def fn(x1, x2):
x1, x2 = _promote_args(numpy_fn.__name__, x1, x2)
# Comparison on complex types are defined as a lexicographic ordering on
# the (real, imag) pair.
if dtypes.issubdtype(dtypes.dtype(x1), np.complexfloating):
rx = lax.real(x1)
ry = lax.real(x2)
return lax.select(lax.eq(rx, ry), lax_fn(lax.imag(x1), lax.imag(x2)),
lax_fn(rx, ry))
return lax_fn(x1, x2)
def nanvar(a,
axis: Optional[Union[int, Tuple[int, ...]]] = None,
dtype=None,
out=None,
ddof=0,
keepdims=False,
where=None):
_check_arraylike("nanvar", a)
lax_internal._check_user_dtype_supported(dtype, "nanvar")
if out is not None:
raise NotImplementedError(
"The 'out' argument to jnp.nanvar is not supported.")
a_dtype, dtype = _var_promote_types(dtypes.dtype(a), dtype)
a_mean = nanmean(a, axis, dtype=a_dtype, keepdims=True, where=where)
centered = _where(lax_internal._isnan(a), 0,
a - a_mean) # double-where trick for gradients.
if dtypes.issubdtype(centered.dtype, np.complexfloating):
centered = lax.real(lax.mul(centered, lax.conj(centered)))
else:
centered = lax.square(centered)
normalizer = sum(lax_internal.bitwise_not(lax_internal._isnan(a)),
axis=axis,
keepdims=keepdims,
where=where)
normalizer = normalizer - ddof
normalizer_mask = lax.le(normalizer, 0)
result = sum(centered, axis, keepdims=keepdims, where=where)
result = _where(normalizer_mask, np.nan, result)
divisor = _where(normalizer_mask, 1, normalizer)
out = lax.div(result, lax.convert_element_type(divisor, result.dtype))
return lax.convert_element_type(out, dtype)
def sign(x):
_check_arraylike('sign', x)
dtype = dtypes.dtype(x)
if dtypes.issubdtype(dtype, np.complexfloating):
re = lax.real(x)
return lax.complex(lax.sign(_where(re != 0, re, lax.imag(x))),
_constant_like(re, 0))
return lax.sign(x)
def rint(x):
_check_arraylike('rint', x)
dtype = dtypes.dtype(x)
if dtypes.issubdtype(dtype, np.integer):
return lax.convert_element_type(x, dtypes.float_)
if dtypes.issubdtype(dtype, np.complexfloating):
return lax.complex(rint(lax.real(x)), rint(lax.imag(x)))
return lax.round(x, lax.RoundingMethod.TO_NEAREST_EVEN)
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 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 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 _var(a,
axis: Optional[Union[int, Tuple[int, ...]]] = None,
dtype=None,
out=None,
ddof=0,
keepdims=False,
*,
where=None):
_check_arraylike("var", a)
lax_internal._check_user_dtype_supported(dtype, "var")
if out is not None:
raise NotImplementedError(
"The 'out' argument to jnp.var is not supported.")
computation_dtype, dtype = _var_promote_types(dtypes.dtype(a), dtype)
a = a.astype(computation_dtype)
a_mean = mean(a, axis, dtype=computation_dtype, keepdims=True, where=where)
centered = lax.sub(a, a_mean)
if dtypes.issubdtype(centered.dtype, np.complexfloating):
centered = lax.real(lax.mul(centered, lax.conj(centered)))
else:
centered = lax.square(centered)
if where is None:
if axis is None:
normalizer = core.dimension_as_value(np.size(a))
else:
normalizer = core.dimension_as_value(_axis_size(a, axis))
else:
normalizer = sum(_broadcast_to(where, np.shape(a)),
axis,
dtype=dtype,
keepdims=keepdims)
normalizer = normalizer - ddof
result = sum(centered, axis, keepdims=keepdims, where=where)
out = lax.div(result, lax.convert_element_type(normalizer, result.dtype))
return lax.convert_element_type(out, dtype)
def real(val):
_check_arraylike("real", val)
return lax.real(val) if np.iscomplexobj(val) else val
def angle(x):
if iscomplexobj(x):
return lax.atan2(lax.imag(x), lax.real(x))
else:
return zeros_like(x)
def real(x):
return lax.real(x) if iscomplexobj(x) else x
