# How to round down coefficients in a constraint in Julia/JuMP?

**URL:** <https://discourse.julialang.org/t/how-to-round-down-coefficients-in-a-constraint-in-julia-jump/29381>\
**Category:** Optimization (Mathematical)\
**Created:** [October 1, 2019, 9:28pm UTC](https://discourse.julialang.org/t/how-to-round-down-coefficients-in-a-constraint-in-julia-jump/29381 "2019-10-01T21:28:01Z")\
**Posts on this page:** 16\
**Page:** 1

<div class="post-metadata">

**Author:** ![Shor](https://avatars.discourse-cdn.com/v4/letter/s/85f322/32.png) [@Shor](https://discourse.julialang.org/u/Shor)\
**Post date:** [October 1, 2019, 9:28pm UTC](https://discourse.julialang.org/t/how-to-round-down-coefficients-in-a-constraint-in-julia-jump/29381/1 "2019-10-01T21:28:01Z")

</div>

Hi, I am new here. I don’t know how to round down coefficients in my constraints. (only coefficients in this constraint. I don’t want to round down elements in the given array)

 ![image](https://global.discourse-cdn.com/julialang/original/3X/9/1/917ed8ad5c479e67a3fc3e67bf53a997589ca6e2.png)  
Anyone can help me? Thanks in advance!

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<div class="post-metadata">

**Author:** ![wenqi\_kou](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/wenqi_kou/32/9348_2.png) [@wenqi\_kou](https://discourse.julialang.org/u/wenqi_kou)\
**Post date:** [October 2, 2019, 3:26am UTC](https://discourse.julialang.org/t/how-to-round-down-coefficients-in-a-constraint-in-julia-jump/29381/2 "2019-10-02T03:26:32Z")

</div>

I have a similar question. I have no idea how to drop some coefficients with real small absolute value.

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<div class="post-metadata">

**Author:** ![Shor](https://avatars.discourse-cdn.com/v4/letter/s/85f322/32.png) [@Shor](https://discourse.julialang.org/u/Shor)\
**Post date:** [October 2, 2019, 4:36am UTC](https://discourse.julialang.org/t/how-to-round-down-coefficients-in-a-constraint-in-julia-jump/29381/3 "2019-10-02T04:36:36Z")

</div>

Anyone know if this can be implemented in Julia/JuMP?

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<div class="post-metadata">

**Author:** ![blegat](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/blegat/32/217090_2.png) [@blegat](https://discourse.julialang.org/u/blegat)\
**Post date:** [October 2, 2019, 11:51am UTC](https://discourse.julialang.org/t/how-to-round-down-coefficients-in-a-constraint-in-julia-jump/29381/4 "2019-10-02T11:51:08Z")

</div>

@Shor You can achieve this with `map_coefficients` or `map_coefficients_inplace`:

```julia
julia> using JuMP

julia> model = Model()
A JuMP Model
Feasibility problem with:
Variables: 0
Model mode: AUTOMATIC
CachingOptimizer state: NO_OPTIMIZER
Solver name: No optimizer attached.

julia> @variable(model, x[1:2])
2-element Array{VariableRef,1}:
 x[1]
 x[2]

julia> A = rand(2, 2)
2×2 Array{Float64,2}:
b 0.842142 0.76944  
 0.893902 0.0591743

julia> b = rand(2)
2-element Array{Float64,1}:
 0.3355544786560043
 0.6001568619069537

julia> func = sum((A * x + b).^2)
1.5082646220201505 x[1]² + 1.4017481381221626 x[2]*x[1] + 0.5955394597878509 x[2]² + 1.638132146198787 x[1] + 0.5874057892258127 x[2] + 0.47278506704010514

julia> map_coefficients_inplace!(a -> round(a, digits=2), func)
1.51 x[1]² + 1.4 x[2]*x[1] + 0.6 x[2]² + 1.64 x[1] + 0.59 x[2] + 0.47

julia> @objective(model, Min, func)
1.51 x[1]² + 1.4 x[2]*x[1] + 0.6 x[2]² + 1.64 x[1] + 0.59 x[2] + 0.47

julia> print(model)
Min 1.51 x[1]² + 1.4 x[2]*x[1] + 0.6 x[2]² + 1.64 x[1] + 0.59 x[2] + 0.47
Subject to

```

@wenqi_kou To drop coefficients of small values you can do

```julia
julia> func = 1e-7x[1] + x[2]
1.0e-7 x[1] + x[2]

julia> map_coefficients_inplace!(a -> abs(a) < 1e-6 ? zero(a) : a, func)
0 x[1] + x[2]

julia> drop_zeros!(func)

julia> func
x[2]

```

---

<div class="post-metadata">

**Author:** ![Shah\_MF](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/shah_mf/32/15196_2.png) [@Shah\_MF](https://discourse.julialang.org/u/Shah_MF)\
**Post date:** [May 27, 2020, 12:59am UTC](https://discourse.julialang.org/t/how-to-round-down-coefficients-in-a-constraint-in-julia-jump/29381/5 "2020-05-27T00:59:27Z")

</div>

Hello, I started using the Gurobi with JuMP on Julia recently. I am receiving numerical errors when running my code (_Numerical trouble encountered_). After doing some research I realized that my problem comes from the large range for the constraint matrices. I wanted to set some of the coefficients to zero. I found this page, however, this code is not working for me. Here is the code that I’m running and the error I’m getting:

code:

```julia
 using JuMP
 model = Model()

 @variable(model, x[1:2])

 A = rand(2, 2)
 b = rand(2)

 func = sum((A * x + b).^2)
 map_coefficients_inplace!(a -> round(a, digits=2), func)

 @objective(model, Min, func)
 print(model)

```

**error** :

```julia
UndefVarError: map_coefficients_inplace! not defined
Stacktrace:
 [1] top-level scope at In[4]:10

```

I would really appreciate it if you help me realize the problem.

---

<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:** [May 27, 2020, 2:36am UTC](https://discourse.julialang.org/t/how-to-round-down-coefficients-in-a-constraint-in-julia-jump/29381/6 "2020-05-27T02:36:13Z")

</div>

This works for me

```nohighlight
julia> using JuMP

julia> model = Model()
A JuMP Model
Feasibility problem with:
Variables: 0
Model mode: AUTOMATIC
CachingOptimizer state: NO_OPTIMIZER
Solver name: No optimizer attached.

julia> @variable(model, x[1:2])
2-element Array{VariableRef,1}:
 x[1]
 x[2]

julia> A = rand(2, 2)
2×2 Array{Float64,2}:
 0.233939 0.587798
 0.559358 0.572598

julia> b = rand(2)
2-element Array{Float64,1}:
 0.11297691388141651
 0.298978646383552  

julia> func = sum((A * x + b).^2)
0.3676088978662473 x[1]² + 0.9155925425691085 x[2]*x[1] + 0.6733753397704672 x[2]² + 0.38733164236038065 x[1] + 0.4752043958662899 x[2] + 0.10215201406351002

julia> map_coefficients_inplace!(a -> round(a, digits=2), func)
0.37 x[1]² + 0.92 x[2]*x[1] + 0.67 x[2]² + 0.39 x[1] + 0.48 x[2] + 0.1

julia> @objective(model, Min, func)
0.37 x[1]² + 0.92 x[2]*x[1] + 0.67 x[2]² + 0.39 x[1] + 0.48 x[2] + 0.1

julia> print(model)
Min 0.37 x[1]² + 0.92 x[2]*x[1] + 0.67 x[2]² + 0.39 x[1] + 0.48 x[2] + 0.1
Subject to

(jump) pkg> st
    Status `/private/tmp/jump/Project.toml`
  [4076af6c] JuMP v0.21.2

```

Please make sure you are on a recent version of JuMP.

---

<div class="post-metadata">

**Author:** ![Shah\_MF](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/shah_mf/32/15196_2.png) [@Shah\_MF](https://discourse.julialang.org/u/Shah_MF)\
**Post date:** [May 27, 2020, 8:11am UTC](https://discourse.julialang.org/t/how-to-round-down-coefficients-in-a-constraint-in-julia-jump/29381/7 "2020-05-27T08:11:56Z")

</div>

Interesting. It does not work for me. I couldn’t understand what did you mean by

```julia
(jump) pkg> st
    Status `/private/tmp/jump/Project.toml`
  [4076af6c] JuMP v0.21.2

```

I used the following code to check the version of my JuMP:

```julia
using Pkg
Pkg.status()

```

and I get

```julia
[4076af6c] JuMP v0.18.6

```

Then I tried to upgrade the version using

```julia
Pkg.update()

```

And I checked the version and it was still the same v0.18.6. I also tried upgrading with `using Pkg Pkg.develop("JuMP") ` but still no luck. Here is the error:

```julia
Path `C:\Users\myaccount\.julia\dev\JuMP` exists and looks like the correct package. Using existing path.
  Resolving package versions...
Unsatisfiable requirements detected for package JuMP [4076af6c]:
 JuMP [4076af6c] log:
 ├─possible versions are: 0.21.2 or uninstalled
 ├─JuMP [4076af6c] is fixed to version 0.21.2
 └─found to have no compatible versions left with JuMPChance [bbd82366] 
   └─JuMPChance [bbd82366] log:
     ├─possible versions are: 0.5.0 or uninstalled
     └─restricted to versions * by an explicit requirement, leaving only versions 0.5.0

```

After all this, I checked the directory on my computer `C:\Users\myaccount\.julia\packages\JuMP` and there are two folders inside. From the `Project.toml` file inside the folders, one contains JuMP v0.18.6 and the other contains JuMP version = “0.21.2”. But from the julia I can only access the JuMP v0.18.6 every time I check, even when I delete the older version.

Also, I don’t know it has anything to do with this issue, but I used ATOM to install initial packages like (IJulia and Juno ) to use Julia with Jupyter Notebook. Sorry if I sound confusing, it is because I am confused at this point.

---

<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:** [May 27, 2020, 1:24pm UTC](https://discourse.julialang.org/t/how-to-round-down-coefficients-in-a-constraint-in-julia-jump/29381/8 "2020-05-27T13:24:23Z")

</div>

Here are the docs for the package manager:  
[https://docs.julialang.org/en/v1/stdlib/Pkg/index.html](https://docs.julialang.org/en/v1/stdlib/Pkg/index.html)

`JuMPChance` is not compatible with recent versions of JuMP. Remove it, then upgrade

```nohighlight
import Pkg
Pkg.rm("JuMPChance")
Pkg.update()

```

If you need to use `JuMPChance`, then you cannot use the code above, and I don’t think there was a good way of doing it in JuMP 0.18.

---

<div class="post-metadata">

**Author:** ![Shah\_MF](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/shah_mf/32/15196_2.png) [@Shah\_MF](https://discourse.julialang.org/u/Shah_MF)\
**Post date:** [May 27, 2020, 6:18pm UTC](https://discourse.julialang.org/t/how-to-round-down-coefficients-in-a-constraint-in-julia-jump/29381/9 "2020-05-27T18:18:26Z")

</div>

I see. Yes, I was using JuMPChance. and this solved the problem regarding the map\_coefficients\_inplace! .

However, it would have taken me much more time to find out this issue if ever without asking here. Appreciate your help.

---

<div class="post-metadata">

**Author:** ![Shah\_MF](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/shah_mf/32/15196_2.png) [@Shah\_MF](https://discourse.julialang.org/u/Shah_MF)\
**Post date:** [May 27, 2020, 7:37pm UTC](https://discourse.julialang.org/t/how-to-round-down-coefficients-in-a-constraint-in-julia-jump/29381/10 "2020-05-27T19:37:49Z")

</div>

Although it is possible to work without JuMPChance, I rather use it because it saves me a lot of modification in my code at this point.  
How about if I detect the small coefficients manually. i.e., let’s say I have the following affine expression:

```julia
JuMP.GenericAffExpr{Float64,Variable}[-5.93e-5, 4.33 ,3.12e-6 x, 2x]

```

and I want to change the first and the third term to zero. Is there any way to do it?

---

<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:** [May 27, 2020, 7:46pm UTC](https://discourse.julialang.org/t/how-to-round-down-coefficients-in-a-constraint-in-julia-jump/29381/11 "2020-05-27T19:46:26Z")

</div>

You will have to poke around the internal fields of `GenericAffExpr`

> <https://github.com/jump-dev/JuMP.jl/blob/a9de4d0de1b34b85d35c3624bea236afec7e5bec/src/affexpr.jl#L22-L26>

and `GenericQuadExpr`

> <https://github.com/jump-dev/JuMP.jl/blob/a9de4d0de1b34b85d35c3624bea236afec7e5bec/src/quadexpr.jl#L23-L28>

---

<div class="post-metadata">

**Author:** ![Shah\_MF](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/shah_mf/32/15196_2.png) [@Shah\_MF](https://discourse.julialang.org/u/Shah_MF)\
**Post date:** [May 27, 2020, 7:48pm UTC](https://discourse.julialang.org/t/how-to-round-down-coefficients-in-a-constraint-in-julia-jump/29381/12 "2020-05-27T19:48:09Z")

</div>

Got it. Thanks.

---

<div class="post-metadata">

**Author:** ![Shah\_MF](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/shah_mf/32/15196_2.png) [@Shah\_MF](https://discourse.julialang.org/u/Shah_MF)\
**Post date:** [May 29, 2020, 6:09am UTC](https://discourse.julialang.org/t/how-to-round-down-coefficients-in-a-constraint-in-julia-jump/29381/13 "2020-05-29T06:09:59Z")

</div>

Thanks to your help I was able to reduce the range of the QMatrix in my problem, but that didn’t fixed my numerical issue. I was wondering if you have any idea about this particular problem that I describe below:  
The problem is that I have a large-scale model, and when I add a certain set of quadratic constraints to it, it gives me a numerical issue. I attached some of the summaries below.  
With the Quadratic Constraint:

```julia
Model has 1343 quadratic constraints
Coefficient statistics:
  Matrix range [4e-11, 4e+02]
  QMatrix range [1e-08, 2e+02]
  Objective range [1e+02, 3e+04]
  Bounds range [3e-02, 1e+01]
  RHS range [8e-19, 1e+01]
  QRHS range [1e-03, 1e+02]
Warning: Model contains large matrix coefficient range
Warning: Quadratic constraints contain large coefficient range
….
Numerical trouble encountered

```

Without that specific quadratic constraint, I don’t have the numerical issue, see below:

```julia
Model has 1157 quadratic constraints
Coefficient statistics:
  Matrix range [4e-11, 4e+02]
  QMatrix range [1e+00, 1e+00]
  Objective range [1e+02, 3e+04]
  Bounds range [3e-02, 1e+01]
  RHS range [8e-19, 1e+01]
  QRHS range [7e-01, 9e+00]
Warning: Model contains large matrix coefficient range
….
Optimal 

```

Looking at the QMatrix range it is quite large, so I thought that is the source of the problem. I reduced the range of the QMatrix coefficients by removing some of the small ones (\<10-3 or even less) but it didn’t solve the problem:

```julia
Model has 1343 quadratic constraints
Coefficient statistics:
  Matrix range [4e-11, 4e+02]
  QMatrix range [1e-03, 2e+02]
  Objective range [1e+02, 3e+04]
  Bounds range [3e-02, 1e+01]
  RHS range [8e-19, 1e+01]
  QRHS range [1e-03, 1e+02]
Warning: Model contains large matrix coefficient range
…..
Numerical trouble encountered

```

Therefore, the QMatrix range is not actually a problem (I even reduced it to smaller values but no luck). Since the model without the extra quadratic constraint is fine, then I suspect something else about this quadratic constraint is bothering the solver.

Any suggestions or ideas where the problem can be?

---

<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:** [May 29, 2020, 2:05pm UTC](https://discourse.julialang.org/t/how-to-round-down-coefficients-in-a-constraint-in-julia-jump/29381/14 "2020-05-29T14:05:16Z")

</div>

The issue is your linear constraints: `Matrix range [4e-11, 4e+02]`. Your coefficients range from 1e-11 to 1e2.

See [https://www.gurobi.com/documentation/9.0/refman/num\_grb\_guidelines\_for\_num.html](https://www.gurobi.com/documentation/9.0/refman/num_grb_guidelines_for_num.html)

---

<div class="post-metadata">

**Author:** ![Shah\_MF](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/shah_mf/32/15196_2.png) [@Shah\_MF](https://discourse.julialang.org/u/Shah_MF)\
**Post date:** [May 29, 2020, 5:28pm UTC](https://discourse.julialang.org/t/how-to-round-down-coefficients-in-a-constraint-in-julia-jump/29381/15 "2020-05-29T17:28:03Z")

</div>

Yes, however, without that specific quadratic constraint I have the same range on linear constraints, `Matrix range [4e-11, 4e+02]` and it was fine. That is where it bothers me. I realize that this range is a problem, however, my model is not created by hand, many parameters are calculated implicitly, which makes it hard to realize where 4e-11 come from…

---

<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:** [May 29, 2020, 8:50pm UTC](https://discourse.julialang.org/t/how-to-round-down-coefficients-in-a-constraint-in-julia-jump/29381/16 "2020-05-29T20:50:31Z")

</div>

> it was fine.

There is no good rule for when you will encounter numerical difficulties.

You should consider changing the units of your problem. For example, instead of talking about 1e-6 meters, talk about 1 micron.