>>> from biseccio import succ_biseccio

---- inici

>>> def f1(x):
...     return 2*x - 6
>>> eps = 1e-3

>>> c = succ_biseccio(f1, 2.9, 3.15, eps)

Valors arrodonits dels extrems dels intervals.

>>> [(round(e, 3), round(d, 3)) for e, d in c]
[(2.9, 3.15), (2.9, 3.025), (2.962, 3.025), (2.994, 3.025), (2.994, 3.009), (2.994, 3.002), (2.998, 3.002), (3.0, 3.002), (3.0, 3.001)]

Només el darrer interval té una longitud més petita que eps.

>>> [abs(e - d) < eps for e, d in c] == [False]*8 + [True]
True

El punt mig del darrer interval s'acosta prou al zero de la funció en
l'interval.

>>> e, d = c[-1]
>>> f1((e + d)/2) < eps
True

---- fi

>>> c = succ_biseccio(f1, 0, 5, eps)
>>> len(c)
14
>>> [abs(e - d) < eps for e, d in c] == [False]*13 + [True]
True
>>> e, d = c[-1]
>>> round(e, 4)
2.9999
>>> round(d, 4)
3.0005
>>> f1((e + d)/2) < eps
True

>>> eps = 1e-5
>>> c = succ_biseccio(f1, 0, 5, eps)
>>> len(c)
20
>>> [abs(e - d) < eps for e, d in c] == [False]*19 + [True]
True
>>> e, d = c[-1]
>>> round(e, 6)
2.999992
>>> round(d, 6)
3.000002
>>> f1((e + d)/2) < eps
True


>>> def f2(x):
...     return (x - 2)*(x + 1)
>>> eps = 1e-3

>>> c = succ_biseccio(f2, 1.9, 2.3, eps)
>>> [(round(e, 3), round(d, 3)) for e, d in c]
[(1.9, 2.3), (1.9, 2.1), (2.0, 2.1), (2.0, 2.05), (2.0, 2.025), (2.0, 2.012), (2.0, 2.006), (2.0, 2.003), (2.0, 2.002), (2.0, 2.001)]
>>> len(c)
10
>>> [abs(e - d) < eps for e, d in c] == [False]*9 + [True]
True
>>> e, d = c[-1]
>>> f2((e + d)/2) < eps*10
True

>>> c = succ_biseccio(f2, 0, 3, eps)
>>> len(c)
13
>>> [abs(e - d) < eps for e, d in c] == [False]*12 + [True]
True
>>> e, d = c[-1]
>>> round(e, 4)
1.9995
>>> round(d, 4)
2.0002
>>> f2((e + d)/2) < eps
True

>>> eps = 1e-5
>>> c = succ_biseccio(f2, 0, 5, eps)
>>> len(c)
20
>>> [abs(e - d) < eps for e, d in c] == [False]*19 + [True]
True
>>> e, d = c[-1]
>>> round(e, 6)
1.999998
>>> round(d, 6)
2.000008
>>> f2((e + d)/2) < eps
True

>>> eps = 1e-3
>>> c = succ_biseccio(f2, -2, -0.5, eps)
>>> [(round(e, 4), round(d, 4)) for e, d in c]
[(-2, -0.5), (-1.25, -0.5), (-1.25, -0.875), (-1.0625, -0.875), (-1.0625, -0.9688), (-1.0156, -0.9688), (-1.0156, -0.9922), (-1.0039, -0.9922), (-1.0039, -0.998), (-1.001, -0.998), (-1.001, -0.9995), (-1.0002, -0.9995)]
>>> len(c)
12
>>> [abs(e - d) < eps for e, d in c] == [False]*11 + [True]
True
>>> e, d = c[-1]
>>> f2((e + d)/2) < eps
True

>>> c = succ_biseccio(f2, -5, 0, eps)
>>> len(c)
14
>>> [abs(e - d) < eps for e, d in c] == [False]*13 + [True]
True
>>> e, d = c[-1]
>>> round(e, 4)
-1.0004
>>> round(d, 4)
-0.9998
>>> f2((e + d)/2) < eps
True

>>> eps = 1e-5
>>> c = succ_biseccio(f2, -4, 1, eps)
>>> len(c)
20
>>> [abs(e - d) < eps for e, d in c] == [False]*19 + [True]
True
>>> e, d = c[-1]
>>> round(e, 6)
-1.000008
>>> round(d, 6)
-0.999998
>>> f2((e + d)/2) < eps
True