Insert values from matrix dataframe into another dataframe using indexes

I have pandas dataframe df_matrix with shape = (4, 5) (Actually it much much much bigger!). It has integer numbers as indexes over rows and columns.

df_matrix =

df_matrix contains data, which I want to put into column depth of another dataframe df_main, according its df_main['row_i'] and df_main['col_i'] columns
So, expected result is like this:

df_main =

I decided it by iterrows:

for index, row in df_main.iterrows():
    df_main.loc[index, 'depth'] = df_matrix.loc[row['row_i'], row['col_i']]

it takes a lot of time while handling 200000+ rows. I believe that pandas has appropriate method, may be merge, but i have no idea which one and how to use it.
Is there decision more pythonic (pandasonic)))?

I'm not sure if merge will be efficient here but you can still try it :

df_main = (
    pd.merge(df_main,
             df_matrix.stack().rename("depth"),
             left_on=["row_i", "col_i"], right_index=True, how="left")
)

​
Output :

print(df_main)

                   datetime   latitude   longitude  row_i  col_i    depth
0       2013-05-29 00:39:44  51.708487  104.366131      0      0   92.576
1       2013-05-29 00:40:44  51.708268  104.362324      0      2  108.308
2       2013-05-29 00:41:44  51.708036  104.358530      1      3  131.331
296448  2022-06-14 03:39:40  51.876903  105.520172      3      4  141.075

This should work as well:

df_main['depth'] = df_matrix.to_numpy()[df_main['row_i'],df_main['col_i']]