def get_Sigma(corstr, p, k, rho):
if corstr == 'exch':
print("Exchangeable covariance matrix")
Sigma = gen.get_exch(p, rho)
elif corstr == '2block':
print("Using '2block' covariance matrix")
Sigma = gen.get_2block(p, k, rho)
elif corstr == 'ar1':
print("Using AR covariance")
Sigma = gen.get_ar(p, rho)
else:
print("Unknown corstr, using exchangeable")
Sigma = gen.get_exch(p, rho)
return Sigma
def sim_wrank(N,
p,
k,
rho,
corstr,
FDR,
offset,
nW,
nsim_x,
nsim_yx,
nsim_uyx,
wtype,
toCSV=True,
tag=''):
if corstr == 'ar1':
Sigma = gen.get_ar(p, rho)
else:
Sigma = gen.get_exch(p, rho)
SigmaChol = np.linalg.cholesky(Sigma)
beta = gen.rand_beta_flat(p, k, es)
fdp = gen.get_fdpfunc(beta)
tpr = gen.get_tprfunc(beta)
fname = "wrank-" + tag + "-nx" + str(nsim_x) + "-nyx" + str(nsim_yx)
fname += "-nuyx" + str(nsim_uyx)
fname += '-N' + str(N) + '-p' + str(p)
fname += '-w' + wtype + '-nW' + str(nW) + '-ar1-rho' + str(
rho) + '-off' + str(offset)
fname += '.csv'
rslt = []
vheader = [
'k', 'N', 'p', 'rho', 'offset', 'nW', 'jx', 'jyx', 'juyx', 'FDR',
'fdp', 'tpr'
]
vheader.extend(["sel{:d}".format(i) for i in range(p)])
vfmt = [
'%d', '%d', '%d', '%.3f', '%d', '%d', '%d', '%d', '%d', '%.3f',
'%.18e', '%.18e'
]
vfmt.extend(['%d' for i in range(p)])
vheader = ','.join(vheader)
gparm = [k, N, p, rho, offset]
for jx in range(nsim_x):
X = gen.gen_X(N, p, SigmaChol) # scaled and centere
Qx, Rx = np.linalg.qr(X, mode='reduced')
G = np.matmul(Rx.T, Rx)
svec = ko.get_svec_ldet(G)
Ginv = np.linalg.inv(G)
Cmat = ko.get_cmat(X, svec, Ginv=Ginv)
for jyx in range(nsim_yx):
Y = gen.gen_Y(X, N, beta, sigma=1)
for juyx in range(nsim_uyx):
sel_consensus = ko.doKnockoff(X,
Y,
FDR,
offset,
svec=svec,
wstat=wtype,
scale=False,
center=False,
Utilde=None,
nrep=nW,
Qx=Qx,
Rx=Rx,
Ginv=Ginv,
G=G,
Cmat=Cmat)
sel_one = ko.doKnockoff(X,
Y,
FDR,
offset,
svec=svec,
wstat=wtype,
scale=False,
center=False,
Utilde=None,
nrep=1,
Qx=Qx,
Rx=Rx,
Ginv=Ginv,
G=G,
Cmat=Cmat)
r1 = gparm + [
1, jx, jyx, juyx, FDR,
fdp(sel_one),
tpr(sel_one)
]
r1.extend((1 * sel_one).tolist())
rc = gparm + [
nW, jx, jyx, juyx, FDR,
fdp(sel_consensus),
tpr(sel_consensus)
]
rc.extend((1 * sel_consensus).tolist())
rslt.append(r1)
rslt.append(rc)
rslt = np.array(rslt)
if toCSV:
np.savetxt(fname,
rslt,
fmt=vfmt,
delimiter=',',
header=vheader,
comments='')
return rslt
else:
return rslt, vheader, vfmt, fname
def power_method(A, p, niter=10):
ek = np.random.normal(size=(p, ))
ek = ek / np.linalg.norm(ek)
for _ in range(niter):
ek1 = np.dot(A, ek)
ek1_norm = np.linalg.norm(ek1)
ek = ek1 / ek1_norm
return np.dot(np.dot(ek.T, A), ek)
if __name__ == "__main__":
p = 200
rho = 0.9
print("p={:d}".format(p))
print("correlation = {:.2f}".format(rho))
Sigma = gen.get_exch(p, rho)
n = 5000
print("n={:d}".format(n))
SigmaChol = np.linalg.cholesky(Sigma)
np.random.seed(1)
X = gen.gen_X(n, p, SigmaChol) # scaled and centered
G = np.dot(X.T, X)
meig_exact = scipy.linalg.eigvalsh(G, eigvals=(0, 0))[0]
print("meig_exact = " + str(meig_exact))
Ginv = scipy.linalg.inv(G)
power_rslt = []
test_iter = np.arange(50) + 1
print("power iterations: ")
for niter in test_iter:
cv = 1 / power_method(Ginv, p, niter)
power_rslt.append(cv)