ERROR: SingularException(4)

[LH1389]

using LinearAlgebra 
    f(x) = (x[1]+10*x[2])^2 + 5*(x[3]-x[4])^2 + (x[2]-2*x[3])^4 + 10*(x[1]-x[4])^4
    f1(x) = 2(x[1]+10*x[2]) + 40(x[1]-x[4])^3
    f2(x) = 20(x[1]+10*x[2]) + 4(x[2]-2*x[3])^3
    f3(x) = 10(x[3]-x[4]) - 8(x[2]-2*x[3])^3
    f4(x) = -10(x[3]-x[4]) - 40(x[1]-x[4])^3
    X(x)  = [f1(x);f2(x);f3(x);f4(x)]
    ;
    f11(x) = 2+120(x[1]-x[4])^2
    f12(x) = 20
    f13(x) = 0
    f14(x) = -120(x[1]-x[4])^2
    f15(x) = [f11(x);f12(x);f13(x);f14(x)]
    f21(x) = 20
    f22(x) = 200+12(x[2]-2*x[3])^2
    f23(x) = -24(x[2]-2*x[3])^2
    f24(x) = 0
    f25(x) = [f21(x);f22(x);f23(x);f24(x)]
    f31(x) = 0
    f32(x) = -24(x[2]-2*x[3])^2
    f33(x) = 10 + 48(x[2]-2*x[3])^2
    f34(x) = -10
    f35(x) = [f31(x);f32(x);f33(x);f34(x)]
    f41(x) = -120(x[1]-x[4])^2
    f42(x) = 0
    f43(x) = -10
    f44(x) = 10 + 120(x[1]-x[4])^2
    f45(x) = [f41(x);f42(x);f43(x);f44(x)]
    F(x) = [f15(x) f25(x) f35(x) f45(x)]
    x = [3,-1,0,1]
    t1 = inv(F(x))
    F([3,-1,0,1])
    dis=1
function newton(x)
while dis > 0.01
    g = X(x)
    t1 = inv(F(x))
    x1 = x - t1 * g
    dis = sqrt((x1[1]-x[1])^2+(x1[2]-x[2])^2+(x1[3]-x[3])^2+(x1[4]-x[4])^2)
    x = x1
    println(x,f(x)) 
end
end
x = [3,-1,0,1]
newton(x)

[LH1389]

ERROR: SingularException(4)
Stacktrace:

checknonsingular at [factorization.jl](vscode-file://vscode-app/d:/Microsoft%20VS%20Code/resources/app/out/vs/code/electron-sandbox/workbench/workbench.html)

checknonsingular at [factorization.jl](vscode-file://vscode-app/d:/Microsoft%20VS%20Code/resources/app/out/vs/code/electron-sandbox/workbench/workbench.html)

#lu!#170 at [lu.jl](vscode-file://vscode-app/d:/Microsoft%20VS%20Code/resources/app/out/vs/code/electron-sandbox/workbench/workbench.html)
lu! at [lu.jl](vscode-file://vscode-app/d:/Microsoft%20VS%20Code/resources/app/out/vs/code/electron-sandbox/workbench/workbench.html)

#lu#176 at [lu.jl](vscode-file://vscode-app/d:/Microsoft%20VS%20Code/resources/app/out/vs/code/electron-sandbox/workbench/workbench.html)

lu at [lu.jl](vscode-file://vscode-app/d:/Microsoft%20VS%20Code/resources/app/out/vs/code/electron-sandbox/workbench/workbench.html) (repeats 2 times)

inv(A::Matrix{Float64}) at [dense.jl](vscode-file://vscode-app/d:/Microsoft%20VS%20Code/resources/app/out/vs/code/electron-sandbox/workbench/workbench.html)

newton(x::Vector{Int64}) at [Untitled-3](vscode-file://vscode-app/d:/Microsoft%20VS%20Code/resources/app/out/vs/code/electron-sandbox/workbench/workbench.html)

top-level scope at [Untitled-3](vscode-file://vscode-app/d:/Microsoft%20VS%20Code/resources/app/out/vs/code/electron-sandbox/workbench/workbench.html)

[LH1389]

Why it cannot stop?

[Kolaru]

The error comes from the fact that sometimes F(x) is not invertible (resulting in a SinguarException).

However this seems to be unrelated to IntervalRootFinding.jl, so I am closing the issue.