def get_tf_scalar_evaluator():
return scalar_sector.get_scalar_manifold_evaluator(
to_scaled_constant=(
lambda x, scale=1: tf.constant(numpy.array(x) * scale)),
expm=tf_cexpm.cexpm,
einsum=tf.einsum,
eye=lambda n: tf.constant(numpy.eye(n), dtype=tf.complex128),
trace=tf.linalg.trace,
concatenate=lambda ts: tf.concat(ts, 0),
complexify=lambda a: tf.cast(a, tf.complex128),
re=tf.math.real,
im=tf.math.imag,
conjugate=tf.math.conj)
mpmath.mpf.shape = ()
mpmath.mpc.shape = ()
# Observe that our E7-definitions have 'numerically exact' structure constants.
#
# So, it actually makes sense to take these as defined, and lift them to mpmath.
#
# >>> set(e7.t_a_ij_kl.reshape(-1))
# >>> {(-2+0j), (-1+0j), -2j, -1j, 0j, 1j, 2j, (1+0j), (2+0j)}
# `mpmath` does not work with numpy.einsum(), so for that reason alone,
# we use opt_einsum's generic-no-backend alternative implementation.
mpmath_scalar_manifold_evaluator = scalar_sector.get_scalar_manifold_evaluator(
frac=lambda p, q: mpmath.mpf(p) / mpmath.mpf(q),
to_scaled_constant=(
lambda x, scale=1: numpy.array(
x, dtype=mpmath.ctx_mp_python.mpc) * scale),
# Wrapping up `expm` is somewhat tricky here, as it returns a mpmath
# matrix-type that numpy does not understand.
expm=lambda m: numpy.array(mpmath.expm(m).tolist()),
einsum=lambda spec, *arrs: opt_einsum.contract(spec, *arrs),
# trace can stay as-is.
eye=lambda n: numpy.eye(n) + mpmath.mpc(0),
complexify=lambda a: a + mpmath.mpc(0),
# re/im are again tricky, since numpy.array(dtype=object)
# does not forward .real / .imag to the contained objects.
re=lambda a: numpy.array([z.real for z in a.reshape(-1)]).reshape(a.shape),
im=lambda a: numpy.array([z.imag for z in a.reshape(-1)]).reshape(a.shape))
