I tried many libraries on Github but all of them did not produce matching results for TradingView so I followed the fo
Here is an option.
I will be touching only on your second bullet
# libraries required
import pandas as pd
import numpy as np
# create dataframe
df = pd.DataFrame({'close':[4724.89, 4378.51,6463.00,9838.96,13716.36,10285.10,
10326.76,6923.91,9246.01,7485.01,6390.07,7730.93,
7011.21,6626.57,6371.93,4041.32,3702.90,3434.10,
3813.69,4103.95,5320.81,8555.00,10854.10]})
df['change'] = df['close'].diff(1) # Calculate change
# calculate gain / loss from every change
df['gain'] = np.select([df['change']>0, df['change'].isna()],
[df['change'], np.nan],
default=0)
df['loss'] = np.select([df['change']<0, df['change'].isna()],
[-df['change'], np.nan],
default=0)
# create avg_gain / avg_loss columns with all nan
df['avg_gain'] = np.nan
df['avg_loss'] = np.nan
n = 14 # what is the window
# keep first occurrence of rolling mean
df['avg_gain'][n] = df['gain'].rolling(window=n).mean().dropna().iloc[0]
df['avg_loss'][n] = df['loss'].rolling(window=n).mean().dropna().iloc[0]
# Alternatively
df['avg_gain'][n] = df.loc[:n, 'gain'].mean()
df['avg_loss'][n] = df.loc[:n, 'loss'].mean()
# This is not a pandas way, looping through the pandas series, but it does what you need
for i in range(n+1, df.shape[0]):
df['avg_gain'].iloc[i] = (df['avg_gain'].iloc[i-1] * (n - 1) + df['gain'].iloc[i]) / n
df['avg_loss'].iloc[i] = (df['avg_loss'].iloc[i-1] * (n - 1) + df['loss'].iloc[i]) / n
# calculate rs and rsi
df['rs'] = df['avg_gain'] / df['avg_loss']
df['rsi'] = 100 - (100 / (1 + df['rs'] ))