def get_p_conn_vec_xpred(tp_src, tp_tgt, w_sigma_x, w_sigma_v, connectivity_radius=1.0):
"""
Calculates the connection probabilities for all source cells targeting one cell.
tp_src = np.array, shape = (n_src, 4)
tp_tgt = (x, y, u, v)
TODO: exp(cos(v_i, x_j - x_i) / (2*sigma_x**2))
"""
n_src = tp_src[:, 0].size
d_ij = utils.torus_distance2D_vec(tp_src[:, 0], tp_tgt[0] * np.ones(n_src), tp_src[:, 1], tp_tgt[1] * np.ones(n_src), w=np.ones(n_src), h=np.ones(n_src))
latency = d_ij / np.sqrt(tp_src[:, 2]**2 + tp_src[:, 3]**2)
x_pred = tp_src[:, 0] + tp_src[:, 2] * latency * connectivity_radius
y_pred = tp_src[:, 1] + tp_src[:, 3] * latency * connectivity_radius
d_pred_tgt = utils.torus_distance2D_vec(x_pred, tp_tgt[0] * np.ones(n_src), y_pred, tp_tgt[1] * np.ones(n_src), w=np.ones(n_src), h=np.ones(n_src))
# v_tuning_diff = utils.torus_distance2D_vec(tp_src[:, 2], tp_tgt[2] * np.ones(n_src), tp_src[:, 3], tp_tgt[3] * np.ones(n_src), w=np.ones(n_src), h=np.ones(n_src))
v_tuning_diff = (tp_src[:, 2] - tp_tgt[2] * np.ones(n_src))**2 + (tp_src[:, 3] - tp_tgt[3] * np.ones(n_src))**2
p = np.exp(- (d_pred_tgt / (2 * w_sigma_x**2))) \
* np.exp(- (v_tuning_diff / (2 * w_sigma_v**2)))
return p, latency
def get_p_conn_vec(tp_src, tp_tgt, w_sigma_x, w_sigma_v, connectivity_radius=1.0, maximal_latency=None):
"""
Calculates the connection probabilities for all source cells targeting one cell.
tp_src = np.array, shape = (n_src, 4)
tp_tgt = (x, y, u, v)
TODO: exp(cos(v_i, x_j - x_i) / (2*sigma_x**2))
"""
n_src = tp_src[:, 0].size
d_ij = utils.torus_distance2D_vec(tp_src[:, 0], tp_tgt[0] * np.ones(n_src), tp_src[:, 1], tp_tgt[1] * np.ones(n_src), w=np.ones(n_src), h=np.ones(n_src))
latency = d_ij / np.sqrt(tp_src[:, 2]**2 + tp_src[:, 3]**2)
# latency = d_ij / connectivity_radius
v_src = np.array((tp_src[:, 2], tp_src[:, 3]))
v_src = v_src.transpose()
v_tgt = np.array([tp_tgt[2], tp_tgt[3]])
v_tgt_norm = tp_tgt[2]**2 + tp_tgt[3]**2
v_src_norm = v_src[:, 0]**2 + v_src[:, 1]**2
v_cos_array = np.dot(v_src, v_tgt)
v_cos_array /= np.sqrt(v_src_norm * v_tgt_norm)
x_src = np.array((tp_src[:, 0], tp_src[:, 1]))
x_src = x_src.transpose()
x_tgt = np.array([tp_tgt[0], tp_tgt[1]])
x_tgt_norm = tp_tgt[0]**2 + tp_tgt[1]**2
x_src_norm = x_src[:, 0]**2 + x_src[:, 1]**2
x_diff = utils.torus(x_tgt[0] * np.ones(n_src) - x_src[:, 0])
y_diff = utils.torus(x_tgt[1] * np.ones(n_src) - x_src[:, 1])
x_diff_ = np.array((x_diff, y_diff))
x_diff_ = x_diff_.transpose()
# norm of x_tgt - x_src
eps = 1e-20
x_norm = x_diff_[:, 0]**2 + x_diff_[:, 1]**2 + eps
x_cos_array = np.dot(x_diff_, v_tgt)
x_cos_array /= np.sqrt(v_tgt_norm * x_norm)
p = np.exp(x_cos_array / (w_sigma_x**2)) * np.exp(v_cos_array/(w_sigma_v**2))
if connectivity_radius < 1.0:
# invalid_idx = latency > connectivity_radius
# invalid_idx = d_ij > connectivity_radius
# invalid_idx = invalid_idx.nonzero()[0]
# p[invalid_idx] = 0.
p[d_ij > connectivity_radius] = 0.
if maximal_latency != None:
p[latency > maximal_latency] = 0.
return p, d_ij
def get_p_conn_direction_and_orientation_based(tp_src, tp_tgt, w_sigma_x, w_sigma_v, w_sigma_theta, connectivity_radius=1.0):
"""
Direction-based + Orientation-tuning based connectivity
--------------------------------------------------------
Calculates the connection probabilities for all source cells targeting one cell.
tp_src = np.array, shape = (n_src, 4)
tp_tgt = (x, y, u, v)
"""
n_src = tp_src[:, 0].size
d_ij = utils.torus_distance2D_vec(tp_src[:, 0], tp_tgt[0] * np.ones(n_src), tp_src[:, 1], tp_tgt[1] * np.ones(n_src), w=np.ones(n_src), h=np.ones(n_src))
# latency = d_ij / np.sqrt(tp_src[:, 2]**2 + tp_src[:, 3]**2)
# latency = d_ij / connectivity_radius
v_src = np.array((tp_src[:, 2], tp_src[:, 3]))
v_src = v_src.transpose()
v_tgt = np.array([tp_tgt[2], tp_tgt[3]])
v_tgt_norm = tp_tgt[2]**2 + tp_tgt[3]**2
v_src_norm = v_src[:, 0]**2 + v_src[:, 1]**2
v_cos_array = np.dot(v_src, v_tgt)
v_cos_array /= np.sqrt(v_src_norm * v_tgt_norm)
x_src = np.array((tp_src[:, 0], tp_src[:, 1]))
x_src = x_src.transpose()
x_tgt = np.array([tp_tgt[0], tp_tgt[1]])
x_tgt_norm = tp_tgt[0]**2 + tp_tgt[1]**2
x_src_norm = x_src[:, 0]**2 + x_src[:, 1]**2
x_diff = utils.torus(x_tgt[0] * np.ones(n_src) - x_src[:, 0])
y_diff = utils.torus(x_tgt[1] * np.ones(n_src) - x_src[:, 1])
x_diff_ = np.array((x_diff, y_diff))
x_diff_ = x_diff_.transpose()
# norm of x_tgt - x_src
eps = 1e-20
x_norm = x_diff_[:, 0]**2 + x_diff_[:, 1]**2 + eps
x_cos_array = np.dot(x_diff_, v_tgt)
x_cos_array /= np.sqrt(v_tgt_norm * x_norm)
p = np.exp(x_cos_array / (w_sigma_x**2)) * np.exp(v_cos_array/(w_sigma_v**2)) * np.exp(np.cos(tp_tgt[4] - tp_src[:, 4]) / w_sigma_theta**2)
if connectivity_radius < 1.0:
# invalid_idx = latency > connectivity_radius
# invalid_idx = d_ij > connectivity_radius
# invalid_idx = invalid_idx.nonzero()[0]
# p[invalid_idx] = 0.
p[d_ij > connectivity_radius] = 0.
return p, d_ij
