CA-EC tested

EC_test.ipynb

@@ -78,6 +78,49 @@
     "plot!(real.(mesh_E), imag.(mesh_E), label=\"contour\")\n",
     "xlims!(0,1)"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "training_points = range(1.35, 0.9, 5)\n",
+    "training_E = Vector{ComplexF64}(undef, length(training_points))\n",
+    "EC_basis = Matrix{ComplexF64}(undef, length(p), length(training_points))\n",
+    "\n",
+    "for (j, c) in enumerate(training_points)\n",
+    "    evals, evecs = eigen(get_H_matrix(V_system(c), p, w))\n",
+    "    i = identify_pole_i(p, evals)\n",
+    "    training_E[j] = evals[i]\n",
+    "    EC_basis[:, j] = evecs[:, i]\n",
+    "end\n",
+    "\n",
+    "EC_basis = hcat(EC_basis, conj.(EC_basis)) # CA-EC\n",
+    "\n",
+    "extrapolate_points = range(0.75, 0.40, 8)\n",
+    "\n",
+    "exact_E = Vector{ComplexF64}(undef, length(extrapolate_points))\n",
+    "extrapolate_E = Vector{ComplexF64}(undef, length(extrapolate_points))\n",
+    "\n",
+    "for (j, c) in enumerate(extrapolate_points)\n",
+    "    exact_E[j] = quick_pole_E(V_system(c))\n",
+    "\n",
+    "    EC_basis_w = EC_basis .* w\n",
+    "    H = get_H_matrix(V_system(c), p, w)\n",
+    "    H_EC = transpose(EC_basis) * H * EC_basis\n",
+    "    N_EC = transpose(EC_basis) * EC_basis\n",
+    "    evals = eigvals(H_EC, N_EC)\n",
+    "    i = argmin(abs.(evals .- exact_E[j]))\n",
+    "    extrapolate_E[j] = evals[i]\n",
+    "end\n",
+    "\n",
+    "scatter(real.(training_E), imag.(training_E), label=\"training\")\n",
+    "scatter!(real.(exact_E), imag.(exact_E), label=\"exact\")\n",
+    "scatter!(real.(extrapolate_E), imag.(extrapolate_E), label=\"extrapolated\")\n",
+    "plot!(real.(mesh_E), imag.(mesh_E), label=\"contour\")\n",
+    "xlims!(-0.7,0.7)"
+   ]
   }
  ],
  "metadata": {