def riesz_energy(points, s):
num_points = len(points)
if num_points < 2:
return gmpy2.zero()
if s == 1:
energy = gmpy2.rec_sqrt(squared_distance(points[0], points[1]))
for j in range(2, num_points):
energy += gmpy2.rec_sqrt(squared_distance(points[0], points[j]))
for i in range(1, num_points):
for j in range(i + 1, num_points):
energy += gmpy2.rec_sqrt(squared_distance(points[i], points[j]))
elif s == 2:
energy = 1 / squared_distance(points[0], points[1])
for j in range(2, num_points):
energy += 1 / squared_distance(points[0], points[j])
for i in range(1, num_points):
for j in range(i + 1, num_points):
energy += 1 / squared_distance(points[i], points[j])
else:
energy = squared_distance(points[0], points[1]) ** (-s/2)
for j in range(2, num_points):
energy += squared_distance(points[0], points[j]) ** (-s/2)
for i in range(1, num_points):
for j in range(i + 1, num_points):
energy += squared_distance(points[i], points[j]) ** (-s/2)
return energy
def riesz_force(points, s):
point_indices = range(len(points))
dim_indices = range(len(points[0]))
force = [[gmpy2.zero() for _ in dim_indices] for _ in point_indices]
if s == 2:
for i in point_indices:
for j in point_indices:
if i != j:
dist, disp = squared_difference(points[i], points[j])
dist = 2 / gmpy2.square(dist)
for k in dim_indices:
force[i][k] += dist * disp[k]
elif s == 1:
for i in point_indices:
for j in point_indices:
if i != j:
dist, disp = squared_difference(points[i], points[j])
dist = gmpy2.rec_sqrt(dist) / dist
for k in dim_indices:
force[i][k] += dist * disp[k]
else:
for i in point_indices:
for j in point_indices:
if i != j:
dist, disp = squared_difference(points[i], points[j])
dist = s * dist**(-s / 2 - 1)
for k in dim_indices:
force[i][k] += dist * disp[k]
return force
def rec_norm(v):
norm_sq = gmpy2.square(v[0])
for i in range(1, len(v)):
norm_sq += gmpy2.square(v[i])
return gmpy2.rec_sqrt(norm_sq)
def rec_norm(self):
"""Return the reciprocal of the Euclidean norm of this MPFRVector."""
return gmpy2.rec_sqrt(self.norm_squared())