def secant(y: sympy.core,
x0: float,
x1: float,
epsilon: float = 0.00001,
maxtime: int = 50) -> (list, list):
'''
弦截法, 使用newton 差商计算,每次只需计算一次f(x)
secant method for finding a zeropoint of a func
y is the func , x0 is the init x val, epsilon is the accurrency
'''
if epsilon < 0: epsilon = -epsilon
ct = 0
x0, x1 = float(x0), float(x1)
li = [x0, x1]
t = y.free_symbols
varsymbol = 'x' if len(t) == 0 else t.pop()
last = y.subs(varsymbol, x0)
vals = [last]
while 1:
cur = y.subs(varsymbol, x1)
vals.append(cur)
x = x1 - cur * (x1 - x0) / (cur - last)
x0, x1 = x1, x
last = cur
li.append(x)
ct += 1
if ct > maxtime:
print(
"after iteration for {} times, I still havn't reach the accurrency.\
Maybe this function havsn't zeropoint\n".format(ct))
return li, vals
if abs(x0 - x1) < epsilon: return li, vals
x0 = x
def newton(y: sympy.core,
x0: float,
epsilon: float = 0.00001,
maxtime: int = 50) -> (list, list):
'''
newton 's iteration method for finding a zeropoint of a func
y is the func, x0 is the init x val: int float epsilon is the accurrency
'''
if epsilon < 0: epsilon = -epsilon
ct = 0
t = y.free_symbols
varsymbol = 'x' if len(t) == 0 else t.pop()
x0 = float(x0)
y_diff = y.diff()
li = [x0]
vals = []
while 1:
val = y.subs(varsymbol, x0)
vals.append(val)
x = x0 - val / y_diff.subs(varsymbol, x0)
li.append(x)
ct += 1
if ct > maxtime:
print(
"after iteration for {} times, I still havn't reach the accurrency.\
Maybe this function havsn't zeropoint\n".format(ct))
return li, val
if abs(x - x0) < epsilon: return li, vals
x0 = x