"""Additional autograd differential operators."""
from functools import wraps
AUTOGRAD_AVAILABLE = True
try:
from autograd import make_vjp as vjp_and_value
from autograd.wrap_util import unary_to_nary
from autograd.builtins import tuple as atuple
from autograd.core import make_vjp
from autograd.extend import vspace
import autograd.numpy as np
except ImportError:
AUTOGRAD_AVAILABLE = False
def _wrapped_unary_to_nary(func):
"""Use functools.wraps with unary_to_nary decorator."""
if AUTOGRAD_AVAILABLE:
return wraps(func)(unary_to_nary(func))
else:
return func
@_wrapped_unary_to_nary
def grad_and_value(fun, x):
"""
Makes a function that returns both gradient and value of a function.
"""
vjp, val = make_vjp(fun, x)
if not vspace(val).size == 1:
raise TypeError("grad_and_value only applies to real scalar-output"
" functions.")
return vjp(vspace(val).ones()), val
@_wrapped_unary_to_nary
def jacobian_and_value(fun, x):
"""
Makes a function that returns both the Jacobian and value of a function.
Assumes that the function `fun` broadcasts along the first dimension of the
input being differentiated with respect to such that a batch of outputs can
be computed concurrently for a batch of inputs.
"""
val = fun(x)
v_vspace = vspace(val)
x_vspace = vspace(x)
x_rep = np.tile(x, (v_vspace.size,) + (1,) * x_vspace.ndim)
vjp_rep, _ = make_vjp(fun, x_rep)
jacobian_shape = v_vspace.shape + x_vspace.shape
basis_vectors = np.array([b for b in v_vspace.standard_basis()])
jacobian = vjp_rep(basis_vectors)
return np.reshape(jacobian, jacobian_shape), val
@_wrapped_unary_to_nary
def mhp_jacobian_and_value(fun, x):
"""
Makes a function that returns MHP, Jacobian and value of a function.
For a vector-valued function `fun` the matrix-Hessian-product (MHP) is here
defined as a function of a matrix `m` corresponding to
mhp(m) = sum(m[:, :, None] * h[:, :, :], axis=(0, 1))
where `h` is the vector-Hessian of `f = fun(x)` wrt `x` i.e. the rank-3
tensor of second-order partial derivatives of the vector-valued function,
such that
h[i, j, k] = ∂²f[i] / (∂x[j] ∂x[k])
Assumes that the function `fun` broadcasts along the first dimension of the
input being differentiated with respect to such that a batch of outputs can
be computed concurrently for a batch of inputs.
"""
mhp, (jacob, val) = make_vjp(
lambda x: atuple(jacobian_and_value(fun)(x)), x)
return lambda m: mhp((m, vspace(val).zeros())), jacob, val
@_wrapped_unary_to_nary
def hessian_grad_and_value(fun, x):
"""
Makes a function that returns the Hessian, gradient & value of a function.
Assumes that the function `fun` broadcasts along the first dimension of the
input being differentiated with respect to such that a batch of outputs can
be computed concurrently for a batch of inputs.
"""
def grad_fun(x):
vjp, val = make_vjp(fun, x)
return vjp(vspace(val).ones()), val
x_vspace = vspace(x)
x_rep = np.tile(x, (x_vspace.size,) + (1,) * x_vspace.ndim)
vjp_grad, (grad, val) = make_vjp(lambda x: atuple(grad_fun(x)), x_rep)
hessian_shape = x_vspace.shape + x_vspace.shape
basis_vectors = np.array([b for b in x_vspace.standard_basis()])
hessian = vjp_grad((basis_vectors, vspace(val).zeros()))
return np.reshape(hessian, hessian_shape), grad[0], val[0]
@_wrapped_unary_to_nary
def mtp_hessian_grad_and_value(fun, x):
"""
Makes a function that returns MTP, Jacobian and value of a function.
For a scalar-valued function `fun` the matrix-Tressian-product (MTP) is
here defined as a function of a matrix `m` corresponding to
mtp(m) = sum(m[:, :] * t[:, :, :], axis=(-1, -2))
where `t` is the 'Tressian' of `f = fun(x)` wrt `x` i.e. the 3D array of
third-order partial derivatives of the scalar-valued function such that
t[i, j, k] = ∂³f / (∂x[i] ∂x[j] ∂x[k])
Assumes that the function `fun` broadcasts along the first dimension of the
input being differentiated with respect to such that a batch of outputs can
be computed concurrently for a batch of inputs.
"""
mtp, (hessian, grad, val) = make_vjp(
lambda x: atuple(hessian_grad_and_value(fun)(x)), x)
return (
lambda m: mtp((m, vspace(grad).zeros(), vspace(val).zeros())),
hessian, grad, val)
