def hypot(x1, x2):
_check_arraylike("hypot", x1, x2)
x1, x2 = _promote_dtypes_inexact(x1, x2)
x1 = lax.abs(x1)
x2 = lax.abs(x2)
x1, x2 = maximum(x1, x2), minimum(x1, x2)
return lax.select(x1 == 0, x1, x1 * lax.sqrt(1 + lax.square(lax.div(x2, lax.select(x1 == 0, lax_internal._ones(x1), x1)))))
def _normalize(x, y):
z = jnp.where(jnp.isinf(x), x, x + y)
zz = jnp.where(
lax.abs(x) > lax.abs(y),
x - z + y,
y - z + x,
)
return z, jnp.where(jnp.isinf(z), 0, zz)
def _add2(x, y):
(x, xx), (y, yy) = x, y
r = x + y
s = jnp.where(
lax.abs(x) > lax.abs(y),
x - r + y + yy + xx,
y - r + x + xx + yy,
)
z = r + s
zz = r - z + s
return (z, zz)
def _sub2(x, y):
(x, xx), (y, yy) = x, y
r = x - y
s = jnp.where(
lax.abs(x) > lax.abs(y),
x - r - y - yy + xx,
-y - r + x + xx - yy,
)
z = r + s
zz = r - z + s
return (z, zz)
def isinf(x):
_check_arraylike("isinf", x)
dtype = dtypes.dtype(x)
if dtypes.issubdtype(dtype, np.floating):
return lax.eq(lax.abs(x), _constant_like(x, np.inf))
elif dtypes.issubdtype(dtype, np.complexfloating):
re = lax.real(x)
im = lax.imag(x)
return lax.bitwise_or(lax.eq(lax.abs(re), _constant_like(re, np.inf)),
lax.eq(lax.abs(im), _constant_like(im, np.inf)))
else:
return lax.full_like(x, False, dtype=np.bool_)
def _normalize_float(x): info = dtypes.finfo(dtypes.dtype(x)) cond = lax.abs(x) < info.tiny x1 = _where(cond, x * _lax_const(x, 1 << info.nmant), x) x2 = _where(cond, lax.full_like(x, -info.nmant, dtype=np.int32), lax.full_like(x, 0, dtype=np.int32)) int_type = _INT_DTYPES[info.bits] return lax.bitcast_convert_type(x1, int_type), x2
def logsumexp(a, axis=None, b=None, keepdims=False, return_sign=False):
if b is not None:
a, b = jnp.broadcast_arrays(a, b)
dims = _reduction_dims(a, axis)
dimadd = lambda x: lax.expand_dims(x, dims)
amax = lax.reduce(a, _constant_like(a, -np.inf), lax.max, dims)
amax = lax.stop_gradient(
lax.select(lax.is_finite(amax), amax, lax.full_like(amax, 0)))
amax_singletons = dimadd(amax)
if b is None:
out = lax.add(
lax.log(
lax.reduce(lax.exp(lax.sub(a, amax_singletons)),
_constant_like(a, 0), lax.add, dims)), amax)
sign = jnp.where(jnp.isnan(out), np.nan, 1.0).astype(out.dtype)
sign = jnp.where(out == -np.inf, 0.0, sign)
else:
sumexp = lax.reduce(lax.mul(lax.exp(lax.sub(a, amax_singletons)), b),
_constant_like(a, 0), lax.add, dims)
sign = lax.stop_gradient(lax.sign(sumexp))
out = lax.add(lax.log(lax.abs(sumexp)), amax)
if return_sign:
return (dimadd(out), dimadd(sign)) if keepdims else (out, sign)
if b is not None:
out = jnp.where(sign < 0, np.nan, out)
return dimadd(out) if keepdims else out
def logsumexp(a, axis=None, b=None, keepdims=False, return_sign=False):
if b is not None:
a, b = _promote_args_inexact("logsumexp", a, b)
a = jnp.where(b != 0, a, -jnp.inf)
pos_dims, dims = _reduction_dims(a, axis)
amax = jnp.max(a, axis=dims, keepdims=keepdims)
amax = lax.stop_gradient(
lax.select(lax.is_finite(amax), amax, lax.full_like(amax, 0)))
amax_with_dims = amax if keepdims else lax.expand_dims(amax, pos_dims)
if b is None:
out = lax.add(
lax.log(
jnp.sum(lax.exp(lax.sub(a, amax_with_dims)),
axis=dims,
keepdims=keepdims)), amax)
sign = jnp.where(jnp.isnan(out), np.nan, 1.0).astype(out.dtype)
sign = jnp.where(out == -np.inf, 0.0, sign)
else:
sumexp = jnp.sum(lax.mul(lax.exp(lax.sub(a, amax_with_dims)), b),
axis=dims,
keepdims=keepdims)
sign = lax.stop_gradient(lax.sign(sumexp))
out = lax.add(lax.log(lax.abs(sumexp)), amax)
if return_sign:
return (out, sign)
if b is not None:
out = jnp.where(sign < 0, np.nan, out)
return out
def svd(a,
full_matrices: bool = True,
compute_uv: bool = True,
hermitian: bool = False):
a, = _promote_dtypes_inexact(jnp.asarray(a))
if hermitian:
w, v = lax_linalg.eigh(a)
s = lax.abs(v)
if compute_uv:
sign = lax.sign(v)
idxs = lax.broadcasted_iota(np.int64,
s.shape,
dimension=s.ndim - 1)
s, idxs, sign = lax.sort((s, idxs, sign), dimension=-1, num_keys=1)
s = lax.rev(s, dimensions=[s.ndim - 1])
idxs = lax.rev(idxs, dimensions=[s.ndim - 1])
sign = lax.rev(sign, dimensions=[s.ndim - 1])
u = jnp.take_along_axis(w, idxs[..., None, :], axis=-1)
vh = _H(u * sign[..., None, :])
return u, s, vh
else:
return lax.rev(lax.sort(s, dimension=-1), dimensions=[s.ndim - 1])
return lax_linalg.svd(a,
full_matrices=full_matrices,
compute_uv=compute_uv)
def _normalize_float(x):
info = dtypes.finfo(dtypes.dtype(x))
int_type = _INT_DTYPES[info.bits]
cond = lax.abs(x) < info.tiny
x1 = _where(cond, x * _lax_const(x, 1 << info.nmant), x)
x2 = _where(cond, int_type(-info.nmant), int_type(0))
return lax.bitcast_convert_type(x1, int_type), x2
def var(a, axis=None, keepdims=False, ddof=0):
if ddof != 0:
raise NotImplementedError("Only implemented for ddof=0.")
centered = subtract(a, mean(a, axis, keepdims=True))
if iscomplexobj(centered):
centered = lax.abs(centered)
return mean(lax.mul(centered, centered), axis, keepdims=keepdims)
def _logaddexp(x1, x2):
"""
Logaddexp while ignoring the custom_jvp rule.
"""
amax = lax.max(x1, x2)
delta = lax.sub(x1, x2)
return lax.select(jnp.isnan(delta),
lax.add(x1, x2), # NaNs or infinities of the same sign.
lax.add(amax, lax.log1p(lax.exp(-lax.abs(delta)))))
def floor_divide(x1, x2):
x1, x2 = _promote_args("floor_divide", x1, x2)
dtype = dtypes.dtype(x1)
if dtypes.issubdtype(dtype, np.integer):
quotient = lax.div(x1, x2)
select = logical_and(lax.sign(x1) != lax.sign(x2), lax.rem(x1, x2) != 0)
# TODO(mattjj): investigate why subtracting a scalar was causing promotion
return _where(select, quotient - 1, quotient)
elif dtypes.issubdtype(dtype, np.complexfloating):
x1r = lax.real(x1)
x1i = lax.imag(x1)
x2r = lax.real(x2)
x2i = lax.imag(x2)
which = lax.ge(lax.abs(x2r), lax.abs(x2i))
rat1 = _where(which, lax.full_like(x2i, 1), lax.div(x2r, x2i))
rat2 = _where(which, lax.div(x2i, x2r), _lax_const(x2i, 1))
out = lax.floor(lax.div(lax.add(lax.mul(x1r, rat1), lax.mul(x1i, rat2)),
lax.add(lax.mul(x2r, rat1), lax.mul(x2i, rat2))))
return lax.convert_element_type(out, dtype)
else:
return _float_divmod(x1, x2)[0]
def logaddexp(x1, x2):
x1, x2 = _promote_args_inexact("logaddexp", x1, x2)
amax = lax.max(x1, x2)
if dtypes.issubdtype(x1.dtype, np.floating):
delta = lax.sub(x1, x2)
return lax.select(lax_internal._isnan(delta),
lax.add(x1, x2), # NaNs or infinities of the same sign.
lax.add(amax, lax.log1p(lax.exp(lax.neg(lax.abs(delta))))))
else:
delta = lax.sub(lax.add(x1, x2), lax.mul(amax, _constant_like(amax, 2)))
out = lax.add(amax, lax.log1p(lax.exp(delta)))
return lax.complex(lax.real(out), _wrap_between(lax.imag(out), np.pi))
def _ndtr(x):
"""Implements ndtr core logic."""
dtype = lax.dtype(x).type
half_sqrt_2 = dtype(0.5) * np.sqrt(2., dtype=dtype)
w = x * half_sqrt_2
z = lax.abs(w)
y = lax.select(
lax.lt(z, half_sqrt_2),
dtype(1.) + lax.erf(w),
lax.select(lax.gt(w, dtype(0.)),
dtype(2.) - lax.erfc(z), lax.erfc(z)))
return dtype(0.5) * y
def logsumexp(a, axis=None, b=None, keepdims=False, return_sign=False):
if b is not None:
a, b = _promote_args_inexact("logsumexp", a, b)
a = jnp.where(b != 0, a, -jnp.inf)
else:
a, = _promote_args_inexact("logsumexp", a)
pos_dims, dims = _reduction_dims(a, axis)
amax = jnp.max(a, axis=dims, keepdims=keepdims)
amax = lax.stop_gradient(
lax.select(jnp.isfinite(amax), amax, lax.full_like(amax, 0)))
amax_with_dims = amax if keepdims else lax.expand_dims(amax, pos_dims)
# fast path if the result cannot be negative.
if b is None and not np.issubdtype(a.dtype, np.complexfloating):
out = lax.add(
lax.log(
jnp.sum(lax.exp(lax.sub(a, amax_with_dims)),
axis=dims,
keepdims=keepdims)), amax)
sign = jnp.where(jnp.isnan(out), out, 1.0)
sign = jnp.where(jnp.isneginf(out), 0.0, sign).astype(out.dtype)
else:
expsub = lax.exp(lax.sub(a, amax_with_dims))
if b is not None:
expsub = lax.mul(expsub, b)
sumexp = jnp.sum(expsub, axis=dims, keepdims=keepdims)
sign = lax.stop_gradient(jnp.sign(sumexp))
if np.issubdtype(sumexp.dtype, np.complexfloating):
if return_sign:
sumexp = sign * sumexp
out = lax.add(lax.log(sumexp), amax)
else:
out = lax.add(lax.log(lax.abs(sumexp)), amax)
if return_sign:
return (out, sign)
if b is not None:
if not np.issubdtype(out.dtype, np.complexfloating):
with jax.debug_nans(False):
out = jnp.where(sign < 0, jnp.array(np.nan, dtype=out.dtype),
out)
return out
def cdf(x, p):
x, p = _promote_args_inexact("gennorm.cdf", x, p)
return .5 * (1 + lax.sign(x) * lax.igamma(1 / p, lax.abs(x)**p))
def logpdf(x, loc=0, scale=1):
x, loc, scale = _promote_args_inexact("laplace.logpdf", x, loc, scale)
two = _constant_like(x, 2)
linear_term = lax.div(lax.abs(lax.sub(x, loc)), scale)
return lax.neg(lax.add(linear_term, lax.log(lax.mul(two, scale))))
def __call__(self, x, training: bool):
"""Normalizes the input using batch statistics.
Args:
x: the input to be normalized.
Returns:
Normalized inputs (the same shape as inputs).
"""
x = jnp.asarray(x, self.dtype)
axis = self.axis if isinstance(self.axis, tuple) else (self.axis, )
axis = _absolute_dims(x.ndim, axis)
feature_shape = tuple(d if i in axis else 1
for i, d in enumerate(x.shape))
reduced_feature_shape = tuple(d for i, d in enumerate(x.shape)
if i in axis)
reduction_axis = tuple(i for i in range(x.ndim) if i not in axis)
# we detect if we're in initialization via empty variable tree.
initializing = not self.has_variable('batch_stats', 'mean')
ra_mean = self.variable('batch_stats', 'mean',
lambda s: jnp.zeros(s, jnp.float32),
reduced_feature_shape)
ra_var = self.variable('batch_stats', 'var',
lambda s: jnp.ones(s, jnp.float32),
reduced_feature_shape)
if not training:
mean, var = ra_mean.value, ra_var.value
else:
mean = jnp.mean(x, axis=reduction_axis, keepdims=False)
var = jnp.mean(lax.abs(x - mean),
axis=reduction_axis,
keepdims=False) * jnp.sqrt(jnp.pi / 2)
if self.axis_name is not None and not initializing:
concatenated_mean = jnp.concatenate([mean, var])
mean, var = jnp.split(
lax.pmean(concatenated_mean,
axis_name=self.axis_name,
axis_index_groups=self.axis_index_groups), 2)
if not initializing:
ra_mean.value = self.momentum * ra_mean.value + (
1 - self.momentum) * mean
ra_var.value = self.momentum * ra_var.value + (
1 - self.momentum) * var
mean = jnp.asarray(mean, self.dtype)
var = jnp.asarray(var, self.dtype)
y = x - mean.reshape(feature_shape)
mul = lax.reciprocal(var + self.epsilon)
if self.use_scale:
scale = self.param('scale', self.scale_init,
reduced_feature_shape).reshape(feature_shape)
scale = jnp.asarray(scale, self.dtype)
mul = mul * scale
y = y * mul
if self.use_bias:
bias = self.param('bias', self.bias_init,
reduced_feature_shape).reshape(feature_shape)
bias = jnp.asarray(bias, self.dtype)
y = y + bias
return jnp.asarray(y, self.dtype)
def _abs2(x):
x, xx = x
sign = jnp.where(lax.sign(x) == lax.sign(xx), 1, -1)
return (lax.abs(x), sign * lax.abs(xx))
def copysign(x1, x2):
x1, x2 = _promote_args_inexact("copysign", x1, x2)
if dtypes.issubdtype(dtypes.dtype(x1), np.complexfloating):
raise TypeError("copysign does not support complex-valued inputs")
return _where(signbit(x2).astype(bool), -lax.abs(x1), lax.abs(x1))
def absolute(x):
_check_arraylike('absolute', x)
dt = dtypes.dtype(x)
return x if dt == np.bool_ or dtypes.issubdtype(
dt, np.unsignedinteger) else lax.abs(x)
def logpdf(x, p):
x, p = _promote_args_inexact("gennorm.logpdf", x, p)
return lax.log(.5 * p) - lax.lgamma(1 / p) - lax.abs(x)**p
def isclose(a, b, rtol=1e-05, atol=1e-08):
a, b = _promote_args("isclose", a, b)
rtol = lax.convert_element_type(rtol, _dtype(a))
atol = lax.convert_element_type(atol, _dtype(a))
return lax.le(lax.abs(lax.sub(a, b)),
lax.add(atol, lax.mul(rtol, lax.abs(b))))
def i1(x):
x, = _promote_args_inexact("i1", x)
return lax.mul(lax.exp(lax.abs(x)), lax.bessel_i1e(x))
def _abs(x):
return lax.abs(x)
