Added pdde_stability native

Author: jarlebring

src/Gallery.jl

@@ -162,6 +162,11 @@ The following list describes the NEP with a certain `name` and the associated pa
     and\\
     X. Huang, Z. Bai, and Y. Su, Nonlinear rank-one modification of the symmetric eigenvalue problem. J. Comput. Math. 28, 2, 218–234, 2010
 
+
+* `nlevp_native_hadeler`\\
+    The benchmark problem from the NLEVP-collection called "hadeler", represented in the native NEP-PACK format. The problem is of the form ``M(λ)=(e^λ-1)B+A0+A2λ^2``. \\
+ Hadeler K.  P.  1967.  Mehrparametrige  und  nichtlineare  Eigenwertaufgaben. Arch.  Rational  Mech. Anal. 27, 4, 306–328.\\
+
 * `nlevp_native_pdde_stability`\\
     The benchmark problem from the NLEVP-collection called "pdde_stability", represented in the native NEP-PACK format.
     This problem is a quadratic eigenvalue with arbitrary given size `n`. See
@@ -211,9 +216,10 @@ julia> norm(compute_Mlincomb(nep,1.0+1.0im,ones(size(nep,1))))
         "periodicdde" => (params...; kwargs...) -> periodic_dde_gallery(PeriodicDDE_NEP, params...; kwargs...),
         "neuron0" => neuron0,
         "nlevp_native_gun" => nlevp_native_gun,
+        "nlevp_native_hadeler" => nlevp_native_hadeler,
         "nlevp_native_cd_player" => nlevp_native_cd_player,
         "nlevp_native_fiber" => nlevp_native_fiber,
-        "nlevp_pdde_stability" => nlevp_native_pdde_stability,
+        "nlevp_native_pdde_stability" => nlevp_native_pdde_stability,
         "beam" => beam,
         "sine" => sine_nep,
     )

src/gallery_extra/NLEVP_native.jl

@@ -137,7 +137,23 @@ function newton_eval(coeffs,S,interp_points)  # This works for λ::Number and λ
 end
 
 
-function pdde_stability(n=15)
+
+function nlevp_native_hadeler(α=100,n=8)
+    i=1:n
+    I2 = ones(n)*i'  # matrix with constant columns 1,2,3,4...n
+    # Identity matrix
+    II = Matrix{typeof(α)}(I,n,n);
+    # Matrices
+    A0= α*II
+    A2 = n*II+1 ./(I2 + I2');
+    B = ((n+1) .- max.(I2',I2)) .* (i*i');
+    # Functions
+    fv= [S->-one(S) ; S->S^2 ; S->(exp(S)-one(S))]
+    nep=SPMF_NEP([A0, A2, B], fv);
+    return nep
+end
+
+function nlevp_native_pdde_stability(n=15)
 
     # default values
     a0 = 2;
@@ -171,4 +187,5 @@ function pdde_stability(n=15)
     return PEP(Av)
 
 
+
 end

test/gallery.jl

@@ -144,6 +144,13 @@ using Test
     @test_throws MethodError nep_gallery("beam", 15, 8)
     @test_throws ErrorException nep_gallery("beam", 15, t=8)
 
+
+    @info "Testing hadeler"
+    nep=nep_gallery("nlevp_native_hadeler")
+    A=compute_Mder(nep,3.0);
+    @test isreal(A)
+
+
     @info "non-existing example"
     @test_throws ErrorException nep_gallery("non-existing example")