How to compute Cumulative values in Shell?

I would like to compute cumulative values from the below data file and writing them into columns after inserting a serial number.

ifile.txt
1 2 3 2 3 1 4 5 1 
3 4 5 2 3 4 1 3 1 
1 3 2 3 2 4 1 2 4 ...............

Where ifile.txt has 3 rows and 9 columns in this example. Desire output:

ofile.txt
1  1   3   1
2  3   7   4
3  6   12  6
4  8   14  9
5  11  17  11
6  12  21  15
7  16  22  16
8  21  25  18
9  22  26  22
.  
.  
.  

Here first column is used for the serial number. So what I did is: I first converted into columns using

awk '{ 
for (i=1; i<=NF; i++)  {
    a[NR,i] = $i
     }
}
NF>p { p = NF }
END {    
for(j=1; j<=p; j++) {
    str=a[1,j]
    for(i=2; i<=NR; i++){
        str=str" "a[i,j];
    }
    print str
    }
 }' ifile.txt > ifile1.txt

Then I use awk

awk '{print m1=$1+m1, m2=$2+m2, m3=$3+m3}' ifile1.txt > ofile.txt

I can’t proceed for the next step i.e. to insert a column of serial number. Also I can’t make it for arbitrary columns and rows.

Answer

for column of serial number

awk '{print i=i+1,m1=$1+m1, m2=$2+m2, m3=$3+m3}' ifile1.txt > ofile.txt

and for complete solution of your logic

awk '{for(i=1;i<=NF;i++){if(i>1)$i=$i+$(i-1);f[i]=f[i]" "$i}if(NF>n)n=NF}END{for(i=1;i<=n;i++)print i,f[i]}'