### Author:  [@Johan-Gronqvist](https://discourse.julialang.org/u/Johan-Gronqvist)
#### Post date: [February 5, 2024, 11:41am UTC](https://discourse.julialang.org/t/symbolics-build-function-issues-on-complicated-expressions/109727/1 "2024-02-05T11:41:42Z")
I am trying to use Symbolics to define and manipulate my problem before moving to numerical methods to actually solve my problem.
After initial manipulations, I want to replace all symbolic variables with their actual values. This worked well for me as long as I used matrices of scalar symbolic variables. I am now trying to move to symbolic arrays, and `substitute` no longer substitutes all symbolic variables. I tried `build_function` which managed better, but which also seems to only work on sufficiently simple expressions.
The behaviour I expected is that all symbolic variables are replaced by numerical values in all cases.
I fail to solve my problem using either of `substitute` or `build_function`, with `build_function` managing more complicated expressions, but not the ones I need it for.
I would appreciate any help.
The following is the smallest test case I have showing the issue:
```julia
import Pkg
Pkg.activate(".")
Pkg.add("Symbolics")
Pkg.status(outdated=true)
import Symbolics
import Symbolics: @variables, get_variables, substitute, build_function
@variables K[1:2, 1:2]
exprs = [-K[1,1] -(K[1,1]) (-K)[1,1] ]
subs = Dict(K[1,1] => 1)
for expr in exprs
println("------------------------")
@show expr get_variables(expr)
try
@show substitute(expr, subs)
catch e
@show e
end
f = build_function(expr, K, expression = false)
@show f([1 2; 3 4])
end
@variables A[1:2, 1:2] B[1:2, 1:1] P[1:2, 1:2]
Pre1 = A*[1.0 0.0 0.0; 0.0 1.0 0.0]
Pre2 = broadcast(+, A*[1.0 0.0 0.0; 0.0 1.0 0.0], B*[0.0 0.0 1.0])
Post = Symbolics.Num[1.0 0.0 0.0 0.0; 0.0 1.0 0.0 0.0; 0.0 0.0 (broadcast(-, K))[1, 1] (broadcast(-, K))[1, 2]]
for expr in [Pre1, Pre2, Post, Pre1*Post, Pre2*Post]
println("---------------------------")
@show expr
fs = build_function(expr, A, B, K, P, expression=false)
for f in fs
try
value = f(randn(2,2), randn(2,1), randn(1,2), randn(2,2))
@show value unique(vcat(get_variables.(value)...))
catch e
end
end
end
```
The output I get is
```julia
Status `~/Workspace/Project.toml`
⌅ [0c5d862f] Symbolics v5.14.1 (
### Author:  [@baggepinnen](https://discourse.julialang.org/u/baggepinnen)
#### Post date: [February 5, 2024, 12:44pm UTC](https://discourse.julialang.org/t/symbolics-build-function-issues-on-complicated-expressions/109727/2 "2024-02-05T12:44:23Z")
Tjena Johan, I think the unfortunate answer here is that array variables are very buggy and mostly do not work as expected. The [list of known issues](https://github.com/JuliaSymbolics/Symbolics.jl/issues?q=is%3Aopen+is%3Aissue+label%3A%22array+variables%22) is rather long, but there are likely several issues not reported here as well.
---
### Author:  [@Johan-Gronqvist](https://discourse.julialang.org/u/Johan-Gronqvist)
#### Post date: [February 5, 2024, 1:44pm UTC](https://discourse.julialang.org/t/symbolics-build-function-issues-on-complicated-expressions/109727/3 "2024-02-05T13:44:23Z")
Tjena, och tack.
That is unfortunate, for me. I was hoping to use `build_function` to quickly repeat the same analysis when parameter values change, but if I have a large number of elements in my matrices, then I end up building functions that take a large number of scalar arguments, instead of a small number of array arguments.
(As you will already know from my name and the variable names `A,B,K,P` appearing, I am analysing stability properties of control systems.)
The problems “it works in simple expressions but not on complex ones” and “it fails with broadcast” appears in several bug reports and it seems to me like it should be relatively simple to solve. It also seems as if the, relatively simple, solution, should enable quite a bit of functionality to become reliable…
Would you agree?
---
### Author:  [@baggepinnen](https://discourse.julialang.org/u/baggepinnen)
#### Post date: [February 5, 2024, 1:59pm UTC](https://discourse.julialang.org/t/symbolics-build-function-issues-on-complicated-expressions/109727/4 "2024-02-05T13:59:02Z")
> [@Johan-Gronqvist](#):
>
> then I end up building functions that take a large number of scalar arguments, instead of a small number of array arguments.
You should stil be able to build function that take arrays as arguments. If you call `array_of_syms = collect(symbolic_array)` you can use `array_of_syms` as input argument to `build_funciton,`, which builds a function that expects a numeric array of the same dimensions.
In general, most things “should work”, if you scalarize the symbolic array expressions using `collect`. The problem you may get instead is that scalar expressions may be come very large, and the generated function may not perform very well and/or take a long time to compile if the scalar expression is very large.
---
### Author:  [@Johan-Gronqvist](https://discourse.julialang.org/u/Johan-Gronqvist)
#### Post date: [February 5, 2024, 2:43pm UTC](https://discourse.julialang.org/t/symbolics-build-function-issues-on-complicated-expressions/109727/5 "2024-02-05T14:43:02Z")
My interpretation of your comment is that I should use the following:
```julia
fs = build_function(Symbolics.scalarize(expr), collect(A), collect(B), collect(K), collect(P), expression=false)
```
That fails for me, because `scalarize` fails on the same subexpression of the same testcase where `build_function` failed.
The call to `scalarize` in
```julia
expr = (broadcast(+, A*[1.0 0.0 0.0; 0.0 1.0 0.0], B*[0.0 0.0 1.0])*Symbolics.Num[1.0 0.0 0.0 0.0; 0.0 1.0 0.0 0.0; 0.0 0.0 (broadcast(-, K))[1, 1] (broadcast(-, K))[1, 2]])[Base.OneTo(2),Base.OneTo(4)]
Symbolics.scalarize(expr)
```
returns
```julia
Symbolics.Num[A[1, 1] A[1, 2] B[1, 1]*(broadcast(-, K))[1, 1] B[1, 1]*(broadcast(-, K))[1, 2]; A[2, 1] A[2, 2] B[2, 1]*(broadcast(-, K))[1, 1] B[2, 1]*(broadcast(-, K))[1, 2]]
```
which did not scalarize the appearances of `K`. The function built by `build_function` throws an `UndefVarError(:K)`, probably because it expects scalars like `K[1,1]`, but not the `K` that appears as an argument to `broadcast`.
---
### Author:  [@baggepinnen](https://discourse.julialang.org/u/baggepinnen)
#### Post date: [February 5, 2024, 4:11pm UTC](https://discourse.julialang.org/t/symbolics-build-function-issues-on-complicated-expressions/109727/6 "2024-02-05T16:11:48Z")
Try calling `collect` on `K` immediately after creating it so you never work with the symbolic arrays at all
```julia
import Symbolics
import Symbolics: @variables, get_variables, substitute, build_function
@variables K[1:2, 1:2]
K = collect(K)
exprs = [-K[1,1] -(K[1,1]) (-K)[1,1] ]
subs = Dict(K[1,1] => 1)
for expr in exprs
println("------------------------")
@show expr get_variables(expr)
try
@show substitute(expr, subs)
catch e
@show e
end
f = build_function(expr, K, expression = false)
@show f([1 2; 3 4])
end
@variables A[1:2, 1:2] B[1:2, 1:1] P[1:2, 1:2]
A,B,P = collect.((A,B,P))
Pre1 = A*[1.0 0.0 0.0; 0.0 1.0 0.0]
Pre2 = broadcast(+, A*[1.0 0.0 0.0; 0.0 1.0 0.0], B*[0.0 0.0 1.0])
Post = Symbolics.Num[1.0 0.0 0.0 0.0; 0.0 1.0 0.0 0.0; 0.0 0.0 (broadcast(-, K))[1, 1] (broadcast(-, K))[1, 2]]
for expr in [Pre1, Pre2, Post, Pre1*Post, Pre2*Post]
println("---------------------------")
@show expr
fs = build_function(expr, A, B, K, P, expression=false)
for f in fs
try
value = f(randn(2,2), randn(2,1), randn(1,2), randn(2,2))
@show value unique(vcat(get_variables.(value)...))
catch e
end
end
end
```
---
### Author:  [@Johan-Gronqvist](https://discourse.julialang.org/u/Johan-Gronqvist)
#### Post date: [February 5, 2024, 4:48pm UTC](https://discourse.julialang.org/t/symbolics-build-function-issues-on-complicated-expressions/109727/7 "2024-02-05T16:48:13Z")
Excellent!
Thanks!