"""滚动窗口、两个收益间隔与样本/总体标准差的独立真值。"""
import json
from math import isclose, sqrt
from statistics import mean, stdev, pstdev


def matches(actual, expected):
    return isclose(actual, expected, rel_tol=0, abs_tol=1e-12)


def calculate(closes):
    rows = []
    for i, close in enumerate(closes):
        if i < 2:
            rows.append({'i': i, 'mean': None, 'return_two_intervals': None,
                         'sample_sd': None, 'population_sd': None, 'signal': 0})
            continue
        window = closes[i-2:i+1]
        average = mean(window)
        rows.append({'i': i, 'mean': average, 'return_two_intervals': close / closes[i-2] - 1,
                     'sample_sd': stdev(window), 'population_sd': pstdev(window),
                     'signal': int(close > average)})
    return rows


xs = [10, 12, 14, 12, 10]
rows = calculate(xs)
assert [r['signal'] for r in rows] == [0, 0, 1, 0, 0]
assert rows[2]['mean'] == 12 and matches(rows[2]['return_two_intervals'], .4)
assert rows[2]['sample_sd'] == 2 and matches(rows[2]['population_sd'], sqrt(8/3))
assert matches(rows[3]['mean'], 38/3) and matches(rows[4]['return_two_intervals'], -2/7)
assert matches(rows[3]['sample_sd'], sqrt(4/3))
assert matches(rows[3]['population_sd'], sqrt(8/9))
assert not matches(1000000, 1000000 + 1e-8)
equal = calculate([10, 12, 11])[-1]
above = calculate([10, 12, 11.01])[-1]
below = calculate([10, 12, 10.99])[-1]
assert equal['mean'] == 11 and equal['signal'] == 0
assert above['signal'] == 1 and below['signal'] == 0
assert not matches(stdev([10, 12, 14]), pstdev([10, 12, 14]))
for cutoff in range(1, len(xs)):
    assert calculate(xs[:cutoff]) == rows[:cutoff]
assert calculate(xs + [10000])[:len(xs)] == rows
print(json.dumps({'truth_rows': rows, 'threshold_equal': equal,
                  'threshold_above': above, 'threshold_below': below,
                  'tolerance_absolute': 1e-12, 'sd_unit': 'price, not return volatility'}))