def gaussian_vector_rbf(a, b, x, eps):
'''VECTOR Gaussian radial basis function. Equals `1/exp(b - a)` in point `(a+b)/2` and 0 far from it.'''
center = (a + b) / 2
edge = b - a
dx = x - center
edge_length = vector_norm(edge)
norm = np.exp(edge_length)
r = vector_norm(dx)
return (edge / edge_length) * np.exp(-(eps * r) ** 2) / edge_length / norm
def edge_cos(a, b, x, eps):
'''REAL cosine similarity fuction with fade out. For `c=(a+b)/2` equals `cos_sim(x-c, b-c)/exp(norm(x-c))`. Positive where `ab` and `x` lay in the same semispace.'''
c = (a + b) / 2
dx = x - c
cs = cos(dx.reshape(1, -1), (b - c).reshape(1, -1))[0][0]
val = cs / np.exp(vector_norm(dx))
return val
def f(x, eps=0.05):
# step 1. Get closest edge points
# # todo: build an index
# cl = SortedList()
# for e, length in cut:
# a, b = G.nodes[e[0]].value, G.nodes[e[1]].value
# center = (a + b) / 2
# if G.nodes[e[0]]._class > G.nodes[e[1]]._class: a, b = b, a
# vect = (b - a) / vector_norm(b - a)
# d = np.dot(center - x, center - x)
# cl.add((d, vect))
vs, cs, rs = set(), SortedList(), SortedList()
tops, hops = edge_index.search_nsw_basic(x, vs, cs, rs, top=100)
summ = 0.
vectors = np.zeros(edge_index.nodes[0].value.shape)
for d, idx in tops:
if d > eps: break
center = edge_index.nodes[idx].value
edge = edge_index.nodes[idx]._class
a, b = G.nodes[edge[0]].value, G.nodes[edge[1]].value
if G.nodes[edge[0]]._class > G.nodes[edge[1]]._class: a, b = b, a
vect = vect = (b - a) / vector_norm(b - a)
# c = 1
c = 2 / (1 + d / eps) - 1
vectors += c * vect
summ += 1
if summ > 0:
vectors /= summ
return vectors
def gen(N=400, border=0.8):
values = []
for i in range(N):
p = np.array([1 - 2 * random.random(), 1 - 2 * random.random()])
cls = 1 if vector_norm(p) > border else 0
values.append((p, cls))
return values
def gen2(N=400, border1=0.3, border2=0.9):
values = []
for i in range(N):
p = np.array([1 - 2 * random.random(), 1 - 2 * random.random()])
cls = 1 if border2 > vector_norm(p) > border1 else 0
values.append((p, cls))
return values
def gen_kd(N=400, k=3, border=0.3, noise=0.0):
values = []
for i in range(N):
p = np.array([1 - 2 * random.random() for _ in range(k)])
cls = 1 if vector_norm(p) > border else 0
if random.random() < noise:
cls = 1 - cls
values.append((p, cls))
return values
def gaussian_rbf(p, x, eps):
'''REAL Gaussian radial basis function. Equals 1 in `p` and 0 far from `p` '''
r = vector_norm(p - x)
return np.exp(-(eps * r) ** 2)
frac = (x-Greens_x[index_x_old])/(Greens_x[index_x_old+1]-Greens_x[index_x_old])
# Cubic interpolation for all values of z
lowx_vals = Greens_G_th_Spline[index_x_old](lnz_arr)
highx_vals = Greens_G_th_Spline[index_x_old+1](lnz_arr)
G_th[index_x_new,:] = (lowx_vals*(1.-frac)+highx_vals*frac)
G_th[index_x_new,:] *= bb_vis*1.e-8
G_th[index_x_new,:] += DI_T_shift[index_x_new,:]*1.e-8
#G_th[index_x_new,:] += Gdist[index_x_new]*df_g
except:
raise ValueError("{} is not in the file range [{},{}] for file '{}'".format(x,Greens_x[0],Greens_x[-1],readfile))
# Begin orthonormlization
# Y distortion
e_Y = Ydist/vector_norm(Ydist)
M_Y = np.dot(e_Y,Mdist)
G_Y = np.dot(e_Y,Gdist)
# Mu distortion
Mperp = Mdist-M_Y*e_Y
e_M = Mperp/vector_norm(Mperp)
G_M = np.dot(e_M,Gdist)
# G distortion
Gperp = Gdist-G_Y*e_Y-G_M*e_M
e_G = Gperp/vector_norm(Gperp)
f_g = np.zeros(Nz_arr)
f_mu = np.zeros(Nz_arr)
f_y = np.zeros(Nz_arr)
# Now, factorize G into orthonormal subspace
for index_z in range(Nz_arr):
