"""Provides functions for aligning traces in a trace set to a reference trace within it."""
import numpy as np
from copy import deepcopy
from fastdtw import fastdtw, dtw
from public import public
from typing import List, Callable, Tuple
from .process import normalize
from .trace import Trace
def _align_reference(
reference: Trace, *traces: Trace, align_func: Callable[[Trace], Tuple[bool, int]]
) -> Tuple[List[Trace], List[int]]:
result = [deepcopy(reference)]
offsets = [0]
for trace in traces:
length = len(trace.samples)
include, offset = align_func(trace)
if not include:
continue
if offset == 0:
result_samples = trace.samples.copy()
else:
result_samples = np.zeros(len(trace.samples), dtype=trace.samples.dtype)
if offset > 0:
result_samples[: length - offset] = trace.samples[offset:]
else:
result_samples[-offset:] = trace.samples[: length + offset]
result.append(trace.with_samples(result_samples))
offsets.append(offset)
return result, offsets
[docs]
@public
def align_correlation(
reference: Trace,
*traces: Trace,
reference_offset: int,
reference_length: int,
max_offset: int,
min_correlation: float = 0.5
) -> Tuple[List[Trace], List[int]]:
"""
Align :paramref:`~.align_correlation.traces` to the :paramref:`~.align_correlation.reference` trace using correlation.
Use the cross-correlation of a part of the reference
trace starting at `reference_offset` with `reference_length` and try to match it to a part of
the trace being matched that is at most `max_offset` mis-aligned from the reference, pick the
alignment offset with the largest cross-correlation. If the maximum cross-correlation of the
trace parts being matched is below `min_correlation`, do not include the trace.
:param reference: Trace to align to.
:param traces: Traces to align.
:param reference_offset: Offset into the reference trace to start the aligning from.
:param reference_length: Length of the part of the reference trace to align.
:param max_offset: Maximum offset to try to align the traces by.
:param min_correlation: Minimal correlation between the aligned trace and the reference trace.
:return: A tuple of: the list of the aligned traces (with the reference) and offsets used in alignment.
"""
reference_centered = normalize(reference)
reference_part = reference_centered.samples[
reference_offset : reference_offset + reference_length
]
def align_func(trace):
length = len(trace.samples)
correlation_start = max(reference_offset - max_offset, 0)
correlation_end = min(
reference_offset + reference_length + max_offset, length - 1
)
trace_part = trace.samples[correlation_start:correlation_end]
trace_part = (trace_part - np.mean(trace_part)) / (
np.std(trace_part) * len(trace_part)
)
correlation = np.correlate(trace_part, reference_part, "same")
max_correlation_offset = correlation.argmax(axis=0)
max_correlation = correlation[max_correlation_offset]
del trace_part
if max_correlation < min_correlation:
return False, 0
left_space = min(max_offset, reference_offset)
shift = left_space + reference_length // 2
return True, max_correlation_offset - shift
return _align_reference(reference, *traces, align_func=align_func)
[docs]
@public
def align_peaks(
reference: Trace,
*traces: Trace,
reference_offset: int,
reference_length: int,
max_offset: int
) -> Tuple[List[Trace], List[int]]:
"""
Align :paramref:`~.align_correlation.traces` to the :paramref:`~.align_correlation.reference` trace using peaks.
Align so that the maximum value within the reference trace
window from `reference_offset` of `reference_length` aligns with the maximum
value of the trace being aligned within `max_offset` of the reference window.
:param reference: Trace to align to.
:param traces: Traces to align.
:param reference_offset: Offset into the reference trace to start the aligning from.
:param reference_length: Length of the part of the reference trace to align.
:param max_offset: Maximum offset to try to align the traces by.
:return: A tuple of: the list of the aligned traces (with the reference) and offsets used in alignment.
"""
reference_part = reference.samples[
reference_offset : reference_offset + reference_length
]
reference_peak = np.argmax(reference_part)
def align_func(trace):
length = len(trace.samples)
window_start = max(reference_offset - max_offset, 0)
window_end = min(reference_offset + reference_length + max_offset, length - 1)
window = trace.samples[window_start:window_end]
window_peak = np.argmax(window)
left_space = min(max_offset, reference_offset)
return True, int(window_peak - reference_peak - left_space)
return _align_reference(reference, *traces, align_func=align_func)
[docs]
@public
def align_offset(
reference: Trace,
*traces: Trace,
reference_offset: int,
reference_length: int,
max_offset: int,
dist_func: Callable[[np.ndarray, np.ndarray], float],
max_dist: float = float("inf")
) -> Tuple[List[Trace], List[int]]:
"""
Align :paramref:`~.align_correlation.traces` to the :paramref:`~.align_correlation.reference` trace using a distance function.
Align so that the value of the `dist_func` is minimized
between the reference trace window from `reference_offset` of `reference_length` and the trace
being aligned within `max_offset` of the reference window.
:param reference: Trace to align to.
:param traces: Traces to align.
:param reference_offset: Offset into the reference trace to start the aligning from.
:param reference_length: Length of the part of the reference trace to align.
:param max_offset: Maximum offset to try to align the traces by.
:param dist_func: Distance function to use.
:param max_dist: Maximum distance between the aligned trace and the reference trace.
:return: A tuple of: the list of the aligned traces (with the reference) and offsets used in alignment.
"""
reference_part = reference.samples[
reference_offset : reference_offset + reference_length
]
def align_func(trace):
length = len(trace.samples)
best_distance = 0.0
best_offset = 0
for offset in range(-max_offset, max_offset):
start = reference_offset + offset
stop = start + reference_length
if start < 0 or stop >= length:
continue
trace_part = trace.samples[start:stop]
distance = dist_func(reference_part, trace_part)
if distance < best_distance:
best_distance = distance
best_offset = offset
if best_distance < max_dist:
return True, best_offset
else:
return False, 0
return _align_reference(reference, *traces, align_func=align_func)
[docs]
@public
def align_sad(
reference: Trace,
*traces: Trace,
reference_offset: int,
reference_length: int,
max_offset: int
) -> Tuple[List[Trace], List[int]]:
"""
Align :paramref:`~.align_correlation.traces` to the :paramref:`~.align_correlation.reference` trace using Sum of Absolute Differences.
Align so that the Sum Of Absolute Differences between the
reference trace window from `reference_offset` of `reference_length` and the trace being aligned
within `max_offset` of the reference window is maximized.
:param reference: Trace to align to.
:param traces: Traces to align.
:param reference_offset: Offset into the reference trace to start the aligning from.
:param reference_length: Length of the part of the reference trace to align.
:param max_offset: Maximum offset to try to align the traces by.
:return: A tuple of: the list of the aligned traces (with the reference) and offsets used in alignment.
"""
def sad(reference_part, trace_part):
return float(np.sum(np.abs(reference_part - trace_part)))
return align_offset(
reference,
*traces,
reference_offset=reference_offset,
reference_length=reference_length,
max_offset=max_offset,
dist_func=sad
)
[docs]
@public
def align_dtw_scale(
reference: Trace, *traces: Trace, radius: int = 1, fast: bool = True
) -> List[Trace]:
"""
Align :paramref:`~.align_correlation.traces` to the :paramref:`~.align_correlation.reference` trace.
Use fastdtw (Dynamic Time Warping) with scaling as per:
Jasper G. J. van Woudenberg, Marc F. Witteman, Bram Bakker:
**Improving Differential Power Analysis by Elastic Alignment**
https://pdfs.semanticscholar.org/aceb/7c307098a414d7c384d6189226e4375cf02d.pdf
:param reference: Trace to align to.
:param traces: Traces to align.
:param radius:
:param fast:
:return: List of the aligned traces (with the reference).
"""
result = [deepcopy(reference)]
reference_samples = reference.samples
for trace in traces:
if fast:
_, path = fastdtw(reference_samples, trace.samples, radius=radius)
else:
_, path = dtw(reference_samples, trace.samples)
result_samples = np.zeros(len(reference_samples), dtype=trace.samples.dtype)
scale = np.zeros(len(reference_samples), dtype=trace.samples.dtype)
for x, y in path:
result_samples[x] += trace.samples[y]
scale[x] += 1
result_samples /= scale
del path
del scale
result.append(trace.with_samples(result_samples))
return result
[docs]
@public
def align_dtw(
reference: Trace, *traces: Trace, radius: int = 1, fast: bool = True
) -> List[Trace]:
"""
Align `traces` to the `reference` trace.
Use fastdtw (Dynamic Time Warping) as per:
Stan Salvador, Philip Chan:
**FastDTW: Toward Accurate Dynamic Time Warping in Linear Time and Space**
https://cs.fit.edu/~pkc/papers/tdm04.pdf
:param reference: Trace to align to.
:param traces: Traces to align.
:param radius:
:param fast:
:return: List of the aligned traces (with the reference).
"""
result = [deepcopy(reference)]
reference_samples = reference.samples
for trace in traces:
if fast:
_, path = fastdtw(reference_samples, trace.samples, radius=radius)
else:
_, path = dtw(reference_samples, trace.samples)
result_samples = np.zeros(
max((len(trace.samples), len(reference_samples))), dtype=trace.samples.dtype
)
pairs = np.array(
np.array(path, dtype=np.dtype("int,int")),
dtype=np.dtype([("x", "int"), ("y", "int")]),
)
result_samples[pairs["x"]] = trace.samples[pairs["y"]]
del pairs
del path
result.append(trace.with_samples(result_samples))
return result
