def test_eigen_circular_ensemble_02(self):
mseeds = [2963416, 235124, 786134]
ce = Circular()
e_cue = ce.eigen_circular_ensemble(seeds=mseeds,
N=5,
nchunks=3,
ensemble='CUE',
parallel=True)
e_coe = ce.eigen_circular_ensemble(seeds=mseeds,
N=5,
nchunks=3,
ensemble='COE',
parallel=True)
e_cse = ce.eigen_circular_ensemble(seeds=mseeds,
N=5,
nchunks=3,
ensemble='CSE',
parallel=True)
e_cse2 = ce.eigen_circular_ensemble(seeds=mseeds,
N=5,
nchunks=3,
ensemble='CSE',
parallel=True,
adir="upper")
n_cue = np.imag(e_cue['c_eigen']).sum()
n_coe = np.imag(e_coe['c_eigen']).sum()
n_cse = np.imag(e_cse['c_eigen']).sum()
n_cse2 = np.imag(e_cse2['c_eigen']).sum()
self.assertTrue(n_cue - 62.284496117511054 < self.epsilon)
self.assertTrue(n_coe + 21.810798433338746 < self.epsilon)
self.assertTrue(np.abs(n_cse) < self.epsilon)
self.assertTrue(np.abs(n_cse2) < self.epsilon)
def test_spectral_density_01(self):
ce = Circular()
mseed = [123,125,124]
Ns = [5, 10, 15]
cSize = 2
nChunks = 3
eigen_data5 = ce.eigen_circular_ensemble(
Ns[0],
cSize=cSize,
nchunks=nChunks,
seeds=mseed,
parallel=False
)
eigen_data10 = ce.eigen_circular_ensemble(
Ns[1],
cSize=cSize,
nchunks=nChunks,
seeds=mseed,
parallel=False
)
eigen_data15 = ce.eigen_circular_ensemble(
Ns[2],
cSize=cSize,
nchunks=nChunks,
seeds=mseed,
parallel=False
)
ensemble_size = cSize*nChunks
eigen_data = {
"N5":eigen_data5,
"N10":eigen_data10,
"N15":eigen_data15
}
ergo = Ergodicity()
Dse = ergo.approach_se(
Ns=Ns,
ensemble_size=ensemble_size,
eigen_data=eigen_data
)
self.assertTrue(len(Dse) == 2)
d0 = -12.287133235052062
d1 = -8.3998021593200445
self.assertTrue(Dse[0]+d0 < self.epsilon)
self.assertTrue(Dse[1]+d1 < self.epsilon)
def test_eigen_circular_ensemble_02(self):
mseeds = [2963416, 235124, 786134]
ce = Circular()
e_cue = ce.eigen_circular_ensemble(
seeds=mseeds,
N=5,
nchunks=3,
ensemble='CUE',
parallel=True
)
e_coe = ce.eigen_circular_ensemble(
seeds=mseeds,
N=5,
nchunks=3,
ensemble='COE',
parallel=True
)
e_cse = ce.eigen_circular_ensemble(
seeds=mseeds,
N=5,
nchunks=3,
ensemble='CSE',
parallel=True
)
e_cse2 = ce.eigen_circular_ensemble(
seeds=mseeds,
N=5,
nchunks=3,
ensemble='CSE',
parallel=True,
adir="upper"
)
n_cue = np.imag(e_cue['c_eigen']).sum()
n_coe = np.imag(e_coe['c_eigen']).sum()
n_cse = np.imag(e_cse['c_eigen']).sum()
n_cse2 = np.imag(e_cse2['c_eigen']).sum()
self.assertTrue(n_cue-234.6608021786007 < self.epsilon)
self.assertTrue(n_coe+61.25284251132706 < self.epsilon)
self.assertTrue(np.abs(n_cse) < self.epsilon)
self.assertTrue(np.abs(n_cse2) < self.epsilon)
def test_test_thirumalai_mountain_01(self):
ce = Circular()
mseed = 2963416
# 5, 10x10 matrices from CUE
N = 10
cSize = 2
nchunks = 5
ensemble_size = cSize * nchunks
eseeds = [978712, 34687, 43124, 67831, 1234]
e_cue = ce.eigen_circular_ensemble(N=N,
ensemble='CUE',
seeds=eseeds,
cSize=cSize,
nchunks=nchunks)
c_eigen_ensemble = e_cue['c_eigen']
ergo = Ergodicity()
tm = ergo.thirumalai_mountain(c_eigen_ensemble, ensemble_size, N)
self.assertTrue(tm.shape == (31, ))
self.assertTrue(tm[6:11].sum() - 0.104 < self.epsilon)
import os
import pickle
from bristol.ensembles import Circular
ce = Circular()
# seed for 4 cpu cores (or chunks if not parallel)
seed_v = [997123, 1091645, 1352, 32718]
data_cue = {}
data_coe = {}
data_cse = {}
range_n = [64, 128, 256, 512, 768, 1024]
for N in range_n:
print("cue N=", N)
tic()
data_cue['N' + str(N)] = ce.eigen_circular_ensemble(N,
cSize=10,
nchunks=4,
seeds=seed_v,
ensemble='CUE')
toc()
print("coe N=", N)
tic()
data_coe['N' + str(N)] = ce.eigen_circular_ensemble(N,
cSize=10,
nchunks=4,
seeds=seed_v,
ensemble='COE')
toc()
print("cse N=", N)
tic()
data_cse['N' + str(N)] = ce.eigen_circular_ensemble(N,
cSize=10,
def spectra_ce(
range_N=[64, 128],
cSize=5,
nchunks=2,
seeds=[997123, 1091645],
ensemble='all',
parallel=False,
):
"""
Generate eigenvalues of matrices of different size
drawn from a circular ensemble.
Author: M.Suzen
params:
range_N set of Size of the rectangular matrix, NxN.
cSize Number of random matrices to generate in a chunk.
nchunks number of cSize chunks.
ensemble One of the circular ensemble
'CUE', 'COE', 'CSE', defaults to 'all'
seeds List of integer to use in random seed
in every chunk.
parallel Run in multicore, number of cores as nchunks,
defaults to False
output:
Dictionary of dictionaries.
* Highest level keys for ensemble `CUE`, `COE` or `CSE`.
* Then, dictionary with keys describing size, such as 'N16.
* Values will be an another dictionary
with keys `local_seed` integers for seeds
used in the chunk, `c_eigen`
numpy array of eigenvalues, `N` matrix size,
`M` number of matrices used to generate `c_eigen`. Note
that `c_eigen` will be length NxM.
Example:
"""
ce = Circular()
data_ce = {'CUE': {}, 'COE': {}, 'CSE': {}}
for N in range_N:
if (ensemble in ['CUE', 'all']):
e_dict = ce.eigen_circular_ensemble(N=N,
cSize=cSize,
nchunks=nchunks,
ensemble='CUE',
seeds=seeds,
parallel=parallel)
data_ce['CUE']['N' + str(N)] = e_dict
if (ensemble in ['COE', 'all']):
e_dict = ce.eigen_circular_ensemble(N=N,
cSize=cSize,
nchunks=nchunks,
ensemble='COE',
seeds=seeds,
parallel=parallel)
data_ce['COE']['N' + str(N)] = e_dict
if (ensemble in ['CSE', 'all']):
e_dict = ce.eigen_circular_ensemble(N=N,
cSize=cSize,
nchunks=nchunks,
ensemble='CSE',
seeds=seeds,
parallel=parallel)
data_ce['COE']['N' + str(N)] = e_dict
return data_ce
