# How to assign value to a matrix in an indicator constraint

**URL:** <https://discourse.julialang.org/t/how-to-assign-value-to-a-matrix-in-an-indicator-constraint/46314>\
**Category:** Optimization (Mathematical)\
**Created:** [September 9, 2020, 9:15am UTC](https://discourse.julialang.org/t/how-to-assign-value-to-a-matrix-in-an-indicator-constraint/46314 "2020-09-09T09:15:34Z")\
**Posts on this page:** 16\
**Page:** 1

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**Author:** ![sogrbilja](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/sogrbilja/32/17521_2.png) [@sogrbilja](https://discourse.julialang.org/u/sogrbilja)\
**Post date:** [September 9, 2020, 9:15am UTC](https://discourse.julialang.org/t/how-to-assign-value-to-a-matrix-in-an-indicator-constraint/46314/1 "2020-09-09T09:15:34Z")

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Is it possible and how to assign values to POSITION[R,C] matrix in the indicator constraint

```julia

    @variable(premex, ROLNA[R in keys(_ROWS), C in keys(_COLS), i_k in keys(_IMAGES_ALL)], Bin)
    @variable(premex, POSITION[R in keys(_ROWS), C in keys(_COLS)], Bin)
    @constraint(
      premex,
      SOMETHING[R in _ROWS, C in _COLS, i_k in keys(_IMAGES_ALL)],
      ROLNA[R, C, i_k] => {
        POSITION[R1 + R - 1, C1 + C - 1]
        # for R1 in collect(UnitRange(1, _IMAGES_ALL[i_k]["ROWS"])), C1 in collect(UnitRange(1, _IMAGES_ALL[i_k]["COLS"])) 
          # if (R1 + R - 1 <= length(_ROWS)) 
            # for C1 in collect(UnitRange(1, _IMAGES_ALL[i_k]["COLS"])) 
              # if (C1 + C - 1 <= length(_ROWS))
        == 1
      }
    )

```

My goal is to assign 1 to some values in POSITION matrix when ROLNA[R, C, i\_k] = 1

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<div class="post-metadata">

**Author:** ![tomerarnon](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tomerarnon/32/3170_2.png) [@tomerarnon](https://discourse.julialang.org/u/tomerarnon)\
**Post date:** [September 9, 2020, 10:01am UTC](https://discourse.julialang.org/t/how-to-assign-value-to-a-matrix-in-an-indicator-constraint/46314/2 "2020-09-09T10:01:51Z")

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What are these objects? Are `ROLNA` and `POSITION` both arrays of `Variable`s?

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<div class="post-metadata">

**Author:** ![sogrbilja](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/sogrbilja/32/17521_2.png) [@sogrbilja](https://discourse.julialang.org/u/sogrbilja)\
**Post date:** [September 9, 2020, 10:14am UTC](https://discourse.julialang.org/t/how-to-assign-value-to-a-matrix-in-an-indicator-constraint/46314/3 "2020-09-09T10:14:05Z")

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I’ve updated my question by adding their definitions.

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<div class="post-metadata">

**Author:** ![tomerarnon](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tomerarnon/32/3170_2.png) [@tomerarnon](https://discourse.julialang.org/u/tomerarnon)\
**Post date:** [September 9, 2020, 10:16am UTC](https://discourse.julialang.org/t/how-to-assign-value-to-a-matrix-in-an-indicator-constraint/46314/4 "2020-09-09T10:16:09Z")

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So it looks like they’re both arrays of binary variables. In that case, at the index of interest, can you simply say `p == 1` and `r == 1`?

Also, I think it is better to omit the constraint name entirely than to name it something like `dsadasd`… unless that actually means something. I hope it isn’t rude to suggest there could be improvement to readability here 😜

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<div class="post-metadata">

**Author:** ![sogrbilja](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/sogrbilja/32/17521_2.png) [@sogrbilja](https://discourse.julialang.org/u/sogrbilja)\
**Post date:** [September 9, 2020, 11:42am UTC](https://discourse.julialang.org/t/how-to-assign-value-to-a-matrix-in-an-indicator-constraint/46314/5 "2020-09-09T11:42:52Z")

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Ok let me write this in C#

```julia
      int[] _ROWS = new int[10];
      int[] _COLS = new int[10];
      int[] _IMAGES = new int[10];
      int[,] POSITION = new int[10, 10];
      int[,,] ROLNA = new int[10, 10, 10];

      int R, C, i_k, R1, C1;

      for (R = 0; R < _ROWS.Length; R++)
      {
        for (C = 0; C < _COLS.Length; C++)
        {
          for (i_k = 0; i_k < _IMAGES.Length; i_k++)
          {
            if (ROLNA[R,C,i_k] == 1)
            {
              for (R1 = 0; R1 < 4; R1++)
              {
                for (C1 = 0; C1 < 4; C1++)
                {
                  if (R1 + R - 1 <= _ROWS.Length && C1 + C - 1 <= _COLS.Length)
                    POSITION[R1 + R - 1,C1 + C - 1] = 1;
                }
              }
            }
          }
        }
      }

```

So, iterate through all ROLNA and if one point is == 1 then assign 1 (ones) to a square in the POSITION matrix that way that upper left point matches the coordinates and add 4 x 4 to the right and down from that point - but really I don;t care this coordinates calculation, I need someone to help me how to assign values to a multidimensional array in indicator constraint and that is it, nothing more .

How to write this in Julia / Jump indicator constraint?

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<div class="post-metadata">

**Author:** ![tomerarnon](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tomerarnon/32/3170_2.png) [@tomerarnon](https://discourse.julialang.org/u/tomerarnon)\
**Post date:** [September 9, 2020, 12:29pm UTC](https://discourse.julialang.org/t/how-to-assign-value-to-a-matrix-in-an-indicator-constraint/46314/6 "2020-09-09T12:29:25Z")

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Is this an accurate translation?

```julia
for cartesian_index in eachindex(ROLNA)
    r, c, i = Tuple(cartesian_index)
    if value(ROLNA[r, c, i]) == 1
        @constraint(premex, [r1 = 0:3, c1 = 0:3], POSITION[r+r1, c+c1] == 1)
    end
end

```

Even if not, the point is you can write all of the logic outside the `@constraint` macro and do the `@constraint` in the same place you seem to be doing it in the C# code. (I did a bit of a hybrid; one of the loops is external and the other is internal, but they can both be internal or both be external and that works too.)

* * *

edit: with both loops external and accounting for the bounds, it now looks like this

```julia
for cartesian_index in eachindex(ROLNA)
    r, c, i = Tuple(cartesian_index)
    if value(ROLNA[r, c, i]) == 1
        for r′ in r:min(r+3, size(ROLNA, 1)),
            c′ in c:min(c+3, size(ROLNA, 2))

            @constraint(premex, POSITION[r′, c′] == 1)
        end
    end
end

```

It’s a bit suspicious though that we’re iterating over the last index (`i`, above) and not using it anywhere. If for each `(r, c)`, if any `i` leads to a 1 constraint the rest don’t matter anymore, you could iterate on each coordinate `(R, C, I)` in a separate loop (like your C# code) and break the `i` loop if you encounter a 1 after setting the constraint. Could save you a tiny bit of repeated constraint setting 🤷‍♂️. You could also use this to inform the loops on r, and c, since they should skip in increments of 4 in those cases… too complicated for me right now.

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**Author:** ![sogrbilja](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/sogrbilja/32/17521_2.png) [@sogrbilja](https://discourse.julialang.org/u/sogrbilja)\
**Post date:** [September 9, 2020, 12:46pm UTC](https://discourse.julialang.org/t/how-to-assign-value-to-a-matrix-in-an-indicator-constraint/46314/7 "2020-09-09T12:46:38Z")

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Thanks, @tomerarnon that is exactly what I’ve needed → so it is quite possible to iterate and then add it to the @constraint macro. Great! I will try this now.

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<div class="post-metadata">

**Author:** ![tomerarnon](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tomerarnon/32/3170_2.png) [@tomerarnon](https://discourse.julialang.org/u/tomerarnon)\
**Post date:** [September 9, 2020, 12:47pm UTC](https://discourse.julialang.org/t/how-to-assign-value-to-a-matrix-in-an-indicator-constraint/46314/8 "2020-09-09T12:47:46Z")

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> [@sogrbilja](#):
>
> so it is quite possible to iterate and then add it to the @constraint macro.

Indeed it is! That is my preferred method, personally.

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<div class="post-metadata">

**Author:** ![sogrbilja](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/sogrbilja/32/17521_2.png) [@sogrbilja](https://discourse.julialang.org/u/sogrbilja)\
**Post date:** [September 9, 2020, 1:02pm UTC](https://discourse.julialang.org/t/how-to-assign-value-to-a-matrix-in-an-indicator-constraint/46314/9 "2020-09-09T13:02:28Z")

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Thanks for your assistance, you’ve opened just another gate for me so I can move on 😄

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<div class="post-metadata">

**Author:** ![odow](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/odow/32/28685_2.png) [@odow](https://discourse.julialang.org/u/odow)\
**Post date:** [September 9, 2020, 8:24pm UTC](https://discourse.julialang.org/t/how-to-assign-value-to-a-matrix-in-an-indicator-constraint/46314/10 "2020-09-09T20:24:32Z")

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This advice is incorrect, because it will be based on the previously solved value of `ROLNA`.

Since both are binary, use

```nohighlight
for r′ in r:min(r+3, size(ROLNA, 1))
    for c′ in c:min(c+3, size(ROLNA, 2))
        @constraint(premex, POSITION[r′, c′] >= ROLNA[r, c, i])
    end
end

```

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<div class="post-metadata">

**Author:** ![tomerarnon](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tomerarnon/32/3170_2.png) [@tomerarnon](https://discourse.julialang.org/u/tomerarnon)\
**Post date:** [September 9, 2020, 8:26pm UTC](https://discourse.julialang.org/t/how-to-assign-value-to-a-matrix-in-an-indicator-constraint/46314/11 "2020-09-09T20:26:43Z")

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> [@odow](#):
>
> This advice is incorrect, because it will be based on the previously solved value of `ROLNA` .

I assumed this was the intention. The fact that the constraint was described as an “indicator” should have suggested that was not so, but I didn’t think through that.

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<div class="post-metadata">

**Author:** ![odow](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/odow/32/28685_2.png) [@odow](https://discourse.julialang.org/u/odow)\
**Post date:** [September 9, 2020, 8:29pm UTC](https://discourse.julialang.org/t/how-to-assign-value-to-a-matrix-in-an-indicator-constraint/46314/12 "2020-09-09T20:29:56Z")

</div>

No worries. It’s useful to see different examples of more advanced things you can do with JuMP (adding constraints conditionally in a loop based on a previous solution).

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<div class="post-metadata">

**Author:** ![sogrbilja](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/sogrbilja/32/17521_2.png) [@sogrbilja](https://discourse.julialang.org/u/sogrbilja)\
**Post date:** [September 9, 2020, 8:36pm UTC](https://discourse.julialang.org/t/how-to-assign-value-to-a-matrix-in-an-indicator-constraint/46314/13 "2020-09-09T20:36:37Z")

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I’ve tried what have @tomerarnon advised but I didn’t get the correct results. Let me explain what I am trying to do here. I want to allow ROLNA to hold only the top-left coordinate of an image from a set of images. Then I would assign all 1 to the remaining points of that image to POSITION matrix, So if POSITION has a value on x,y ROLNA cannot. How to write that.

Here is what I’ve tried from the last suggestion:

```julia
    @timeit to "02. this should put ones to POSITION matrix" begin
      for R in _ROWS, C in _COLS, i_k in keys(_IMAGES_ALL)
        if ROLNA[R, C, i_k] == 1
          for R1 in collect(UnitRange(1, _IMAGES_ALL[i_k]["ROWS"])),
            C1 in collect(UnitRange(1, _IMAGES_ALL[i_k]["COLS"])) 
            if (R1 == 1 && C1 == 1)
              @constraint(premex, ROLNA[R, C, i_k] => {POSITION[R, C] == 0})
            elseif (R1 + R - 1 <= length(_ROWS)) && (C1 + C - 1 <= length(_COLS))
              @constraint(premex, ROLNA[R, C, i_k] => {POSITION[R1 + R - 1, C1 + C - 1] == 1})
            end            
          end            
        end
      end
    end

    @timeit to "03.this will prohibit ROLNA to take place that POSITION already holds" begin
      for i_k in keys(_IMAGES_ALL)
        @constraint(
          premex,
          [R in _ROWS, C in _COLS],
          POSITION[R, C] => {ROLNA[R, C, i_k] == 0}
        )
      end
    end

```

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<div class="post-metadata">

**Author:** ![tomerarnon](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tomerarnon/32/3170_2.png) [@tomerarnon](https://discourse.julialang.org/u/tomerarnon)\
**Post date:** [September 9, 2020, 8:52pm UTC](https://discourse.julialang.org/t/how-to-assign-value-to-a-matrix-in-an-indicator-constraint/46314/14 "2020-09-09T20:52:01Z")

</div>

I think the way to do this is:

```julia
1 - POSITION[R, C] >= ROLNA[R, C, I_k]

```

so when `p == 1` you get `0 >= r` (ROLNA is 0), and when `p == 0`, `1 >= r`, which does nothing to a binary variable.

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<div class="post-metadata">

**Author:** ![sogrbilja](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/sogrbilja/32/17521_2.png) [@sogrbilja](https://discourse.julialang.org/u/sogrbilja)\
**Post date:** [September 9, 2020, 9:13pm UTC](https://discourse.julialang.org/t/how-to-assign-value-to-a-matrix-in-an-indicator-constraint/46314/15 "2020-09-09T21:13:01Z")

</div>

Yes, that is a good idea too, so the thing here is to build a huge amount of constraints (predefined) with all possible indexes, is that the way this works?

So if I have an image, let’s say 500 x 200 mm and I divide ROLE to mm grid, so to assign all 1 (ones) to POSITION system will have to create 500 x 200 constraints, is that?

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**Author:** ![tomerarnon](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tomerarnon/32/3170_2.png) [@tomerarnon](https://discourse.julialang.org/u/tomerarnon)\
**Post date:** [September 10, 2020, 9:37am UTC](https://discourse.julialang.org/t/how-to-assign-value-to-a-matrix-in-an-indicator-constraint/46314/16 "2020-09-10T09:37:34Z")

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> [@sogrbilja](#):
>
> is that the way this works?

Honestly, I don’t know… Maybe? I think posing this problem (I looked at the previous threads) as an MIP like you’re doing is more intuitive to conceptualize, but computationally will be difficult to solve. I have been wondering if the problem can be posed as e.g. a geometric program (and solved with Convex.jl), but I don’t know of some simple mapping that will make it so. Anyway, for me this is uncharted territory, so I can’t predict what the results of this approach will be 😅  
Good luck!