Going from monthly average dataframe to an interpolated daily timeseries - python-3.x

Question

I am interested in taking average monthly values, for each month, and set the monthly average values to be the value on the 15th day of each month (within a daily timeseries).
I start with the following (these are the monthly average values I am given):
m_avg = pd.DataFrame({'Month': ['1.527013956', '1.899169054', '1.669356146','1.44920871', '1.188557788', '1.017035727', '0.950243755', '1.022453993', '1.203913739', '1.369545041','1.441827406','1.48621651']
EDIT: I added one more value to the dataframe so that there are now 12 values.
Next, I want to put each of these monthly values on the 15th day (within each month) for the following time period:
ts = pd.date_range(start='1/1/1950', end='12/31/1999', freq='D')
I know how to pull out the date on 15th day of an already existing daily timeseries by using:
df= df.loc[(df.index.day==15)] # Where df is any daily timeseries
Lastly, I know how to interpolate the values once I have the average monthly values on the 15th day of each month, using:
df.loc[:, ['Col1']] = df.loc[:, ['Col1']].interpolate(method='linear', limit_direction='both', limit=100)
How do I get from the monthly DataFrame to an interpolated daily DataFrame, where I linearly interpolate between the 15th day of each month, which is the monthly value of my original DataFrame by construction?
EDIT:
Your suggestion to use np.tile() was good, but I ended up needing to do this for multiple columns. Instead of np.tile, I used:
index = pd.date_range(start='1/1/1950', end='12/31/1999', freq='MS')
m_avg = pd.concat([month]*49,axis=0).set_index(index)
There may be a better solution out there, but this is working for my needs so far.

Answer 1

Here is one way to do it:
import pandas as pd
import numpy as np
# monthly averages, note these should be cast to float
month = np.array(['1.527013956', '1.899169054', '1.669356146',
'1.44920871', '1.188557788', '1.017035727',
'0.950243755', '1.022453993', '1.203913739',
'1.369545041', '1.441827406', '1.48621651'], dtype='float')
# expand this to 51 years, with the same monthly averages repeating each year
# (obviously not very efficient, probably there are better ways to attack the problem,
# but this was the question)
month = np.tile(month, 51)
# create DataFrame with these values
m_avg = pd.DataFrame({'Month': month})
# set the date index to the desired time period
m_avg.index = pd.date_range(start='1/1/1950', end='12/1/2000', freq='MS')
# shift the index by 14 days to get the 15th of each month
m_avg = m_avg.tshift(14, freq='D')
# expand the index to daily frequency
daily = m_avg.asfreq(freq='D')
# interpolate (linearly) the missing values
daily = daily.interpolate()
# show result
display(daily)
Output:
Month
1950-01-15 1.527014
1950-01-16 1.539019
1950-01-17 1.551024
1950-01-18 1.563029
1950-01-19 1.575034
... ...
2000-12-11 1.480298
2000-12-12 1.481778
2000-12-13 1.483257
2000-12-14 1.484737
2000-12-15 1.486217
18598 rows × 1 columns