Add tests and fix typos

Author: eeshan9815

perf/linear_eq_tabular.txt

@@ -39,26 +39,11 @@ Gauss Seidel
 
 Gauss Elimination
 
-20×3 DataFrames.DataFrame
-│ Row │ n  │ Base.\\     │ Gauss Elimination │
-├─────┼────┼─────────────┼───────────────────┤
-│ 1   │ 1  │ 1.0859e-5   │ 1.0402e-5         │
-│ 2   │ 10 │ 0.00037311  │ 0.000372278       │
-│ 3   │ 11 │ 0.000457845 │ 0.000457603       │
-│ 4   │ 12 │ 0.000543028 │ 0.00054428        │
-│ 5   │ 13 │ 0.000642694 │ 0.00064314        │
-│ 6   │ 14 │ 0.00076788  │ 0.000766503       │
-│ 7   │ 15 │ 0.000877223 │ 0.000874887       │
-│ 8   │ 16 │ 0.00102177  │ 0.00102244        │
-│ 9   │ 17 │ 0.00114972  │ 0.00115541        │
-│ 10  │ 18 │ 0.00150682  │ 0.00153407        │
-│ 11  │ 19 │ 0.00172544  │ 0.00170808        │
-│ 12  │ 2  │ 2.6519e-5   │ 2.5677e-5         │
-│ 13  │ 20 │ 0.00192433  │ 0.0019773         │
-│ 14  │ 3  │ 4.6299e-5   │ 4.6316e-5         │
-│ 15  │ 4  │ 7.2201e-5   │ 7.2106e-5         │
-│ 16  │ 5  │ 0.000101941 │ 0.000102027       │
-│ 17  │ 6  │ 0.000139823 │ 0.000139717       │
-│ 18  │ 7  │ 0.000189156 │ 0.000188991       │
-│ 19  │ 8  │ 0.000239304 │ 0.000238721       │
-│ 20  │ 9  │ 0.000305721 │ 0.000305388       │
+5×3 DataFrames.DataFrame
+│ Row │ n │ Base.\\    │ Gauss Elimination │
+├─────┼───┼────────────┼───────────────────┤
+│ 1   │ 1 │ 1.84e-6    │ 8.127e-6          │
+│ 2   │ 2 │ 3.1615e-6  │ 1.0029e-5         │
+│ 3   │ 3 │ 4.53986e-6 │ 1.1211e-5         │
+│ 4   │ 4 │ 6.8655e-6  │ 1.4342e-5         │
+│ 5   │ 5 │ 1.0773e-5  │ 1.7725e-5         │

src/IntervalRootFinding.jl

@@ -21,10 +21,8 @@ export
     bisect, newton1d, slope,
     slope_newton1d,
     gauss_seidel_interval, gauss_seidel_interval!,
-    gauss_seidel_contractor, gauss_seidel_contractor!
-    # gauss_seidel_interval_static1, gauss_seidel_interval_static1!
-    # gauss_seidel_interval_static2, gauss_seidel_interval_static2!
-    # gauss_seidel_interval_static, gauss_seidel_interval_static!
+    gauss_seidel_contractor, gauss_seidel_contractor!,
+    gauss_elimination_interval, gauss_elimination_interval!
 
 export isunique, root_status
 

src/linear_eq.jl

@@ -1,4 +1,3 @@
-using IntervalArithmetic
 """
 Preconditions the matrix A and b with the inverse of mid(A)
 """
@@ -81,16 +80,14 @@ function gauss_elimination_interval(A::AbstractMatrix, b::AbstractArray; precond
     n = size(A, 1)
     x = fill(-1e16..1e16, n)
 
-    x = gauss_seidel_interval!(x, A, b, precondition=precondition)
+    x = gauss_elimination_interval!(x, A, b, precondition=precondition)
 
     return x
 end
 """
-Iteratively solves the system of interval linear
-equations and returns the solution set. Uses the
-Gauss-Seidel method (Hansen-Sengupta version) to solve the system.
-Keyword `precondition` to turn preconditioning off.
-Eldon Hansen and G. William Walster : Global Optimization Using Interval Analysis - Chapter 5 - Page 115
+Solves the system of linear equations using Gaussian Elimination,
+with (or without) preconditioning. (kwarg - `precondition`)
+Luc Jaulin, Michel Kieffer, Olivier Didrit and Eric Walter - Applied Interval Analysis - Page 72
 """
 function gauss_elimination_interval!(x::AbstractArray, a::AbstractMatrix, b::AbstractArray; precondition=true)
 
@@ -132,16 +129,12 @@ function gauss_elimination_interval1(A::AbstractMatrix, b::AbstractArray; precon
     n = size(A, 1)
     x = fill(-1e16..1e16, n)
 
-    x = gauss_seidel_interval!(x, A, b, precondition=precondition)
+    x = gauss_elimination_interval1!(x, A, b, precondition=precondition)
 
     return x
 end
 """
-Iteratively solves the system of interval linear
-equations and returns the solution set. Uses the
-Gauss-Seidel method (Hansen-Sengupta version) to solve the system.
-Keyword `precondition` to turn preconditioning off.
-Eldon Hansen and G. William Walster : Global Optimization Using Interval Analysis - Chapter 5 - Page 115
+Using `Base.\``
 """
 function gauss_elimination_interval1!(x::AbstractArray, a::AbstractMatrix, b::AbstractArray; precondition=true)
 

test/linear_eq.jl

@@ -1,6 +1,6 @@
 using IntervalArithmetic, StaticArrays, IntervalRootFinding
 
-@testset "Testing Gauss Seidel Method" begin
+@testset "Linear Equations" begin
 
     A = [[2..3 0..1;1..2 2..3], ]
     b = [[0..120, 60..240], ]
@@ -9,7 +9,7 @@ using IntervalArithmetic, StaticArrays, IntervalRootFinding
 
     for i in 1:length(A)
         for precondition in (false, true)
-            for f in (gauss_seidel_interval, gauss_seidel_contractor)
+            for f in (gauss_seidel_interval, gauss_seidel_contractor, gauss_elimination_interval)
                 @test all(x[i] .⊆ f(A[i], b[i]))
             end
         end