Code takes forever to come up with a solution - python-3.x

Question

What I basically want, is comparing a timevalue (t1 and tuit)(in hours) to determine which method to use to calculate 'S' and 'k' in a function called 'stijghoogteverlaging'. Then a fitted curve can be made with those values.
I tried multiple things, like putting 'return s' underneath both s-methods.
if t1[i] < tuit:
s = Q / (4 * np.pi * k * D) * exp1(S * r**2 / (4 * k * D * t))
return s
else:
s = Q / (4 * np.pi * k * D) * ((exp1(S * r**2 / (4 * k * D * t))) - (exp1(S * r**2 / (4 * k * D * (t - tuit)))))
return s
But then I got a wrong fitted curve as can be seen in the image below.
Now I tried putting only one 'return s', but then it takes forever to calculate and I have to interrupt the kernel.
data = read_csv("pompproef_data.csv", sep = ';')
pb1 = data.iloc[1:,1].values-1.87
pb2 = data.iloc[1:,2].values-1.86
t1 = data.iloc[1:,0].values / (60*24)
volume = 10/1000 #m3
duur = [128,136, 150, 137, 143, 141] #seconden
totaal = np.sum(duur)
debiet = (((len(duur) * volume)/totaal)) * (60*60*24) #m3/d
print(debiet)
print(t1)
print(pb1)
tuit = 15/(24*60)
D = 2.0
Q = debiet
def stijghoogteverlaging(t, k, S):
for i in range(len(t1)):
if t1[i] < tuit:
s = Q / (4 * np.pi * k * D) * exp1(S * r**2 / (4 * k * D * t))
else:
s = Q / (4 * np.pi * k * D) * ((exp1(S * r**2 / (4 * k * D * t))) - (exp1(S * r**2 / (4 * k * D * (t - tuit)))))
return s
r = 4.0 #afstand peilbuis1 tot put
poptpb1, pcovpb1 = curve_fit(stijghoogteverlaging, t1, pb1, p0=[100, 1e-25], maxfev = 10000000)
print('optimale waarde van k voor peilbuis1:', poptpb1[0])
print('optimale waarde van S voor peilbuis1:', poptpb1[1])
tijd = data.iloc[1:,0].values
t = np.linspace(0.00069*(24*60), 0.021*(24*60), 1000)
s1 = stijghoogteverlaging(t, poptpb1[0], poptpb1[1])
plt.plot(tijd, pb1, 'r.', label = 'Gemeten bij 4 meter')
plt.plot(t, s1, 'b', label = 'fitted bij 4 m')
Does anyone have a solution?
Used values for t1 and pb1:
Plot with a wrong fitted curve(time in minutes).

Answer 1

The function stijghoogteverlaging is performing a nonsense operation over and over:
def stijghoogteverlaging(t, k, S):
for i in range(len(t1)):
if t1[i] < tuit:
s = Q / (4 * np.pi * k * D) * exp1(S * r**2 / (4 * k * D * t))
else:
s = Q / (4 * np.pi * k * D) * ((exp1(S * r**2 / (4 * k * D * t))) - (exp1(S * r**2 / (4 * k * D * (t - tuit)))))
return s
You are iterating len(t1) times, and at each iteration, you are computing the full vectorized value of s each and every time. That means that you are computing len(t)**2 values per call, and using a Python for loop as your outer loop to do it. As a minor point, you are accessing the x-data as the global variable t1 instead of the local value t, which gets passed in.
Your function should probably look more like this:
def stijghoogteverlaging(t, k, S):
return np.where(t < tuit,
Q / (4 * np.pi * k * D) * exp1(S * r**2 / (4 * k * D * t)),
Q / (4 * np.pi * k * D) * ((exp1(S * r**2 / (4 * k * D * t))) - (exp1(S * r**2 / (4 * k * D * (t - tuit)))))
)
This computes len(t) * 2 values per call, not len(t)**2, and selects a value from the appropriate result for each value of t.