Question about for loop

Question

How can I get the results of a "for" loop for each iteration? For example, I have the following for loop and would like to know how I can get the value of S1 for each i value in the output. Also, I am just wondering is there any way to show the name of the variable in the output (e.g: S1 = {{1,2},{2,3}}) and not just {{1,2},{2,3}}?

Thank you and regards,

For [i=1,10,++

   For [j=1,20,++

      S1=?

       ]
]```

Answer 1

As recommend in comments, better to use Table or Do.

how I can get the value of S1 for each i value in the output.

For For you can still use Sow and Reap as well

result = First@Last@Reap@For[i = 1, i <= 3, i++,
     For[j = 1, j <= 3, j++,
      Sow[{i, j}]
      ]
     ]

to show the name of the variable in the output (e.g: S1 = {{1,2},{2,3}}) and not just {{1,2},{2,3}}?

What do you mean by show S1={...}? In Mathematica x=1 is assignment, and Mathematica displays back 1, not x=1. To show x=1 you would need to force things into strings. Something like

 ("S = " <> ToString[#]) & /@ result

an example with Table application

result = First@Last@Reap@Do[
     Do[
      Sow[{i, j}]
      ,
      {j, 1, 3}
      ],
     {i, 1, 3}
     ]

Or to make it do something more interesting

result = First@Last@Reap@Do[
      Do[
       Sow[{ Row[{"S[", i, ",", j, "]=", i + j}], i + j}]
       ,
       {j, 1, 3}
       ],
      {i, 1, 3}
      ];

And now the actual computation result is stored in result[[All,2]] and the display part is stored separately in result[[All,1]]

result[[All, 2]]

result[[All, 1]] // Column