def dihotomiaMethodGetTable(f, epsilon, a, b):
data = {
'a': [],
'b': [],
'Отношение длин': [],
'x1': [],
'x2': [],
'f(x1)': [],
'f(x2)': []
}
delta = epsilon / 4
x1 = (a + b) / 2 - delta
x2 = (a + b) / 2 + delta
f1 = f(x1)
f2 = f(x2)
prev_length = None
u.writeRow(data, a, b, prev_length, x1, x2, f1, f2)
count = 0
while True:
count += 1
prev_length = abs(b - a)
if f1 < f2:
b = x2
else:
a = x1
x1 = (a + b) / 2 - delta
x2 = (a + b) / 2 + delta
f1 = f(x1)
f2 = f(x2)
u.writeRow(data, a, b, prev_length, x1, x2, f1, f2)
if abs(b - a) < epsilon:
break
return (count, pd.DataFrame(data))
def dihotomiaMethod(f, epsilon, a, b):
delta = epsilon / 4
x1 = (a + b) / 2 - delta
x2 = (a + b) / 2 + delta
f1 = f(x1)
f2 = f(x2)
while True:
if f1 < f2:
b = x2
else:
a = x1
x1 = (a + b) / 2 - delta
x2 = (a + b) / 2 + delta
f1 = f(x1)
f2 = f(x2)
if abs(b - a) < epsilon:
break
return (a + b) / 2
def fibonacciMethod(f, n, a, b):
x1 = a + (b - a) * fibonacci(n - 2) / fibonacci(n)
x2 = a + (b - a) * fibonacci(n - 1) / fibonacci(n)
f1 = f(x1)
f2 = f(x2)
while True:
n -= 1
if f1 > f2:
a = x1
x1 = x2
x2 = b - (x1 - a)
f1 = f2
f2 = f(x2)
else:
b = x2
x2 = x1
x1 = a + (b - x2)
f2 = f1
f1 = f(x1)
if n == 1:
return (x1 + x2) / 2
def goldenRatioMethodGetTable(f, epsilon, a, b):
data = {
'a': [],
'b': [],
'Отношение длин': [],
'x1': [],
'x2': [],
'f(x1)': [],
'f(x2)': []
}
F = (1 + math.sqrt(5)) / 2
x1 = b - (b - a) / F
x2 = a + (b - a) / F
f1 = f(x1)
f2 = f(x2)
prev_length = None
count = 0
u.writeRow(data, a, b, prev_length, x1, x2, f1, f2)
while True:
count += 1
prev_length = abs(b - a)
if f1 < f2:
b = x2
x2 = x1
f2 = f1
x1 = b - (b - a) / F
f1 = f(x1)
else:
a = x1
x1 = x2
f1 = f2
x2 = a + (b - a) / F
f2 = f(x2)
u.writeRow(data, a, b, prev_length, x1, x2, f1, f2)
if abs(b - a) < epsilon:
break
return (count, pd.DataFrame(data))
def goldenRatioMethod(f, epsilon, a, b):
F = (1 + math.sqrt(5)) / 2
x1 = b - (b - a) / F
x2 = a + (b - a) / F
f1 = f(x1)
f2 = f(x2)
while True:
if f1 < f2:
b = x2
x2 = x1
f2 = f1
x1 = b - (b - a) / F
f1 = f(x1)
else:
a = x1
x1 = x2
f1 = f2
x2 = a + (b - a) / F
f2 = f(x2)
if abs(b - a) < epsilon:
break
return 0.5 * (a + b)
def fibonacciMethodGetTable(f, n, a, b):
data = {
'a': [],
'b': [],
'Отношение длин': [],
'x1': [],
'x2': [],
'f(x1)': [],
'f(x2)': []
}
x1 = a + (b - a) * fibonacci(n - 2) / fibonacci(n)
x2 = a + (b - a) * fibonacci(n - 1) / fibonacci(n)
f1 = f(x1)
f2 = f(x2)
prev_length = None
count = 0
u.writeRow(data, a, b, prev_length, x1, x2, f1, f2)
while True:
count += 1
prev_length = abs(b - a)
n -= 1
if f1 > f2:
a = x1
x1 = x2
x2 = b - (x1 - a)
f1 = f2
f2 = f(x2)
else:
b = x2
x2 = x1
x1 = a + (b - x2)
f2 = f1
f1 = f(x1)
u.writeRow(data, a, b, prev_length, x1, x2, f1, f2)
if n == 1:
break
return (count, pd.DataFrame(data))
def brandtMethod(f, epsilon, a, c):
K = (3 - math.sqrt(5)) / 2
x = (a + c) / 2
w = (a + c) / 2
v = (a + c) / 2
fx = f(x)
fw = f(w)
fv = f(v)
d = e = c - a
u = None
count = 0
while True:
count += 1
prev_u = u
g = e
e = d
if x != w and x != v and w != v and fx != fw and fx != fv and fw != fv:
#u = w - (((w - x) ** 2) * (fw - fv) - ((w - v) ** 2) * (fw - fx)) / 2 / (
# (w - x) * (w - v) - (w - v) * (w - x))
u = calculateX_hat(x, w, v, fx, fw, fv)
if a + epsilon <= u and u <= c - epsilon and abs(u - x) < g / 2:
d = abs(u - x)
else:
u = None
if u is None:
if x < (c + a) / 2:
u = x + K * (c - x)
d = c - x
else:
u = x - K * (x - a)
d = x - a
if abs(u - x) < epsilon:
u = x + sign(u - x) * epsilon
fu = f(u)
if fu <= fx:
if u >= x:
a = x
else:
c = x
v = w
w = x
x = u
fv = fw
fw = fx
fx = fu
else:
if u >= x:
c = u
else:
a = u
if fu <= fw or w == x:
v = w
w = u
fv = fw
fw = fu
elif fu <= fv or v == x or v == w:
v = u
fv = fu
if count != 1:
if abs(prev_u - u) < epsilon:
break
return (a + c) / 2