1import math
 2import numpy as np
 3
 4def weighted_quantile(v, w, mass):
 5    o = np.argsort(v, kind='mergesort')
 6    c = np.cumsum(w[o] / np.sum(w))
 7    return float(v[o][np.searchsorted(c, mass, side='left')])
 8
 9def conformal_q(scores, alpha):
10    a = np.sort(np.asarray(scores, float)); n = len(a)
11    k = min(n, int(math.ceil((n + 1) * (1-alpha))))
12    return float(a[k-1])
13
14def main():
15    v=np.array([1.,2.,10.,20.]); w=np.array([.1,.2,.3,.4])
16    assert weighted_quantile(v,w,.9)==20 and weighted_quantile(v,w,.5)==10
17    assert conformal_q(np.arange(1.,11.),.1)==10
18    rng=np.random.default_rng(7); r=rng.lognormal(size=(50,64)); ws=np.ones(64)/64
19    qs=[]
20    for g in (.01,.05,.10,.25):
21        s=np.array([weighted_quantile(row,ws,1-g) for row in r]); qs.append(float(np.mean(s)))
22        assert np.all((r <= s[:,None]).mean(1) >= 1-g-1e-12)
23    assert all(qs[i] >= qs[i+1] for i in range(len(qs)-1))
24    out={'weighted_order_statistic':True,'finite_sample_indexing':True,'gamma_mean_scores':qs,'monotone_tightening':True}
25    print(out)
26if __name__=='__main__': main()