def __init__(self, x, y, m):
"""
m is a vector of integers giving each layer dimension
z_i ∈ R^{m_i}, i ∈ [0,n-1]
x ∈ R^{ x.shape[0], q }
y ∈ R^{ m[n-1] , q }
A[i] ∈ R^{ m[i], m[i-1] }
A[0] ∈ R^{ m[0], x.shape[0] }
b[i] ∈ R^{ m[i] }
"""
self.sigmoid = sig.poly1()
assert x.shape[1] == y.shape[1]
assert y.shape[0] == m[-1]
self.x = x
self.y = y
self.n = len(m)
self.z = []
self.A = []
self.b = []
for i in range(self.n):
if i == 0:
self.A.append(randn(m[0], x.shape[0]))
else:
self.A.append(randn(m[i], m[i - 1]))
self.b.append(randn(m[i]))
self.z.append(randn(m[i]))
self.train()
def test():
n = 2
a = randn(n)
b = randn(1)
c = randn(n)
d = randn(1)
P = poly.rand(n,1,1)
problem = linear_fractional(a,b,c,d,P)
problem.solve()
print(problem)
def test():
print('\n'+'_'*80 + '\nk_means [see ./fig/k_means.png]')
import random
n = 2
m = 20
k = 4
s = randn(n,m)+np.kron(ones(1,m),10*randn(n,1))
for i in range(k-1):
s = np.hstack((s,randn(n,m)+np.kron(ones(1,m),10*randn(n,1))))
k_means(s,k).plot()
def __init__(self,s,k):
# s = vectors
# x = means
m = s.shape[1]
n = s.shape[0]# s[i] = column vector as matrix in R^n
x = randn(n,k)
for loop in range(10):
d = zeros(k,m)
for j in range(m):
for i in range(k):
d[i,j] = norm.l_p(s[:,j] - x[:,i], 2)
min_d = np.full((m), np.inf)
for j in range(m):
for i in range(k):
if d[i,j] < min_d[j]:
min_d[j] = d[i,j]
b = zeros(k,m)
for j in range(m):
for i in range(k):
if d[i,j] == min_d[j]:
b[i,j] = 1
else:
b[i,j] = 0
for i in range(k):
num = zeros(n,1)
den = 0
for j in range(m):
num += b[i,j]*s[:,j]
den += b[i,j]
if den != 0:
x[:,i] = num / den
else:
x[:,i] += random.gauss(0,1) # random walk
self.s = s
self.x = x
def test():
print('\n'+'_'*80 + '\npoly_cells [see ./fig/Voronoi.png]')
n = 2
m = 100
x = randn(n,m)
obj = poly_cells(x)
obj.plot_poly_cells()
obj.plot_poly_center()
def test():
n = 5
m = 10
q = 100
x = randn(n,q)
y = zeros(m,q)
while True:
A,r = sprandn(m,n,0.1)
if r < m*n:
break
for i in range(q):
y[:,i] = A * x[:,i]
print(min_complexity_model(x,y,1))
print('\nA_data = \n' + str(sparse(A))+'\n')
def test():
x = randn(2, 100)
y = randn(3, 100)
m = (2, 2, y.shape[0])
nn(x, y, m)
def test():
n = 2
s = randn(n,100)
sampled_convex_set(s)