Add examples

examples/linear_eq.jl

@@ -0,0 +1,32 @@
+# Examples from Luc Jaulin, Michel Kieffer, Olivier Didrit and Eric Walter - Applied Interval Analysis
+
+using IntervalArithmetic, IntervalRootFinding, StaticArrays
+
+A = [4..5 -1..1 1.5..2.5; -0.5..0.5 -7.. -5 1..2; -1.5.. -0.5 -0.7.. -0.5 2..3]
+sA = SMatrix{3}{3}(A)
+mA = MMatrix{3}{3}(A)
+
+b = [3..4, 0..2, 3..4]
+sb = SVector{3}(b)
+mb = MVector{3}(b)
+
+p = fill(-1e16..1e16, 3)
+
+rts = gauss_seidel_interval!(p, A, b, precondition=true) # Gauss-Seidel Method; precondition=true by default
+rts = gauss_seidel_interval!(p, sA, sb, precondition=true) # Gauss-Seidel Method; precondition=true by default
+rts = gauss_seidel_interval!(p, mA, mb, precondition=true) # Gauss-Seidel Method; precondition=true by default
+
+rts = gauss_seidel_interval(A, b, precondition=true) # Gauss-Seidel Method; precondition=true by default
+rts = gauss_seidel_interval(sA, sb, precondition=true) # Gauss-Seidel Method; precondition=true by default
+rts = gauss_seidel_interval(mA, mb, precondition=true) # Gauss-Seidel Method; precondition=true by default
+
+rts = gauss_seidel_contractor!(p, A, b, precondition=true) # Gauss-Seidel Method (Vectorized); precondition=true by default
+rts = gauss_seidel_contractor!(p, sA, sb, precondition=true) # Gauss-Seidel Method (Vectorized); precondition=true by default
+rts = gauss_seidel_contractor!(p, mA, mb, precondition=true) # Gauss-Seidel Method (Vectorized); precondition=true by default
+
+rts = gauss_seidel_contractor(A, b, precondition=true) # Gauss-Seidel Method (Vectorized); precondition=true by default
+rts = gauss_seidel_contractor(sA, sb, precondition=true) # Gauss-Seidel Method (Vectorized); precondition=true by default
+rts = gauss_seidel_contractor(mA, mb, precondition=true) # Gauss-Seidel Method (Vectorized); precondition=true by default
+
+rts = gauss_elimination_interval!(p, A, b, precondition=true) # Gaussian Elimination; precondition=true by default
+rts = gauss_elimination_interval(A, b, precondition=true) # Gaussian Elimination; precondition=true by default

src/linear_eq.jl

@@ -13,8 +13,8 @@ end
 function gauss_seidel_interval(A::AbstractMatrix, b::AbstractArray; precondition=true, maxiter=100)
 
     n = size(A, 1)
-    x = fill(-1e16..1e16, n)
-
+    x = similar(b)
+    x .= -1e16..1e16
     gauss_seidel_interval!(x, A, b, precondition=precondition, maxiter=maxiter)
     return x
 end
@@ -47,7 +47,8 @@ end
 function gauss_seidel_contractor(A::AbstractMatrix, b::AbstractArray; precondition=true, maxiter=100)
 
     n = size(A, 1)
-    x = fill(-1e16..1e16, n)
+    x = similar(b)
+    x .= -1e16..1e16
     x = gauss_seidel_contractor!(x, A, b, precondition=precondition, maxiter=maxiter)
     return x
 end
@@ -78,8 +79,8 @@ end
 function gauss_elimination_interval(A::AbstractMatrix, b::AbstractArray; precondition=true)
 
     n = size(A, 1)
-    x = fill(-1e16..1e16, n)
-
+    x = similar(b)
+    x .= -1e16..1e16
     x = gauss_elimination_interval!(x, A, b, precondition=precondition)
 
     return x