How to add vertical values in three dimensional matrix

I have a netcdf file, with following details. The variable 'rf' is gridded rainfall value, and it is basically daily rainfall data from 1901 to 2018, resulting to 43099 values. When i read this netcdf file and assigned a variable for gridded rainfall, then my matrix was 135*129*43099, 135*129 being the number of grids, with each grid having 43099 values. I want to convert this daily rainfall data to monthly rainfall data, by adding the one month value to get a single value and get 12 values a year and get total 1416 values for all time period, considering all leap years and different number of days in a month. Hence my final resultant array should be 135*129*1416.

Dimensions:
           time = 43099 (UNLIMITED)
           lon  = 135
           lat  = 129
Variables:
    time
           Size:       43099x1
           Dimensions: time
           Datatype:   double
           Attributes:
                       standard_name = 'time'
                       units         = 'hours since 1-1-1 00:00:00'
                       calendar      = 'standard'
                       axis          = 'T'
    lon 
           Size:       135x1
           Dimensions: lon
           Datatype:   single
           Attributes:
                       standard_name = 'longitude'
                       long_name     = 'longitude'
                       units         = 'degrees_east'
                       axis          = 'X'
    lat 
           Size:       129x1
           Dimensions: lat
           Datatype:   single
           Attributes:
                       standard_name = 'latitude'
                       long_name     = 'latitude'
                       units         = 'degrees_north'
                       axis          = 'Y'
    rf  
           Size:       135x129x43099
           Dimensions: lon,lat,time
           Datatype:   single
           Attributes:
                       long_name     = 'GRIDDED RAINFALL'
                       _FillValue    = -999
                       missing_value = -999

Answer 1

[KSSV]

1. Convert your time into datevec. This will give you day, month, year etc.
2. Run loop for each month.
3. Pick the months indices from time. Like use: idx = month == 1 (this will pick Jan)
4. Pick the data using the baove indices idx. Like use: data_jan = data(:,:,idx) ;
5. Convert the above 3D data into 2D. Use

 T = permute(data_jan,[1 3 2]);
 T = reshape(T,[],size(data_jan,2),1) ; 

5. The above 2D matrix is for Jan for all the years.

6. You can process it.

There are some inbuilt functions also to achieve this. I don't remember the function name and I have never used too.

[Suman Dhamala]

I created a time vector with number of rows being equal to number of days, like in one column year, in another month and in another day. But since, this time vector and gridded rainfall are two different matrices, how do i link them, so that while running loop for time vector, I can add rainfall vaues for each grid?

[KSSV]

I already shown you how to index right? Step 3 and step 4.