def batch_shape(self):
# loc.shape should be [..., d]
# self.scale_tril shoule be [..., d, d]
# broadcasted... should be [..., d]
return lax.broadcast_shapes(self.loc.shape, self.scale_tril[:-1])[:-1]
def log_prob(self, value):
shape = lax.broadcast_shapes(self.batch_shape, np.shape(value)[:-1])
return np.broadcast_to(self.log_factor, shape)
def testBroadcastShapesReturnsPythonInts(self): shape1, shape2 = (1, 2, 3), (2, 3) out_shape = lax.broadcast_shapes(shape1, shape2) self.assertTrue(all(type(s) is int for s in out_shape))
def test_multinomial_shape(p, shape):
rng = random.PRNGKey(0)
n = 10000
expected_shape = lax.broadcast_shapes(p.shape[:-1], shape) + p.shape[-1:]
assert np.shape(multinomial(rng, p, n, shape)) == expected_shape
def log_prob(self, value):
shape = lax.broadcast_shapes(self.batch_shape,
jnp.shape(value)[:max(jnp.ndim(value) - self.event_dim, 0)])
log_prob = self.base_dist.log_prob(value)
return jnp.broadcast_to(log_prob, shape)
def __init__(self, loc=0., scale=1., validate_args=None):
self.loc, self.scale = promote_shapes(loc, scale)
batch_shape = lax.broadcast_shapes(np.shape(loc), np.shape(scale))
super(Cauchy, self).__init__(batch_shape=batch_shape,
validate_args=validate_args)
def test_standard_gamma_shape(alpha, shape):
rng = random.PRNGKey(0)
expected_shape = lax.broadcast_shapes(np.shape(alpha), shape)
assert np.shape(standard_gamma(rng, alpha, shape=shape)) == expected_shape
def infer_shapes(predictor, cutpoints):
batch_shape = lax.broadcast_shapes(predictor, cutpoints[:-1])
event_shape = ()
return batch_shape, event_shape
def infer_shapes(logits, total_count):
batch_shape = lax.broadcast_shapes(logits[:-1], total_count)
event_shape = logits[-1:]
return batch_shape, event_shape
def infer_shapes(concentration, total_count=()):
batch_shape = lax.broadcast_shapes(concentration[:-1], total_count)
event_shape = concentration[-1:]
return batch_shape, event_shape
def log_prob(self, value):
if self._validate_args:
self._validate_sample(value)
batch_shape = lax.broadcast_shapes(self.batch_shape, np.shape(value))
return -np.zeros(batch_shape)
def kl_divergence(p, q):
kl = kl_divergence(p.base_dist, q.base_dist)
shape = lax.broadcast_shapes(p.batch_shape, q.batch_shape)
return jnp.broadcast_to(kl, shape)
def batch_shape(self):
return lax.broadcast_shapes(self.minval.shape, self.maxval.shape)
def batch_shape(self):
return lax.broadcast_shapes(self.loc.shape, self.scale.shape)
def inverse_shape(self, shape):
return lax.broadcast_shapes(shape, getattr(self.exponent, "shape", ()))
def _xlog1py_jvp_lhs(g, ans, x, y):
shape = lax.broadcast_shapes(np.shape(g), np.shape(y))
g = np.broadcast_to(g, shape)
y = np.broadcast_to(y, shape)
g, y = _promote_args_like(osp_special.xlog1py, g, y)
return lax._safe_mul(g, np.log1p(y))
def __init__(self, concentration, rate=1., validate_args=None):
self.concentration, self.rate = promote_shapes(concentration, rate)
batch_shape = lax.broadcast_shapes(np.shape(concentration),
np.shape(rate))
super(Gamma, self).__init__(batch_shape=batch_shape,
validate_args=validate_args)
def _xlog1py_jvp_rhs(g, ans, x, y):
shape = lax.broadcast_shapes(np.shape(g), np.shape(x))
g = np.broadcast_to(g, shape)
x = np.broadcast_to(x, shape)
x, y = _promote_args_like(osp_special.xlog1py, x, y)
return g * lax._safe_mul(x, np.reciprocal(1 + y))
def __init__(self, low=0., high=1., validate_args=None):
self.low, self.high = promote_shapes(low, high)
batch_shape = lax.broadcast_shapes(np.shape(low), np.shape(high))
super(Uniform, self).__init__(batch_shape=batch_shape,
validate_args=validate_args)
def __init__(self, probs, total_count=1, validate_args=None):
self.probs, self.total_count = promote_shapes(probs, total_count)
batch_shape = lax.broadcast_shapes(np.shape(probs), np.shape(total_count))
super(BinomialProbs, self).__init__(batch_shape=batch_shape, validate_args=validate_args)
def test_categorical_shape(p, shape):
rng = random.PRNGKey(0)
expected_shape = lax.broadcast_shapes(p.shape[:-1], shape)
assert np.shape(categorical(rng, p, shape)) == expected_shape
def __init__(self, logits, total_count=1, validate_args=None):
self.logits, self.total_count = promote_shapes(logits, total_count)
batch_shape = lax.broadcast_shapes(jnp.shape(logits),
jnp.shape(total_count))
super(BinomialLogits, self).__init__(batch_shape=batch_shape,
validate_args=validate_args)
def _cofactor_solve(a, b):
"""Equivalent to det(a)*solve(a, b) for nonsingular mat.
Intermediate function used for jvp and vjp of det.
This function borrows heavily from jax.numpy.linalg.solve and
jax.numpy.linalg.slogdet to compute the gradient of the determinant
in a way that is well defined even for low rank matrices.
This function handles two different cases:
* rank(a) == n or n-1
* rank(a) < n-1
For rank n-1 matrices, the gradient of the determinant is a rank 1 matrix.
Rather than computing det(a)*solve(a, b), which would return NaN, we work
directly with the LU decomposition. If a = p @ l @ u, then
det(a)*solve(a, b) =
prod(diag(u)) * u^-1 @ l^-1 @ p^-1 b =
prod(diag(u)) * triangular_solve(u, solve(p @ l, b))
If a is rank n-1, then the lower right corner of u will be zero and the
triangular_solve will fail.
Let x = solve(p @ l, b) and y = det(a)*solve(a, b).
Then y_{n}
x_{n} / u_{nn} * prod_{i=1...n}(u_{ii}) =
x_{n} * prod_{i=1...n-1}(u_{ii})
So by replacing the lower-right corner of u with prod_{i=1...n-1}(u_{ii})^-1
we can avoid the triangular_solve failing.
To correctly compute the rest of y_{i} for i != n, we simply multiply
x_{i} by det(a) for all i != n, which will be zero if rank(a) = n-1.
For the second case, a check is done on the matrix to see if `solve`
returns NaN or Inf, and gives a matrix of zeros as a result, as the
gradient of the determinant of a matrix with rank less than n-1 is 0.
This will still return the correct value for rank n-1 matrices, as the check
is applied *after* the lower right corner of u has been updated.
Args:
a: A square matrix or batch of matrices, possibly singular.
b: A matrix, or batch of matrices of the same dimension as a.
Returns:
det(a) and cofactor(a)^T*b, aka adjugate(a)*b
"""
a = _promote_arg_dtypes(jnp.asarray(a))
b = _promote_arg_dtypes(jnp.asarray(b))
a_shape = jnp.shape(a)
b_shape = jnp.shape(b)
a_ndims = len(a_shape)
if not (a_ndims >= 2 and a_shape[-1] == a_shape[-2]
and b_shape[-2:] == a_shape[-2:]):
msg = ("The arguments to _cofactor_solve must have shapes "
"a=[..., m, m] and b=[..., m, m]; got a={} and b={}")
raise ValueError(msg.format(a_shape, b_shape))
if a_shape[-1] == 1:
return a[0, 0], b
# lu contains u in the upper triangular matrix and l in the strict lower
# triangular matrix.
# The diagonal of l is set to ones without loss of generality.
lu, pivots, permutation = lax_linalg.lu(a)
dtype = lax.dtype(a)
batch_dims = lax.broadcast_shapes(lu.shape[:-2], b.shape[:-2])
x = jnp.broadcast_to(b, batch_dims + b.shape[-2:])
lu = jnp.broadcast_to(lu, batch_dims + lu.shape[-2:])
# Compute (partial) determinant, ignoring last diagonal of LU
diag = jnp.diagonal(lu, axis1=-2, axis2=-1)
parity = jnp.count_nonzero(pivots != jnp.arange(a_shape[-1]), axis=-1)
sign = jnp.array(-2 * (parity % 2) + 1, dtype=dtype)
# partial_det[:, -1] contains the full determinant and
# partial_det[:, -2] contains det(u) / u_{nn}.
partial_det = jnp.cumprod(diag, axis=-1) * sign[..., None]
lu = ops.index_update(lu, ops.index[..., -1, -1],
1.0 / partial_det[..., -2])
permutation = jnp.broadcast_to(permutation, batch_dims + (a_shape[-1], ))
iotas = jnp.ix_(*(lax.iota(jnp.int32, b) for b in batch_dims + (1, )))
# filter out any matrices that are not full rank
d = jnp.ones(x.shape[:-1], x.dtype)
d = lax_linalg.triangular_solve(lu, d, left_side=True, lower=False)
d = jnp.any(jnp.logical_or(jnp.isnan(d), jnp.isinf(d)), axis=-1)
d = jnp.tile(d[..., None, None], d.ndim * (1, ) + x.shape[-2:])
x = jnp.where(d, jnp.zeros_like(x), x) # first filter
x = x[iotas[:-1] + (permutation, slice(None))]
x = lax_linalg.triangular_solve(lu,
x,
left_side=True,
lower=True,
unit_diagonal=True)
x = jnp.concatenate(
(x[..., :-1, :] * partial_det[..., -1, None, None], x[..., -1:, :]),
axis=-2)
x = lax_linalg.triangular_solve(lu, x, left_side=True, lower=False)
x = jnp.where(d, jnp.zeros_like(x), x) # second filter
return partial_det[..., -1], x
def __init__(self, gate, rate=1., validate_args=None):
batch_shape = lax.broadcast_shapes(jnp.shape(gate), jnp.shape(rate))
self.gate, self.rate = promote_shapes(gate, rate)
super(ZeroInflatedPoisson, self).__init__(batch_shape,
validate_args=validate_args)
def log_prob(self, value):
batch_shape = jnp.shape(value)[:jnp.ndim(value) - len(self.event_shape)]
batch_shape = lax.broadcast_shapes(batch_shape, self.batch_shape)
return jnp.zeros(batch_shape)
def inverse_shape(self, shape):
if len(shape) < 1:
raise ValueError("Too few dimensions on input")
return lax.broadcast_shapes(shape, self.loc.shape, self.scale_tril.shape[:-1])
def polygamma(n, x):
assert jnp.issubdtype(lax.dtype(n), jnp.integer)
n, x = _promote_args_inexact("polygamma", n, x)
shape = lax.broadcast_shapes(n.shape, x.shape)
return _polygamma(jnp.broadcast_to(n, shape), jnp.broadcast_to(x, shape))
def forward_shape(self, shape):
return lax.broadcast_shapes(shape, getattr(self.exponent, "shape", ()))
def inverse_shape(self, shape):
return lax.broadcast_shapes(shape, getattr(self.loc, "shape", ()),
getattr(self.scale, "shape", ()))
def __init__(self, low=0., loc=0., scale=1., validate_args=None):
self.low, self.loc, self.scale = promote_shapes(low, loc, scale)
batch_shape = lax.broadcast_shapes(np.shape(low), np.shape(loc), np.shape(scale))
self._normal = Normal(self.loc, self.scale)
super(TruncatedNormal, self).__init__(batch_shape=batch_shape, validate_args=validate_args)
