Condition on the data of table

Question

If you have a table and want to separate some data into columns according to certain conditions:

Let's assume we have the following table:

fr = Subscript[x, 1] Subscript[x, 2] + 
   Subscript[x, 1] Subscript[x, 3] - 
   Subscript[x, 1] Subscript[x, 2] Subscript[x, 3] ;
(data = Tuples[{0, 1}, 3]) // MatrixForm; LLR1 = {Block[{Subscript}, 
    Do[Subscript[x, j] = Transpose[data][[j]], {j, 3}]; 
    fr]}/(Binomial[2, {data[[All, 1]] + data[[All, 2]]}] Binomial[
     1, {data[[All, 3]]}]);
(table = Prepend[
    Transpose@
     Join[{Range@Length@data}, 
      Transpose@
       data, {data[[All, 1]] + data[[All, 2]]}, {data[[All, 3]]}, 
      LLR1], Flatten[{"order", Subscript["x", #] & /@ Range[3], "l1", 
      "l2", "f", "h0", "h1", "h2"}]]) // Grid[#, Frame -> All] &

We set the condition to form column h2:

(If $x_1x_2=1$ take the value of f)

We set the condition to form column h1:

(h1=f-h2)

We set the condition to form column h0:

(h0 is the complement of f)

The result should be as follows

Thanks for the help

Answer 1

You can use ReplaceAll to replace each row (omitting the header row). By using patterns instead of indices, you minimize the risk of mismatching the values.

table /. {data : 
 PatternSequence[order_?NumericQ, x1_, x2_, x3_, l1_, l2_, f_], ___} :> 
   With[{h2 = If[x1 x2 == 1, f, 0]}, {data, 1 - f, f - h2, h2}] // 
 Grid[#, Frame -> All] &

Note that ?NumericQ is there to assure you do not modify the first (header) row.

Answer 2

It is easier to work with the columns of the table as a list and eliminate the header:

tmp = Transpose[(Join[#, {0, 0, 0}]) & /@ table[[2 ;;]]];

Next we insert the missing columns:

tmp = Join[Transpose[table[[2 ;;]]], ConstantArray[0, {3, 8}]];

Now we apply the conditions:

tmp[[10]] = tmp[[7]] ((If[# == 1, 1, #]) & /@ (tmp[[2]]  tmp[[3]]));
tmp[[9]] = tmp[[7]] - tmp[[10]];
tmp[[8]] = (Switch[#, 1, 0, 0, 1, _, #]) & /@ tmp[[7]];

Finally we transpose tmp to get the original table back and reinsert the headings:

tmp = Prepend[Transpose[tmp], table[[1, All]]];

Now we can display the change table:

tmp // Grid[#, Frame -> All] &