def random_naub_pos(self):
a = Vec2d(350, 0)
b = Vec2d(0, 220)
if random() < 0.5:
a,b = b,a
if random() < 0.5:
b = -b
return random_vec(a.x, a.y) + b
def spam_naub_pair(self):
pos = self.random_naub_pos()
rot = random() * math.pi * 2
a, b = self.create_naub_pair(pos, rot)
impulse = lambda: random_vec(50, 50)
a.body.apply_impulse(impulse())
b.body.apply_impulse(impulse())
a.color = self.random_naub_color()
b.color = self.random_naub_color()
self.add_naubs(a, b)
def slq(A, step, nv, f):
"""
input:
A : sparse positive semi-definite matrix (real symmetric)
step :
nv :
f :
output:
tr(f(L))
"""
N = A.shape[0]
sum_of_gauss_quadrature = 0
for l in range(nv):
x = random_vec(N)
z = normalize_vec(x)
T, _ = lanczos(A, z, step)
w, vs = LA.eigh(T) # if T is not symmetric, use eig(T)
ts = vs[0] # frist elements of eigenvectors
sum_of_gauss_quadrature += np.dot((ts**2),
f(w)) # sum(t**2 f(eigenval))
return (N / nv) * sum_of_gauss_quadrature
elif Gtype == "adjacency":
L = nx.adjacency_matrix(G)
def f(x):
return np.power(x, k)
return slq(L.astype(np.float64), step, nv, f)
if __name__ == "__main__":
# ---- generate matrix A
n = 4
step = 100
sqrtA = np.random.rand(n, n) - 0.5
A = np.dot(sqrtA, np.transpose(sqrtA))
print("A:")
print(A)
A = csr_matrix(A)
x = random_vec(n)
z = normalize_vec(x)
T, V = lanczos(A, z, step)
print("T:")
print(T)
print("V:")
print(V)
print("V.T A V")
V = csr_matrix(V)
print(V.T.dot(A).dot(V).toarray())