How to calculate Relative Strength Index (RSI) and Exponential Moving Average (EMA) from a list in pandas

I have created a pandas dataframe (called df) as follows:

import pandas as pd
import numpy as np

ds = {'col1' : [[10,23,45],[54,67,65],[76,43,21]]}

df = pd.DataFrame(data=ds)

The dataframe looks like this:

print(df)

           col1
0  [10, 23, 45]
1  [54, 67, 65]
2  [76, 43, 21]

I need to create two new columns:

a columns called RSI_2, which shows the 2-period Relative Strength Index (RSI) of the list contained in col1 (so, the RSI_2 column will contain the 2-period RSI of 10,23,45 and then the 2-period RSI of 54,67,65, etc.)
a column called EMA_2, which shows the 2-period Exponential Moving Average (EMA) of the list contained in col1(so, the EMA_2 column will contain the 2-period EMA of 10,23,45 and then the 2-period EMA of 54,67,65, etc.)

Solution

One possible way to do this is to define two functions. One for computing the RSI and one to calculate the EMA (note that in this one I chose the preiod 2, as you required, but it can be changed if needed).

A word of advice. In the future, do put a little bit of context and possibly explanations of what you are aiming for. That will increase your chances for a reply. Not everybody is used to stock markets.

Given you data, this would be:

import pandas as pd
import numpy as np

ds = {'col1': [[10, 23, 45], [54, 67, 65], [76, 43, 21]]}
df = pd.DataFrame(data=ds)

def calculate_rsi(values):
    gains = []
    losses = []
    for i in range(1, len(values)):
        difference = values[i] - values[i-1]
        if difference > 0:
            gains.append(difference)
        else:
            losses.append(abs(difference))
    
    average_gain = np.mean(gains) if gains else 0
    average_loss = np.mean(losses) if losses else 0
    
    if average_loss == 0:  
        return 100
    else:
        rs = average_gain / average_loss
        rsi = 100 - (100 / (1 + rs))
        return rsi

def calculate_ema(values, periods=2):
    weights = np.exp(np.linspace(-1., 0., periods))
    weights /= weights.sum()
    ema = np.convolve(values, weights, mode='full')[:len(values)]
    ema[:periods] = ema[periods]  
    return ema[-1]

df['RSI_2'] = df['col1'].apply(calculate_rsi)
df['EMA_2'] = df['col1'].apply(lambda x: calculate_ema(x, 2))

print(df)

Which retunrs:

           col1       RSI_2      EMA_2
0  [10, 23, 45]  100.000000  28.916711
1  [54, 67, 65]   86.666667  66.462117
2  [76, 43, 21]    0.000000  37.083289