad,
val,
)
def grad_and_value(fun, x):
"""
Returns a function that returns both gradient and value of a function.
"""
vjp, val = _make_vjp(fun, x)
if not vspace(val).size == 1:
raise TypeError("grad_and_value only applies to real scalar-output "
"functions.")
return vjp(vspace(val).ones()), val
def grad_and_value(fun, x):
"""
Returns a function that returns both gradient and value of a function.
"""
vjp, val = make_vjp(fun, x)
if not vspace(val).size == 1:
raise TypeError("grad_and_value only applies to real scalar-output"
" functions.")
return vjp(vspace(val).ones()), val
def _grad_with_forward(fun, x):
"""This function is a replica of ``autograd.grad``, with the only
difference being that it returns both the gradient *and* the forward pass
value."""
vjp, ans = _make_vjp(fun, x)
if not vspace(ans).size == 1:
raise TypeError(
"Grad only applies to real scalar-output functions. "
"Try jacobian, elementwise_grad or holomorphic_grad.")
grad_value = vjp(vspace(ans).ones())
return grad_value, ans
def jacobian_pkl(fun, x):
vjp, ans = _make_vjp(fun, x)
ans_vspace = vspace(ans)
jacobian_shape = ans_vspace.shape + vspace(x).shape
grads = map(vjp, ans_vspace.standard_basis())
grads_out = np.stack(grads)
if (np.prod(jacobian_shape) == np.prod(grads_out.shape)):
return np.reshape(grads_out, jacobian_shape)
else:
my_jacobian_shape = ans_vspace.shape + vspace(x).shape + (
2, ) # 2 to support real/im
re_im_grads = np.squeeze(np.reshape(grads_out, my_jacobian_shape))
out = re_im_grads[..., 0] + 1j * re_im_grads[..., 1]
return out
def jacobian_and_value(fun, x):
"""
Returns a function that returns both the Jacobian and value of a function.
Assumes that the function `fun` broadcasts along the first dimension of the
input being differentiated with respect to such that a batch of outputs can
be computed concurrently for a batch of inputs.
"""
val = fun(x)
v_vspace = vspace(val)
x_vspace = vspace(x)
x_rep = np.tile(x, (v_vspace.size, ) + (1, ) * x_vspace.ndim)
vjp_rep, _ = _make_vjp(fun, x_rep)
jacobian_shape = v_vspace.shape + x_vspace.shape
basis_vectors = np.array([b for b in v_vspace.standard_basis()])
jacobian = vjp_rep(basis_vectors)
return np.reshape(jacobian, jacobian_shape), val
def get_shape(x):
""" Gets the shape of x, even if it is not an array """
if isinstance(x, float) or isinstance(x, int):
return (1, )
elif isinstance(x, tuple) or isinstance(x, list):
return (len(x), )
else:
return vspace(x).shape
def irfft_grad(get_args, rfft_fun, ans, x, *args, **kwargs):
axes, gs, norm = get_args(x, *args, **kwargs)
vs = vspace(x)
gvs = vspace(ans)
check_no_repeated_axes(axes)
if gs is None: gs = [gvs.shape[i] for i in axes]
check_even_shape(gs)
# gs is the full fft shape
# s is the compressed shape
s = list(gs)
s[-1] = s[-1] // 2 + 1
def vjp(g):
r = match_complex(x, truncate_pad((rfft_fun(g, *args, **kwargs)), vs.shape))
fac = make_rfft_factors(axes, vs.shape, s, gs, norm)
r = anp.conj(r) * fac
return r
return vjp
def jacobian_and_value(fun, x):
"""
Returns a function that returns both the Jacobian and value of a
function.
Assumes that the function `fun` broadcasts along the first dimension of
the input being differentiated with respect to such that a batch of
outputs can be computed concurrently for a batch of inputs.
"""
val = fun(x)
v_vspace = vspace(val)
x_vspace = vspace(x)
x_rep = np.tile(x, (v_vspace.size,) + (1,) * x_vspace.ndim)
vjp_rep, _ = make_vjp(fun, x_rep)
jacobian_shape = v_vspace.shape + x_vspace.shape
basis_vectors = np.array([b for b in v_vspace.standard_basis()])
jacobian = vjp_rep(basis_vectors)
return np.reshape(jacobian, jacobian_shape), val
def rfft_grad(get_args, irfft_fun, ans, x, *args, **kwargs):
axes, s, norm = get_args(x, *args, **kwargs)
vs = vspace(x)
gvs = vspace(ans)
check_no_repeated_axes(axes)
if s is None: s = [vs.shape[i] for i in axes]
check_even_shape(s)
# s is the full fft shape
# gs is the compressed shape
gs = list(s)
gs[-1] = gs[-1] // 2 + 1
fac = make_rfft_factors(axes, gvs.shape, gs, s, norm)
def vjp(g):
g = anp.conj(g / fac)
r = match_complex(x, truncate_pad((irfft_fun(g, *args, **kwargs)), vs.shape))
return r
return vjp
def fixed_point_vjp(ans, f, a, x0, distance, tol):
def rev_iter(params):
a, x_star, x_star_bar = params
vjp_x, _ = make_vjp(f(a))(x_star)
vs = vspace(x_star)
return lambda g: vs.add(vjp_x(g), x_star_bar)
vjp_a, _ = make_vjp(lambda x, y: f(x)(y))(a, ans)
return lambda g: vjp_a(fixed_point(rev_iter, tuple((a, ans, g)),
vspace(x0).zeros(), distance, tol))
def jacobian_forward(fun, x):
""" Compute jacobian of fun with respect to x using forward mode differentiation"""
jvp = make_jvp(fun, x)
# ans = fun(x)
val_grad = map(lambda b: jvp(b), vspace(x).standard_basis())
vals, grads = zip(*val_grad)
ans = np.zeros((list(vals)[0].size,)) # fake answer so that dont have to compute it twice
m, n = _jac_shape(x, ans)
return np.reshape(np.stack(grads), (m, n)).T
def hessian_grad_and_value(fun, x):
"""
Returns a function that returns Hessian, gradient and value of a function.
Assumes that the function `fun` broadcasts along the first dimension of the
input being differentiated with respect to such that a batch of outputs can
be computed concurrently for a batch of inputs.
"""
def grad_fun(x):
vjp, val = _make_vjp(fun, x)
return vjp(vspace(val).ones()), val
x_vspace = vspace(x)
x_rep = np.tile(x, (x_vspace.size, ) + (1, ) * x_vspace.ndim)
vjp_grad, (grad, val) = _make_vjp(lambda x: atuple(grad_fun(x)), x_rep)
hessian_shape = x_vspace.shape + x_vspace.shape
basis_vectors = np.array([b for b in x_vspace.standard_basis()])
hessian = vjp_grad((basis_vectors, vspace(val).zeros()))
return np.reshape(hessian, hessian_shape), grad[0], val[0]
def hessian_grad_and_value(fun, x):
"""
Returns a function that returns the Hessian, gradient and value of a
function.
Assumes that the function `fun` broadcasts along the first dimension of
the input being differentiated with respect to such that a batch of
outputs can be computed concurrently for a batch of inputs.
"""
def grad_fun(x):
vjp, val = make_vjp(fun, x)
return vjp(vspace(val).ones()), val
x_vspace = vspace(x)
x_rep = np.tile(x, (x_vspace.size,) + (1,) * x_vspace.ndim)
vjp_grad, (grad, val) = make_vjp(lambda x: atuple(grad_fun(x)), x_rep)
hessian_shape = x_vspace.shape + x_vspace.shape
basis_vectors = np.array([b for b in x_vspace.standard_basis()])
hessian = vjp_grad((basis_vectors, vspace(val).zeros()))
return np.reshape(hessian, hessian_shape), grad[0], val[0]
def view_update(data, view_fun):
view_vjp, item = make_vjp(view_fun)(data)
item_vs = vspace(item)
def update(new_item):
assert item_vs == vspace(new_item), \
"Please ensure new_item shape and dtype match the data view."
diff = view_vjp(
item_vs.add(new_item, item_vs.scalar_mul(item, -np.uint64(1))))
return vspace(data).add(data, diff)
return item, update
def irfft_grad(get_args, rfft_fun, ans, x, *args, **kwargs):
axes, gs, norm = get_args(x, *args, **kwargs)
vs = vspace(x)
gvs = vspace(ans)
check_no_repeated_axes(axes)
if gs is None: gs = [gvs.shape[i] for i in axes]
check_even_shape(gs)
# gs is the full fft shape
# s is the compressed shape
s = list(gs)
s[-1] = s[-1] // 2 + 1
def vjp(g):
r = match_complex(
x, truncate_pad((rfft_fun(g, *args, **kwargs)), vs.shape))
fac = make_rfft_factors(axes, vs.shape, s, gs, norm)
r = anp.conj(r) * fac
return r
return vjp
def rfft_grad(get_args, irfft_fun, ans, x, *args, **kwargs):
axes, s, norm = get_args(x, *args, **kwargs)
vs = vspace(x)
gvs = vspace(ans)
check_no_repeated_axes(axes)
if s is None: s = [vs.shape[i] for i in axes]
check_even_shape(s)
# s is the full fft shape
# gs is the compressed shape
gs = list(s)
gs[-1] = gs[-1] // 2 + 1
fac = make_rfft_factors(axes, gvs.shape, gs, s, norm)
def vjp(g):
g = anp.conj(g / fac)
r = match_complex(
x, truncate_pad((irfft_fun(g, *args, **kwargs)), vs.shape))
return r
return vjp
def ans_jacobian(function, argnum):
"""
Get the value and the jacobian of a function.
This differential operator follows autograd's jacobian implementation:
https://github.com/HIPS/autograd/blob/master/autograd/differential_operators.py
Args:
function :: any -> any - the function to differentiate
argnum :: int - the argument number to differentiate with respect to
Returns:
ans_jacobian any -> tuple(any :: any, jacobian :: ndarray) - a function
that returns the value of `function` and the jacobian
of `function` evaluated at a given argument of `function`
"""
vjp, ans = _make_vjp(function, argnum)
ans_vspace = vspace(ans)
jacobian_shape = ans_vspace.shape + vspace(argnum).shape
grads = list(map(vjp, ans_vspace.standard_basis()))
jacobian = np.reshape(np.stack(grads), jacobian_shape)
return ans, jacobian
def ans_jacobian(function, argnum):
"""
Get the value and the jacobian of a function.
This differential operator supports numpy and pycuda arrays.
Args:
function :: any -> any - the function to differentiate
argnum :: int - the argument number to differentiate with respect to
Returns:
ans_jacobian any -> tuple(any :: any, jacobian :: ndarray) - a function
that returns the value of `function` and the jacobian
of `function` evaluated at a given argument of `function`
"""
vjp, ans = _make_vjp(function, argnum)
ans_vspace = vspace(ans)
jacobian_shape = ans_vspace.shape + vspace(argnum).shape
grads = list(map(vjp, ans_vspace.standard_basis()))
if isinstance(grads[0], np.ndarray):
jacobian = np.reshape(np.stack(grads), jacobian_shape)
elif isinstance(grads[0], GPUArray):
jacobian = stack_gpu(grads).reshape(jacobian_shape)
return ans, jacobian
def mtp_hessian_grad_and_value(fun, x):
"""
Returns a function that returns MTP, Jacobian and value of a function.
For a scalar-valued function `fun` the matrix-Tressian-product (MTP) is
here defined as a function of a matrix `m` corresponding to
mtp(m) = sum(m[:, :] * t[:, :, :], axis=(-1, -2))
where `t` is the 'Tressian' of `f = fun(x)` wrt `x` i.e. the rank-3
tensor of third-order partial derivatives of the scalar-valued function
such that
t[i, j, k] = d**3 f / (dx[i] * dx[j] * dx[k])
Assumes that the function `fun` broadcasts along the first dimension of
the input being differentiated with respect to such that a batch of
outputs can be computed concurrently for a batch of inputs.
"""
mtp, (hessian, grad, val) = make_vjp(
lambda x: atuple(hessian_grad_and_value(fun)(x)), x)
return (
lambda m: mtp((m, vspace(grad).zeros(), vspace(val).zeros())),
hessian, grad, val)
def __new__(self, name, base, dic):
cls = type.__new__(container_mateclass, name, base, dic)
cls.register(_np.ndarray)
for type_ in [
float, _np.float64, _np.float32, _np.float16, complex,
_np.complex64, _np.complex128
]:
cls.register(type_)
for method_name in nondiff_methods + diff_methods:
setattr(cls, method_name, anp.__dict__[method_name])
setattr(cls, 'flatten', anp.__dict__['ravel'])
defvjp(func(cls.__getitem__),
lambda ans, A, idx: lambda g: untake(g, idx, vspace(A)))
defjvp(func(cls.__getitem__), 'same')
defjvp(untake, 'same')
setattr(cls, 'reshape', wrapped_reshape)
return cls
def mhp_jacobian_and_value(fun, x):
"""
Returns a function that returns MHP, Jacobian and value of a function.
For a vector-valued function `fun` the matrix-Hessian-product (MHP) is here
defined as a function of a matrix `m` corresponding to
mhp(m) = sum(m[:, :] * h[:, :, :], axis=(-1, -2))
where `h` is the vector-Hessian of `f = fun(x)` wrt `x` i.e. the rank-3
tensor of second-order partial derivatives of the vector-valued function,
such that
h[k, i, j] = (d**2 f[i]) / (dx[j] * dx[k])
Assumes that the function `fun` broadcasts along the first dimension of the
input being differentiated with respect to such that a batch of outputs can
be computed concurrently for a batch of inputs.
"""
mhp, (jacob, val) = _make_vjp(lambda x: atuple(jacobian_and_value(fun)(x)),
x)
return lambda m: mhp((m, vspace(val).zeros())), jacob, val
def mhp_jacobian_and_value(fun, x):
"""
Returns a function that returns MHP, Jacobian and value of a function.
For a vector-valued function `fun` the matrix-Hessian-product (MHP) is
here defined as a function of a matrix `m` corresponding to
mhp(m) = sum(m[:, :] * h[:, :, :], axis=(-1, -2))
where `h` is the vector-Hessian of `f = fun(x)` wrt `x` i.e. the rank-3
tensor of second-order partial derivatives of the vector-valued
function, such that
h[k, i, j] = (d**2 f[i]) / (dx[j] * dx[k])
Assumes that the function `fun` broadcasts along the first dimension of
the input being differentiated with respect to such that a batch of
outputs can be computed concurrently for a batch of inputs.
"""
mhp, (jacob, val) = make_vjp(
lambda x: atuple(jacobian_and_value(fun)(x)), x)
return lambda m: mhp((m, vspace(val).zeros())), jacob, val
@primitive
def untake(x, idx, vs):
if isinstance(idx, list) and (len(idx) == 0
or not isinstance(idx[0], slice)):
idx = onp.array(idx, dtype='int64')
def mut_add(A):
onp.add.at(A, idx, x)
return A
return SparseObject(vs, mut_add)
defvjp(func(ArrayBox.__getitem__),
lambda ans, A, idx: lambda g: untake(g, idx, vspace(A)))
defvjp(untake, lambda ans, x, idx, _: lambda g: g[idx])
def _unpad(array, width):
if anp.isscalar(width):
width = [[width, width]]
elif anp.shape(width) == (1, ):
width = [anp.concatenate((width, width))]
elif anp.shape(width) == (2, ):
width = [width]
if anp.shape(width)[0] == 1:
width = anp.repeat(width, anp.ndim(array), 0)
idxs = tuple(slice(l, -u or None) for l, u in width)
return array[idxs]
def grad_fun(x):
vjp, val = make_vjp(fun, x)
return vjp(vspace(val).ones()), val
def grad_fun(x):
vjp, val = _make_vjp(fun, x)
return vjp(vspace(val).ones()), val
from . import numpy_wrapper as anp
from .numpy_vjps import (untake, balanced_eq, match_complex, replace_zero,
dot_adjoint_0, dot_adjoint_1, tensordot_adjoint_0,
tensordot_adjoint_1, nograd_functions)
from autograd.extend import (defjvp, defjvp_argnum, def_linear, vspace, JVPNode,
register_notrace)
from ..util import func
from .numpy_boxes import ArrayBox
for fun in nograd_functions:
register_notrace(JVPNode, fun)
defjvp(func(ArrayBox.__getitem__), 'same')
defjvp(untake, 'same')
defjvp_argnum(anp.array_from_args, lambda argnum, g, ans, args, kwargs: untake(g, argnum-2, vspace(ans)))
defjvp(anp._array_from_scalar_or_array, None, None,
lambda g, ans, args, kwargs, _: anp._array_from_scalar_or_array(args, kwargs, g))
# ----- Functions that are constant w.r.t. continuous inputs -----
defjvp(anp.nan_to_num, lambda g, ans, x: anp.where(anp.isfinite(x), g, 0.))
# ----- Binary ufuncs (linear) -----
def_linear(anp.multiply)
# ----- Binary ufuncs -----
defjvp(anp.add, lambda g, ans, x, y : broadcast(g, ans),
lambda g, ans, x, y : broadcast(g, ans))
defjvp(anp.subtract, lambda g, ans, x, y : broadcast(g, ans),
lambda g, ans, x, y : broadcast(-g, ans))
defjvp(anp.divide, 'same',
dot_adjoint_0, dot_adjoint_1, tensordot_adjoint_0,
tensordot_adjoint_1, nograd_functions)
from autograd.extend import (defjvp, defjvp_argnum, def_linear, vspace,
JVPNode, register_notrace)
from ..util import func
from .numpy_boxes import ArrayBox
for fun in nograd_functions:
register_notrace(JVPNode, fun)
defjvp(func(ArrayBox.__getitem__), 'same')
defjvp(untake, 'same')
defjvp_argnum(
anp.array_from_args,
lambda argnum, g, ans, args, kwargs: untake(g, argnum - 2, vspace(ans)))
defjvp(
anp._array_from_scalar_or_array, None, None,
lambda g, ans, args, kwargs, _: anp._array_from_scalar_or_array(
args, kwargs, g))
# ----- Functions that are constant w.r.t. continuous inputs -----
defjvp(anp.nan_to_num, lambda g, ans, x: anp.where(anp.isfinite(x), g, 0.))
# ----- Binary ufuncs (linear) -----
def_linear(anp.multiply)
# ----- Binary ufuncs -----
defjvp(anp.add, lambda g, ans, x, y: broadcast(g, ans),
lambda g, ans, x, y: broadcast(g, ans))
defjvp(anp.subtract, lambda g, ans, x, y: broadcast(g, ans),
def jacobian_reverse(fun, x):
""" Compute jacobian of fun with respect to x using reverse mode differentiation"""
vjp, ans = make_vjp(fun, x)
grads = map(vjp, vspace(ans).standard_basis())
m, n = _jac_shape(x, ans)
return npa.reshape(npa.stack(grads), (n, m))
def rev_iter(params):
a, x_star, x_star_bar = params
vjp_x, _ = make_vjp(f(a))(x_star)
vs = vspace(x_star)
return lambda g: vs.add(vjp_x(g), x_star_bar)
irfft_grad(get_fftn_args, rfftn, *args, **kwargs))
defvjp(fftshift, lambda ans, x, axes=None : lambda g:
match_complex(x, anp.conj(ifftshift(anp.conj(g), axes))))
defvjp(ifftshift, lambda ans, x, axes=None : lambda g:
match_complex(x, anp.conj(fftshift(anp.conj(g), axes))))
@primitive
def truncate_pad(x, shape):
# truncate/pad x to have the appropriate shape
slices = [slice(n) for n in shape]
pads = list(zip(anp.zeros(len(shape), dtype=int),
anp.maximum(0, anp.array(shape) - anp.array(x.shape))))
return anp.pad(x, pads, 'constant')[slices]
defvjp(truncate_pad, lambda ans, x, shape: lambda g:
match_complex(x, truncate_pad(g, vspace(x).shape)))
## TODO: could be made less stringent, to fail only when repeated axis has different values of s
def check_no_repeated_axes(axes):
axes_set = set(axes)
if len(axes) != len(axes_set):
raise NotImplementedError("FFT gradient for repeated axes not implemented.")
def check_even_shape(shape):
if shape[-1] % 2 != 0:
raise NotImplementedError("Real FFT gradient for odd lengthed last axes is not implemented.")
def get_fft_args(a, d=None, axis=-1, norm=None, *args, **kwargs):
axes = [axis]
if d is not None: d = [d]
return axes, d, norm
def fft_grad(get_args, fft_fun, ans, x, *args, **kwargs):
axes, s, norm = get_args(x, *args, **kwargs)
check_no_repeated_axes(axes)
vs = vspace(x)
return lambda g: match_complex(
x, truncate_pad(fft_fun(g, *args, **kwargs), vs.shape))
def balanced_eq(x, z, y):
return (x == z) / (1.0 + (x == y))
def replace_zero(x, val):
return anp.where(x, x, val)
# ----- extra functions used internally -----
def array_from_args_gradmaker(argnum, ans, args, kwargs):
return lambda g: g[argnum-2]
defvjp_argnum(anp.array_from_args, array_from_args_gradmaker)
def array_from_scalar_or_array_gradmaker(ans, array_args, array_kwargs, scarray):
ndmin = array_kwargs.get('ndmin', 0)
scarray_ndim = anp.ndim(scarray)
if ndmin > scarray_ndim:
return lambda g: anp.squeeze(g, axis=tuple(range(ndmin - scarray_ndim)))
else:
return lambda g: g
defvjp(anp._array_from_scalar_or_array, array_from_scalar_or_array_gradmaker, argnums=(2,3))
@primitive
def untake(x, idx, vs):
def mut_add(A):
onp.add.at(A, idx, x)
return A
return SparseObject(vs, mut_add)
defvjp(func(ArrayBox.__getitem__), lambda ans, A, idx: lambda g: untake(g, idx, vspace(A)))
defvjp(untake, lambda ans, x, idx, _: lambda g: g[idx])
def elementwise_grad(fun, x, initial_grad=None):
vjp, ans = _make_vjp(fun, x)
if vspace(ans).iscomplex:
raise TypeError(
"Elementwise_grad only applies to real-output functions.")
return vjp(vspace(ans).ones() if initial_grad is None else initial_grad)
else:
return lambda g: g
defvjp(
acp._array_from_scalar_or_array,
array_from_scalar_or_array_gradmaker,
argnums=(2, 3),
)
@primitive
def untake(x, idx, vs):
def mut_add(A):
# in numpy codebase, this used to be:
# onp.add.at(A, idx, x)
# according to https://docs-cupy.chainer.org/en/stable/reference/ufunc.html?highlight=ufunc.at,
# scatter_add is the correct function to use.
# TODO: PR into cupy codebase the ability to use scatter_add with float64?
ocpx.scatter_add(A, idx, x)
return A
return SparseObject(vs, mut_add)
defvjp(
func(container.__getitem__),
lambda ans, A, idx: lambda g: untake(g, idx, vspace(A)), # noqa: E501
)
defvjp(untake, lambda ans, x, idx, _: lambda g: g[idx])
def fft_grad(get_args, fft_fun, ans, x, *args, **kwargs):
axes, s, norm = get_args(x, *args, **kwargs)
check_no_repeated_axes(axes)
vs = vspace(x)
return lambda g: match_complex(x, truncate_pad(fft_fun(g, *args, **kwargs), vs.shape))
def array_from_scalar_or_array_gradmaker(ans, array_args, array_kwargs, scarray):
ndmin = array_kwargs.get('ndmin', 0)
scarray_ndim = anp.ndim(scarray)
if ndmin > scarray_ndim:
return lambda g: anp.squeeze(g, axis=tuple(range(ndmin - scarray_ndim)))
else:
return lambda g: g
defvjp(anp._array_from_scalar_or_array, array_from_scalar_or_array_gradmaker, argnums=(2,3))
@primitive
def untake(x, idx, vs):
def mut_add(A):
onp.add.at(A, idx, x)
return A
return SparseObject(vs, mut_add)
defvjp(func(ArrayBox.__getitem__), lambda ans, A, idx: lambda g: untake(g, idx, vspace(A)))
defvjp(untake, lambda ans, x, idx, _: lambda g: g[idx])
def _unpad(array, width):
if anp.isscalar(width):
width = [[width, width]]
elif anp.shape(width) == (1,):
width = [anp.concatenate((width, width))]
elif anp.shape(width) == (2,):
width = [width]
if anp.shape(width)[0] == 1:
width = anp.repeat(width, anp.ndim(array), 0)
idxs = [slice(l, -u or None) for l, u in width]
return array[idxs]
def pad_vjp(ans, array, pad_width, mode, **kwargs):
@primitive
def truncate_pad(x, shape):
# truncate/pad x to have the appropriate shape
slices = [slice(n) for n in shape]
pads = list(
zip(anp.zeros(len(shape), dtype=int),
anp.maximum(0,
anp.array(shape) - anp.array(x.shape))))
return anp.pad(x, pads, 'constant')[slices]
defvjp(
truncate_pad, lambda ans, x, shape: lambda g: match_complex(
x, truncate_pad(g,
vspace(x).shape)))
## TODO: could be made less stringent, to fail only when repeated axis has different values of s
def check_no_repeated_axes(axes):
axes_set = set(axes)
if len(axes) != len(axes_set):
raise NotImplementedError(
"FFT gradient for repeated axes not implemented.")
def check_even_shape(shape):
if shape[-1] % 2 != 0:
raise NotImplementedError(
"Real FFT gradient for odd lengthed last axes is not implemented.")