# 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_SIG_JOIN, CUSIG_SIG_JOIN_CUDA
from .sig_length import sig_length, _infer_scalar_term
from .data_handlers import SigInputHandler, SigOutputHandler
[docs]
def sig_join(
sig : Union[np.ndarray, torch.tensor],
displacement : Union[np.ndarray, torch.tensor],
dimension : int,
degree : int,
*,
prepend : bool = False,
n_jobs : int = 1
) -> Union[np.ndarray, torch.tensor]:
"""
Extends a truncated signature by a single displacement vector. This is equivalent to
computing ``sig_combine(sig, linear_sig(displacement))``, but is more efficient as it
avoids constructing the intermediate linear signature.
Given a signature :math:`S(x)` and a displacement :math:`v`, this computes
.. math::
S(x * v) = S(x) \\otimes S(v),
where :math:`S(v)` is the signature of the linear path defined by :math:`v`.
:param sig: The existing truncated signature, of shape ``(sig_length,)`` or ``(batch_size, sig_length)``.
:type sig: numpy.ndarray | torch.tensor
:param displacement: The displacement vector, of shape ``(dimension,)`` or ``(batch_size, dimension)``.
:type displacement: numpy.ndarray | torch.tensor
:param dimension: Dimension of the underlying space, :math:`d`.
:type dimension: int
:param degree: Truncation level of the signature, :math:`N`.
:type degree: int
:param prepend: If True, prepend the linear segment to the front of the path rather than
appending it at the end. In that case this computes :math:`S(v) \\otimes S(x) = S(v * x)`.
Default is False.
:type prepend: bool
: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 signature, :math:`S(x * v)`.
:rtype: numpy.ndarray | torch.tensor
Example usage::
import pysiglib
import numpy as np
dimension = 5
degree = 3
path = np.random.uniform(size=(100, dimension))
sig = pysiglib.sig(path, degree)
displacement = np.random.uniform(size=(dimension,))
extended_sig = pysiglib.sig_join(sig, 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)
scalar_term = _infer_scalar_term(sig, dimension, degree)
sig_len = sig_length(dimension, degree, scalar_term=scalar_term)
sig_data = SigInputHandler(sig, sig_len, "sig")
disp_data = SigInputHandler(displacement, dimension, "displacement")
if sig_data.type_ != disp_data.type_:
raise ValueError("sig and displacement must both be numpy arrays or both torch tensors")
if sig_data.dtype != disp_data.dtype:
raise ValueError("sig and displacement must have the same dtype")
if sig_data.batch_shape != disp_data.batch_shape:
raise ValueError("sig and displacement must have the same batch shape")
if sig_data.device != disp_data.device:
raise ValueError("sig and displacement must be on the same device")
result = SigOutputHandler(sig_data, sig_len)
if sig_data.batch_size == 0:
return result.data
if sig_data.device == "cpu":
err_code = CPSIG_SIG_JOIN[sig_data.dtype](
sig_data.data_ptr, disp_data.data_ptr, result.data_ptr,
sig_data.batch_size, dimension, degree, prepend, scalar_term, n_jobs)
else:
err_code = CUSIG_SIG_JOIN_CUDA[sig_data.dtype](
sig_data.data_ptr, disp_data.data_ptr, result.data_ptr,
sig_data.batch_size, dimension, degree, prepend, scalar_term)
if err_code:
raise Exception("Error in pysiglib.sig_join: " + err_msg(err_code))
return result.data
