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# -------------------------------------------------------------------------------
# Core routines for computing properties of symmetric random matrices.
# -------------------------------------------------------------------------------
import numpy as np
ra = np.random
la = np.linalg
def GOE(N):
"""Creates an NxN element of the Gaussian Orthogonal Ensemble"""
m = ra.standard_normal((N, N))
m += m.T
return m / 2
def center_eigenvalue_diff(mat):
"""Compute the eigvals of mat and then find the center eigval difference."""
N = len(mat)
evals = np.sort(la.eigvals(mat))
diff = np.abs(evals[N / 2] - evals[N / 2 - 1])
return diff
def ensemble_diffs(num, N):
"""Return num eigenvalue diffs for the NxN GOE ensemble."""
diffs = np.empty(num)
for i in range(num):
mat = GOE(N)
diffs[i] = center_eigenvalue_diff(mat)
return diffs
def normalize_diffs(diffs):
"""Normalize an array of eigenvalue diffs."""
return diffs / diffs.mean()
def normalized_ensemble_diffs(num, N):
"""Return num *normalized* eigenvalue diffs for the NxN GOE ensemble."""
diffs = ensemble_diffs(num, N)
return normalize_diffs(diffs)
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