# Source code for netket.jax._math

```# Copyright 2022 The NetKet Authors - All rights reserved.
#
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#
# Unless required by applicable law or agreed to in writing, software
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and

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))

```