Numerical Fredholm integration using loop

Question

I have a code line having two Do loops, one within other. In certain situation arising within inner loop, I want the outer Do loop to break. How to achieve it ?

Here is a simplified example.

X = {{-10, 1, 1}, { 8, 2, 2},  {-7, 3, 1}, {2, 4, 2}};
XX = Reap[
   Do[Do[If[X[[k, 1]] < 0, R = m*X[[k, 2]]; Sow[R], R = m*X[[k, 3]]; 
      Sow[R]], {k, 1, 4}], {m, 1, 5}]][[2]]

The o/p of this code is

{{1, 2, 3, 2, 2, 4, 6, 4, 3, 6, 9, 6, 4, 8, 12, 8, 5, 10, 15, 10}}

Now for example, the element "9" appears in the o/p for the m = 3 cycle. I want to break the m loop for the next value of m as soon as "9" appears in the o/p. So in this case, the m cycle should stop at m = 3 instead of going up to 5. The o/p in that case should be

{{1, 2, 3, 2, 2, 4, 6, 4, 3, 6, 9, 6}}

I tried the beard combination of Break & Catch/Throw as shown below, but not able to make it work.

    X = {{-10, 1, 1}, { 8, 2, 2},  {-7, 3, 1}, {2, 4, 2}};
XX = Reap[
       Do[Catch[
         Do[If[X[[k, 1]] < 0, R = m*X[[k, 2]]; Sow[R]; 
           If[R == 9, Throw[Break[]]], R = m*X[[k, 3]];
           Sow[R]]; If[R == 9, Throw[Break[]]], {k, 1, 4}]], {m, 1, 
         5}]][[2]]

Will appreciate any help.

thanks

Answer 1

Throw/Catch would probably work:

Catch[
  Do[
    Do[Print[{i, j}];
       If[j == 7, Throw[7]],
    {j, 10}],
  {i, 10}]]

(*    {1,1}    *)
(*    {1,2}    *)
(*    {1,3}    *)
(*    {1,4}    *)
(*    {1,5}    *)
(*    {1,6}    *)
(*    {1,7}    *)

(*    7    *)

The advantage of Throw over Break is that the latter quits only the innermost loop, whereas for the former you can decide how many loops to quit by setting the Catch appropriately.

Update: you seem to want to break only the outer loop but let the inner one finish the current iteration. This could work:

X = {{-10, 1, 1}, {8, 2, 2}, {-7, 3, 1}, {2, 4, 2}};
stop = False;
XX = Reap[Do[Do[If[X[[k, 1]] < 0, R = m*X[[k, 2]]; Sow[R];
                If[R == 9, stop = True], R = m*X[[k, 3]];
                Sow[R]]; If[R == 9, stop = True], {k, 1, 4}];
             If[stop, Break[]], {m, 1, 5}]][[2, 1]]
(*    {1, 2, 3, 2, 2, 4, 6, 4, 3, 6, 9, 6}    *)

The trick here is to set a flag stop in the inner loop, and at the end of the inner loop check this flag and conditionally break the outer loop.