# Copyright 2025 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
from .error_codes import err_msg
from .data_handlers import PathInputHandler, SigOutputHandler, PathOutputHandler, MultipleSigInputHandler, DeviceToHost
from .dtypes import CPSIG_SIG_BACKPROP, CPSIG_BATCH_SIG_BACKPROP, CPSIG_SIG_COMBINE_BACKPROP, CPSIG_BATCH_SIG_COMBINE_BACKPROP
from .sig_length import sig_length
def sig_combine_backprop_(sig_data, sig1_deriv, sig2_deriv, dimension, degree):
err_code = CPSIG_SIG_COMBINE_BACKPROP[sig_data.dtype](
sig_data.sig_ptr[2],
sig1_deriv.data_ptr,
sig2_deriv.data_ptr,
sig_data.sig_ptr[0],
sig_data.sig_ptr[1],
dimension,
degree
)
if err_code:
raise Exception("Error in pysiglib.sig_combine_backprop: " + err_msg(err_code))
return sig1_deriv.data, sig2_deriv.data
def batch_sig_combine_backprop_(sig_data, sig1_deriv, sig2_deriv, dimension, degree, n_jobs):
err_code = CPSIG_BATCH_SIG_COMBINE_BACKPROP[sig_data.dtype](
sig_data.sig_ptr[2],
sig1_deriv.data_ptr,
sig2_deriv.data_ptr,
sig_data.sig_ptr[0],
sig_data.sig_ptr[1],
sig_data.batch_size,
dimension,
degree,
n_jobs
)
if err_code:
raise Exception("Error in pysiglib.sig_combine_backprop: " + err_msg(err_code))
return sig1_deriv.data, sig2_deriv.data
[docs]
def sig_combine_backprop(
deriv : Union[np.ndarray, torch.tensor],
sig1 : Union[np.ndarray, torch.tensor],
sig2 : Union[np.ndarray, torch.tensor],
dimension : int,
degree : int,
time_aug : bool = False,
lead_lag : bool = False,
n_jobs : int = 1
):
"""
This function is required to backpropagate through ``pysiglib.sig_combine``.
Given the derivatives of a scalar function :math:`F` with respect to the
result of ``pysiglib.sig_combine``, :math:`\\partial F / \\partial S(x_1 * x_2)`,
returns the derivatives of :math:`F` with respect to the original two signatures,
:math:`\\partial F / \\partial S(x_1)` and :math:`\\partial F / \\partial S(x_2)`.
:param deriv: Derivative with respect to the combined signature,
:math:`\\partial F / \\partial S(x_1 * x_2)`
:type sig_combine_deriv: numpy.ndarray | torch.tensor
:param sig1: The first truncated signature
:type sig1: numpy.ndarray | torch.tensor
:param sig2: The second truncated signature. Must have the same degree and dimension as the first.
:type sig2: numpy.ndarray | torch.tensor
:param dimension: Dimension of the underlying space, :math:`d`.
:type dimension: int
:param degree: Truncation level of the signatures, :math:`N`
:type degree: int
:param time_aug: Whether time augmentation was applied before computing
the signature.
:type time_aug: bool
:param lead_lag: Whether the lead lag transformation was applied before computing
the signature.
:type lead_lag: 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: Derivatives with respect to ``sig1`` and ``sig2``
:rtype: Tuple[numpy.ndarray | torch.tensor, numpy.ndarray | torch.tensor]
"""
check_type(dimension, "dimension", int)
check_non_neg(dimension, "dimension")
check_type(degree, "degree", int)
check_non_neg(degree, "degree")
check_type(time_aug, "time_aug", bool)
check_type(lead_lag, "lead_lag", bool)
device_handler = DeviceToHost([deriv, sig1, sig2], ["deriv", "sig1", "sig2"])
deriv, sig1, sig2 = device_handler.data
check_type(dimension, "dimension", int)
check_type(degree, "degree", int)
aug_dimension = (2 * dimension if lead_lag else dimension) + (1 if time_aug else 0)
sig_len = sig_length(aug_dimension, degree)
sig_data = MultipleSigInputHandler([sig1, sig2, deriv], sig_len, ["sig1", "sig2", "sig_combined_deriv"])
sig1_deriv = SigOutputHandler(sig_data, sig_len)
sig2_deriv = SigOutputHandler(sig_data, sig_len)
if sig_data.is_batch:
check_type(n_jobs, "n_jobs", int)
if n_jobs == 0:
raise ValueError("n_jobs cannot be 0")
res1, res2 = batch_sig_combine_backprop_(sig_data, sig1_deriv, sig2_deriv, aug_dimension, degree, n_jobs)
else:
res1, res2 = sig_combine_backprop_(sig_data, sig1_deriv, sig2_deriv, aug_dimension, degree)
if device_handler.device is not None:
res1 = res1.to(device_handler.device)
res2 = res2.to(device_handler.device)
return res1, res2
def sig_backprop_(path_data, sig_data, result, degree):
err_code = CPSIG_SIG_BACKPROP[path_data.dtype](
path_data.data_ptr,
result.data_ptr,
sig_data.sig_ptr[1],
sig_data.sig_ptr[0],
path_data.data_dimension,
path_data.data_length,
degree,
path_data. time_aug,
path_data.lead_lag,
path_data.end_time
)
if err_code:
raise Exception("Error in pysiglib.sig_backprop: " + err_msg(err_code))
return result.data
def batch_sig_backprop_(path_data, sig_data, result, degree, n_jobs):
err_code = CPSIG_BATCH_SIG_BACKPROP[path_data.dtype](
path_data.data_ptr,
result.data_ptr,
sig_data.sig_ptr[1],
sig_data.sig_ptr[0],
path_data.batch_size,
path_data.data_dimension,
path_data.data_length,
degree,
path_data.time_aug,
path_data.lead_lag,
path_data.end_time,
n_jobs
)
if err_code:
raise Exception("Error in pysiglib.sig_backprop: " + err_msg(err_code))
return result.data
[docs]
def sig_backprop(
path : Union[np.ndarray, torch.tensor],
sig : Union[np.ndarray, torch.tensor],
sig_derivs : Union[np.ndarray, torch.tensor],
degree : int,
time_aug : bool = False,
lead_lag : bool = False,
end_time : float = 1.,
n_jobs : int = 1
) -> Union[np.ndarray, torch.tensor]:
"""
This function is required to backpropagate through the signature computation.
Given the derivatives of a scalar function :math:`F` with respect to the
signature, :math:`\\partial F / \\partial S(x)`, returns the
derivatives of :math:`F` with respect to the underlying path,
:math:`\\partial F / \\partial x`.
:param path: The underlying path or batch of paths, given as a `numpy.ndarray` or `torch.tensor`.
For a single path, this must be of shape ``(length, dimension)``. For a batch of paths, this must
be of shape ``(batch_size, length, dimension)``.
:type path: numpy.ndarray | torch.tensor
:param sig: Signature(s) of the path or batch of paths.
:type sig: numpy.ndarray | torch.tensor
:param sig_derivs: Derivatives of the scalar function :math:`F` with respect to the signature(s),
:math:`\\partial F / \\partial S(x)`. This must be an array of the same shape as the
provided signature(s).
:type sig_derivs: numpy.ndarray | torch.tensor
:param degree: The truncation level of the signature, :math:`N`.
:type degree: int
:param time_aug: If set to True, will compute the signature of the time-augmented path, :math:`\\hat{x}_t := (t, x_t)`,
defined as the original path with an extra channel set to time, :math:`t`. This channel spans :math:`[0, t_L]`,
where :math:`t_L` is given by the parameter ``end_time``.
:type time_aug: bool
:param lead_lag: If set to True, will compute the signature of the path after applying the lead-lag transformation.
:type lead_lag: bool
:param end_time: End time for time-augmentation, :math:`t_L`.
:type end_time: float
:return: Derivatives of the scalar function :math:`F` with respect to the path(s), :math:`\\partial F / \\partial x`.
This is an array of the same shape as the provided path(s).
:rtype: numpy.ndarray | torch.tensor
"""
check_type(degree, "degree", int)
check_non_neg(degree, "degree")
check_type(time_aug, "time_aug", bool)
check_type(lead_lag, "lead_lag", bool)
check_type(end_time, "end_time", float)
device_handler = DeviceToHost([path, sig, sig_derivs], ["path", "sig", "sig_derivs"])
path, sig, sig_derivs = device_handler.data
path_data = PathInputHandler(path, time_aug, lead_lag, end_time, "path")
sig_len = sig_length(path_data.dimension, degree)
sig_data = MultipleSigInputHandler([sig, sig_derivs], sig_len, ["sig", "sig_derivs"])
if path_data.type_ != sig_data.type_:
raise ValueError("path, sig and sig_derivs must all be numpy arrays or torch tensors")
if path_data.dtype != sig_data.dtype:
raise ValueError("path, sig and sig_derivs must have the same dtype")
result = PathOutputHandler(path_data.data_length, path_data.data_dimension, path_data)
if path_data.is_batch != sig_data.is_batch or path_data.batch_size != sig_data.batch_size:
raise ValueError("path, sig and sig_derivs must have the same batch sizes")
if path_data.is_batch:
check_type(n_jobs, "n_jobs", int)
if n_jobs == 0:
raise ValueError("n_jobs cannot be 0")
res = batch_sig_backprop_(path_data, sig_data, result, degree, n_jobs)
else:
res = sig_backprop_(path_data, sig_data, result, degree)
if device_handler.device is not None:
res = res.to(device_handler.device)
return res
