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add erf and erfc rules #3051

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May 19, 2020
Merged

add erf and erfc rules #3051

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29 changes: 29 additions & 0 deletions jax/experimental/jet.py
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Original file line number Diff line number Diff line change
Expand Up @@ -211,7 +211,36 @@ def linear_prop(prim, primals_in, series_in, **params):
deflinear(lax_fft.fft_p)
deflinear(xla.device_put_p)

def def_deriv(prim, deriv):
"""
Define the jet rule for a primitive in terms of its first derivative.
"""
jet_rules[prim] = partial(deriv_prop, prim, deriv)

def deriv_prop(prim, deriv, primals_in, series_in):
x, = primals_in
series, = series_in
primal_out = prim.bind(x)
c0, cs = jet(deriv, primals_in, series_in)
c = [c0] + cs
u = [x] + series
v = [primal_out] + [None] * len(series)
for k in range(1, len(v)):
v[k] = fact(k-1) * sum(_scale(k, j) * c[k-j] * u[j] for j in range(1, k + 1))
primal_out, *series_out = v
return primal_out, series_out


def_deriv(lax.erf_p, lambda x: lax.mul(lax._const(x, 2. / onp.sqrt(onp.pi)), lax.exp(lax.neg(lax.square(x)))))

def def_comp(prim, comp):
"""
Define the jet rule for a primitive in terms of a composition of simpler primitives.
"""
jet_rules[prim] = partial(jet, comp)


def_comp(lax.erfc_p, lambda x: 1 - lax.erf(x))

### More complicated rules

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4 changes: 4 additions & 0 deletions tests/jet_test.py
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Expand Up @@ -225,6 +225,10 @@ def test_asinh(self): self.unary_check(lax.asinh, lims=[-100, 100])
def test_acosh(self): self.unary_check(lax.acosh, lims=[-100, 100])
@jtu.skip_on_devices("tpu")
def test_atanh(self): self.unary_check(lax.atanh, lims=[-1, 1])
@jtu.skip_on_devices("tpu")
def test_erf(self): self.unary_check(lax.erf)
@jtu.skip_on_devices("tpu")
def test_erfc(self): self.unary_check(lax.erfc)

@jtu.skip_on_devices("tpu")
def test_div(self): self.binary_check(lambda x, y: x / y, lims=[0.8, 4.0])
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