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"""
This module provides functions for aligning traces in a trace set to a reference trace within it.
"""
import numpy as np
from copy import copy, 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]]) -> List[Trace]:
result = [deepcopy(reference)]
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(copy(trace.title), copy(trace.data), result_samples))
return result
@public
def align_correlation(reference: Trace, *traces: Trace,
reference_offset: int, reference_length: int,
max_offset: int, min_correlation: float = 0.5) -> List[Trace]:
"""
Align `traces` to the reference `trace`. Using 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:
:param traces:
:param reference_offset:
:param reference_length:
:param max_offset:
:param min_correlation:
:return:
"""
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)
@public
def align_peaks(reference: Trace, *traces: Trace,
reference_offset: int, reference_length: int, max_offset: int) -> List[Trace]:
"""
Align `traces` to the reference `trace` 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:
:param traces:
:param reference_offset:
:param reference_length:
:param max_offset:
:return:
"""
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)
@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")) -> List[Trace]:
"""
Align `traces` to the reference `trace` 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:
:param traces:
:param reference_offset:
:param reference_length:
:param max_offset:
:param dist_func:
:return:
"""
reference_part = reference.samples[reference_offset: reference_offset + reference_length]
def align_func(trace):
length = len(trace.samples)
best_distance = 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)
@public
def align_sad(reference: Trace, *traces: Trace,
reference_offset: int, reference_length: int, max_offset: int) -> List[Trace]:
"""
Align `traces` to the reference `trace` 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:
:param traces:
:param reference_offset:
:param reference_length:
:param max_offset:
:return:
"""
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)
@public
def align_dtw_scale(reference: Trace, *traces: Trace, radius: int = 1,
fast: bool = True) -> List[Trace]:
"""
Align `traces` to the reference `trace`.
Using 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:
:param traces:
:param radius:
:param fast:
:return:
"""
result = [deepcopy(reference)]
reference_samples = reference.samples
for trace in traces:
if fast:
dist, path = fastdtw(reference_samples, trace.samples, radius=radius)
else:
dist, path = dtw(reference_samples, trace.samples)
result_samples = np.zeros(len(trace.samples), dtype=trace.samples.dtype)
scale = np.ones(len(trace.samples), dtype=trace.samples.dtype)
for x, y in path:
result_samples[x] = trace.samples[y]
scale[x] += 1
result_samples //= scale
del scale
result.append(Trace(copy(trace.title), copy(trace.data), result_samples))
return result
@public
def align_dtw(reference: Trace, *traces: Trace, radius: int = 1, fast: bool = True) -> List[Trace]:
"""
Align `traces` to the reference `trace`. Using 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:
:param traces:
:param radius:
:param fast:
:return:
"""
result = [deepcopy(reference)]
reference_samples = reference.samples
for trace in traces:
if fast:
dist, path = fastdtw(reference_samples, trace.samples, radius=radius)
else:
dist, path = dtw(reference_samples, trace.samples)
result_samples = np.zeros(len(trace.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
# or manually:
# for x, y in path:
# result_samples[x] = trace.samples[y]
result.append(Trace(copy(trace.title), copy(trace.data), result_samples))
return result
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