Develop Reference

Python's `.loc` is really slow on selecting subsets of Data

I'm having a large multindexed (y,t) single valued DataFrame df. Currently, I'm selecting a subset via df.loc[(Y,T), :] and create a dictionary out of it. The following MWE works, but the selection is very slow for large subsets.
import numpy as np
import pandas as pd
# Full DataFrame
y_max = 50
Y_max = range(1, y_max+1)
t_max = 100
T_max = range(1, t_max+1)
idx_max = tuple((y,t) for y in Y_max for t in T_max)
df = pd.DataFrame(np.random.sample(y_max*t_max), index=idx_max, columns=['Value'])
# Create Dictionary of Subset of Data
y1 = 4
yN = 10
Y = range(y1, yN+1)
t1 = 5
tN = 9
T = range(t1, tN+1)
idx_sub = tuple((y,t) for y in Y for t in T)
data_sub = df.loc[(Y,T), :] #This is really slow
dict_sub = dict(zip(idx_sub, data_sub['Value']))
# result, e.g. (y,t) = (5,7)
dict_sub[5,7] == df.loc[(5,7), 'Value']
I was thinking of using df.loc[(y1,t1),(yN,tN), :], but it does not work properly, as the second index is only bounded in the final year yN.

One idea is use Index.isin with itertools.product in boolean indexing:
from itertools import product
idx_sub = tuple(product(Y, T))
dict_sub = df.loc[df.index.isin(idx_sub),'Value'].to_dict()
print (dict_sub)

Calculate 2.5% below and 2.5% above the mean in Python

How do I print the dataframe, where the population is within 5% of the mean? (2.5% below and 2.5% above)
Here is what I've tried:
mean = df['population'].mean()
minimum = mean - (0.025*mean)
maximum = mean + (0.025*mean)
df[df.population < maximum]

Use:
df.loc[(df['population'] > minimum) & (df['population'] < maximum)]

import pandas as pd
df = pd.read_csv("fileName.csv")
#suppose this dataFrame contains the population in the int format
mean = df['population'].mean()
minimum = mean - (0.025*mean)
maximum = mean + (0.025*mean)
ans = df.loc[(df['population']>minimum) & (df['population'] <maximum)]
ans
you can use this

I built this dataframe for testing.
import numpy as np
import pandas as pd
random_data = np.random.randint(1_000_000, 100_000_000, 200)
random_df = pd.DataFrame(random_data, columns=['population'])
random_df
Here's the answer to specifically what you were asking for.
pop = random_df.population
top_boundary = pop.mean() + pop.mean() * 0.025
low_boundary = pop.mean() - pop.mean() * 0.025
criteria_boundary_limits = random_df.population.between(low_boundary, top_boundary)
criteria_boundary_df = random_df.loc[criteria_boundary_limits]
criteria_boundary_df
But, maybe, another answer could be had by using quantiles. I used 40 quantiles because 1/40 = 0.025.
groups_list = list(range(1,41))
random_df['groups'] = pd.qcut(random_df['population'], 40, labels = groups_list)
criteria_groups_limits = random_df.groups.between(20,21)
criteria_groups_df = random_df.loc[criteria_groups_limits]
criteria_groups_df

Maximum and minimum in a range of independent variable

Based on the answer from #Peaceful James, I am attempting to reduce the confusion. Thus, editing the question.
Edited
I am trying to find a maximum (and minimum) in the range of an independent variable, i.e. X. My code looks like the following. Note, this is just a representative function.
import numpy as np
import matplotlib.pyplot as plt
from pandas import *
X = np.arange(2, 11, 0.2)
Z = np.zeros((len(X),1))
for i in range(0,len(X)):
Z[i] = 0.1*np.sin(X[i]-5)
print(DataFrame(Z))
A = np.argmax(Z, axis = 0)
B = np.argmin(Z, axis = 0)
C = print("Maximum =",Z[A[0]])
D = print("Minimum =", Z[B[0]])
plt.plot(X,Z,'r-', linewidth = 2)
plt.xlabel('$X$ (-)')
plt.ylabel('$Z$ (-)')
1: A = np.argmax(Z, axis = 0) the maximum is 0.09995736 (index: (23,0)) which is between the X values 6 and 8.
2: A = np.argmin(Z, axis = 0) the min is -0.09995736 (index: (7,0)) which is between the X values 2 and 4. However, there is another minimum between the X values 8 and 10. I am wondering if there is a way to pass some kind of upper and lower limit values of X to np.argmin (or to similar command) to get the second minimum of function Z.
Any help is appreciated. Thanks !

Use numpy.argsort:
https://numpy.org/devdocs/reference/generated/numpy.argsort.html
import numpy as np
X = np.arange(2, 11, 0.2)
Z = np.zeros((len(X),1))
for i in range(0,len(X)):
Z[i] = 0.1*np.sin(X[i]-5)
C = np.argsort(Z, axis=0)
C = C.flatten() # flatten because it is currently an array of 1-dim arrays.
print("Maximum =",Z[C[-1]])
print("Second Maximum =",Z[C[-2]])
print("Second Minimum =",Z[C[1]])
print("Minimum =",Z[C[0]])

Dataframe with Monte Carlo Simulation calculation next row Problem

I want to build up a Dataframe from scratch with calculations based on the Value before named Barrier option. I know that i can use a Monte Carlo simulation to solve it but it just wont work the way i want it to.
The formula is:
Value in row before * np.exp((r-sigma**2/2)*T/TradingDays+sigma*np.sqrt(T/TradingDays)*z)
The first code I write just calculates the first column. I know that I need a second loop but can't really manage it.
The result should be, that for each simulation it will calculate a new value using the the value before, for 500 Day meaning S_1 should be S_500 with a total of 1000 simulations. (I need to generate new columns based on the value before using the formular.)
similar to this:
So for the 1. Simulations 500 days, 2. Simulation 500 day and so on...
import numpy as np
import pandas as pd
from scipy.stats import norm
import random as rd
import math
simulation = 0
S_0 = 42
T = 2
r = 0.02
sigma = 0.20
TradingDays = 500
df = pd.DataFrame()
for i in range (0,TradingDays):
z = norm.ppf(rd.random())
simulation = simulation + 1
S_1 = S_0*np.exp((r-sigma**2/2)*T/TradingDays+sigma*np.sqrt(T/TradingDays)*z)
df = df.append ({
'S_1':S_1,
'S_0':S_0
}, ignore_index=True)
df = df.round ({'Z':6,
'S_T':2
})
df.index += 1
df.index.name = 'Simulation'
print(df)
I found another possible code which i found here and it does solve the problem but just for one row, the next row is just the same calculation. Generate a Dataframe that follow a mathematical function for each column / row
If i just replace it with my formular i get the same problem.
replacing:
exp(r - q * sqrt(sigma))*T+ (np.random.randn(nrows) * sqrt(deltaT)))
with:
exp((r-sigma**2/2)*T/nrows+sigma*np.sqrt(T/nrows)*z))
import numpy as np
import pandas as pd
from scipy.stats import norm
import random as rd
import math
S_0 = 42
T = 2
r = 0.02
sigma = 0.20
TradingDays = 50
Simulation = 100
df = pd.DataFrame({'s0': [S_0] * Simulation})
for i in range(1, TradingDays):
z = norm.ppf(rd.random())
df[f's{i}'] = df.iloc[:, -1] * np.exp((r-sigma**2/2)*T/TradingDays+sigma*np.sqrt(T/TradingDays)*z)
print(df)
I would work more likely with the last code and solve the problem with it.

How about just overwriting the value of S_0 by the new value of S_1 while you loop and keeping all simulations in a list?
Like this:
import numpy as np
import pandas as pd
import random
from scipy.stats import norm
S_0 = 42
T = 2
r = 0.02
sigma = 0.20
trading_days = 50
output = []
for i in range(trading_days):
z = norm.ppf(random.random())
value = S_0*np.exp((r - sigma**2 / 2) * T / trading_days + sigma * np.sqrt(T/trading_days) * z)
output.append(value)
S_0 = value
df = pd.DataFrame({'simulation': output})
Perhaps I'm missing something, but I don't see the need for a second loop.
Also, this eliminates calling df.append() in a loop, which should be avoided. (See here)

Solution based on the the answer of bartaelterman, thank you very much!
import numpy as np
import pandas as pd
from scipy.stats import norm
import random as rd
import math
#Dividing the list in chunks to later append it to the dataframe in the right order
def chunk_list(lst, chunk_size):
for i in range(0, len(lst), chunk_size):
yield lst[i:i + chunk_size]
def blackscholes():
d1 = ((math.log(S_0/K)+(r+sigma**2/2)*T)/(sigma*np.sqrt(2)))
d2 = ((math.log(S_0/K)+(r-sigma**2/2)*T)/(sigma*np.sqrt(2)))
preis_call_option = S_0*norm.cdf(d1)-K*np.exp(-r*T)*norm.cdf(d2)
return preis_call_option
K = 40
S_0 = 42
T = 2
r = 0.02
sigma = 0.2
U = 38
simulation = 10000
trading_days = 500
trading_days = trading_days -1
#creating 2 lists for the first and second loop
loop_simulation = []
loop_trading_days = []
#first loop calculates the first column in a list
for j in range (0,simulation):
print("Progressbar_1_2 {:2.2%}".format(j / simulation), end="\n\r")
S_Tag_new = 0
NORM_S_INV = norm.ppf(rd.random())
S_Tag = S_0*np.exp((r-sigma**2/2)*T/trading_days+sigma*np.sqrt(T/trading_days)*NORM_S_INV)
S_Tag_new = S_Tag
loop_simulation.append(S_Tag)
#second loop calculates the the rows for the columns in a list
for i in range (0,trading_days):
NORM_S_INV = norm.ppf(rd.random())
S_Tag = S_Tag_new*np.exp((r-sigma**2/2)*T/trading_days+sigma*np.sqrt(T/trading_days)*NORM_S_INV)
loop_trading_days.append(S_Tag)
S_Tag_new = S_Tag
#values from the second loop will be divided in number of Trading days per Simulation
loop_trading_days_chunked = list(chunk_list(loop_trading_days,trading_days))
#First dataframe with just the first results from the firstloop for each simulation
df1 = pd.DataFrame({'S_Tag 1': loop_simulation})
#Appending the the chunked list from the second loop to a second dataframe
df2 = pd.DataFrame(loop_trading_days_chunked)
#Merging both dataframe into one
df3 = pd.concat([df1, df2], axis=1)

Pandas DataFrame Logic - Python

Trying to backtest trading logic for fun but I can seem to comprehend how to utilize numpy to make decisions. For example, I want to set df['position'] = 1 or -1 based on whether the data is below or above the upper and lower lines. If Data <= the lower line I want to set position = 1 and keep it at 1 until Data it is >= the upper line. Once data is >= the upper line I want to set position = -1 and keep at -1 then repeat.
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
data = np.random.standard_normal((5, 100)).flatten()
data = data.cumsum()
df = pd.DataFrame({'Data': data})
df['std'] = df['Data'].rolling(50).std()
df['SMA'] = df['Data'].rolling(50).mean()
df['upper'] = df['SMA'] + (2 * df['std'])
df['lower'] = df['SMA'] - (2 * df['std'])
df[['Data', 'SMA', 'upper', 'lower']].plot(figsize=(10, 6))
df['position'] = 0
plt.show()
Here I try to do just that but fail because I don't know how to do this properly.
df['islower'] = np.where(df['Data'] < df['lower'], 1, 0)
df['isupper'] = np.where(df['Data'] > df['upper'], 1, 0)
df['position'] = np.where(df['isupper']==1, -1, 0) | np.where(df['islower']==1, 1, 0)

I think what you want to do is:
df['islower'] = df['islower'].where(df['Data'] < df['lower'], 1, 0)
df['isupper'] = df['isupper'].where(df['Data'] < df['upper'], 1, 0)