Algorithm for progressive matrix - algorithm

Question

I want to construct a matrix like so:
[ 0 1 2 3 4 5 ....
1 2 3 4 5 6 ....
2 3 4 5 6 7 ....
3 4 5 6 7 8 ....
4 5 6 7 8 9 ....
5 6 7 8 9 10 ... ] etc
The main goal is to use the algorithm to put to the power the elements of an already existing matrix.
I am programming in Fortran, and I used the following code but it's not working:
do i = 1, m+1
do j = 1, m+1
do while ( w < 2*m )
if ( i > j ) then
ma(i,j) = 0
else
w = i-1
ma(i, j) = w
w = w +1
end if
end do
end do
end do

Answer 1

I suggest you to use an implied-do in the array constructor syntax, possibly initialized in the same declaration:
integer, parameter :: n = 10, m = 5
integer :: i, j
integer :: ma(m,n) = reshape([((i+j, j=0, m-1), i=0, n-1)], [m,n])
The [...] syntax is posible in Fortran 2003 or higher. (/.../) should be used otherwise. My result with gfortran v7.1.1 is:
do i = 1, m
print *, ma(i, :)
end do
$gfortran test.f90 -o main
$main
0 1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9 10
2 3 4 5 6 7 8 9 10 11
3 4 5 6 7 8 9 10 11 12
4 5 6 7 8 9 10 11 12 13
Note: The initialization in the declaration would only be possible if n and m are constants (parameter). You could initialize it normally in the program body, otherwise, with the same implied-do syntax.
If you plan to read the values of m and n at runtime, you should make ma an allocatable array.

Answer 2

While there is nothing wrong with Rodrigo's answer personally I think it much clearer to just use two loops
ian#eris:~/work/stackoverflow$ cat floyd.f90
Program yes
Implicit None
Integer, Parameter :: n = 5
Integer, Dimension( 1:n, 1:n ) :: elp
Integer :: base, offset
Integer :: i, j
Do i = 1, n
base = i - 1
Do j = 1, n
offset = j - 1
elp( j, i ) = base + offset
End Do
End Do
Do j = 1, n
Write( *, '( 1000( i3, 1x ) )' ) elp( j, : )
End Do
End Program yes
ian#eris:~/work/stackoverflow$ gfortran -Wall -Wextra -std=f2003 -fcheck=all -O floyd.f90 -o genesis
ian#eris:~/work/stackoverflow$ ./genesis
0 1 2 3 4
1 2 3 4 5
2 3 4 5 6
3 4 5 6 7
4 5 6 7 8

Answer 3

I've seen that others already made an algorithm that solves your problem. But i also bring another algorithm that works for a non-square matrix. NI is the number of columns of the matrix, and NJ is the number of lines. MAT is the matrix you want.
PROGRAM MATRIX
IMPLICIT NONE
INTEGER :: I, J, NI, NJ
INTEGER, ALLOCATABLE :: MAT(:,:)
NI = 8
NJ = 5
ALLOCATE(MAT(NI,NJ))
DO I = 1, NI
MAT(I,1) = I-1
ENDDO
DO J = 2,NJ
MAT(:,J) = MAT(:,J-1) + 1
ENDDO
DO J = 1, NJ
WRITE(*,'(8I3)') MAT(:,J)
ENDDO
END PROGRAM

Answer 4

Thanks for the feedback, I managed to do it using the following code:
do i = 1, m+1
w = i-1
do j = 1, m+1
ma(i, j) = u**w
w = w+1
end do
end do
I would like to state that i'm using Fortran 90 and only 90 because of my circumstances, otherwise I would've went with c++, (university life !!).
Please note that I used the desired series to put to the power the elements of the matrix.
Finally, I noticed some "complex" answers maybe, or maybe I'm just a beginner, but i would really love to learn if there are some rules and or dos and don'ts and or advice to get better at coding ( scientific code, not development code).
Thank you very much for the feed back, and waiting for any responses.