def __call__(self, data: InputData) -> ResultData:
(x, y) = data.initial
path = [(x, y)]
grad = (data.df_dx1(x, y), data.df_dx2(x, y))
calls_count = 2
f_calls = 0
while (grad[0]**2 + grad[1]**2) >= data.eps**2:
(t_x, t_y) = (x - self.alpha * grad[0], y - self.alpha * grad[1])
f_calls += 2
if data.function(t_x, t_y) > data.function(
x,
y) - self.delta * self.alpha * (grad[0]**2 + grad[1]**2):
self.alpha *= self.delta
continue
(x, y) = (t_x, t_y)
grad = (data.df_dx1(x, y), data.df_dx2(x, y))
calls_count += 2
path.append((x, y))
return ResultData(self.name, (x, y), data.function(x, y), f_calls,
calls_count, path)
def __call__(self, data: InputData) -> ResultData:
(x, y) = data.initial
x0 = (x, y)
x1 = (x + self.length, y)
x2 = (x, y + self.length)
xk = [x0, x1, x2]
f_calls = 3
path = [x0]
fk = [data.function(xi[0], xi[1]) for xi in xk]
while sum([(xk[i][0] - xk[0][0])**2 + (xk[i][1] - xk[0][1])**2
for i in range(1, 3)]) / 2 > data.eps**2:
min_i = min(range(3), key=lambda i: fk[i])
max_i = max(range(3), key=lambda i: fk[i])
c_x = 0
c_y = 0
for i in range(3):
if i != max_i:
c_x += xk[i][0]
c_y += xk[i][1]
c_x /= 2
c_y /= 2
u_k = (2 * c_x - xk[max_i][0], 2 * c_y - xk[max_i][1])
f_u = data.function(u_k[0], u_k[1])
if f_u < fk[max_i]:
xk[max_i] = u_k
fk[max_i] = f_u
f_calls += 1
else:
for i in range(0, 3):
xk[i] = ((xk[i][0] + xk[min_i][0]) / 2,
(xk[i][1] + xk[min_i][1]) / 2)
fk[i] = data.function(xk[i][0], xk[i][1])
f_calls += 2
path.append(xk[0])
return ResultData(self.name, xk[0], fk[0], f_calls, 0, path)
def __call__(self, data: InputData) -> ResultData:
(x, y) = data.initial
h = self.h
calls_count = 0
path = [(x, y)]
while h > self.delta:
x1 = x
y1 = y
f = data.function(x, y)
if data.function(x + h, y) < f:
x1 += h
if data.function(x - h, y) < f:
x1 -= h
if data.function(x, y + h) < f:
y1 += h
if data.function(x, y - h) < f:
y1 -= h
calls_count += 5
if (x1, y1) == (x, y):
h /= 2
continue
x += self.lambd * (x1 - x)
y += self.lambd * (y1 - y)
path.append((x, y))
return ResultData(self.name, (x, y), data.function(x, y), calls_count,
0, path)
def __call__(self, data: InputData) -> ResultData:
(x, y) = data.initial
path = [(x, y)]
grad = (data.df_dx1(x, y), data.df_dx2(x, y))
calls_count = 2
while (grad[0] * grad[0] + grad[1] * grad[1]) >= data.eps * data.eps:
(x, y) = (x - self.alpha * grad[0], y - self.alpha * grad[1])
grad = (data.df_dx1(x, y), data.df_dx2(x, y))
calls_count += 2
path.append((x, y))
return ResultData(self.name, (x, y), data.function(x, y), 0,
calls_count, path)
def __call__(self, data: InputData) -> ResultData:
(x, y) = data.initial
path = [(x, y)]
dx = data.df_dx1(x, y)
x1 = x - self.alpha * dx
dy = data.df_dx2(x1, y)
y1 = y - self.alpha * dy
calls_count = 2
f_calls = 0
while ((x1 - x)**2 + (y1 - y)**2) >= data.eps**2:
(x, y) = (x1, y1)
dx = data.df_dx1(x, y)
x1 = x - self.alpha * dx
dy = data.df_dx2(x1, y)
y1 = y - self.alpha * dy
calls_count += 2
path.append((x, y))
path.append((x1, y1))
return ResultData(self.name, (x1, y1), data.function(x, y), f_calls,
calls_count, path)