add gaussjordan for steps of a matrix inversion

Author: jbytecode

CHANGELOG.md

@@ -1,8 +1,12 @@
-### 0.2.4 (Upcoming Release)
+### 0.2.5 (Upcoming Release)
+
+
+### 0.2.4
 
 - Rename `mmethodcorrection()` to `mmethodcorrection!()` just because the function mutates its input.
 - Add documentation for `simplexiterations`.
-- Add additional tests for Simplex
+- Add additional tests for Simplex.
+- Add `gaussjordan()` method to calculate the inverse of a matrix with iteration steps.
 
 
 ### 0.2.3 

Project.toml

@@ -1,7 +1,7 @@
 name = "OperationsResearchModels"
 uuid = "8042aa49-e599-49ec-a8f7-b5b80cc82a88"
 authors = ["Mehmet Hakan Satman <mhsatman@gmail.com>"]
-version = "0.2.3"
+version = "0.2.4"
 
 [deps]
 HiGHS = "87dc4568-4c63-4d18-b0c0-bb2238e4078b"

docs/src/algorithms.md

@@ -87,3 +87,8 @@ OperationsResearchModels.travelingsalesman
 OperationsResearchModels.createsimplexproblem
 ```
 
+### Gauss Jordan steps for matrix inversion
+```@docs
+OperationsResearchModels.gaussjordan
+```
+

src/OperationsResearchModels.jl

@@ -58,7 +58,7 @@ import .Latex: latex
 import .Johnsons: JohnsonResult, johnsons, JohnsonException, makespan, johnsons_ga
 import .RandomKeyGA: Chromosome, run_ga
 import .TravelingSalesman: TravelinSalesmenResult, travelingsalesman
-import .Simplex: SimplexProblem, simplexiterations, createsimplexproblem
+import .Simplex: SimplexProblem, simplexiterations, createsimplexproblem, gaussjordan
 
 export TransportationProblem, TransportationResult, balance, isbalanced, northwestcorner
 export Connection, ShortestPathResult, MaximumFlowResult, nodes
@@ -76,7 +76,7 @@ export latex
 export Chromosome, run_ga
 export JohnsonResult, johnsons, JohnsonException, makespan, johnsons_ga
 export TravelinSalesmenResult, travelingsalesman
-export simplexiterations, SimplexProblem, createsimplexproblem
+export simplexiterations, SimplexProblem, createsimplexproblem, gaussjordan
 
 export JuMP, HiGHS
 

src/simplex.jl

@@ -12,6 +12,7 @@ export simplexiterations
 export simplexpretty
 export createsimplexproblem
 export solve!
+export gaussjordan
 
 import ..Utility: numround
 
@@ -545,5 +546,52 @@ function createsimplexproblem(
     return s
 end
 
+"""
+    gaussjordan(A::Matrix; verbose::Bool = true)::Matrix
+
+Description:
+
+    Attaches an Identity matrix to the right of the given matrix A and applies the Gauss-Jordan elimination method to find the inverse of the given matrix.
+
+Arguments:
+
+- A::Matrix: The matrix to find the inverse.
+- verbose::Bool: If true, the intermediate steps are displayed. Default is true.
+
+Returns:
+
+    The inverse of the given matrix.
+
+Example:
+
+```julia
+julia> A = [1.0 2.0 3.0; 4.0 5.0 6.0; 7.0 8.0 10.0]
+julia> invA = gaussjordan(A, verbose = false)
+3×3 Matrix{Float64}:
+ -0.666667  -1.33333   1.0
+ -0.666667   3.66667  -2.0
+  1.0       -2.0       1.0
+```
+"""
+function gaussjordan(A::Matrix{Float64}; verbose::Bool = true)::Matrix{Float64}
+    n, p = size(A)
+    b = zeros(Float64,n, n)
+    for i in 1:n
+        b[i, i] = 1.0
+    end
+    Z = Float64[A b]
+    @inbounds @fastmath @simd for i in 1:n
+        @fastmath @simd for j in 1:n
+            if i != j 
+                Z[j, :] .= view(Z, j, :) .- (Z[j, i] / Z[i, i]) .* view(Z, i, :)
+            else
+                Z[j, :] .= (1.0 / Z[i, j]) .* view(Z, j, :)
+            end
+            verbose && display(Z)
+        end
+    end
+    return Z[:, (p+1):end]
+end
+
 
 end # end of module Simplex 

test/testsimplex.jl

@@ -1,4 +1,20 @@
 @testset "Simplex" begin
+
+    @testset "Gauss Jordan" begin 
+
+        m = Float64[1.0 2 7; -1 6 5; 9 8 -3]
+
+        expected = [
+            0.142157  -0.151961    0.0784314;
+            -0.102941   0.161765    0.0294118;
+             0.151961  -0.0245098  -0.0196078           
+        ]
+
+        result = gaussjordan(m, verbose = false)
+
+        @test isapprox(result, expected, atol = 0.0001)
+    end 
+
     @testset "Maximization Problem" begin
 
         eps = 0.0001