Source code for netket.jax._math

# Copyright 2022 The NetKet Authors - All rights reserved.
# Licensed under the Apache License, Version 2.0 (the "License");
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from typing import Optional

import jax
import jax.numpy as jnp
from jax.scipy.special import logsumexp

from ._utils_dtype import dtype_complex

[docs] def logsumexp_cplx(a: jax.Array, b: Optional[jax.Array] = None, **kwargs) -> jax.Array: """Compute the log of the sum of exponentials of input elements, always returning a complex number. Equivalent to, but more numerically stable than, `np.log(np.sum(b*np.exp(a)))`. If the optional argument `b` is omitted, `np.log(np.sum(np.exp(a)))` is returned. Wraps `jax.scipy.special.logsumexp` but uses `return_sign=True` if both `a` and `b` are real numbers in order to support `b<0` instead of returning `nan`. See the JAX function for details of the calling sequence; `return_sign` is not supported. """ if jnp.iscomplexobj(a) or jnp.iscomplexobj(b): # logsumexp uses complex algebra anyway return logsumexp(a, b=b, **kwargs) else: a, sgn = logsumexp(a, b=b, **kwargs, return_sign=True) a = a + jnp.where(sgn < 0, 1j * jnp.pi, 0j) return a
[docs] def logdet_cmplx(A: jax.Array) -> jax.Array: r"""Log-determinant, with automatic upconversion to a complex output dtype in order to encode the sign. This is a thin wrapper on top of {func}`jax.numpy.linalg.slogdet`. The mathematical formula is: .. math:: \log(|A |) Args: A: A square matrix, or batch of matrices. The shape should be `(..., N, N)` Return: A scalar or batch of scalars with the smallest complex dtype computed from the input dtype. If the input has shape `(..., N, N)` the output has shape `(...)` """ sign, logabsdet = jnp.linalg.slogdet(A) cplx_type = dtype_complex(A.dtype) return logabsdet.astype(cplx_type) + jnp.log(sign.astype(cplx_type))