def get_sigma_input(self, mu, C=None):
"""
Standard deviation of input given presynaptic activity mu
(and correlations C)
For C=None: formula (6) in Helias14
For C given: formula (13) in Helias14
mu: averages rates
C: average correlations
"""
mu = np.array(mu)
if np.shape(mu) != (2,):
raise ValueError(
'Mean activity needs to be given for both populations.')
if C is None:
C = np.array([[0., 0.],
[0., 0.]])
else:
C = np.array(C)
if np.shape(C) != (2, 2):
raise ValueError(
'Correlation needs to be given for all combinations of both populations.')
a = bhlp.get_sigma2(mu)
sigma_shared = np.dot(self.K * self.J * self.J, a)
sigma_corr = np.diag(
np.dot(np.dot(self.K * self.J, C), (self.K * self.J).T))
return np.sqrt(sigma_shared + sigma_corr)
def get_c_meanfield(self, mu, C=None):
"""
Self-consistent correlations
Formula (24) without external input in Helias14
mu: average rates
"""
a = bhlp.get_sigma2(mu)
A = np.zeros(2)
A[0] = a[0] * 1. / self.NE if self.NE > 0 else 0.
A[1] = a[1] * 1. / self.NI if self.NI > 0 else 0.
W = self.get_w_meanfield(mu, C)
M = np.array([[2. - 2. * W[0, 0], -2. * W[0, 1], 0.],
[-1. * W[1, 0], 2. - (W[0, 0] + W[1, 1]), -1. * W[0, 1]],
[0, -2. * W[1, 0], 2. - 2. * W[1, 1]]])
B = np.array([[2. * W[0, 0], 0],
[W[1, 0], W[0, 1]],
[0, 2. * W[1, 1]]])
rhs = np.dot(B, A)
c = np.linalg.solve(M, rhs)
C = np.array([[c[0], c[1]],
[c[1], c[2]]])
return C
