def jvp(g):
ret = []
ng = np.broadcast_to(g, np.shape(ans))
shape = np.shape(ng)
for idx in range(shape[axis]):
ret.append(np.take(ng, idx, axis=axis))
return tuple(ret)
def repeat_to_match_shape(g, shape, dtype, axis, keepdims):
"""Returns the array g repeated along axis to fit vector space vs.
Also returns the number of repetitions of the array."""
with ua.set_backend(numpy_backend, coerce=True):
if shape == ():
return g, 1
axis = list(axis) if isinstance(axis, tuple) else axis
new_shape = np.array(shape, dtype=int)
new_shape[axis] = 1
num_reps = np.prod(np.array(shape)[axis])
return np.broadcast_to(np.reshape(g, new_shape), shape), num_reps
def __setitem__(self, k, v):
if isinstance(k, DiffArray):
if not k.var:
raise ValueError("k does not have a set var")
k = k.var
if not isinstance(k, Variable):
raise ValueError("k must be a Variable")
if not isinstance(v, DiffArray):
v = DiffArray(v)
v = np.broadcast_to(v, self.shape)
super().__setitem__(k, v)
def __ua_function__(func, args, kwargs, skip_vars=None):
from udiff import SKIP_SELF
from ._func_diff_registry import global_registry
if skip_vars is None:
skip_vars = set()
extracted_args = func.arg_extractor(*args, **kwargs)
arr_args = tuple(x.value for x in extracted_args if x.type is np.ndarray)
input_args = tuple(x.value for x in extracted_args
if x.coercible and x.type is np.ndarray)
with SKIP_SELF:
if len(arr_args) == 0:
out = func(*args, **kwargs)
return DiffArray(out)
a, kw = replace_arrays(func, args, kwargs,
(x.arr if x is not None else None
for x in arr_args))
out_arr = func(*a, **kw)
out = DiffArray(out_arr)
diff_keys = set.union(*(set(d_j.diffs.keys()) for d_j in input_args))
with ua.set_backend(NoRecurseBackend(set.union(skip_vars, diff_keys))):
for k in diff_keys - skip_vars:
diff_args = []
for arr in arr_args:
if arr is None:
diff_args.append(None)
continue
if k in arr.diffs:
diff_args.append((arr, arr.diffs[k]))
else:
diff_args.append((arr, np.broadcast_to(0, arr.shape)))
a, kw = replace_arrays(func, args, kwargs, diff_args)
if func is np.ufunc.__call__:
diff_arr = global_registry[a[0]](*a[1:], **kw)
else:
diff_arr = global_registry[func](*a, **kw)
out.diffs[k] = diff_arr
return out
def __ua_function__(func, args, kwargs, tree=None):
from udiff import SKIP_SELF
from ._func_diff_registry import global_registry
extracted_args = func.arg_extractor(*args, **kwargs)
arr_args = tuple(x.value for x in extracted_args if x.type is np.ndarray)
input_args = tuple(
x.value for x in extracted_args if x.coercible and x.type is np.ndarray
)
if tree is None:
tree = compute_diff_tree(*input_args)
with SKIP_SELF:
if len(arr_args) == 0:
out = func(*args, **kwargs)
return DiffArray(out)
a, kw = replace_arrays(
func, args, kwargs, (x.arr if x is not None else None for x in arr_args)
)
out_arr = func(*a, **kw)
out = DiffArray(out_arr)
for k in tree:
diff_args = []
for arr in arr_args:
if arr is None:
diff_args.append(None)
continue
if k in arr.diffs:
diff_args.append((arr, arr.diffs[k]))
else:
diff_args.append((arr, np.broadcast_to(0, arr.shape)))
a, kw = replace_arrays(func, args, kwargs, diff_args)
with ua.set_backend(NoRecurseBackend(tree[k])):
if func is np.ufunc.__call__:
diff_arr = global_registry[a[0]](*a[1:], **kw)
else:
diff_arr = global_registry[func](*a, **kw)
out.diffs[k] = diff_arr
return out
register_diff(np.true_divide, divide_diff) register_diff(np.power, pow_diff) register_diff(np.positive, lambda x: +x[1]) register_diff(np.negative, lambda x: -x[1]) register_diff(np.conj, lambda x: np.conj(x[1])) register_diff(np.conj, lambda x: np.conj(x[1])) register_diff(np.exp, lambda x: x[1] * np.exp(x[0])) register_diff(np.exp2, lambda x: x[1] * np.log(2) * np.exp(x[0])) register_diff(np.log, lambda x: x[1] / x[0]) register_diff(np.log2, lambda x: x[1] / (np.log(2) * x[0])) register_diff(np.log10, lambda x: x[1] / (np.log(10) * x[0])) register_diff(np.sqrt, lambda x: x[1] / (2 * np.sqrt(x[0]))) register_diff(np.square, lambda x: 2 * x[1] * x[0]) register_diff(np.cbrt, lambda x: x[1] / (3 * (x[0]**(2 / 3)))) register_diff(np.reciprocal, lambda x: -x[1] / np.square(x[0])) register_diff(np.broadcast_to, lambda x, shape: np.broadcast_to(x[1], shape)) register_diff(np.sin, lambda x: x[1] * np.cos(x[0])) register_diff(np.cos, lambda x: -x[1] * np.sin(x[0])) register_diff(np.tan, lambda x: x[1] / np.square(np.cos(x[0]))) register_diff(np.arcsin, lambda x: x[1] / np.sqrt(1 - np.square(x[0]))) register_diff(np.arccos, lambda x: -x[1] / np.sqrt(1 - np.square(x[0]))) register_diff(np.arctan, lambda x: x[1] / (1 + np.square(x[0]))) register_diff(np.arctan2, arctan2_diff) register_diff(np.sinh, lambda x: x[1] * np.cosh(x[0])) register_diff(np.cosh, lambda x: x[1] * np.sinh(x[0])) register_diff(np.tanh, lambda x: x[1] / np.square(np.cosh(x[0]))) register_diff(np.arcsinh, lambda x: x[1] / np.sqrt(1 + np.square(x[0]))) register_diff(np.arccosh, lambda x: x[1] / np.sqrt(1 - np.square(x[0]))) register_diff(np.arctanh, lambda x: x[1] / (1 - np.square(x[0])))
defjvp,
defjvp_argnum,
def_linear,
)
# ----- Functions that are constant w.r.t. continuous inputs -----
defjvp(np.nan_to_num,
lambda ans, x: lambda g: np.where(np.isfinite(x), g, 0.0))
# ----- Binary ufuncs (linear) -----
def_linear(np.multiply)
# ----- Binary ufuncs -----
defjvp(
np.add,
lambda ans, x, y: lambda g: np.broadcast_to(g, np.shape(ans)),
lambda ans, x, y: lambda g: np.broadcast_to(g, np.shape(ans)),
)
defjvp(
np.subtract,
lambda ans, x, y: lambda g: np.broadcast_to(g, np.shape(ans)),
lambda ans, x, y: lambda g: np.broadcast_to(-g, np.shape(ans)),
)
defjvp(
np.multiply,
lambda ans, x, y: lambda g: np.broadcast_to(g * y, np.shape(ans)),
lambda ans, x, y: lambda g: np.broadcast_to(x * g, np.shape(ans)),
)
defjvp(np.divide, "same", lambda ans, x, y: lambda g: -g * x / y**2)
defjvp(
np.maximum,
gfpof = x1[1] / x1[0] * x2[0]
return ftog * (gplogf + gfpof)
def matmul_diff(x1, x2):
return x1[0] @ x2[1] + x1[1] @ x2[0]
def arctan2_diff(x1, x2):
return (x1[1] * x2[0] - x1[0] * x2[1]) / (np.square(x1[0]) +
np.square(x2[0]))
register_diff(
np.sign,
lambda x: np.broadcast_to(np.where(x[0].arr == 0, float("nan"), 0), x[1].
shape),
)
register_diff(np.add, lambda x1, x2: x1[1] + x2[1])
register_diff(np.subtract, lambda x1, x2: x1[1] - x2[1])
register_diff(np.multiply, multiply_diff)
register_diff(np.matmul, matmul_diff)
register_diff(np.divide, divide_diff)
register_diff(np.true_divide, divide_diff)
register_diff(np.power, pow_diff)
register_diff(
np.absolute,
lambda x: x[1] * np.where(np.sign(x[0]) == 0, float("nan"), np.sign(x[0])),
)
register_diff(np.positive, lambda x: +x[1])
register_diff(np.negative, lambda x: -x[1])
register_diff(np.conj, lambda x: np.conj(x[1]))
gplogf = np.log(x1[0]) * x2[1]
gfpof = x1[1] / x1[0] * x2[0]
return ftog * (gplogf + gfpof)
def matmul_diff(x1, x2):
return x1[0] @ x2[1] + x1[1] @ x2[0]
def arctan2_diff(x1, x2):
return (x1[1] * x2[0] - x1[0] * x2[1]) / (np.square(x1[0]) +
np.square(x2[0]))
register_diff(
np.sign, lambda x: np.broadcast_to(
np.where(x[0].arr == 0, float('nan'), 0), x[1].shape))
register_diff(np.add, lambda x1, x2: x1[1] + x2[1])
register_diff(np.subtract, lambda x1, x2: x1[1] - x2[1])
register_diff(np.multiply, multiply_diff)
register_diff(np.matmul, matmul_diff)
register_diff(np.divide, divide_diff)
register_diff(np.true_divide, divide_diff)
register_diff(np.power, pow_diff)
register_diff(
np.absolute,
lambda x: x[1] * np.where(np.sign(x[0]) == 0, float('nan'), np.sign(x[0])))
register_diff(np.positive, lambda x: +x[1])
register_diff(np.negative, lambda x: -x[1])
register_diff(np.conj, lambda x: np.conj(x[1]))
register_diff(np.exp, lambda x: x[1] * np.exp(x[0]))
register_diff(np.exp2, lambda x: x[1] * np.log(2) * np.exp2(x[0]))
