different methods for log determinants

log_det.py

import numpy as np
import time

# generate data
X = np.random.randn(1000, 10000)

t0 = time.time()
K = X.dot(X.T) + 1e-9*np.eye(X.shape[0])
tK = time.time() - t0
print "tK:", tK

# np function
t0 = time.time()
np.linalg.slogdet(K)
tnp = time.time() - t0 + tK
print "tslogdet:", tnp

# np function
t0 = time.time()
np.log(np.linalg.det(K))
tnp = time.time() - t0 + tK
print "tdet:", tnp


# using eigh
t0 = time.time()
S1, U1 = np.linalg.eigh(K)
np.log(S1[S1 > 1e-9]).sum()
teig = time.time() - t0 + tK
print "teig:", teig

# using svd
t0 = time.time()
U,S,V = np.linalg.svd(X, full_matrices=False)
S2 = S*S
np.log(S2[S2 > 1e-9]).sum()
tsvd = time.time() - t0
print "tsvd:", tsvd

# using cholesky (creates lower-triagular matrix, for which eigenvalues can be read off the diagonal)
t0 = time.time()
L = np.linalg.cholesky(K)
log_det_chol = np.log(np.diag(L)**2).sum()
tcho = time.time() - t0 + tK
print "tcho:", tcho


"""
output:
tK: 0.680999994278
tnp: 0.746999979019
teig: 1.02300000191
tsvd: 4.94499993324
tcho: 0.770999908447

verdict:
use cholesky if other operations are done on matrices
if only log det is needed, slogdet is fine (uses LU factorzation internally)
"""