# clingo[LP]
`clingo[LP]` extends the ASP solver `clingo` with linear constraints as dealt with in Linear Programming (LP).
## Install
Install via conda:
```sh
conda install -c potassco -c conda-forge clingo-lp
```
## CPLEX
The clingoLP propagator requires an LP solver.
The default is [lpsolve](https://sourceforge.net/projects/lpsolve/) but [cplex](https://www.ibm.com/support/knowledgecenter/SSSA5P_12.7.0/ilog.odms.cplex.help/CPLEX/GettingStarted/topics/set_up/Python_setup.html) can be used optionally.
IBM also provides a promotional version of `cplex` that is sufficient to solve small problems limited to 1000 variables and 1000 constraints.
```sh
conda install -c ibmdecisionoptimization cplex`
```
To solve larger problems, you need to use the full version of CPLEX Studio.
## Syntax
LP constraints can be expressed as follows:
| LP constraints | ClingoLP Syntax |
| :------------------------------------------------------------------ | :------------------------------------------------------------------------------------------------------ |
| w<sub>1</sub>x<sub>1</sub>+...+w<sub>n</sub>x<sub>n</sub> >= k | `&sum{`w<sub>1</sub>`*`x<sub>1</sub>`;`...`;`w<sub>n</sub>`*`x<sub>n</sub>`} >=` k |
| domain(x)={l,...,u} | `&dom{`l`..`u`} =` x |
| maximize: w<sub>1</sub>x<sub>1</sub>+...+w<sub>n</sub>x<sub>n</sub> | `&maximize{`w<sub>1</sub>`*`x<sub>1</sub>`;`...`;`w<sub>n</sub>`*`x<sub>1</sub>`}` (minimize analogous) |
To avoid syntax clashes, you must quote `"` real numbers. Instead of `1.5` write `"1.5"`.
## Usage
```txt
clingoLP [number] [options] [files]
Options:
--lp-solver=<arg> : Set LP solver
<arg>: {lps,cplx} (default lp-solver=lps)
--[no-]show-lp-solution : Show LP solution and value of objective function
--accuracy=n : Set decimal position of LP solver accuracy (default accuracy=3)
--epsilon=n,m : Set epsilon to convert lhs > k into lhs >= k+n*10^-m (default epsilon=1,3)
--[no-]trace : Enables detailed output of theory propagation
--core-confl=n : Searches for core conflicts if at least n% of the theory atoms are decided
(default core-confl=20)
--prop-heur=n : Starts a solve call of the LP solver if at least n% of the theory atoms are decided
(default prop-heur=0)
--[no-]ilp : Sets the LP solver to solve an Integer Linear Programming (ILP) problem
```
Example:
```sh
clingoLP 0 --show-lp-solution example_encoding.lp example_instance.lp
```
For more options you can ask for help as follows:
```sh
clingoLP --help
```
## Publication
[Clingo goes linear constraints over reals and integers, Janhunen, T., Kaminski, R., Ostrowski, M., Schellhorn, S., Wanko, P., Schaub, T. (2017), TPLP, 17(5-6), 872–888.](https://www.cs.uni-potsdam.de/wv/publications/DBLP_journals/tplp/JanhunenKOSWS17.pdf)
