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"""This module provides statistical tests usable on groups of traces sample-wise (Welch's and Student's t-test, ...)."""
from typing import Sequence, Optional, Tuple
import numpy as np
from public import public
from scipy.stats import ttest_ind, ks_2samp, t
from .trace import Trace, CombinedTrace
from .combine import average_and_variance
from .edit import trim
def _ttest_func(
first_set: Sequence[Trace], second_set: Sequence[Trace], equal_var: bool
) -> Optional[CombinedTrace]:
if not first_set or not second_set or len(first_set) == 0 or len(second_set) == 0:
return None
first_stack = np.stack([first.samples for first in first_set])
second_stack = np.stack([second.samples for second in second_set])
result = ttest_ind(first_stack, second_stack, axis=0, equal_var=equal_var)
return CombinedTrace(result[0])
@public
def welch_ttest(
first_set: Sequence[Trace],
second_set: Sequence[Trace],
dof: bool = False,
p_value: bool = False,
) -> Optional[Tuple[CombinedTrace, ...]]:
"""
Perform the Welch's t-test sample wise on two sets of traces :paramref:`~.welch_ttest.first_set` and :paramref:`~.welch_ttest.second_set`.
Useful for Test Vector Leakage Analysis (TVLA).
:param first_set:
:param second_set:
:param dof: Whether to compute and return the degrees-of-freedom.
:param p_value: Whether to compute and return the p-values.
:return: Welch's t-values (samplewise) (+ degrees-of-freedom, + p-values)
"""
if not first_set or not second_set or len(first_set) == 0 or len(second_set) == 0:
return None
n0 = len(first_set)
n1 = len(second_set)
mean_0, var_0 = average_and_variance(*first_set)
mean_1, var_1 = average_and_variance(*second_set)
if len(mean_0) < len(mean_1):
mean_1 = trim(mean_1, end=len(mean_0))
var_1 = trim(var_1, end=len(mean_0))
if len(mean_1) < len(mean_0):
mean_0 = trim(mean_0, end=len(mean_1))
var_0 = trim(var_0, end=len(mean_1))
varn_0 = var_0.samples / n0
varn_1 = var_1.samples / n1
tval = (mean_0.samples - mean_1.samples) / np.sqrt(varn_0 + varn_1)
result = [CombinedTrace(tval)]
if dof or p_value:
top = (varn_0 + varn_1) ** 2
bot = (varn_0 ** 2 / (n0 - 1)) + (varn_1 ** 2 / (n1 - 1))
df = top / bot
del top
del bot
result.append(CombinedTrace(df))
if p_value:
atval = np.abs(tval)
p = 2 * t.sf(atval, df)
del atval
result.append(CombinedTrace(p))
return tuple(result)
@public
def student_ttest(
first_set: Sequence[Trace], second_set: Sequence[Trace]
) -> Optional[CombinedTrace]:
"""
Perform the Students's t-test sample wise on two sets of traces :paramref:`~.student_ttest.first_set` and :paramref:`~.student_ttest.second_set`.
Useful for Test Vector Leakage Analysis (TVLA).
:param first_set:
:param second_set:
:return: Student's t-values (samplewise)
"""
return _ttest_func(first_set, second_set, True)
@public
def ks_test(
first_set: Sequence[Trace], second_set: Sequence[Trace]
) -> Optional[CombinedTrace]:
"""
Perform the Kolmogorov-Smirnov two sample test on equality of distributions sample wise on two sets of traces :paramref:`~.ks_test.first_set` and :paramref:`~.ks_test.second_set`.
:param first_set:
:param second_set:
:return: Kolmogorov-Smirnov test statistic values (samplewise)
"""
if not first_set or not second_set or len(first_set) == 0 or len(second_set) == 0:
return None
first_stack = np.stack([first.samples for first in first_set])
second_stack = np.stack([second.samples for second in second_set])
results = np.empty(len(first_set[0].samples), dtype=first_set[0].samples.dtype)
for i in range(len(first_set[0].samples)):
results[i] = ks_2samp(first_stack[..., i], second_stack[..., i])[0]
return CombinedTrace(results)
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