# Copyright 2026 Daniil Shmelev
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# =========================================================================
from typing import Union
import numpy as np
import torch
from .param_checks import check_type, check_non_neg, check_n_jobs
from .error_codes import err_msg
from .dtypes import CPSIG_LOG_SIG_JOIN, CUSIG_LOG_SIG_JOIN_CUDA
from .sig_length import log_sig_length
from .data_handlers import SigInputHandler, SigOutputHandler
[docs]
def log_sig_join(
log_sig : Union[np.ndarray, torch.tensor],
displacement : Union[np.ndarray, torch.tensor],
dimension : int,
degree : int,
*,
n_jobs : int = 1
) -> Union[np.ndarray, torch.tensor]:
"""
Extends a truncated log-signature by a single displacement vector using the
Baker-Campbell-Hausdorff (BCH) formula. This is the log-signature analogue of
``sig_join``.
Given a log-signature :math:`L(x)` and a displacement :math:`v`, this computes
.. math::
L(x * v) = \\text{BCH}(L(x), v),
where :math:`v` is embedded as a degree-1 element of the free Lie algebra.
.. note::
``log_sig`` is expected in the Lyndon bracket basis (``method=2`` output). You
must call ``pysiglib.prepare_log_sig(dimension, degree, method=2)`` before using
this function. This precomputes the Lyndon basis and BCH coefficients needed
internally.
:param log_sig: The existing truncated log-signature, of shape ``(..., log_sig_length)``.
:type log_sig: numpy.ndarray | torch.tensor
:param displacement: The displacement vector, of shape ``(..., dimension)``.
Leading batch dimensions must match those of ``log_sig``.
:type displacement: numpy.ndarray | torch.tensor
:param dimension: Dimension of the underlying space, :math:`d`.
:type dimension: int
:param degree: Truncation level of the log-signature, :math:`N`.
:type degree: int
:param n_jobs: Number of threads to run in parallel. If n_jobs = 1, the computation is run serially.
If set to -1, all available threads are used. For n_jobs below -1, (max_threads + 1 + n_jobs)
threads are used. For example if n_jobs = -2, all threads but one are used.
:type n_jobs: int
:return: Extended log-signature, :math:`L(x * v)`.
:rtype: numpy.ndarray | torch.tensor
Example:
---------
.. code-block:: python
import pysiglib
import numpy as np
dimension = 5
degree = 3
pysiglib.prepare_log_sig(dimension, degree, method=2)
path = np.random.uniform(size=(100, dimension))
ls = pysiglib.log_sig(path, degree, method=2)
displacement = np.random.uniform(size=(dimension,))
extended_ls = pysiglib.log_sig_join(ls, displacement, dimension, degree)
"""
check_type(dimension, "dimension", int)
check_non_neg(dimension, "dimension")
check_type(degree, "degree", int)
check_non_neg(degree, "degree")
check_n_jobs(n_jobs)
ls_len = log_sig_length(dimension, degree)
logsig_data = SigInputHandler(log_sig, ls_len, "log_sig")
disp_data = SigInputHandler(displacement, dimension, "displacement")
if logsig_data.type_ != disp_data.type_:
raise ValueError("log_sig and displacement must both be numpy arrays or both torch tensors")
if logsig_data.dtype != disp_data.dtype:
raise ValueError("log_sig and displacement must have the same dtype")
if logsig_data.batch_shape != disp_data.batch_shape:
raise ValueError("log_sig and displacement must have the same batch shape")
if logsig_data.device != disp_data.device:
raise ValueError("log_sig and displacement must be on the same device")
result = SigOutputHandler(logsig_data, ls_len)
if logsig_data.batch_size == 0:
return result.data
if logsig_data.device == "cpu":
err_code = CPSIG_LOG_SIG_JOIN[logsig_data.dtype](
logsig_data.data_ptr, disp_data.data_ptr, result.data_ptr,
logsig_data.batch_size, dimension, degree, n_jobs)
else:
err_code = CUSIG_LOG_SIG_JOIN_CUDA[logsig_data.dtype](
logsig_data.data_ptr, disp_data.data_ptr, result.data_ptr,
logsig_data.batch_size, dimension, degree)
if err_code:
raise Exception("Error in pysiglib.log_sig_join: " + err_msg(err_code))
return result.data
