{
"cells": [
{
"cell_type": "markdown",
"source": [
"# Self-consistent field methods"
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"In the Introduction to density-functional theory we concluded that the non-linear eigenvalue\n",
"problem underlying DFT can be written as the fixed-point problem\n",
"$$\n",
"\\rho = D(V(\\rho)),\n",
"$$\n",
"where $V$ is the potential depending on the density $\\rho$ and $D(V)$ is the potential-to-density\n",
"map, that is the construction of the DFT Hamiltonian $H(ρ) = -\\frac12 Δ + V(ρ)$,\n",
"followed its diagonalization to obtain its eigenpairs $(\\varepsilon_{k i}, \\psi_{ki})$\n",
"and from these a new density\n",
"$$\n",
"\\rho(r) = \\sum_i f\\left(\\varepsilon_{i}\\right) \\, \\psi_{ki}(r) \\, \\psi_{ki}^\\ast(r)\n",
"$$\n",
"with the Fermi level in the occupation function $f$ chosen such that the number of electrons is conserved.\n",
"\n",
"In this chapter we will investigate the convergence properties of density-mixing SCF algorithms,\n",
"that is **damped, preconditioned fixed-point iterations**\n",
"$$\n",
"\\rho_{n+1} = \\rho_n + \\alpha P^{-1} (D(V(\\rho_n)) - \\rho_n),\n",
"$$\n",
"where\n",
"* $\\alpha$ is a damping parameter, typically chosen between $0$ and $1$.\n",
"* $P^{-1}$ is a preconditioner, which aims to improve convergence (details discussed further down).\n",
"* the iterations start from an initial guess $\\rho_0$.\n",
"Our presentation follows [^HL2021], where more details can be found.\n",
"\n",
"## SCF convergence analysis\n",
"\n",
"We investigate the convergence properties of damped, preconditioned\n",
"iterations, in order to understand the choices for the preconditioning\n",
"stratege $P^{-1}$ as well as the damping parameter $\\alpha$ to be made.\n",
"\n",
"Near the fixed point $\\rho_\\ast = D(V(\\rho_\\ast))$ the error $e_n = \\rho_n - \\rho_\\ast$ is small and we can expand to first order:\n",
"$$\n",
"\\begin{align*}\n",
"D(V(\\rho_\\ast + e_n)) &\\simeq D\\left[V(\\rho_\\ast) + V'|_{\\rho_\\ast} e_n\\right] \\\\\n",
"&\\simeq D(V(\\rho_\\ast)) + D'|_{V(\\rho_\\ast)} V'|_{\\rho_\\ast} e_n\\\\\n",
"&= \\rho_\\ast + D'|_{V(\\rho_\\ast)} V'|_{\\rho_\\ast} e_n\n",
"\\end{align*}\n",
"$$\n",
"\n",
"The derivatives $D'$ and $V'$ are again important quantities and are given special symbols:\n",
"- Hartree-exchange-correlation **kernel** $K = V'$\n",
"- Independent-particle **susceptibility** $\\chi_0 = D'$\n",
"\n",
"where for simplicity it has been dropped that these quantities are evaluated at the fixed-point,\n",
" i.e. at $\\rho_\\ast$ and $V(\\rho_\\ast)$, respectively.\n",
"\n",
"The above expansion allows to relate the **error between SCF iterations** (near the fixed point):\n",
"$$\n",
"\\begin{align*}\n",
"e_{n+1} = \\rho_{n+1} - \\rho_\\ast\n",
"&= \\rho_{n} - \\rho_\\ast + \\alpha P^{-1} [D(V(\\rho_\\ast + e_n)) - \\rho_n] \\\\\n",
"&\\simeq \\rho_{n} - \\rho_\\ast + \\alpha P^{-1} [\\rho_\\ast + \\chi_0 K e_n - \\rho_n] \\\\\n",
"&= e_n - \\alpha P^{-1} [1 - \\chi_0 K] e_n.\n",
"\\end{align*}\n",
"$$\n",
"\n",
"Introducing the **dielectric matrix** adjoint\n",
"$$\n",
"\\varepsilon^\\dagger = [1 - \\chi_0 K]\n",
"$$\n",
"leads to the final relationship\n",
"$$\n",
"e_{n+1} \\simeq [1 - \\alpha P^{-1} \\varepsilon^\\dagger] e_n = [1 - \\alpha P^{-1} \\varepsilon^\\dagger]^n e_0\n",
"$$\n",
"with $e_0$ being the initial error. The SCF Jacobian is\n",
"$1 - \\alpha P^{-1} \\varepsilon^\\dagger.$\n",
"\n",
"In other words:\n",
"$$\n",
"\\text{SCF converges} \\qquad \\Leftrightarrow \\qquad \\text{eigenvalues of $1 - \\alpha P^{-1} \\varepsilon^\\dagger$ are between $-1$ and $1$}\n",
"$$\n",
"\n",
"This implies that the **convergence** properties of an SCF\n",
"are related to $\\varepsilon$, the dielectric operator,\n",
"which **depends on** the **dielectric properties** of the system under study.\n",
"\n",
"In other words it depends on the conduction and screening properties, i.e. whether the material is an insulator, a semiconductor, a metal etc."
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"## Making an SCF converge\n",
"\n",
"It turns out that for the largest chunk of cases the eigenvalues of\n",
"$\\varepsilon^\\dagger$ are positive. Moreover near a local minimiser\n",
"$\\varepsilon^\\dagger$ always has non-degative spectrum.\n",
"\n",
"To make the SCF converge one can therefore:\n",
"- Choose $\\alpha$ small enough. Even for $P = I$ this always works, but convergence can be painfully slow. (see e.g. the proof in [^HL2022])\n",
"- Find a good $P^{-1} \\simeq (\\varepsilon^\\dagger)^{-1}$. Then the eigenvalues of $(P^{-1} \\varepsilon^\\dagger)$ are close to 1, $\\alpha \\simeq 1$ is a good choice and the SCF converges in few steps. Hooray!\n",
"- The optimal $\\alpha$ and the optimal rate of convergence are directly related to the eigenvalues of $P^{-1} \\varepsilon^\\dagger$. Denoting by $\\lambda_\\text{min} > 0$ and $\\lambda_\\text{max}$ the smallest and largest eigenvalues of $P^{-1} \\varepsilon^\\dagger$, then the optimal damping is\n",
" $$\n",
" \\alpha = \\frac{2}{\\lambda_\\text{min} + \\lambda_\\text{max}}\n",
" $$\n",
" and the rate of convergence is (for large $\\kappa$)\n",
" $$\n",
" r \\simeq 1 - \\frac{2}{\\kappa}\n",
" $$\n",
" where the (spectral) condition number\n",
" $$\n",
" \\kappa = \\frac{\\lambda_\\text{max}}{\\lambda_\\text{min}}.\n",
" $$\n",
" Thus the smaller the condition number, the better the convergence.\n",
"\n",
"**Note:** If the preconditioner is very bad, the eigenvalues of\n",
"$(P^{-1} \\varepsilon^\\dagger)$ might even be worse than $\\varepsilon^\\dagger$, such\n",
"that convergence is actually hampered by the preconditioner."
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"## Damped iterations\n",
"We start our practical investigation of typical SCF algorithms using the most simple case of $P=I$\n",
"and $α = 1$, i.e. the fixed-point iterations\n",
"$$\n",
"\\rho_{n+1} = F(\\rho_n),\n",
"$$\n",
"where thus the density is just sent through the SCF step function $F(\\rho) = D(V(ρ))$\n",
"over and over again, starting from a hopefully good initial guess $\\rho_0$ until\n",
"two successive densities differ by less than a desired threshold.\n",
"\n",
"DFTK automatically provides a reasonable\n",
"guess density as well as function to evaluate $F(ρ)$,\n",
"such that we only need to take care of the iterations themselves.\n",
"In the language of DFTK this algorithm is written as:"
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"using DFTK\n",
"using LinearAlgebra\n",
"\n",
"function fixed_point_iteration(F, ρ0, info0; maxiter, tol=1e-10)\n",
" # F: The SCF step function\n",
" # ρ0: The initial guess density\n",
" # info0: The initial metadata\n",
" # maxiter: The maximal number of iterations to be performed\n",
"\n",
" ρ = ρ0\n",
" info = info0\n",
" for n = 1:maxiter\n",
" Fρ, info = F(ρ, info)\n",
" # If the change is less than the tolerance, break iteration.\n",
" if norm(Fρ - ρ) < tol\n",
" break\n",
" end\n",
" ρ = Fρ\n",
" end\n",
"\n",
" # Return some stuff DFTK needs ...\n",
" (; fixpoint=ρ, info)\n",
"end;"
],
"metadata": {},
"execution_count": 1
},
{
"cell_type": "markdown",
"source": [
"> **Convergence checks in DFTK**\n",
">\n",
"> The ad-hoc convergence criterion in the example above is included only for\n",
"> pedagogical purposes. It does not yet include the correct scaling,\n",
"> which depends on the discretization.\n",
"> It is preferred to use the provided DFTK utilities for specifying\n",
"> convergence, that can be shared across different solvers. For the more\n",
"> advanced version, see the tutorial on custom SCF solvers."
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"To test this algorithm we use the following simple setting, which builds and discretizes\n",
"a PBE model for an aluminium supercell."
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"using AtomsBuilder\n",
"using PseudoPotentialData\n",
"\n",
"function aluminium_setup(repeat=1; Ecut=13.0, kgrid=[2, 2, 2])\n",
" al_supercell = bulk(:Al; cubic=true) * (repeat, 1, 1)\n",
" pd_pbe_family = PseudoFamily(\"dojo.nc.sr.pbe.v0_4_1.standard.upf\")\n",
" model = model_DFT(al_supercell;\n",
" functionals=PBE(), temperature=1e-3, symmetries=false,\n",
" pseudopotentials=pd_pbe_family)\n",
" PlaneWaveBasis(model; Ecut, kgrid)\n",
"end;"
],
"metadata": {},
"execution_count": 2
},
{
"cell_type": "markdown",
"source": [
"Now use this setup together with the `fixed_point_iteration` solver above\n",
"within an SCF. Note that the `damping` and `mixing` parameters are needed\n",
"here to disable some DFTK defaults we don't want to use just yet."
],
"metadata": {}
},
{
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"n Energy log10(ΔE) log10(Δρ) Diag Δtime\n",
"--- --------------- --------- --------- ---- ------\n",
" 1 -9.186851634535 -1.09 6.8 7.40s\n",
" 2 -9.187803424194 -3.02 -2.40 1.0 241ms\n",
" 3 -9.187984828647 -3.74 -2.68 8.5 474ms\n",
" 4 -9.187869555984 + -3.94 -2.20 2.0 210ms\n",
" 5 -9.186929201981 + -3.03 -1.74 3.2 303ms\n",
" 6 -9.183449872345 + -2.46 -1.41 5.1 415ms\n",
" 7 -9.176395067738 + -2.15 -1.21 4.9 440ms\n",
" 8 -9.162810743391 + -1.87 -1.06 5.0 457ms\n",
" 9 -9.140007516547 + -1.64 -0.93 5.4 803ms\n",
" 10 -9.103021128748 + -1.43 -0.82 7.1 569ms\n",
" 11 -9.018617559277 + -1.07 -0.69 8.0 585ms\n",
" 12 -8.764436074438 + -0.59 -0.51 7.4 598ms\n",
" 13 -8.415516763926 + -0.46 -0.35 9.4 673ms\n",
" 14 -7.800420117148 + -0.21 -0.22 10.8 751ms\n",
" 15 -7.551794032574 + -0.60 -0.15 9.0 776ms\n",
" 16 -7.001873507578 + -0.26 -0.10 10.9 820ms\n",
" 17 -7.025585446598 -1.63 -0.07 11.2 857ms\n",
" 18 -6.773461294544 + -0.60 -0.06 10.4 838ms\n",
" 19 -6.900061424449 -0.90 -0.06 10.9 1.15s\n",
" 20 -6.679746406121 + -0.66 -0.05 10.5 582ms\n",
" 21 -6.763168034150 -1.08 -0.05 11.5 853ms\n",
" 22 -6.620839154162 + -0.85 -0.04 10.5 809ms\n",
" 23 -6.651888301532 -1.51 -0.04 11.4 893ms\n",
" 24 -6.596149165262 + -1.25 -0.04 11.0 858ms\n",
" 25 -6.625083710254 -1.54 -0.04 11.4 855ms\n",
" 26 -6.601592239557 + -1.63 -0.04 12.2 886ms\n",
" 27 -6.617981866340 -1.79 -0.04 11.1 871ms\n",
" 28 -6.606876320377 + -1.95 -0.04 11.9 872ms\n",
" 29 -6.615320237043 -2.07 -0.04 11.2 1.15s\n",
" 30 -6.609815084069 + -2.26 -0.04 12.1 664ms\n",
"┌ Warning: SCF not converged.\n",
"└ @ DFTK ~/work/DFTK.jl/DFTK.jl/src/scf/scf_callbacks.jl:60\n"
]
}
],
"cell_type": "code",
"source": [
"self_consistent_field(aluminium_setup(1); solver=fixed_point_iteration, damping=1.0,\n",
" maxiter=30, mixing=SimpleMixing());"
],
"metadata": {},
"execution_count": 3
},
{
"cell_type": "markdown",
"source": [
"As can be observed this algorithm is not very good and in fact even fails to converge albeit we are only looking at a very simple system.\n",
"\n",
"This is a known limitation of this algorithm, which is indeed why in practice one at least includes\n",
"the damping parameter $\\alpha$ (with values usually between $0$ and $1$). One now iterates as follows:\n",
"$$\n",
"\\rho_{n+1} = \\rho_{n} + \\alpha (F(\\rho_n) - \\rho_n)\n",
"$$\n",
"\n",
"> **Exercise 1**\n",
">\n",
"> Modify `fixed_point_iteration` such that it supports this *damped*\n",
"> fixed-point iteration. In other words implement damping *inside* your\n",
"> algorithm and not by changing the `damping` parameter of the\n",
"> `self_consistent_field` function driving the SCF.\n",
"\n",
" Using your algorithm try different values for $\\alpha$ between $0$ and\n",
" $1$ and estimate roughly the $\\alpha$ which gives fastest convergence.\n",
" For which $\\alpha$ do you observe no convergence at all?"
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"## Acceleration techniques\n",
"Before moving on to cases with $P \\neq I$ we will briefly consider an orthogonal strategy\n",
"leading to faster SCF convergence, namely acceleration techniques.\n",
"Our discussion will focus on **Anderson acceleration**. In this approach one\n",
"exploits that the update $R(\\rho) = F(\\rho) - \\rho$ is also the residual of\n",
"the fixed-point problem $F(\\rho) = \\rho$, i.e. how far away we are from the\n",
"fixed-point density. A good next density $\\rho_{n+1}$ therefore should be\n",
"found by minimising an approximation for $R(\\rho_{n+1})$. Assuming the SCF\n",
"was linear in the density (which it is not), a good idea is to find a linear\n",
"combination of residuals\n",
"$$\n",
"\\min_{\\beta_i} \\left\\| \\sum_i \\beta_i R(\\rho_i) \\right\\|^2\n",
"$$\n",
"which has the smallest possible norm and to use these coefficients $\\beta_i$ to extrapolate the next\n",
"density\n",
"$$\n",
"\\rho_{n+1} = \\sum_i \\beta_i (\\rho_i + \\alpha R(\\rho_i))\n",
"$$\n",
"where you notice the \"standard\" damped fixed-point iteration in the summed terms.\n",
"\n",
"This simple idea has been rediscovered a few times in different communities with only minor variations to the theme. This makes Anderson acceleration variably known as e.g. Anderson mixing, Pulay mixing or direct inversion of the iterative subspace (DIIS). The mathematical analysis of such methods is not yet exhaustive, see [M. Chupin, M. Dupuy, G. Legendre, É. Séré. *Math. Model. Num. Anal.* **55** 2785 (2021) DOI: 10.1051/m2an/2021069](http://dx.doi.org/10.1051/m2an/2021069) for a recent paper providing a good review of the state of the art.\n",
"\n",
"A key result has been obtained by [Walker and Ni](https://doi.org/10.1137/10078356X), namely the equivalence of Anderson to the GMRES algorithm for linear problems. Based on this analysis Anderson-accelerated SCF procedures Anderson can be expected to inherit the GMRES convergence properties near a fixed point, resulting in a rate of convergence of\n",
"$$\n",
"r \\simeq 1 - \\frac{2}{\\sqrt{\\kappa}}.\n",
"$$\n",
"In terms of an algorithm Anderson iteration is"
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"function anderson_iteration(F, ρ0, info0; maxiter)\n",
" # F: The SCF step function\n",
" # ρ0: The initial guess density\n",
" # info0: The initial metadata\n",
" # maxiter: The maximal number of iterations to be performed\n",
"\n",
" info = info0\n",
" ρ = ρ0\n",
" ρs = []\n",
" Rs = []\n",
" for n = 1:maxiter\n",
" Fρ, info = F(ρ, info)\n",
" if info.converged\n",
" break\n",
" end\n",
" Rρ = Fρ - ρ\n",
"\n",
" ρnext = vec(ρ) .+ vec(Rρ)\n",
" if !isempty(Rs)\n",
" M = hcat(Rs...) .- vec(Rρ)\n",
" βs = -(M \\ vec(Rρ))\n",
"\n",
" for (iβ, β) in enumerate(βs)\n",
" ρnext .+= β .* (ρs[iβ] .- vec(ρ) .+ Rs[iβ] .- vec(Rρ))\n",
" end\n",
" end\n",
"\n",
" push!(ρs, vec(ρ))\n",
" push!(Rs, vec(Rρ))\n",
" ρ = reshape(ρnext, size(ρ0)...)\n",
" end\n",
"\n",
" # Return some stuff DFTK needs ...\n",
" (; fixpoint=ρ, info)\n",
"end;"
],
"metadata": {},
"execution_count": 4
},
{
"cell_type": "markdown",
"source": [
"To work with this algorithm we will use DFTK's intrinsic mechanism to choose a damping. The syntax for this is\n",
"\n",
"```julia\n",
"repeat = 1\n",
"self_consistent_field(aluminium_setup(repeat);\n",
" solver=anderson_iteration,\n",
" damping=0.8, maxiter=40,\n",
" mixing=SimpleMixing());\n",
"```\n",
"to choose a damping of $\\alpha = 0.8$ and run for at most `maxiter` iterations.\n",
"\n",
"> **Exercise 2**\n",
">\n",
"> Based on this Anderson implementation verify (by making a few experiments) that the algorithm converges for `repeat=1` for any $0 < \\alpha \\leq 2$. You may now use the `damping` parameter for changing the value $\\alpha$ used by the SCF. State the number of iterations and runtimes you observe.\n",
"\n",
"> **Exercise 3**\n",
">\n",
"> Pick $\\alpha = 0.8$ and make the problem harder by increasing `repeat` (e.g. `2`, `4`, `6`, `8`). Can you make Anderson fail to converge? What do you notice in terms of the number of iterations and runtimes?"
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"DFTK actually employs a numerically more stable Anderson acceleration implementation by default\n",
"if the `solver` keyword argument is not provided to `self_consistent_field`.\n",
"For practical calculations this should be used instead of a custom version."
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"## Metals and charge sloshing\n",
"\n",
"Anderson allows us to push the boundary for SCF methods, but for larger or\n",
"more challenging systems it is not fully sufficient. The next ingredient for\n",
"a stable SCF procedure is based on the insight that the convergence\n",
"properties of an SCF provably depend on the dielectric properties of\n",
"materials, which is simulated. Amongst others this is to say that insulators\n",
"(like glass), semiconductors (like silicon) or metals (like aluminium) have\n",
"rather differing SCF behaviours. As a result the ideal SCF procedure should\n",
"be slightly different for each material.\n",
"\n",
"To investigate this further theoretically\n",
"Recall the definition $\\varepsilon^\\dagger = 1 - \\chi_0 K$. The Hartree-exchange-correlation kernel can be further decomposed into\n",
"$$\n",
"K = v_c + K_\\text{xc},\n",
"$$\n",
"where $v_c$ is the classical Coulomb kernel we introduced previously and $K_\\text{xc} = d^2 E_\\text{xc}(\\rho)$ is the Hessian of the exchange-correlation energy functional.\n",
"\n",
"For well-behaved systems the smallest eigenvalue of $\\varepsilon^\\dagger$ is around $1$ while the largest eigenvalue is of order $10$ (or less). Due to a number of instabilities in the modelled systems either the smallest eigenvalue can decrease or the largest eigenvalue can increase, thus giving a larker condition number $\\kappa$ and worse convergence. For a detailed discussion, see Section 2 of [^HL2021].\n",
"\n",
"In this discussion we will restrict ourselves to a single source of instabilities, namely the one due to the long range divergence of the Coulomb kernel $v_c$. Indeed, if $\\hat{\\rho}(q)$ are the Fourier coefficients of the density, then\n",
"$$\n",
"\\widehat{(v_c \\rho)}(q) = \\frac{4\\pi \\hat{\\rho}(q)}{|q|^2},\n",
"$$\n",
"which diverges for small $q$ (long wavelength). If this divergence is not compensated by $\\chi_0$, this can manifest in large eigenvalues of $\\varepsilon^\\dagger$. (Note that $\\chi_0$ is a non-positive operator and $K_\\text{xc}$ has usually little influence on the large eigenmodes of $\\varepsilon^\\dagger$.)\n",
"\n",
"For **metals** it turns out that $\\chi_0$ is approximately constant in the long-wavelength limit ($q \\to 0$), namely the negative density of states $D$ (per volume) at the Fermi level:\n",
"$$\n",
"\\lim_{q\\to0} \\chi_0(q) \\simeq -D.\n",
"$$\n",
"Therefore as one treats larger and larger metallic systems, smaller wavelengths $q$ become accessible in the discretised problem, which causes $\\lambda_\\text{max}$ to increase --- in theory quadratically with system size. This phaenomenon, known as **charge sloshing** makes it difficult to treat large metallic systems without proper preconditioning.\n",
"\n",
"In contrast for **insulators** and **semiconductors** a good approximation of $\\chi_0(q)$ for small $q$ is $-q^T \\sigma_0 q$, where $\\sigma_0$ is a material-dependent symmetric positive matrix. Therefore the $1/q^2$ instability is compensated and treating larger cells is less difficult."
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"## Preconditioning strategies (mixing methods)\n",
"\n",
"The natural approach to deal with the large-wavelength instabilities mentioned in the previous section, is to develop an approximate dielectric model $P \\simeq \\varepsilon^\\dagger$, which can be used to compensate the large eigenvalues of $\\varepsilon^\\dagger$, i.e. such that $P^{-1} \\varepsilon^\\dagger$ keeps a manageable condition number $\\kappa$ and thus a fast SCF convergence.\n",
"\n",
"To simplify the discussion we will employ the so-called **random-phase approximation**, where we set $K \\simeq v_c$, i.e. $\\varepsilon^\\dagger = 1 - \\chi_0 v_c$. This approximatiion is justified for analysing the large-wavelength limit, where $v_c$ dominates over $K$."
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"### Bulk dielectric models\n",
"\n",
"The most practical strategy is to directly propose analytical expressions directly for $P^{-1}$. The rationale is that these are fast to evaluate and their cost can thus be neglected in an SCF. For **bulk materials** this is feasible building on the justified approximation to ignore lattice-scale details. Mathematically one may (a) take the $q\\to0$ limit and (b) model $\\chi_0$ as a translation-independent operator. Such operators (compare to the Kinetic energy) are diagonal in Fourier space and are fully characterised by their Fourier multiplier $\\chi_0(q)$. Since $v_c$ is also translation-independent, this implies that the resulting model for the dielectric operator $P \\simeq \\varepsilon^\\dagger$ is translation-independent and its inverse can be directly computed as $P^{-1}(q) = \\frac{1}{P(q)}$ enabling an analytical computation of the inverse of the preconditioner from a dielectric model.\n",
"\n",
"For **metals** the observation $\\lim_{q\\to0} \\chi_0(q) \\simeq -D$ directly leads to the **Kerker preconditioner**\n",
"$$\n",
"P_\\text{Kerker}^{-1}(q) = \\left( 1 - \\frac{4\\pi -D}{|q|^2} \\right)^{-1} = \\frac{|q|^2}{|q|^2 + 4\\pi D}.\n",
"$$\n",
"The Kerker preconditioner is available in DFTK as `KerkerMixing` and `KerkerDosMixing` (which automatically determines the density of states from the current orbitals and occupations).\n",
"\n",
"For **semiconductors** and **insulators** one can identify $\\varepsilon_r = \\varepsilon(q = 0) = 1 + 4\\pi \\sigma_0$ (in the case of isotropic $\\sigma_0$), where $\\varepsilon_r$ can be interpreted as the macroscopic electronic dielectric constant. From this limit for long wavelengths a number of empirical models for $\\chi_0(q)$ and $\\varepsilon^\\dagger(q)$ have been proposed in the literature. A simple, two-parameter model is\n",
"$$\n",
"P_\\text{Dielectric}^{-1}(q) = \\frac{\\varepsilon_r + (\\varepsilon_r-1) \\frac{|q|^2}{k_\\text{TF}^2}}{1 + (\\varepsilon_r-1) \\frac{|q|^2}{k_\\text{TF}^2}},\n",
"$$\n",
"where $k_\\text{TF}$ is another parameter.\n",
"This model is available in DFTK as `DielectricMixing`.\n",
"\n",
"Below is a sketch of the three models using the appropriate setups for aluminium (a metal), gallium arsenide (a semiconductor, $\\varepsilon_r = 14.9$) and silica (an insulator, $\\varepsilon_r = 1.5$) for comparison:"
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "Plot{Plots.GRBackend() n=3}",
"image/png": "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",
"text/html": [
"<?xml version=\"1.0\" encoding=\"utf-8\"?>\n",
"<svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"600\" height=\"400\" viewBox=\"0 0 2400 1600\">\n",
"<defs>\n",
" <clipPath id=\"clip790\">\n",
" <rect x=\"0\" y=\"0\" width=\"2400\" height=\"1600\"/>\n",
" </clipPath>\n",
"</defs>\n",
"<path clip-path=\"url(#clip790)\" d=\"M0 1600 L2400 1600 L2400 0 L0 0 Z\" fill=\"#ffffff\" fill-rule=\"evenodd\" fill-opacity=\"1\"/>\n",
"<defs>\n",
" <clipPath id=\"clip791\">\n",
" <rect x=\"480\" y=\"0\" width=\"1681\" height=\"1600\"/>\n",
" </clipPath>\n",
"</defs>\n",
"<path clip-path=\"url(#clip790)\" d=\"M202.227 1423.18 L2352.76 1423.18 L2352.76 47.2441 L202.227 47.2441 Z\" fill=\"#ffffff\" fill-rule=\"evenodd\" fill-opacity=\"1\"/>\n",
"<defs>\n",
" <clipPath id=\"clip792\">\n",
" <rect x=\"202\" y=\"47\" width=\"2152\" height=\"1377\"/>\n",
" </clipPath>\n",
"</defs>\n",
"<polyline clip-path=\"url(#clip792)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"620.787,1423.18 620.787,47.2441 \"/>\n",
"<polyline clip-path=\"url(#clip792)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"1053.78,1423.18 1053.78,47.2441 \"/>\n",
"<polyline clip-path=\"url(#clip792)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"1486.77,1423.18 1486.77,47.2441 \"/>\n",
"<polyline clip-path=\"url(#clip792)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"1919.76,1423.18 1919.76,47.2441 \"/>\n",
"<polyline clip-path=\"url(#clip792)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"202.227,1423.18 2352.76,1423.18 \"/>\n",
"<polyline clip-path=\"url(#clip792)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"202.227,993.2 2352.76,993.2 \"/>\n",
"<polyline clip-path=\"url(#clip792)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"202.227,563.22 2352.76,563.22 \"/>\n",
"<polyline clip-path=\"url(#clip792)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"202.227,133.24 2352.76,133.24 \"/>\n",
"<polyline clip-path=\"url(#clip790)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"202.227,1423.18 2352.76,1423.18 \"/>\n",
"<polyline clip-path=\"url(#clip790)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"620.787,1423.18 620.787,1404.28 \"/>\n",
"<polyline clip-path=\"url(#clip790)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"1053.78,1423.18 1053.78,1404.28 \"/>\n",
"<polyline clip-path=\"url(#clip790)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"1486.77,1423.18 1486.77,1404.28 \"/>\n",
"<polyline clip-path=\"url(#clip790)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"1919.76,1423.18 1919.76,1404.28 \"/>\n",
"<path clip-path=\"url(#clip790)\" d=\"M598.495 1454.1 Q594.884 1454.1 593.055 1457.66 Q591.25 1461.2 591.25 1468.33 Q591.25 1475.44 593.055 1479.01 Q594.884 1482.55 598.495 1482.55 Q602.129 1482.55 603.935 1479.01 Q605.764 1475.44 605.764 1468.33 Q605.764 1461.2 603.935 1457.66 Q602.129 1454.1 598.495 1454.1 M598.495 1450.39 Q604.305 1450.39 607.361 1455 Q610.44 1459.58 610.44 1468.33 Q610.44 1477.06 607.361 1481.67 Q604.305 1486.25 598.495 1486.25 Q592.685 1486.25 589.606 1481.67 Q586.551 1477.06 586.551 1468.33 Q586.551 1459.58 589.606 1455 Q592.685 1450.39 598.495 1450.39 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M618.657 1479.7 L623.541 1479.7 L623.541 1485.58 L618.657 1485.58 L618.657 1479.7 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M647.893 1466.95 Q651.249 1467.66 653.124 1469.93 Q655.023 1472.2 655.023 1475.53 Q655.023 1480.65 651.504 1483.45 Q647.986 1486.25 641.504 1486.25 Q639.328 1486.25 637.013 1485.81 Q634.722 1485.39 632.268 1484.54 L632.268 1480.02 Q634.213 1481.16 636.527 1481.74 Q638.842 1482.32 641.365 1482.32 Q645.763 1482.32 648.055 1480.58 Q650.37 1478.84 650.37 1475.53 Q650.37 1472.48 648.217 1470.77 Q646.087 1469.03 642.268 1469.03 L638.24 1469.03 L638.24 1465.19 L642.453 1465.19 Q645.902 1465.19 647.731 1463.82 Q649.56 1462.43 649.56 1459.84 Q649.56 1457.18 647.662 1455.77 Q645.787 1454.33 642.268 1454.33 Q640.347 1454.33 638.148 1454.75 Q635.949 1455.16 633.31 1456.04 L633.31 1451.88 Q635.972 1451.14 638.287 1450.77 Q640.625 1450.39 642.685 1450.39 Q648.009 1450.39 651.111 1452.83 Q654.212 1455.23 654.212 1459.35 Q654.212 1462.22 652.569 1464.21 Q650.925 1466.18 647.893 1466.95 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M1031.08 1454.1 Q1027.47 1454.1 1025.64 1457.66 Q1023.84 1461.2 1023.84 1468.33 Q1023.84 1475.44 1025.64 1479.01 Q1027.47 1482.55 1031.08 1482.55 Q1034.72 1482.55 1036.52 1479.01 Q1038.35 1475.44 1038.35 1468.33 Q1038.35 1461.2 1036.52 1457.66 Q1034.72 1454.1 1031.08 1454.1 M1031.08 1450.39 Q1036.89 1450.39 1039.95 1455 Q1043.03 1459.58 1043.03 1468.33 Q1043.03 1477.06 1039.95 1481.67 Q1036.89 1486.25 1031.08 1486.25 Q1025.27 1486.25 1022.19 1481.67 Q1019.14 1477.06 1019.14 1468.33 Q1019.14 1459.58 1022.19 1455 Q1025.27 1450.39 1031.08 1450.39 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M1051.24 1479.7 L1056.13 1479.7 L1056.13 1485.58 L1051.24 1485.58 L1051.24 1479.7 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M1076.89 1466.44 Q1073.74 1466.44 1071.89 1468.59 Q1070.06 1470.74 1070.06 1474.49 Q1070.06 1478.22 1071.89 1480.39 Q1073.74 1482.55 1076.89 1482.55 Q1080.04 1482.55 1081.87 1480.39 Q1083.72 1478.22 1083.72 1474.49 Q1083.72 1470.74 1081.87 1468.59 Q1080.04 1466.44 1076.89 1466.44 M1086.17 1451.78 L1086.17 1456.04 Q1084.42 1455.21 1082.61 1454.77 Q1080.83 1454.33 1079.07 1454.33 Q1074.44 1454.33 1071.98 1457.45 Q1069.55 1460.58 1069.21 1466.9 Q1070.57 1464.89 1072.63 1463.82 Q1074.69 1462.73 1077.17 1462.73 Q1082.38 1462.73 1085.39 1465.9 Q1088.42 1469.05 1088.42 1474.49 Q1088.42 1479.82 1085.27 1483.03 Q1082.12 1486.25 1076.89 1486.25 Q1070.9 1486.25 1067.73 1481.67 Q1064.55 1477.06 1064.55 1468.33 Q1064.55 1460.14 1068.44 1455.28 Q1072.33 1450.39 1078.88 1450.39 Q1080.64 1450.39 1082.42 1450.74 Q1084.23 1451.09 1086.17 1451.78 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M1464.25 1454.1 Q1460.64 1454.1 1458.81 1457.66 Q1457 1461.2 1457 1468.33 Q1457 1475.44 1458.81 1479.01 Q1460.64 1482.55 1464.25 1482.55 Q1467.88 1482.55 1469.69 1479.01 Q1471.52 1475.44 1471.52 1468.33 Q1471.52 1461.2 1469.69 1457.66 Q1467.88 1454.1 1464.25 1454.1 M1464.25 1450.39 Q1470.06 1450.39 1473.11 1455 Q1476.19 1459.58 1476.19 1468.33 Q1476.19 1477.06 1473.11 1481.67 Q1470.06 1486.25 1464.25 1486.25 Q1458.44 1486.25 1455.36 1481.67 Q1452.3 1477.06 1452.3 1468.33 Q1452.3 1459.58 1455.36 1455 Q1458.44 1450.39 1464.25 1450.39 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M1484.41 1479.7 L1489.29 1479.7 L1489.29 1485.58 L1484.41 1485.58 L1484.41 1479.7 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M1499.62 1484.86 L1499.62 1480.6 Q1501.38 1481.44 1503.18 1481.88 Q1504.99 1482.32 1506.72 1482.32 Q1511.35 1482.32 1513.79 1479.21 Q1516.24 1476.09 1516.59 1469.75 Q1515.24 1471.74 1513.18 1472.8 Q1511.12 1473.87 1508.62 1473.87 Q1503.44 1473.87 1500.41 1470.74 Q1497.4 1467.59 1497.4 1462.15 Q1497.4 1456.83 1500.54 1453.61 Q1503.69 1450.39 1508.92 1450.39 Q1514.92 1450.39 1518.07 1455 Q1521.24 1459.58 1521.24 1468.33 Q1521.24 1476.51 1517.35 1481.39 Q1513.48 1486.25 1506.93 1486.25 Q1505.17 1486.25 1503.37 1485.9 Q1501.56 1485.56 1499.62 1484.86 M1508.92 1470.21 Q1512.07 1470.21 1513.9 1468.06 Q1515.75 1465.9 1515.75 1462.15 Q1515.75 1458.43 1513.9 1456.27 Q1512.07 1454.1 1508.92 1454.1 Q1505.78 1454.1 1503.92 1456.27 Q1502.1 1458.43 1502.1 1462.15 Q1502.1 1465.9 1503.92 1468.06 Q1505.78 1470.21 1508.92 1470.21 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M1887.72 1481.64 L1895.35 1481.64 L1895.35 1455.28 L1887.04 1456.95 L1887.04 1452.69 L1895.31 1451.02 L1899.98 1451.02 L1899.98 1481.64 L1907.62 1481.64 L1907.62 1485.58 L1887.72 1485.58 L1887.72 1481.64 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M1917.07 1479.7 L1921.95 1479.7 L1921.95 1485.58 L1917.07 1485.58 L1917.07 1479.7 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M1936.16 1481.64 L1952.48 1481.64 L1952.48 1485.58 L1930.54 1485.58 L1930.54 1481.64 Q1933.2 1478.89 1937.78 1474.26 Q1942.39 1469.61 1943.57 1468.27 Q1945.82 1465.74 1946.7 1464.01 Q1947.6 1462.25 1947.6 1460.56 Q1947.6 1457.8 1945.65 1456.07 Q1943.73 1454.33 1940.63 1454.33 Q1938.43 1454.33 1935.98 1455.09 Q1933.55 1455.86 1930.77 1457.41 L1930.77 1452.69 Q1933.59 1451.55 1936.05 1450.97 Q1938.5 1450.39 1940.54 1450.39 Q1945.91 1450.39 1949.1 1453.08 Q1952.3 1455.77 1952.3 1460.26 Q1952.3 1462.39 1951.49 1464.31 Q1950.7 1466.2 1948.59 1468.8 Q1948.02 1469.47 1944.91 1472.69 Q1941.81 1475.88 1936.16 1481.64 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M1267.61 1550.25 Q1267.61 1556.71 1270.25 1560.4 Q1272.92 1564.07 1277.57 1564.07 Q1282.22 1564.07 1284.89 1560.4 Q1287.57 1556.71 1287.57 1550.25 Q1287.57 1543.79 1284.89 1540.13 Q1282.22 1536.44 1277.57 1536.44 Q1272.92 1536.44 1270.25 1540.13 Q1267.61 1543.79 1267.61 1550.25 M1287.57 1562.7 Q1285.72 1565.88 1282.89 1567.44 Q1280.09 1568.97 1276.14 1568.97 Q1269.68 1568.97 1265.6 1563.81 Q1261.56 1558.65 1261.56 1550.25 Q1261.56 1541.85 1265.6 1536.69 Q1269.68 1531.54 1276.14 1531.54 Q1280.09 1531.54 1282.89 1533.1 Q1285.72 1534.62 1287.57 1537.81 L1287.57 1532.4 L1293.42 1532.4 L1293.42 1581.6 L1287.57 1581.6 L1287.57 1562.7 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><polyline clip-path=\"url(#clip790)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"202.227,1423.18 202.227,47.2441 \"/>\n",
"<polyline clip-path=\"url(#clip790)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"202.227,1423.18 221.125,1423.18 \"/>\n",
"<polyline clip-path=\"url(#clip790)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"202.227,993.2 221.125,993.2 \"/>\n",
"<polyline clip-path=\"url(#clip790)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"202.227,563.22 221.125,563.22 \"/>\n",
"<polyline clip-path=\"url(#clip790)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"202.227,133.24 221.125,133.24 \"/>\n",
"<path clip-path=\"url(#clip790)\" d=\"M154.283 1408.98 Q150.672 1408.98 148.843 1412.54 Q147.038 1416.08 147.038 1423.21 Q147.038 1430.32 148.843 1433.89 Q150.672 1437.43 154.283 1437.43 Q157.917 1437.43 159.723 1433.89 Q161.552 1430.32 161.552 1423.21 Q161.552 1416.08 159.723 1412.54 Q157.917 1408.98 154.283 1408.98 M154.283 1405.27 Q160.093 1405.27 163.149 1409.88 Q166.227 1414.46 166.227 1423.21 Q166.227 1431.94 163.149 1436.55 Q160.093 1441.13 154.283 1441.13 Q148.473 1441.13 145.394 1436.55 Q142.339 1431.94 142.339 1423.21 Q142.339 1414.46 145.394 1409.88 Q148.473 1405.27 154.283 1405.27 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M145.325 975.92 L163.681 975.92 L163.681 979.855 L149.607 979.855 L149.607 988.327 Q150.626 987.98 151.644 987.818 Q152.663 987.633 153.681 987.633 Q159.468 987.633 162.848 990.804 Q166.227 993.975 166.227 999.392 Q166.227 1004.97 162.755 1008.07 Q159.283 1011.15 152.964 1011.15 Q150.788 1011.15 148.519 1010.78 Q146.274 1010.41 143.866 1009.67 L143.866 1004.97 Q145.95 1006.1 148.172 1006.66 Q150.394 1007.22 152.871 1007.22 Q156.876 1007.22 159.214 1005.11 Q161.552 1003 161.552 999.392 Q161.552 995.781 159.214 993.674 Q156.876 991.568 152.871 991.568 Q150.996 991.568 149.121 991.985 Q147.269 992.401 145.325 993.281 L145.325 975.92 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M114.931 576.565 L122.57 576.565 L122.57 550.199 L114.26 551.866 L114.26 547.607 L122.524 545.94 L127.2 545.94 L127.2 576.565 L134.839 576.565 L134.839 580.5 L114.931 580.5 L114.931 576.565 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M154.283 549.019 Q150.672 549.019 148.843 552.583 Q147.038 556.125 147.038 563.255 Q147.038 570.361 148.843 573.926 Q150.672 577.468 154.283 577.468 Q157.917 577.468 159.723 573.926 Q161.552 570.361 161.552 563.255 Q161.552 556.125 159.723 552.583 Q157.917 549.019 154.283 549.019 M154.283 545.315 Q160.093 545.315 163.149 549.921 Q166.227 554.505 166.227 563.255 Q166.227 571.982 163.149 576.588 Q160.093 581.171 154.283 581.171 Q148.473 581.171 145.394 576.588 Q142.339 571.982 142.339 563.255 Q142.339 554.505 145.394 549.921 Q148.473 545.315 154.283 545.315 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M115.927 146.585 L123.566 146.585 L123.566 120.219 L115.256 121.886 L115.256 117.627 L123.519 115.96 L128.195 115.96 L128.195 146.585 L135.834 146.585 L135.834 150.52 L115.927 150.52 L115.927 146.585 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M145.325 115.96 L163.681 115.96 L163.681 119.895 L149.607 119.895 L149.607 128.367 Q150.626 128.02 151.644 127.858 Q152.663 127.673 153.681 127.673 Q159.468 127.673 162.848 130.844 Q166.227 134.016 166.227 139.432 Q166.227 145.011 162.755 148.113 Q159.283 151.191 152.964 151.191 Q150.788 151.191 148.519 150.821 Q146.274 150.451 143.866 149.71 L143.866 145.011 Q145.95 146.145 148.172 146.701 Q150.394 147.256 152.871 147.256 Q156.876 147.256 159.214 145.15 Q161.552 143.043 161.552 139.432 Q161.552 135.821 159.214 133.715 Q156.876 131.608 152.871 131.608 Q150.996 131.608 149.121 132.025 Q147.269 132.441 145.325 133.321 L145.325 115.96 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M44.7797 785.692 Q44.0158 789.257 41.947 791.167 Q39.91 793.076 36.9499 793.076 Q32.4621 793.076 29.9476 789.448 Q27.465 785.851 27.465 779.613 Q27.465 777.194 27.8469 774.488 Q28.2289 771.783 28.9928 768.664 L34.3081 768.664 Q33.3851 771.751 32.9713 774.297 Q32.5576 776.876 32.5576 779.135 Q32.5576 782.923 34.0217 785.119 Q35.4858 787.347 37.5228 787.347 Q39.7508 787.347 41.1831 785.183 Q42.5836 783.05 42.5836 779.358 L42.5836 774.425 L47.4215 774.425 L47.4215 779.135 Q47.4215 783.496 49.0447 785.788 Q50.8271 788.27 53.6281 788.27 Q56.4926 788.27 58.275 785.597 Q60.0574 782.891 60.0574 778.085 Q60.0574 775.125 59.4845 772.42 Q58.8798 769.714 57.7021 767.454 L63.1448 767.454 Q64.036 770.319 64.4816 772.992 Q64.9272 775.698 64.9272 778.244 Q64.9272 785.819 62.0308 789.925 Q59.1344 794.031 53.6281 794.031 Q50.1906 794.031 47.8671 791.835 Q45.5436 789.639 44.7797 785.692 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M14.5426 742.819 Q21.8632 747.084 29.0246 749.153 Q36.186 751.222 43.5384 751.222 Q50.8908 751.222 58.1159 749.153 Q65.3091 747.052 72.5979 742.819 L72.5979 747.912 Q65.1182 752.686 57.8931 755.073 Q50.668 757.428 43.5384 757.428 Q36.4406 757.428 29.2474 755.073 Q22.0542 752.718 14.5426 747.912 L14.5426 742.819 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M46.212 727.955 Q52.6732 727.955 56.3653 725.313 Q60.0256 722.64 60.0256 717.993 Q60.0256 713.346 56.3653 710.672 Q52.6732 707.999 46.212 707.999 Q39.7508 707.999 36.0905 710.672 Q32.3984 713.346 32.3984 717.993 Q32.3984 722.64 36.0905 725.313 Q39.7508 727.955 46.212 727.955 M58.657 707.999 Q61.8398 709.845 63.3994 712.677 Q64.9272 715.478 64.9272 719.425 Q64.9272 725.886 59.771 729.96 Q54.6147 734.002 46.212 734.002 Q37.8093 734.002 32.6531 729.96 Q27.4968 725.886 27.4968 719.425 Q27.4968 715.478 29.0564 712.677 Q30.5842 709.845 33.7671 707.999 L28.3562 707.999 L28.3562 702.142 L77.5631 702.142 L77.5631 707.999 L58.657 707.999 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M14.5426 691.002 L14.5426 685.91 Q22.0542 681.135 29.2474 678.78 Q36.4406 676.393 43.5384 676.393 Q50.668 676.393 57.8931 678.78 Q65.1182 681.135 72.5979 685.91 L72.5979 691.002 Q65.3091 686.769 58.1159 684.7 Q50.8908 682.599 43.5384 682.599 Q36.186 682.599 29.0246 684.7 Q21.8632 686.769 14.5426 691.002 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><polyline clip-path=\"url(#clip792)\" style=\"stroke:#009af9; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"202.227,-858623 202.401,-838320 202.574,-818729 202.748,-799815 202.921,-781547 203.095,-763898 203.268,-746839 203.442,-730344 203.615,-714388 203.962,-684004 204.309,-655514 204.656,-628765 205.003,-603617 205.35,-579945 205.696,-557635 206.043,-536586 206.39,-516704 206.737,-497904 207.084,-480109 207.431,-463249 207.778,-447259 208.125,-432081 208.472,-417660 208.819,-403947 209.165,-390897 209.512,-378467 209.859,-366618 210.206,-355316 210.553,-344526 211.247,-324365 211.941,-305917 212.634,-288994 213.328,-273430 214.022,-259086 214.716,-245836 215.41,-233572 216.103,-222199 216.797,-211632 217.491,-201797 218.185,-192628 218.879,-184066 220.266,-168560 221.654,-154920 222.348,-148708 223.041,-142859 223.735,-137346 224.429,-132143 226.461,-118484 228.492,-106819 230.524,-96777.9 232.556,-88073 234.588,-80477.3 236.619,-73809.9 238.651,-67925.5 240.683,-62706.2 244.746,-53893.3 248.81,-46781.8 252.873,-40960.4 256.937,-36134.8 265.064,-28666.9 273.191,-23227.8 281.318,-19144 289.445,-16000 305.699,-11549.4 321.953,-8615.98 338.207,-6581.07 354.461,-5111.94 384.706,-3282.94 414.951,-2134.53 455.491,-1162.64 496.031,-548.315 563.029,64.8796 625.329,401.411 703.538,663.699 773.692,815.326 853.993,933.548 914.017,997.514 990.79,1059.36 1060.86,1102.17 1140.61,1139.86 1203.83,1163.65 1282.37,1187.66 1342.52,1202.83 1427.32,1220.59 1490.69,1231.65 1562.76,1242.43 1634.13,1251.55 1712.66,1260.14 1772.63,1265.86 1848.32,1272.21 1918.32,1277.36 1990.52,1282.06 2063.69,1286.28 2140.1,1290.18 2200.3,1292.95 2337.38,1298.41 2352.76,1298.96 \"/>\n",
"<polyline clip-path=\"url(#clip792)\" style=\"stroke:#e26f46; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" stroke-dasharray=\"16, 10\" points=\"202.227,143.499 207.778,145.016 213.328,147.017 218.879,149.497 224.429,152.449 232.556,157.61 240.683,163.742 248.81,170.814 256.937,178.792 265.064,187.637 273.191,197.307 281.318,207.756 289.445,218.939 305.699,243.307 321.953,270.005 338.207,298.622 354.461,328.752 369.583,357.804 384.706,387.538 399.829,417.682 414.951,447.996 435.221,488.519 455.491,528.52 475.761,567.646 496.031,605.624 512.781,635.994 529.53,665.36 546.279,693.664 563.029,720.872 578.604,745.173 594.179,768.507 609.754,790.881 625.329,812.309 644.882,837.897 664.434,862.072 683.986,884.889 703.538,906.408 721.077,924.659 738.615,941.963 756.154,958.368 773.692,973.919 793.767,990.728 813.842,1006.54 833.917,1021.43 853.993,1035.44 884.005,1054.88 914.017,1072.68 952.403,1093.29 990.79,1111.75 1025.83,1126.96 1060.86,1140.78 1100.73,1155 1140.61,1167.82 1172.22,1177.09 1203.83,1185.65 1282.37,1204.29 1342.52,1216.41 1427.32,1230.95 1490.69,1240.22 1562.76,1249.39 1634.13,1257.27 1712.66,1264.81 1772.63,1269.88 1848.32,1275.56 1918.32,1280.22 1990.52,1284.49 2063.69,1288.36 2140.1,1291.96 2200.3,1294.53 2337.38,1299.63 2352.76,1300.15 \"/>\n",
"<polyline clip-path=\"url(#clip792)\" style=\"stroke:#3da44d; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" stroke-dasharray=\"16, 8, 2, 8\" points=\"202.227,1294.19 207.778,1294.19 213.328,1294.19 218.879,1294.2 224.429,1294.2 256.937,1294.24 289.445,1294.29 321.953,1294.37 354.461,1294.47 384.706,1294.58 414.951,1294.71 455.491,1294.91 496.031,1295.14 529.53,1295.36 563.029,1295.59 594.179,1295.83 625.329,1296.07 664.434,1296.41 703.538,1296.77 738.615,1297.1 773.692,1297.46 853.993,1298.33 914.017,1299.02 990.79,1299.95 1060.86,1300.84 1140.61,1301.88 1203.83,1302.72 1282.37,1303.79 1342.52,1304.61 1427.32,1305.77 1490.69,1306.63 1562.76,1307.61 1634.13,1308.56 1712.66,1309.59 1772.63,1310.36 1848.32,1311.31 1918.32,1312.17 1990.52,1313.03 2063.69,1313.87 2140.1,1314.73 2200.3,1315.38 2337.38,1316.8 2352.76,1316.95 \"/>\n",
"<path clip-path=\"url(#clip790)\" d=\"M1502.9 300.469 L2281.07 300.469 L2281.07 93.1086 L1502.9 93.1086 Z\" fill=\"#ffffff\" fill-rule=\"evenodd\" fill-opacity=\"1\"/>\n",
"<polyline clip-path=\"url(#clip790)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"1502.9,300.469 2281.07,300.469 2281.07,93.1086 1502.9,93.1086 1502.9,300.469 \"/>\n",
"<polyline clip-path=\"url(#clip790)\" style=\"stroke:#009af9; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"1526.79,144.949 1670.16,144.949 \"/>\n",
"<path clip-path=\"url(#clip790)\" d=\"M1707.46 149.196 Q1702.3 149.196 1700.3 150.377 Q1698.31 151.557 1698.31 154.405 Q1698.31 156.673 1699.8 158.016 Q1701.3 159.335 1703.87 159.335 Q1707.41 159.335 1709.54 156.835 Q1711.69 154.312 1711.69 150.145 L1711.69 149.196 L1707.46 149.196 M1715.95 147.437 L1715.95 162.229 L1711.69 162.229 L1711.69 158.293 Q1710.24 160.655 1708.06 161.789 Q1705.88 162.9 1702.74 162.9 Q1698.75 162.9 1696.39 160.678 Q1694.05 158.432 1694.05 154.682 Q1694.05 150.307 1696.97 148.085 Q1699.91 145.863 1705.72 145.863 L1711.69 145.863 L1711.69 145.446 Q1711.69 142.507 1709.75 140.909 Q1707.83 139.289 1704.33 139.289 Q1702.11 139.289 1700 139.821 Q1697.9 140.354 1695.95 141.419 L1695.95 137.483 Q1698.29 136.581 1700.49 136.141 Q1702.69 135.678 1704.77 135.678 Q1710.4 135.678 1713.18 138.594 Q1715.95 141.511 1715.95 147.437 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M1724.73 126.21 L1728.99 126.21 L1728.99 162.229 L1724.73 162.229 L1724.73 126.21 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M1737.46 151.997 L1737.46 136.303 L1741.72 136.303 L1741.72 151.835 Q1741.72 155.516 1743.15 157.368 Q1744.59 159.196 1747.46 159.196 Q1750.91 159.196 1752.9 156.997 Q1754.91 154.798 1754.91 151.002 L1754.91 136.303 L1759.17 136.303 L1759.17 162.229 L1754.91 162.229 L1754.91 158.247 Q1753.36 160.608 1751.3 161.766 Q1749.26 162.9 1746.55 162.9 Q1742.09 162.9 1739.77 160.122 Q1737.46 157.344 1737.46 151.997 M1748.17 135.678 L1748.17 135.678 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M1788.13 141.28 Q1789.73 138.409 1791.95 137.044 Q1794.17 135.678 1797.18 135.678 Q1801.23 135.678 1803.43 138.525 Q1805.63 141.349 1805.63 146.581 L1805.63 162.229 L1801.35 162.229 L1801.35 146.719 Q1801.35 142.993 1800.03 141.187 Q1798.71 139.382 1796 139.382 Q1792.69 139.382 1790.77 141.581 Q1788.85 143.78 1788.85 147.576 L1788.85 162.229 L1784.56 162.229 L1784.56 146.719 Q1784.56 142.969 1783.24 141.187 Q1781.92 139.382 1779.17 139.382 Q1775.91 139.382 1773.99 141.604 Q1772.06 143.803 1772.06 147.576 L1772.06 162.229 L1767.78 162.229 L1767.78 136.303 L1772.06 136.303 L1772.06 140.331 Q1773.52 137.946 1775.56 136.812 Q1777.6 135.678 1780.4 135.678 Q1783.22 135.678 1785.19 137.113 Q1787.18 138.548 1788.13 141.28 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M1814.12 136.303 L1818.38 136.303 L1818.38 162.229 L1814.12 162.229 L1814.12 136.303 M1814.12 126.21 L1818.38 126.21 L1818.38 131.604 L1814.12 131.604 L1814.12 126.21 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M1848.85 146.581 L1848.85 162.229 L1844.59 162.229 L1844.59 146.719 Q1844.59 143.039 1843.15 141.21 Q1841.72 139.382 1838.85 139.382 Q1835.4 139.382 1833.41 141.581 Q1831.42 143.78 1831.42 147.576 L1831.42 162.229 L1827.13 162.229 L1827.13 136.303 L1831.42 136.303 L1831.42 140.331 Q1832.94 137.993 1835 136.835 Q1837.09 135.678 1839.79 135.678 Q1844.26 135.678 1846.55 138.456 Q1848.85 141.21 1848.85 146.581 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M1857.34 136.303 L1861.6 136.303 L1861.6 162.229 L1857.34 162.229 L1857.34 136.303 M1857.34 126.21 L1861.6 126.21 L1861.6 131.604 L1857.34 131.604 L1857.34 126.21 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M1870.07 151.997 L1870.07 136.303 L1874.33 136.303 L1874.33 151.835 Q1874.33 155.516 1875.77 157.368 Q1877.2 159.196 1880.07 159.196 Q1883.52 159.196 1885.51 156.997 Q1887.53 154.798 1887.53 151.002 L1887.53 136.303 L1891.79 136.303 L1891.79 162.229 L1887.53 162.229 L1887.53 158.247 Q1885.98 160.608 1883.91 161.766 Q1881.88 162.9 1879.17 162.9 Q1874.7 162.9 1872.39 160.122 Q1870.07 157.344 1870.07 151.997 M1880.79 135.678 L1880.79 135.678 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M1920.74 141.28 Q1922.34 138.409 1924.56 137.044 Q1926.79 135.678 1929.79 135.678 Q1933.85 135.678 1936.04 138.525 Q1938.24 141.349 1938.24 146.581 L1938.24 162.229 L1933.96 162.229 L1933.96 146.719 Q1933.96 142.993 1932.64 141.187 Q1931.32 139.382 1928.61 139.382 Q1925.3 139.382 1923.38 141.581 Q1921.46 143.78 1921.46 147.576 L1921.46 162.229 L1917.18 162.229 L1917.18 146.719 Q1917.18 142.969 1915.86 141.187 Q1914.54 139.382 1911.79 139.382 Q1908.52 139.382 1906.6 141.604 Q1904.68 143.803 1904.68 147.576 L1904.68 162.229 L1900.4 162.229 L1900.4 136.303 L1904.68 136.303 L1904.68 140.331 Q1906.14 137.946 1908.17 136.812 Q1910.21 135.678 1913.01 135.678 Q1915.84 135.678 1917.8 137.113 Q1919.79 138.548 1920.74 141.28 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M1972.04 126.257 Q1968.94 131.581 1967.43 136.789 Q1965.93 141.997 1965.93 147.344 Q1965.93 152.692 1967.43 157.946 Q1968.96 163.178 1972.04 168.479 L1968.34 168.479 Q1964.86 163.039 1963.13 157.784 Q1961.41 152.53 1961.41 147.344 Q1961.41 142.182 1963.13 136.951 Q1964.84 131.72 1968.34 126.257 L1972.04 126.257 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M1992.04 132.275 L1985.7 149.474 L1998.41 149.474 L1992.04 132.275 M1989.4 127.669 L1994.7 127.669 L2007.87 162.229 L2003.01 162.229 L1999.86 153.363 L1984.28 153.363 L1981.14 162.229 L1976.21 162.229 L1989.4 127.669 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M2012.73 126.21 L2016.99 126.21 L2016.99 162.229 L2012.73 162.229 L2012.73 126.21 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M2025.23 126.257 L2028.94 126.257 Q2032.41 131.72 2034.12 136.951 Q2035.86 142.182 2035.86 147.344 Q2035.86 152.53 2034.12 157.784 Q2032.41 163.039 2028.94 168.479 L2025.23 168.479 Q2028.31 163.178 2029.82 157.946 Q2031.34 152.692 2031.34 147.344 Q2031.34 141.997 2029.82 136.789 Q2028.31 131.581 2025.23 126.257 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><polyline clip-path=\"url(#clip790)\" style=\"stroke:#e26f46; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" stroke-dasharray=\"16, 10\" points=\"1526.79,196.789 1670.16,196.789 \"/>\n",
"<path clip-path=\"url(#clip790)\" d=\"M1712.97 200.805 Q1712.97 196.175 1711.05 193.629 Q1709.15 191.083 1705.7 191.083 Q1702.27 191.083 1700.35 193.629 Q1698.45 196.175 1698.45 200.805 Q1698.45 205.411 1700.35 207.958 Q1702.27 210.504 1705.7 210.504 Q1709.15 210.504 1711.05 207.958 Q1712.97 205.411 1712.97 200.805 M1717.23 210.851 Q1717.23 217.471 1714.29 220.689 Q1711.35 223.93 1705.28 223.93 Q1703.04 223.93 1701.05 223.582 Q1699.05 223.258 1697.18 222.564 L1697.18 218.42 Q1699.05 219.439 1700.88 219.925 Q1702.71 220.411 1704.61 220.411 Q1708.8 220.411 1710.88 218.212 Q1712.97 216.036 1712.97 211.615 L1712.97 209.508 Q1711.65 211.8 1709.59 212.934 Q1707.53 214.069 1704.66 214.069 Q1699.89 214.069 1696.97 210.434 Q1694.05 206.8 1694.05 200.805 Q1694.05 194.786 1696.97 191.152 Q1699.89 187.518 1704.66 187.518 Q1707.53 187.518 1709.59 188.652 Q1711.65 189.786 1712.97 192.078 L1712.97 188.143 L1717.23 188.143 L1717.23 210.851 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M1737.78 201.036 Q1732.62 201.036 1730.63 202.217 Q1728.64 203.397 1728.64 206.245 Q1728.64 208.513 1730.12 209.856 Q1731.62 211.175 1734.19 211.175 Q1737.74 211.175 1739.86 208.675 Q1742.02 206.152 1742.02 201.985 L1742.02 201.036 L1737.78 201.036 M1746.28 199.277 L1746.28 214.069 L1742.02 214.069 L1742.02 210.133 Q1740.56 212.495 1738.38 213.629 Q1736.21 214.74 1733.06 214.74 Q1729.08 214.74 1726.72 212.518 Q1724.38 210.272 1724.38 206.522 Q1724.38 202.147 1727.3 199.925 Q1730.24 197.703 1736.05 197.703 L1742.02 197.703 L1742.02 197.286 Q1742.02 194.347 1740.07 192.749 Q1738.15 191.129 1734.66 191.129 Q1732.43 191.129 1730.33 191.661 Q1728.22 192.194 1726.28 193.259 L1726.28 189.323 Q1728.61 188.421 1730.81 187.981 Q1733.01 187.518 1735.1 187.518 Q1740.72 187.518 1743.5 190.434 Q1746.28 193.351 1746.28 199.277 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M1755.05 178.05 L1759.31 178.05 L1759.31 214.069 L1755.05 214.069 L1755.05 178.05 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M1768.22 178.05 L1772.48 178.05 L1772.48 214.069 L1768.22 214.069 L1768.22 178.05 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M1781.39 188.143 L1785.65 188.143 L1785.65 214.069 L1781.39 214.069 L1781.39 188.143 M1781.39 178.05 L1785.65 178.05 L1785.65 183.444 L1781.39 183.444 L1781.39 178.05 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M1794.12 203.837 L1794.12 188.143 L1798.38 188.143 L1798.38 203.675 Q1798.38 207.356 1799.82 209.208 Q1801.25 211.036 1804.12 211.036 Q1807.57 211.036 1809.56 208.837 Q1811.58 206.638 1811.58 202.842 L1811.58 188.143 L1815.84 188.143 L1815.84 214.069 L1811.58 214.069 L1811.58 210.087 Q1810.03 212.448 1807.97 213.606 Q1805.93 214.74 1803.22 214.74 Q1798.75 214.74 1796.44 211.962 Q1794.12 209.184 1794.12 203.837 M1804.84 187.518 L1804.84 187.518 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M1844.79 193.12 Q1846.39 190.249 1848.61 188.884 Q1850.84 187.518 1853.85 187.518 Q1857.9 187.518 1860.1 190.365 Q1862.29 193.189 1862.29 198.421 L1862.29 214.069 L1858.01 214.069 L1858.01 198.559 Q1858.01 194.833 1856.69 193.027 Q1855.37 191.222 1852.67 191.222 Q1849.35 191.222 1847.43 193.421 Q1845.51 195.62 1845.51 199.416 L1845.51 214.069 L1841.23 214.069 L1841.23 198.559 Q1841.23 194.809 1839.91 193.027 Q1838.59 191.222 1835.84 191.222 Q1832.57 191.222 1830.65 193.444 Q1828.73 195.643 1828.73 199.416 L1828.73 214.069 L1824.45 214.069 L1824.45 188.143 L1828.73 188.143 L1828.73 192.171 Q1830.19 189.786 1832.23 188.652 Q1834.26 187.518 1837.06 187.518 Q1839.89 187.518 1841.86 188.953 Q1843.85 190.388 1844.79 193.12 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M1897.64 201.036 Q1892.48 201.036 1890.49 202.217 Q1888.5 203.397 1888.5 206.245 Q1888.5 208.513 1889.98 209.856 Q1891.48 211.175 1894.05 211.175 Q1897.6 211.175 1899.73 208.675 Q1901.88 206.152 1901.88 201.985 L1901.88 201.036 L1897.64 201.036 M1906.14 199.277 L1906.14 214.069 L1901.88 214.069 L1901.88 210.133 Q1900.42 212.495 1898.24 213.629 Q1896.07 214.74 1892.92 214.74 Q1888.94 214.74 1886.58 212.518 Q1884.24 210.272 1884.24 206.522 Q1884.24 202.147 1887.16 199.925 Q1890.1 197.703 1895.91 197.703 L1901.88 197.703 L1901.88 197.286 Q1901.88 194.347 1899.93 192.749 Q1898.01 191.129 1894.52 191.129 Q1892.29 191.129 1890.19 191.661 Q1888.08 192.194 1886.14 193.259 L1886.14 189.323 Q1888.48 188.421 1890.67 187.981 Q1892.87 187.518 1894.96 187.518 Q1900.58 187.518 1903.36 190.434 Q1906.14 193.351 1906.14 199.277 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M1929.93 192.124 Q1929.22 191.708 1928.36 191.522 Q1927.53 191.314 1926.51 191.314 Q1922.9 191.314 1920.95 193.675 Q1919.03 196.013 1919.03 200.411 L1919.03 214.069 L1914.75 214.069 L1914.75 188.143 L1919.03 188.143 L1919.03 192.171 Q1920.37 189.809 1922.53 188.675 Q1924.68 187.518 1927.76 187.518 Q1928.2 187.518 1928.73 187.587 Q1929.26 187.634 1929.91 187.749 L1929.93 192.124 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M1950.93 188.907 L1950.93 192.934 Q1949.12 192.009 1947.18 191.546 Q1945.23 191.083 1943.15 191.083 Q1939.98 191.083 1938.38 192.055 Q1936.81 193.027 1936.81 194.971 Q1936.81 196.453 1937.94 197.309 Q1939.08 198.143 1942.5 198.907 L1943.96 199.231 Q1948.5 200.203 1950.4 201.985 Q1952.32 203.745 1952.32 206.916 Q1952.32 210.527 1949.45 212.633 Q1946.6 214.74 1941.6 214.74 Q1939.52 214.74 1937.25 214.323 Q1935 213.93 1932.5 213.12 L1932.5 208.721 Q1934.86 209.948 1937.16 210.573 Q1939.45 211.175 1941.69 211.175 Q1944.7 211.175 1946.32 210.157 Q1947.94 209.115 1947.94 207.24 Q1947.94 205.504 1946.76 204.578 Q1945.6 203.652 1941.65 202.796 L1940.16 202.448 Q1936.21 201.615 1934.45 199.902 Q1932.69 198.166 1932.69 195.157 Q1932.69 191.499 1935.28 189.509 Q1937.87 187.518 1942.64 187.518 Q1945 187.518 1947.09 187.865 Q1949.17 188.212 1950.93 188.907 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M1981.28 200.041 L1981.28 202.124 L1961.69 202.124 Q1961.97 206.522 1964.33 208.837 Q1966.72 211.129 1970.95 211.129 Q1973.41 211.129 1975.7 210.527 Q1978.01 209.925 1980.28 208.721 L1980.28 212.749 Q1977.99 213.721 1975.58 214.231 Q1973.17 214.74 1970.7 214.74 Q1964.49 214.74 1960.86 211.129 Q1957.25 207.518 1957.25 201.36 Q1957.25 194.995 1960.67 191.268 Q1964.12 187.518 1969.96 187.518 Q1975.19 187.518 1978.22 190.897 Q1981.28 194.254 1981.28 200.041 M1977.02 198.791 Q1976.97 195.296 1975.05 193.212 Q1973.15 191.129 1970 191.129 Q1966.44 191.129 1964.28 193.143 Q1962.16 195.157 1961.83 198.814 L1977.02 198.791 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M2009.82 198.421 L2009.82 214.069 L2005.56 214.069 L2005.56 198.559 Q2005.56 194.879 2004.12 193.05 Q2002.69 191.222 1999.82 191.222 Q1996.37 191.222 1994.38 193.421 Q1992.39 195.62 1992.39 199.416 L1992.39 214.069 L1988.1 214.069 L1988.1 188.143 L1992.39 188.143 L1992.39 192.171 Q1993.91 189.833 1995.97 188.675 Q1998.06 187.518 2000.77 187.518 Q2005.23 187.518 2007.53 190.296 Q2009.82 193.05 2009.82 198.421 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M2018.31 188.143 L2022.57 188.143 L2022.57 214.069 L2018.31 214.069 L2018.31 188.143 M2018.31 178.05 L2022.57 178.05 L2022.57 183.444 L2018.31 183.444 L2018.31 178.05 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M2048.54 192.078 L2048.54 178.05 L2052.8 178.05 L2052.8 214.069 L2048.54 214.069 L2048.54 210.18 Q2047.2 212.495 2045.14 213.629 Q2043.1 214.74 2040.23 214.74 Q2035.53 214.74 2032.57 210.99 Q2029.63 207.24 2029.63 201.129 Q2029.63 195.018 2032.57 191.268 Q2035.53 187.518 2040.23 187.518 Q2043.1 187.518 2045.14 188.652 Q2047.2 189.763 2048.54 192.078 M2034.03 201.129 Q2034.03 205.828 2035.95 208.513 Q2037.9 211.175 2041.28 211.175 Q2044.65 211.175 2046.6 208.513 Q2048.54 205.828 2048.54 201.129 Q2048.54 196.43 2046.6 193.768 Q2044.65 191.083 2041.28 191.083 Q2037.9 191.083 2035.95 193.768 Q2034.03 196.43 2034.03 201.129 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M2083.75 200.041 L2083.75 202.124 L2064.17 202.124 Q2064.45 206.522 2066.81 208.837 Q2069.19 211.129 2073.43 211.129 Q2075.88 211.129 2078.17 210.527 Q2080.49 209.925 2082.76 208.721 L2082.76 212.749 Q2080.46 213.721 2078.06 214.231 Q2075.65 214.74 2073.17 214.74 Q2066.97 214.74 2063.34 211.129 Q2059.72 207.518 2059.72 201.36 Q2059.72 194.995 2063.15 191.268 Q2066.6 187.518 2072.43 187.518 Q2077.66 187.518 2080.7 190.897 Q2083.75 194.254 2083.75 200.041 M2079.49 198.791 Q2079.45 195.296 2077.53 193.212 Q2075.63 191.129 2072.48 191.129 Q2068.91 191.129 2066.76 193.143 Q2064.63 195.157 2064.31 198.814 L2079.49 198.791 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M2116.04 178.097 Q2112.94 183.421 2111.44 188.629 Q2109.93 193.837 2109.93 199.184 Q2109.93 204.532 2111.44 209.786 Q2112.96 215.018 2116.04 220.319 L2112.34 220.319 Q2108.87 214.879 2107.13 209.624 Q2105.42 204.37 2105.42 199.184 Q2105.42 194.022 2107.13 188.791 Q2108.84 183.56 2112.34 178.097 L2116.04 178.097 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M2148.06 209.138 L2148.06 199.856 L2140.42 199.856 L2140.42 196.013 L2152.69 196.013 L2152.69 210.851 Q2149.98 212.772 2146.71 213.768 Q2143.45 214.74 2139.75 214.74 Q2131.65 214.74 2127.06 210.018 Q2122.5 205.272 2122.5 196.823 Q2122.5 188.351 2127.06 183.629 Q2131.65 178.884 2139.75 178.884 Q2143.13 178.884 2146.16 179.717 Q2149.21 180.55 2151.78 182.171 L2151.78 187.147 Q2149.19 184.948 2146.27 183.837 Q2143.36 182.726 2140.14 182.726 Q2133.8 182.726 2130.6 186.268 Q2127.43 189.809 2127.43 196.823 Q2127.43 203.814 2130.6 207.356 Q2133.8 210.897 2140.14 210.897 Q2142.62 210.897 2144.56 210.481 Q2146.51 210.041 2148.06 209.138 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M2172.83 201.036 Q2167.66 201.036 2165.67 202.217 Q2163.68 203.397 2163.68 206.245 Q2163.68 208.513 2165.16 209.856 Q2166.67 211.175 2169.24 211.175 Q2172.78 211.175 2174.91 208.675 Q2177.06 206.152 2177.06 201.985 L2177.06 201.036 L2172.83 201.036 M2181.32 199.277 L2181.32 214.069 L2177.06 214.069 L2177.06 210.133 Q2175.6 212.495 2173.43 213.629 Q2171.25 214.74 2168.1 214.74 Q2164.12 214.74 2161.76 212.518 Q2159.42 210.272 2159.42 206.522 Q2159.42 202.147 2162.34 199.925 Q2165.28 197.703 2171.09 197.703 L2177.06 197.703 L2177.06 197.286 Q2177.06 194.347 2175.12 192.749 Q2173.2 191.129 2169.7 191.129 Q2167.48 191.129 2165.37 191.661 Q2163.27 192.194 2161.32 193.259 L2161.32 189.323 Q2163.66 188.421 2165.86 187.981 Q2168.06 187.518 2170.14 187.518 Q2175.77 187.518 2178.54 190.434 Q2181.32 193.351 2181.32 199.277 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M2201.83 184.115 L2195.49 201.314 L2208.2 201.314 L2201.83 184.115 M2199.19 179.509 L2204.49 179.509 L2217.66 214.069 L2212.8 214.069 L2209.65 205.203 L2194.08 205.203 L2190.93 214.069 L2186 214.069 L2199.19 179.509 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M2239.05 188.907 L2239.05 192.934 Q2237.25 192.009 2235.3 191.546 Q2233.36 191.083 2231.27 191.083 Q2228.1 191.083 2226.51 192.055 Q2224.93 193.027 2224.93 194.971 Q2224.93 196.453 2226.07 197.309 Q2227.2 198.143 2230.63 198.907 L2232.08 199.231 Q2236.62 200.203 2238.52 201.985 Q2240.44 203.745 2240.44 206.916 Q2240.44 210.527 2237.57 212.633 Q2234.72 214.74 2229.72 214.74 Q2227.64 214.74 2225.37 214.323 Q2223.13 213.93 2220.63 213.12 L2220.63 208.721 Q2222.99 209.948 2225.28 210.573 Q2227.57 211.175 2229.82 211.175 Q2232.83 211.175 2234.45 210.157 Q2236.07 209.115 2236.07 207.24 Q2236.07 205.504 2234.89 204.578 Q2233.73 203.652 2229.77 202.796 L2228.29 202.448 Q2224.33 201.615 2222.57 199.902 Q2220.81 198.166 2220.81 195.157 Q2220.81 191.499 2223.4 189.509 Q2226 187.518 2230.76 187.518 Q2233.13 187.518 2235.21 187.865 Q2237.29 188.212 2239.05 188.907 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M2246.55 178.097 L2250.26 178.097 Q2253.73 183.56 2255.44 188.791 Q2257.18 194.022 2257.18 199.184 Q2257.18 204.37 2255.44 209.624 Q2253.73 214.879 2250.26 220.319 L2246.55 220.319 Q2249.63 215.018 2251.14 209.786 Q2252.66 204.532 2252.66 199.184 Q2252.66 193.837 2251.14 188.629 Q2249.63 183.421 2246.55 178.097 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><polyline clip-path=\"url(#clip790)\" style=\"stroke:#3da44d; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" stroke-dasharray=\"16, 8, 2, 8\" points=\"1526.79,248.629 1670.16,248.629 \"/>\n",
"<path clip-path=\"url(#clip790)\" d=\"M1712.48 240.747 L1712.48 244.774 Q1710.68 243.849 1708.73 243.386 Q1706.79 242.923 1704.7 242.923 Q1701.53 242.923 1699.93 243.895 Q1698.36 244.867 1698.36 246.811 Q1698.36 248.293 1699.49 249.149 Q1700.63 249.983 1704.05 250.747 L1705.51 251.071 Q1710.05 252.043 1711.95 253.825 Q1713.87 255.585 1713.87 258.756 Q1713.87 262.367 1711 264.473 Q1708.15 266.58 1703.15 266.58 Q1701.07 266.58 1698.8 266.163 Q1696.55 265.77 1694.05 264.96 L1694.05 260.561 Q1696.42 261.788 1698.71 262.413 Q1701 263.015 1703.24 263.015 Q1706.25 263.015 1707.87 261.997 Q1709.49 260.955 1709.49 259.08 Q1709.49 257.344 1708.31 256.418 Q1707.16 255.492 1703.2 254.636 L1701.72 254.288 Q1697.76 253.455 1696 251.742 Q1694.24 250.006 1694.24 246.997 Q1694.24 243.339 1696.83 241.349 Q1699.43 239.358 1704.19 239.358 Q1706.55 239.358 1708.64 239.705 Q1710.72 240.052 1712.48 240.747 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M1720.65 239.983 L1724.91 239.983 L1724.91 265.909 L1720.65 265.909 L1720.65 239.983 M1720.65 229.89 L1724.91 229.89 L1724.91 235.284 L1720.65 235.284 L1720.65 229.89 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M1733.82 229.89 L1738.08 229.89 L1738.08 265.909 L1733.82 265.909 L1733.82 229.89 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M1746.99 239.983 L1751.25 239.983 L1751.25 265.909 L1746.99 265.909 L1746.99 239.983 M1746.99 229.89 L1751.25 229.89 L1751.25 235.284 L1746.99 235.284 L1746.99 229.89 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M1778.82 240.978 L1778.82 244.96 Q1777.02 243.964 1775.19 243.478 Q1773.38 242.969 1771.53 242.969 Q1767.39 242.969 1765.1 245.608 Q1762.8 248.224 1762.8 252.969 Q1762.8 257.714 1765.1 260.353 Q1767.39 262.969 1771.53 262.969 Q1773.38 262.969 1775.19 262.483 Q1777.02 261.973 1778.82 260.978 L1778.82 264.913 Q1777.04 265.747 1775.12 266.163 Q1773.22 266.58 1771.07 266.58 Q1765.21 266.58 1761.76 262.899 Q1758.31 259.219 1758.31 252.969 Q1758.31 246.626 1761.79 242.992 Q1765.28 239.358 1771.35 239.358 Q1773.31 239.358 1775.19 239.775 Q1777.06 240.168 1778.82 240.978 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M1798.01 252.876 Q1792.85 252.876 1790.86 254.057 Q1788.87 255.237 1788.87 258.085 Q1788.87 260.353 1790.35 261.696 Q1791.86 263.015 1794.42 263.015 Q1797.97 263.015 1800.1 260.515 Q1802.25 257.992 1802.25 253.825 L1802.25 252.876 L1798.01 252.876 M1806.51 251.117 L1806.51 265.909 L1802.25 265.909 L1802.25 261.973 Q1800.79 264.335 1798.61 265.469 Q1796.44 266.58 1793.29 266.58 Q1789.31 266.58 1786.95 264.358 Q1784.61 262.112 1784.61 258.362 Q1784.61 253.987 1787.53 251.765 Q1790.47 249.543 1796.28 249.543 L1802.25 249.543 L1802.25 249.126 Q1802.25 246.187 1800.3 244.589 Q1798.38 242.969 1794.89 242.969 Q1792.67 242.969 1790.56 243.501 Q1788.45 244.034 1786.51 245.099 L1786.51 241.163 Q1788.85 240.261 1791.05 239.821 Q1793.24 239.358 1795.33 239.358 Q1800.95 239.358 1803.73 242.274 Q1806.51 245.191 1806.51 251.117 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M1840.58 229.937 Q1837.48 235.261 1835.98 240.469 Q1834.47 245.677 1834.47 251.024 Q1834.47 256.372 1835.98 261.626 Q1837.5 266.858 1840.58 272.159 L1836.88 272.159 Q1833.41 266.719 1831.67 261.464 Q1829.96 256.21 1829.96 251.024 Q1829.96 245.862 1831.67 240.631 Q1833.38 235.4 1836.88 229.937 L1840.58 229.937 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M1869.75 232.483 L1869.75 237.043 Q1867.09 235.77 1864.73 235.145 Q1862.36 234.52 1860.17 234.52 Q1856.35 234.52 1854.26 236.001 Q1852.2 237.483 1852.2 240.214 Q1852.2 242.506 1853.57 243.687 Q1854.96 244.844 1858.8 245.562 L1861.62 246.14 Q1866.85 247.136 1869.33 249.659 Q1871.83 252.159 1871.83 256.372 Q1871.83 261.395 1868.45 263.987 Q1865.1 266.58 1858.59 266.58 Q1856.14 266.58 1853.36 266.024 Q1850.6 265.469 1847.64 264.381 L1847.64 259.566 Q1850.49 261.163 1853.22 261.973 Q1855.95 262.784 1858.59 262.784 Q1862.6 262.784 1864.77 261.21 Q1866.95 259.636 1866.95 256.719 Q1866.95 254.173 1865.37 252.737 Q1863.82 251.302 1860.26 250.585 L1857.41 250.029 Q1852.18 248.987 1849.84 246.765 Q1847.5 244.543 1847.5 240.585 Q1847.5 236.001 1850.72 233.362 Q1853.96 230.724 1859.63 230.724 Q1862.06 230.724 1864.59 231.163 Q1867.11 231.603 1869.75 232.483 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M1878.94 239.983 L1883.2 239.983 L1883.2 265.909 L1878.94 265.909 L1878.94 239.983 M1878.94 229.89 L1883.2 229.89 L1883.2 235.284 L1878.94 235.284 L1878.94 229.89 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M1906.32 234.52 Q1901.23 234.52 1898.22 238.316 Q1895.23 242.112 1895.23 248.663 Q1895.23 255.191 1898.22 258.987 Q1901.23 262.784 1906.32 262.784 Q1911.41 262.784 1914.38 258.987 Q1917.36 255.191 1917.36 248.663 Q1917.36 242.112 1914.38 238.316 Q1911.41 234.52 1906.32 234.52 M1906.32 230.724 Q1913.59 230.724 1917.94 235.608 Q1922.29 240.469 1922.29 248.663 Q1922.29 256.835 1917.94 261.719 Q1913.59 266.58 1906.32 266.58 Q1899.03 266.58 1894.66 261.719 Q1890.3 256.858 1890.3 248.663 Q1890.3 240.469 1894.66 235.608 Q1899.03 230.724 1906.32 230.724 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M1931.16 263.27 L1940.97 263.27 L1940.97 265.909 L1927.13 265.909 L1927.13 263.362 Q1927.92 262.645 1929.38 261.348 Q1937.34 254.288 1937.34 252.112 Q1937.34 250.585 1936.14 249.659 Q1934.93 248.71 1932.97 248.71 Q1931.76 248.71 1930.35 249.126 Q1928.94 249.52 1927.27 250.33 L1927.27 247.483 Q1929.05 246.835 1930.58 246.511 Q1932.13 246.187 1933.45 246.187 Q1936.81 246.187 1938.82 247.714 Q1940.84 249.242 1940.84 251.742 Q1940.84 254.96 1933.17 261.534 Q1931.88 262.645 1931.16 263.27 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip790)\" d=\"M1947.76 229.937 L1951.46 229.937 Q1954.93 235.4 1956.65 240.631 Q1958.38 245.862 1958.38 251.024 Q1958.38 256.21 1956.65 261.464 Q1954.93 266.719 1951.46 272.159 L1947.76 272.159 Q1950.84 266.858 1952.34 261.626 Q1953.87 256.372 1953.87 251.024 Q1953.87 245.677 1952.34 240.469 Q1950.84 235.261 1947.76 229.937 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /></svg>\n"
],
"image/svg+xml": [
"<?xml version=\"1.0\" encoding=\"utf-8\"?>\n",
"<svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"600\" height=\"400\" viewBox=\"0 0 2400 1600\">\n",
"<defs>\n",
" <clipPath id=\"clip760\">\n",
" <rect x=\"0\" y=\"0\" width=\"2400\" height=\"1600\"/>\n",
" </clipPath>\n",
"</defs>\n",
"<path clip-path=\"url(#clip760)\" d=\"M0 1600 L2400 1600 L2400 0 L0 0 Z\" fill=\"#ffffff\" fill-rule=\"evenodd\" fill-opacity=\"1\"/>\n",
"<defs>\n",
" <clipPath id=\"clip761\">\n",
" <rect x=\"480\" y=\"0\" width=\"1681\" height=\"1600\"/>\n",
" </clipPath>\n",
"</defs>\n",
"<path clip-path=\"url(#clip760)\" d=\"M202.227 1423.18 L2352.76 1423.18 L2352.76 47.2441 L202.227 47.2441 Z\" fill=\"#ffffff\" fill-rule=\"evenodd\" fill-opacity=\"1\"/>\n",
"<defs>\n",
" <clipPath id=\"clip762\">\n",
" <rect x=\"202\" y=\"47\" width=\"2152\" height=\"1377\"/>\n",
" </clipPath>\n",
"</defs>\n",
"<polyline clip-path=\"url(#clip762)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"620.787,1423.18 620.787,47.2441 \"/>\n",
"<polyline clip-path=\"url(#clip762)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"1053.78,1423.18 1053.78,47.2441 \"/>\n",
"<polyline clip-path=\"url(#clip762)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"1486.77,1423.18 1486.77,47.2441 \"/>\n",
"<polyline clip-path=\"url(#clip762)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"1919.76,1423.18 1919.76,47.2441 \"/>\n",
"<polyline clip-path=\"url(#clip762)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"202.227,1423.18 2352.76,1423.18 \"/>\n",
"<polyline clip-path=\"url(#clip762)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"202.227,993.2 2352.76,993.2 \"/>\n",
"<polyline clip-path=\"url(#clip762)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"202.227,563.22 2352.76,563.22 \"/>\n",
"<polyline clip-path=\"url(#clip762)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"202.227,133.24 2352.76,133.24 \"/>\n",
"<polyline clip-path=\"url(#clip760)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"202.227,1423.18 2352.76,1423.18 \"/>\n",
"<polyline clip-path=\"url(#clip760)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"620.787,1423.18 620.787,1404.28 \"/>\n",
"<polyline clip-path=\"url(#clip760)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"1053.78,1423.18 1053.78,1404.28 \"/>\n",
"<polyline clip-path=\"url(#clip760)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"1486.77,1423.18 1486.77,1404.28 \"/>\n",
"<polyline clip-path=\"url(#clip760)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"1919.76,1423.18 1919.76,1404.28 \"/>\n",
"<path clip-path=\"url(#clip760)\" d=\"M598.495 1454.1 Q594.884 1454.1 593.055 1457.66 Q591.25 1461.2 591.25 1468.33 Q591.25 1475.44 593.055 1479.01 Q594.884 1482.55 598.495 1482.55 Q602.129 1482.55 603.935 1479.01 Q605.764 1475.44 605.764 1468.33 Q605.764 1461.2 603.935 1457.66 Q602.129 1454.1 598.495 1454.1 M598.495 1450.39 Q604.305 1450.39 607.361 1455 Q610.44 1459.58 610.44 1468.33 Q610.44 1477.06 607.361 1481.67 Q604.305 1486.25 598.495 1486.25 Q592.685 1486.25 589.606 1481.67 Q586.551 1477.06 586.551 1468.33 Q586.551 1459.58 589.606 1455 Q592.685 1450.39 598.495 1450.39 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M618.657 1479.7 L623.541 1479.7 L623.541 1485.58 L618.657 1485.58 L618.657 1479.7 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M647.893 1466.95 Q651.249 1467.66 653.124 1469.93 Q655.023 1472.2 655.023 1475.53 Q655.023 1480.65 651.504 1483.45 Q647.986 1486.25 641.504 1486.25 Q639.328 1486.25 637.013 1485.81 Q634.722 1485.39 632.268 1484.54 L632.268 1480.02 Q634.213 1481.16 636.527 1481.74 Q638.842 1482.32 641.365 1482.32 Q645.763 1482.32 648.055 1480.58 Q650.37 1478.84 650.37 1475.53 Q650.37 1472.48 648.217 1470.77 Q646.087 1469.03 642.268 1469.03 L638.24 1469.03 L638.24 1465.19 L642.453 1465.19 Q645.902 1465.19 647.731 1463.82 Q649.56 1462.43 649.56 1459.84 Q649.56 1457.18 647.662 1455.77 Q645.787 1454.33 642.268 1454.33 Q640.347 1454.33 638.148 1454.75 Q635.949 1455.16 633.31 1456.04 L633.31 1451.88 Q635.972 1451.14 638.287 1450.77 Q640.625 1450.39 642.685 1450.39 Q648.009 1450.39 651.111 1452.83 Q654.212 1455.23 654.212 1459.35 Q654.212 1462.22 652.569 1464.21 Q650.925 1466.18 647.893 1466.95 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M1031.08 1454.1 Q1027.47 1454.1 1025.64 1457.66 Q1023.84 1461.2 1023.84 1468.33 Q1023.84 1475.44 1025.64 1479.01 Q1027.47 1482.55 1031.08 1482.55 Q1034.72 1482.55 1036.52 1479.01 Q1038.35 1475.44 1038.35 1468.33 Q1038.35 1461.2 1036.52 1457.66 Q1034.72 1454.1 1031.08 1454.1 M1031.08 1450.39 Q1036.89 1450.39 1039.95 1455 Q1043.03 1459.58 1043.03 1468.33 Q1043.03 1477.06 1039.95 1481.67 Q1036.89 1486.25 1031.08 1486.25 Q1025.27 1486.25 1022.19 1481.67 Q1019.14 1477.06 1019.14 1468.33 Q1019.14 1459.58 1022.19 1455 Q1025.27 1450.39 1031.08 1450.39 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M1051.24 1479.7 L1056.13 1479.7 L1056.13 1485.58 L1051.24 1485.58 L1051.24 1479.7 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M1076.89 1466.44 Q1073.74 1466.44 1071.89 1468.59 Q1070.06 1470.74 1070.06 1474.49 Q1070.06 1478.22 1071.89 1480.39 Q1073.74 1482.55 1076.89 1482.55 Q1080.04 1482.55 1081.87 1480.39 Q1083.72 1478.22 1083.72 1474.49 Q1083.72 1470.74 1081.87 1468.59 Q1080.04 1466.44 1076.89 1466.44 M1086.17 1451.78 L1086.17 1456.04 Q1084.42 1455.21 1082.61 1454.77 Q1080.83 1454.33 1079.07 1454.33 Q1074.44 1454.33 1071.98 1457.45 Q1069.55 1460.58 1069.21 1466.9 Q1070.57 1464.89 1072.63 1463.82 Q1074.69 1462.73 1077.17 1462.73 Q1082.38 1462.73 1085.39 1465.9 Q1088.42 1469.05 1088.42 1474.49 Q1088.42 1479.82 1085.27 1483.03 Q1082.12 1486.25 1076.89 1486.25 Q1070.9 1486.25 1067.73 1481.67 Q1064.55 1477.06 1064.55 1468.33 Q1064.55 1460.14 1068.44 1455.28 Q1072.33 1450.39 1078.88 1450.39 Q1080.64 1450.39 1082.42 1450.74 Q1084.23 1451.09 1086.17 1451.78 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M1464.25 1454.1 Q1460.64 1454.1 1458.81 1457.66 Q1457 1461.2 1457 1468.33 Q1457 1475.44 1458.81 1479.01 Q1460.64 1482.55 1464.25 1482.55 Q1467.88 1482.55 1469.69 1479.01 Q1471.52 1475.44 1471.52 1468.33 Q1471.52 1461.2 1469.69 1457.66 Q1467.88 1454.1 1464.25 1454.1 M1464.25 1450.39 Q1470.06 1450.39 1473.11 1455 Q1476.19 1459.58 1476.19 1468.33 Q1476.19 1477.06 1473.11 1481.67 Q1470.06 1486.25 1464.25 1486.25 Q1458.44 1486.25 1455.36 1481.67 Q1452.3 1477.06 1452.3 1468.33 Q1452.3 1459.58 1455.36 1455 Q1458.44 1450.39 1464.25 1450.39 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M1484.41 1479.7 L1489.29 1479.7 L1489.29 1485.58 L1484.41 1485.58 L1484.41 1479.7 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M1499.62 1484.86 L1499.62 1480.6 Q1501.38 1481.44 1503.18 1481.88 Q1504.99 1482.32 1506.72 1482.32 Q1511.35 1482.32 1513.79 1479.21 Q1516.24 1476.09 1516.59 1469.75 Q1515.24 1471.74 1513.18 1472.8 Q1511.12 1473.87 1508.62 1473.87 Q1503.44 1473.87 1500.41 1470.74 Q1497.4 1467.59 1497.4 1462.15 Q1497.4 1456.83 1500.54 1453.61 Q1503.69 1450.39 1508.92 1450.39 Q1514.92 1450.39 1518.07 1455 Q1521.24 1459.58 1521.24 1468.33 Q1521.24 1476.51 1517.35 1481.39 Q1513.48 1486.25 1506.93 1486.25 Q1505.17 1486.25 1503.37 1485.9 Q1501.56 1485.56 1499.62 1484.86 M1508.92 1470.21 Q1512.07 1470.21 1513.9 1468.06 Q1515.75 1465.9 1515.75 1462.15 Q1515.75 1458.43 1513.9 1456.27 Q1512.07 1454.1 1508.92 1454.1 Q1505.78 1454.1 1503.92 1456.27 Q1502.1 1458.43 1502.1 1462.15 Q1502.1 1465.9 1503.92 1468.06 Q1505.78 1470.21 1508.92 1470.21 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M1887.72 1481.64 L1895.35 1481.64 L1895.35 1455.28 L1887.04 1456.95 L1887.04 1452.69 L1895.31 1451.02 L1899.98 1451.02 L1899.98 1481.64 L1907.62 1481.64 L1907.62 1485.58 L1887.72 1485.58 L1887.72 1481.64 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M1917.07 1479.7 L1921.95 1479.7 L1921.95 1485.58 L1917.07 1485.58 L1917.07 1479.7 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M1936.16 1481.64 L1952.48 1481.64 L1952.48 1485.58 L1930.54 1485.58 L1930.54 1481.64 Q1933.2 1478.89 1937.78 1474.26 Q1942.39 1469.61 1943.57 1468.27 Q1945.82 1465.74 1946.7 1464.01 Q1947.6 1462.25 1947.6 1460.56 Q1947.6 1457.8 1945.65 1456.07 Q1943.73 1454.33 1940.63 1454.33 Q1938.43 1454.33 1935.98 1455.09 Q1933.55 1455.86 1930.77 1457.41 L1930.77 1452.69 Q1933.59 1451.55 1936.05 1450.97 Q1938.5 1450.39 1940.54 1450.39 Q1945.91 1450.39 1949.1 1453.08 Q1952.3 1455.77 1952.3 1460.26 Q1952.3 1462.39 1951.49 1464.31 Q1950.7 1466.2 1948.59 1468.8 Q1948.02 1469.47 1944.91 1472.69 Q1941.81 1475.88 1936.16 1481.64 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M1267.61 1550.25 Q1267.61 1556.71 1270.25 1560.4 Q1272.92 1564.07 1277.57 1564.07 Q1282.22 1564.07 1284.89 1560.4 Q1287.57 1556.71 1287.57 1550.25 Q1287.57 1543.79 1284.89 1540.13 Q1282.22 1536.44 1277.57 1536.44 Q1272.92 1536.44 1270.25 1540.13 Q1267.61 1543.79 1267.61 1550.25 M1287.57 1562.7 Q1285.72 1565.88 1282.89 1567.44 Q1280.09 1568.97 1276.14 1568.97 Q1269.68 1568.97 1265.6 1563.81 Q1261.56 1558.65 1261.56 1550.25 Q1261.56 1541.85 1265.6 1536.69 Q1269.68 1531.54 1276.14 1531.54 Q1280.09 1531.54 1282.89 1533.1 Q1285.72 1534.62 1287.57 1537.81 L1287.57 1532.4 L1293.42 1532.4 L1293.42 1581.6 L1287.57 1581.6 L1287.57 1562.7 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><polyline clip-path=\"url(#clip760)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"202.227,1423.18 202.227,47.2441 \"/>\n",
"<polyline clip-path=\"url(#clip760)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"202.227,1423.18 221.125,1423.18 \"/>\n",
"<polyline clip-path=\"url(#clip760)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"202.227,993.2 221.125,993.2 \"/>\n",
"<polyline clip-path=\"url(#clip760)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"202.227,563.22 221.125,563.22 \"/>\n",
"<polyline clip-path=\"url(#clip760)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"202.227,133.24 221.125,133.24 \"/>\n",
"<path clip-path=\"url(#clip760)\" d=\"M154.283 1408.98 Q150.672 1408.98 148.843 1412.54 Q147.038 1416.08 147.038 1423.21 Q147.038 1430.32 148.843 1433.89 Q150.672 1437.43 154.283 1437.43 Q157.917 1437.43 159.723 1433.89 Q161.552 1430.32 161.552 1423.21 Q161.552 1416.08 159.723 1412.54 Q157.917 1408.98 154.283 1408.98 M154.283 1405.27 Q160.093 1405.27 163.149 1409.88 Q166.227 1414.46 166.227 1423.21 Q166.227 1431.94 163.149 1436.55 Q160.093 1441.13 154.283 1441.13 Q148.473 1441.13 145.394 1436.55 Q142.339 1431.94 142.339 1423.21 Q142.339 1414.46 145.394 1409.88 Q148.473 1405.27 154.283 1405.27 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M145.325 975.92 L163.681 975.92 L163.681 979.855 L149.607 979.855 L149.607 988.327 Q150.626 987.98 151.644 987.818 Q152.663 987.633 153.681 987.633 Q159.468 987.633 162.848 990.804 Q166.227 993.975 166.227 999.392 Q166.227 1004.97 162.755 1008.07 Q159.283 1011.15 152.964 1011.15 Q150.788 1011.15 148.519 1010.78 Q146.274 1010.41 143.866 1009.67 L143.866 1004.97 Q145.95 1006.1 148.172 1006.66 Q150.394 1007.22 152.871 1007.22 Q156.876 1007.22 159.214 1005.11 Q161.552 1003 161.552 999.392 Q161.552 995.781 159.214 993.674 Q156.876 991.568 152.871 991.568 Q150.996 991.568 149.121 991.985 Q147.269 992.401 145.325 993.281 L145.325 975.92 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M114.931 576.565 L122.57 576.565 L122.57 550.199 L114.26 551.866 L114.26 547.607 L122.524 545.94 L127.2 545.94 L127.2 576.565 L134.839 576.565 L134.839 580.5 L114.931 580.5 L114.931 576.565 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M154.283 549.019 Q150.672 549.019 148.843 552.583 Q147.038 556.125 147.038 563.255 Q147.038 570.361 148.843 573.926 Q150.672 577.468 154.283 577.468 Q157.917 577.468 159.723 573.926 Q161.552 570.361 161.552 563.255 Q161.552 556.125 159.723 552.583 Q157.917 549.019 154.283 549.019 M154.283 545.315 Q160.093 545.315 163.149 549.921 Q166.227 554.505 166.227 563.255 Q166.227 571.982 163.149 576.588 Q160.093 581.171 154.283 581.171 Q148.473 581.171 145.394 576.588 Q142.339 571.982 142.339 563.255 Q142.339 554.505 145.394 549.921 Q148.473 545.315 154.283 545.315 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M115.927 146.585 L123.566 146.585 L123.566 120.219 L115.256 121.886 L115.256 117.627 L123.519 115.96 L128.195 115.96 L128.195 146.585 L135.834 146.585 L135.834 150.52 L115.927 150.52 L115.927 146.585 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M145.325 115.96 L163.681 115.96 L163.681 119.895 L149.607 119.895 L149.607 128.367 Q150.626 128.02 151.644 127.858 Q152.663 127.673 153.681 127.673 Q159.468 127.673 162.848 130.844 Q166.227 134.016 166.227 139.432 Q166.227 145.011 162.755 148.113 Q159.283 151.191 152.964 151.191 Q150.788 151.191 148.519 150.821 Q146.274 150.451 143.866 149.71 L143.866 145.011 Q145.95 146.145 148.172 146.701 Q150.394 147.256 152.871 147.256 Q156.876 147.256 159.214 145.15 Q161.552 143.043 161.552 139.432 Q161.552 135.821 159.214 133.715 Q156.876 131.608 152.871 131.608 Q150.996 131.608 149.121 132.025 Q147.269 132.441 145.325 133.321 L145.325 115.96 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M44.7797 785.692 Q44.0158 789.257 41.947 791.167 Q39.91 793.076 36.9499 793.076 Q32.4621 793.076 29.9476 789.448 Q27.465 785.851 27.465 779.613 Q27.465 777.194 27.8469 774.488 Q28.2289 771.783 28.9928 768.664 L34.3081 768.664 Q33.3851 771.751 32.9713 774.297 Q32.5576 776.876 32.5576 779.135 Q32.5576 782.923 34.0217 785.119 Q35.4858 787.347 37.5228 787.347 Q39.7508 787.347 41.1831 785.183 Q42.5836 783.05 42.5836 779.358 L42.5836 774.425 L47.4215 774.425 L47.4215 779.135 Q47.4215 783.496 49.0447 785.788 Q50.8271 788.27 53.6281 788.27 Q56.4926 788.27 58.275 785.597 Q60.0574 782.891 60.0574 778.085 Q60.0574 775.125 59.4845 772.42 Q58.8798 769.714 57.7021 767.454 L63.1448 767.454 Q64.036 770.319 64.4816 772.992 Q64.9272 775.698 64.9272 778.244 Q64.9272 785.819 62.0308 789.925 Q59.1344 794.031 53.6281 794.031 Q50.1906 794.031 47.8671 791.835 Q45.5436 789.639 44.7797 785.692 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M14.5426 742.819 Q21.8632 747.084 29.0246 749.153 Q36.186 751.222 43.5384 751.222 Q50.8908 751.222 58.1159 749.153 Q65.3091 747.052 72.5979 742.819 L72.5979 747.912 Q65.1182 752.686 57.8931 755.073 Q50.668 757.428 43.5384 757.428 Q36.4406 757.428 29.2474 755.073 Q22.0542 752.718 14.5426 747.912 L14.5426 742.819 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M46.212 727.955 Q52.6732 727.955 56.3653 725.313 Q60.0256 722.64 60.0256 717.993 Q60.0256 713.346 56.3653 710.672 Q52.6732 707.999 46.212 707.999 Q39.7508 707.999 36.0905 710.672 Q32.3984 713.346 32.3984 717.993 Q32.3984 722.64 36.0905 725.313 Q39.7508 727.955 46.212 727.955 M58.657 707.999 Q61.8398 709.845 63.3994 712.677 Q64.9272 715.478 64.9272 719.425 Q64.9272 725.886 59.771 729.96 Q54.6147 734.002 46.212 734.002 Q37.8093 734.002 32.6531 729.96 Q27.4968 725.886 27.4968 719.425 Q27.4968 715.478 29.0564 712.677 Q30.5842 709.845 33.7671 707.999 L28.3562 707.999 L28.3562 702.142 L77.5631 702.142 L77.5631 707.999 L58.657 707.999 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M14.5426 691.002 L14.5426 685.91 Q22.0542 681.135 29.2474 678.78 Q36.4406 676.393 43.5384 676.393 Q50.668 676.393 57.8931 678.78 Q65.1182 681.135 72.5979 685.91 L72.5979 691.002 Q65.3091 686.769 58.1159 684.7 Q50.8908 682.599 43.5384 682.599 Q36.186 682.599 29.0246 684.7 Q21.8632 686.769 14.5426 691.002 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><polyline clip-path=\"url(#clip762)\" style=\"stroke:#009af9; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"202.227,-858623 202.401,-838320 202.574,-818729 202.748,-799815 202.921,-781547 203.095,-763898 203.268,-746839 203.442,-730344 203.615,-714388 203.962,-684004 204.309,-655514 204.656,-628765 205.003,-603617 205.35,-579945 205.696,-557635 206.043,-536586 206.39,-516704 206.737,-497904 207.084,-480109 207.431,-463249 207.778,-447259 208.125,-432081 208.472,-417660 208.819,-403947 209.165,-390897 209.512,-378467 209.859,-366618 210.206,-355316 210.553,-344526 211.247,-324365 211.941,-305917 212.634,-288994 213.328,-273430 214.022,-259086 214.716,-245836 215.41,-233572 216.103,-222199 216.797,-211632 217.491,-201797 218.185,-192628 218.879,-184066 220.266,-168560 221.654,-154920 222.348,-148708 223.041,-142859 223.735,-137346 224.429,-132143 226.461,-118484 228.492,-106819 230.524,-96777.9 232.556,-88073 234.588,-80477.3 236.619,-73809.9 238.651,-67925.5 240.683,-62706.2 244.746,-53893.3 248.81,-46781.8 252.873,-40960.4 256.937,-36134.8 265.064,-28666.9 273.191,-23227.8 281.318,-19144 289.445,-16000 305.699,-11549.4 321.953,-8615.98 338.207,-6581.07 354.461,-5111.94 384.706,-3282.94 414.951,-2134.53 455.491,-1162.64 496.031,-548.315 563.029,64.8796 625.329,401.411 703.538,663.699 773.692,815.326 853.993,933.548 914.017,997.514 990.79,1059.36 1060.86,1102.17 1140.61,1139.86 1203.83,1163.65 1282.37,1187.66 1342.52,1202.83 1427.32,1220.59 1490.69,1231.65 1562.76,1242.43 1634.13,1251.55 1712.66,1260.14 1772.63,1265.86 1848.32,1272.21 1918.32,1277.36 1990.52,1282.06 2063.69,1286.28 2140.1,1290.18 2200.3,1292.95 2337.38,1298.41 2352.76,1298.96 \"/>\n",
"<polyline clip-path=\"url(#clip762)\" style=\"stroke:#e26f46; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" stroke-dasharray=\"16, 10\" points=\"202.227,143.499 207.778,145.016 213.328,147.017 218.879,149.497 224.429,152.449 232.556,157.61 240.683,163.742 248.81,170.814 256.937,178.792 265.064,187.637 273.191,197.307 281.318,207.756 289.445,218.939 305.699,243.307 321.953,270.005 338.207,298.622 354.461,328.752 369.583,357.804 384.706,387.538 399.829,417.682 414.951,447.996 435.221,488.519 455.491,528.52 475.761,567.646 496.031,605.624 512.781,635.994 529.53,665.36 546.279,693.664 563.029,720.872 578.604,745.173 594.179,768.507 609.754,790.881 625.329,812.309 644.882,837.897 664.434,862.072 683.986,884.889 703.538,906.408 721.077,924.659 738.615,941.963 756.154,958.368 773.692,973.919 793.767,990.728 813.842,1006.54 833.917,1021.43 853.993,1035.44 884.005,1054.88 914.017,1072.68 952.403,1093.29 990.79,1111.75 1025.83,1126.96 1060.86,1140.78 1100.73,1155 1140.61,1167.82 1172.22,1177.09 1203.83,1185.65 1282.37,1204.29 1342.52,1216.41 1427.32,1230.95 1490.69,1240.22 1562.76,1249.39 1634.13,1257.27 1712.66,1264.81 1772.63,1269.88 1848.32,1275.56 1918.32,1280.22 1990.52,1284.49 2063.69,1288.36 2140.1,1291.96 2200.3,1294.53 2337.38,1299.63 2352.76,1300.15 \"/>\n",
"<polyline clip-path=\"url(#clip762)\" style=\"stroke:#3da44d; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" stroke-dasharray=\"16, 8, 2, 8\" points=\"202.227,1294.19 207.778,1294.19 213.328,1294.19 218.879,1294.2 224.429,1294.2 256.937,1294.24 289.445,1294.29 321.953,1294.37 354.461,1294.47 384.706,1294.58 414.951,1294.71 455.491,1294.91 496.031,1295.14 529.53,1295.36 563.029,1295.59 594.179,1295.83 625.329,1296.07 664.434,1296.41 703.538,1296.77 738.615,1297.1 773.692,1297.46 853.993,1298.33 914.017,1299.02 990.79,1299.95 1060.86,1300.84 1140.61,1301.88 1203.83,1302.72 1282.37,1303.79 1342.52,1304.61 1427.32,1305.77 1490.69,1306.63 1562.76,1307.61 1634.13,1308.56 1712.66,1309.59 1772.63,1310.36 1848.32,1311.31 1918.32,1312.17 1990.52,1313.03 2063.69,1313.87 2140.1,1314.73 2200.3,1315.38 2337.38,1316.8 2352.76,1316.95 \"/>\n",
"<path clip-path=\"url(#clip760)\" d=\"M1502.9 300.469 L2281.07 300.469 L2281.07 93.1086 L1502.9 93.1086 Z\" fill=\"#ffffff\" fill-rule=\"evenodd\" fill-opacity=\"1\"/>\n",
"<polyline clip-path=\"url(#clip760)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"1502.9,300.469 2281.07,300.469 2281.07,93.1086 1502.9,93.1086 1502.9,300.469 \"/>\n",
"<polyline clip-path=\"url(#clip760)\" style=\"stroke:#009af9; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"1526.79,144.949 1670.16,144.949 \"/>\n",
"<path clip-path=\"url(#clip760)\" d=\"M1707.46 149.196 Q1702.3 149.196 1700.3 150.377 Q1698.31 151.557 1698.31 154.405 Q1698.31 156.673 1699.8 158.016 Q1701.3 159.335 1703.87 159.335 Q1707.41 159.335 1709.54 156.835 Q1711.69 154.312 1711.69 150.145 L1711.69 149.196 L1707.46 149.196 M1715.95 147.437 L1715.95 162.229 L1711.69 162.229 L1711.69 158.293 Q1710.24 160.655 1708.06 161.789 Q1705.88 162.9 1702.74 162.9 Q1698.75 162.9 1696.39 160.678 Q1694.05 158.432 1694.05 154.682 Q1694.05 150.307 1696.97 148.085 Q1699.91 145.863 1705.72 145.863 L1711.69 145.863 L1711.69 145.446 Q1711.69 142.507 1709.75 140.909 Q1707.83 139.289 1704.33 139.289 Q1702.11 139.289 1700 139.821 Q1697.9 140.354 1695.95 141.419 L1695.95 137.483 Q1698.29 136.581 1700.49 136.141 Q1702.69 135.678 1704.77 135.678 Q1710.4 135.678 1713.18 138.594 Q1715.95 141.511 1715.95 147.437 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M1724.73 126.21 L1728.99 126.21 L1728.99 162.229 L1724.73 162.229 L1724.73 126.21 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M1737.46 151.997 L1737.46 136.303 L1741.72 136.303 L1741.72 151.835 Q1741.72 155.516 1743.15 157.368 Q1744.59 159.196 1747.46 159.196 Q1750.91 159.196 1752.9 156.997 Q1754.91 154.798 1754.91 151.002 L1754.91 136.303 L1759.17 136.303 L1759.17 162.229 L1754.91 162.229 L1754.91 158.247 Q1753.36 160.608 1751.3 161.766 Q1749.26 162.9 1746.55 162.9 Q1742.09 162.9 1739.77 160.122 Q1737.46 157.344 1737.46 151.997 M1748.17 135.678 L1748.17 135.678 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M1788.13 141.28 Q1789.73 138.409 1791.95 137.044 Q1794.17 135.678 1797.18 135.678 Q1801.23 135.678 1803.43 138.525 Q1805.63 141.349 1805.63 146.581 L1805.63 162.229 L1801.35 162.229 L1801.35 146.719 Q1801.35 142.993 1800.03 141.187 Q1798.71 139.382 1796 139.382 Q1792.69 139.382 1790.77 141.581 Q1788.85 143.78 1788.85 147.576 L1788.85 162.229 L1784.56 162.229 L1784.56 146.719 Q1784.56 142.969 1783.24 141.187 Q1781.92 139.382 1779.17 139.382 Q1775.91 139.382 1773.99 141.604 Q1772.06 143.803 1772.06 147.576 L1772.06 162.229 L1767.78 162.229 L1767.78 136.303 L1772.06 136.303 L1772.06 140.331 Q1773.52 137.946 1775.56 136.812 Q1777.6 135.678 1780.4 135.678 Q1783.22 135.678 1785.19 137.113 Q1787.18 138.548 1788.13 141.28 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M1814.12 136.303 L1818.38 136.303 L1818.38 162.229 L1814.12 162.229 L1814.12 136.303 M1814.12 126.21 L1818.38 126.21 L1818.38 131.604 L1814.12 131.604 L1814.12 126.21 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M1848.85 146.581 L1848.85 162.229 L1844.59 162.229 L1844.59 146.719 Q1844.59 143.039 1843.15 141.21 Q1841.72 139.382 1838.85 139.382 Q1835.4 139.382 1833.41 141.581 Q1831.42 143.78 1831.42 147.576 L1831.42 162.229 L1827.13 162.229 L1827.13 136.303 L1831.42 136.303 L1831.42 140.331 Q1832.94 137.993 1835 136.835 Q1837.09 135.678 1839.79 135.678 Q1844.26 135.678 1846.55 138.456 Q1848.85 141.21 1848.85 146.581 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M1857.34 136.303 L1861.6 136.303 L1861.6 162.229 L1857.34 162.229 L1857.34 136.303 M1857.34 126.21 L1861.6 126.21 L1861.6 131.604 L1857.34 131.604 L1857.34 126.21 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M1870.07 151.997 L1870.07 136.303 L1874.33 136.303 L1874.33 151.835 Q1874.33 155.516 1875.77 157.368 Q1877.2 159.196 1880.07 159.196 Q1883.52 159.196 1885.51 156.997 Q1887.53 154.798 1887.53 151.002 L1887.53 136.303 L1891.79 136.303 L1891.79 162.229 L1887.53 162.229 L1887.53 158.247 Q1885.98 160.608 1883.91 161.766 Q1881.88 162.9 1879.17 162.9 Q1874.7 162.9 1872.39 160.122 Q1870.07 157.344 1870.07 151.997 M1880.79 135.678 L1880.79 135.678 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M1920.74 141.28 Q1922.34 138.409 1924.56 137.044 Q1926.79 135.678 1929.79 135.678 Q1933.85 135.678 1936.04 138.525 Q1938.24 141.349 1938.24 146.581 L1938.24 162.229 L1933.96 162.229 L1933.96 146.719 Q1933.96 142.993 1932.64 141.187 Q1931.32 139.382 1928.61 139.382 Q1925.3 139.382 1923.38 141.581 Q1921.46 143.78 1921.46 147.576 L1921.46 162.229 L1917.18 162.229 L1917.18 146.719 Q1917.18 142.969 1915.86 141.187 Q1914.54 139.382 1911.79 139.382 Q1908.52 139.382 1906.6 141.604 Q1904.68 143.803 1904.68 147.576 L1904.68 162.229 L1900.4 162.229 L1900.4 136.303 L1904.68 136.303 L1904.68 140.331 Q1906.14 137.946 1908.17 136.812 Q1910.21 135.678 1913.01 135.678 Q1915.84 135.678 1917.8 137.113 Q1919.79 138.548 1920.74 141.28 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M1972.04 126.257 Q1968.94 131.581 1967.43 136.789 Q1965.93 141.997 1965.93 147.344 Q1965.93 152.692 1967.43 157.946 Q1968.96 163.178 1972.04 168.479 L1968.34 168.479 Q1964.86 163.039 1963.13 157.784 Q1961.41 152.53 1961.41 147.344 Q1961.41 142.182 1963.13 136.951 Q1964.84 131.72 1968.34 126.257 L1972.04 126.257 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M1992.04 132.275 L1985.7 149.474 L1998.41 149.474 L1992.04 132.275 M1989.4 127.669 L1994.7 127.669 L2007.87 162.229 L2003.01 162.229 L1999.86 153.363 L1984.28 153.363 L1981.14 162.229 L1976.21 162.229 L1989.4 127.669 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M2012.73 126.21 L2016.99 126.21 L2016.99 162.229 L2012.73 162.229 L2012.73 126.21 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M2025.23 126.257 L2028.94 126.257 Q2032.41 131.72 2034.12 136.951 Q2035.86 142.182 2035.86 147.344 Q2035.86 152.53 2034.12 157.784 Q2032.41 163.039 2028.94 168.479 L2025.23 168.479 Q2028.31 163.178 2029.82 157.946 Q2031.34 152.692 2031.34 147.344 Q2031.34 141.997 2029.82 136.789 Q2028.31 131.581 2025.23 126.257 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><polyline clip-path=\"url(#clip760)\" style=\"stroke:#e26f46; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" stroke-dasharray=\"16, 10\" points=\"1526.79,196.789 1670.16,196.789 \"/>\n",
"<path clip-path=\"url(#clip760)\" d=\"M1712.97 200.805 Q1712.97 196.175 1711.05 193.629 Q1709.15 191.083 1705.7 191.083 Q1702.27 191.083 1700.35 193.629 Q1698.45 196.175 1698.45 200.805 Q1698.45 205.411 1700.35 207.958 Q1702.27 210.504 1705.7 210.504 Q1709.15 210.504 1711.05 207.958 Q1712.97 205.411 1712.97 200.805 M1717.23 210.851 Q1717.23 217.471 1714.29 220.689 Q1711.35 223.93 1705.28 223.93 Q1703.04 223.93 1701.05 223.582 Q1699.05 223.258 1697.18 222.564 L1697.18 218.42 Q1699.05 219.439 1700.88 219.925 Q1702.71 220.411 1704.61 220.411 Q1708.8 220.411 1710.88 218.212 Q1712.97 216.036 1712.97 211.615 L1712.97 209.508 Q1711.65 211.8 1709.59 212.934 Q1707.53 214.069 1704.66 214.069 Q1699.89 214.069 1696.97 210.434 Q1694.05 206.8 1694.05 200.805 Q1694.05 194.786 1696.97 191.152 Q1699.89 187.518 1704.66 187.518 Q1707.53 187.518 1709.59 188.652 Q1711.65 189.786 1712.97 192.078 L1712.97 188.143 L1717.23 188.143 L1717.23 210.851 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M1737.78 201.036 Q1732.62 201.036 1730.63 202.217 Q1728.64 203.397 1728.64 206.245 Q1728.64 208.513 1730.12 209.856 Q1731.62 211.175 1734.19 211.175 Q1737.74 211.175 1739.86 208.675 Q1742.02 206.152 1742.02 201.985 L1742.02 201.036 L1737.78 201.036 M1746.28 199.277 L1746.28 214.069 L1742.02 214.069 L1742.02 210.133 Q1740.56 212.495 1738.38 213.629 Q1736.21 214.74 1733.06 214.74 Q1729.08 214.74 1726.72 212.518 Q1724.38 210.272 1724.38 206.522 Q1724.38 202.147 1727.3 199.925 Q1730.24 197.703 1736.05 197.703 L1742.02 197.703 L1742.02 197.286 Q1742.02 194.347 1740.07 192.749 Q1738.15 191.129 1734.66 191.129 Q1732.43 191.129 1730.33 191.661 Q1728.22 192.194 1726.28 193.259 L1726.28 189.323 Q1728.61 188.421 1730.81 187.981 Q1733.01 187.518 1735.1 187.518 Q1740.72 187.518 1743.5 190.434 Q1746.28 193.351 1746.28 199.277 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M1755.05 178.05 L1759.31 178.05 L1759.31 214.069 L1755.05 214.069 L1755.05 178.05 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M1768.22 178.05 L1772.48 178.05 L1772.48 214.069 L1768.22 214.069 L1768.22 178.05 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M1781.39 188.143 L1785.65 188.143 L1785.65 214.069 L1781.39 214.069 L1781.39 188.143 M1781.39 178.05 L1785.65 178.05 L1785.65 183.444 L1781.39 183.444 L1781.39 178.05 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M1794.12 203.837 L1794.12 188.143 L1798.38 188.143 L1798.38 203.675 Q1798.38 207.356 1799.82 209.208 Q1801.25 211.036 1804.12 211.036 Q1807.57 211.036 1809.56 208.837 Q1811.58 206.638 1811.58 202.842 L1811.58 188.143 L1815.84 188.143 L1815.84 214.069 L1811.58 214.069 L1811.58 210.087 Q1810.03 212.448 1807.97 213.606 Q1805.93 214.74 1803.22 214.74 Q1798.75 214.74 1796.44 211.962 Q1794.12 209.184 1794.12 203.837 M1804.84 187.518 L1804.84 187.518 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M1844.79 193.12 Q1846.39 190.249 1848.61 188.884 Q1850.84 187.518 1853.85 187.518 Q1857.9 187.518 1860.1 190.365 Q1862.29 193.189 1862.29 198.421 L1862.29 214.069 L1858.01 214.069 L1858.01 198.559 Q1858.01 194.833 1856.69 193.027 Q1855.37 191.222 1852.67 191.222 Q1849.35 191.222 1847.43 193.421 Q1845.51 195.62 1845.51 199.416 L1845.51 214.069 L1841.23 214.069 L1841.23 198.559 Q1841.23 194.809 1839.91 193.027 Q1838.59 191.222 1835.84 191.222 Q1832.57 191.222 1830.65 193.444 Q1828.73 195.643 1828.73 199.416 L1828.73 214.069 L1824.45 214.069 L1824.45 188.143 L1828.73 188.143 L1828.73 192.171 Q1830.19 189.786 1832.23 188.652 Q1834.26 187.518 1837.06 187.518 Q1839.89 187.518 1841.86 188.953 Q1843.85 190.388 1844.79 193.12 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M1897.64 201.036 Q1892.48 201.036 1890.49 202.217 Q1888.5 203.397 1888.5 206.245 Q1888.5 208.513 1889.98 209.856 Q1891.48 211.175 1894.05 211.175 Q1897.6 211.175 1899.73 208.675 Q1901.88 206.152 1901.88 201.985 L1901.88 201.036 L1897.64 201.036 M1906.14 199.277 L1906.14 214.069 L1901.88 214.069 L1901.88 210.133 Q1900.42 212.495 1898.24 213.629 Q1896.07 214.74 1892.92 214.74 Q1888.94 214.74 1886.58 212.518 Q1884.24 210.272 1884.24 206.522 Q1884.24 202.147 1887.16 199.925 Q1890.1 197.703 1895.91 197.703 L1901.88 197.703 L1901.88 197.286 Q1901.88 194.347 1899.93 192.749 Q1898.01 191.129 1894.52 191.129 Q1892.29 191.129 1890.19 191.661 Q1888.08 192.194 1886.14 193.259 L1886.14 189.323 Q1888.48 188.421 1890.67 187.981 Q1892.87 187.518 1894.96 187.518 Q1900.58 187.518 1903.36 190.434 Q1906.14 193.351 1906.14 199.277 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M1929.93 192.124 Q1929.22 191.708 1928.36 191.522 Q1927.53 191.314 1926.51 191.314 Q1922.9 191.314 1920.95 193.675 Q1919.03 196.013 1919.03 200.411 L1919.03 214.069 L1914.75 214.069 L1914.75 188.143 L1919.03 188.143 L1919.03 192.171 Q1920.37 189.809 1922.53 188.675 Q1924.68 187.518 1927.76 187.518 Q1928.2 187.518 1928.73 187.587 Q1929.26 187.634 1929.91 187.749 L1929.93 192.124 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M1950.93 188.907 L1950.93 192.934 Q1949.12 192.009 1947.18 191.546 Q1945.23 191.083 1943.15 191.083 Q1939.98 191.083 1938.38 192.055 Q1936.81 193.027 1936.81 194.971 Q1936.81 196.453 1937.94 197.309 Q1939.08 198.143 1942.5 198.907 L1943.96 199.231 Q1948.5 200.203 1950.4 201.985 Q1952.32 203.745 1952.32 206.916 Q1952.32 210.527 1949.45 212.633 Q1946.6 214.74 1941.6 214.74 Q1939.52 214.74 1937.25 214.323 Q1935 213.93 1932.5 213.12 L1932.5 208.721 Q1934.86 209.948 1937.16 210.573 Q1939.45 211.175 1941.69 211.175 Q1944.7 211.175 1946.32 210.157 Q1947.94 209.115 1947.94 207.24 Q1947.94 205.504 1946.76 204.578 Q1945.6 203.652 1941.65 202.796 L1940.16 202.448 Q1936.21 201.615 1934.45 199.902 Q1932.69 198.166 1932.69 195.157 Q1932.69 191.499 1935.28 189.509 Q1937.87 187.518 1942.64 187.518 Q1945 187.518 1947.09 187.865 Q1949.17 188.212 1950.93 188.907 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M1981.28 200.041 L1981.28 202.124 L1961.69 202.124 Q1961.97 206.522 1964.33 208.837 Q1966.72 211.129 1970.95 211.129 Q1973.41 211.129 1975.7 210.527 Q1978.01 209.925 1980.28 208.721 L1980.28 212.749 Q1977.99 213.721 1975.58 214.231 Q1973.17 214.74 1970.7 214.74 Q1964.49 214.74 1960.86 211.129 Q1957.25 207.518 1957.25 201.36 Q1957.25 194.995 1960.67 191.268 Q1964.12 187.518 1969.96 187.518 Q1975.19 187.518 1978.22 190.897 Q1981.28 194.254 1981.28 200.041 M1977.02 198.791 Q1976.97 195.296 1975.05 193.212 Q1973.15 191.129 1970 191.129 Q1966.44 191.129 1964.28 193.143 Q1962.16 195.157 1961.83 198.814 L1977.02 198.791 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M2009.82 198.421 L2009.82 214.069 L2005.56 214.069 L2005.56 198.559 Q2005.56 194.879 2004.12 193.05 Q2002.69 191.222 1999.82 191.222 Q1996.37 191.222 1994.38 193.421 Q1992.39 195.62 1992.39 199.416 L1992.39 214.069 L1988.1 214.069 L1988.1 188.143 L1992.39 188.143 L1992.39 192.171 Q1993.91 189.833 1995.97 188.675 Q1998.06 187.518 2000.77 187.518 Q2005.23 187.518 2007.53 190.296 Q2009.82 193.05 2009.82 198.421 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M2018.31 188.143 L2022.57 188.143 L2022.57 214.069 L2018.31 214.069 L2018.31 188.143 M2018.31 178.05 L2022.57 178.05 L2022.57 183.444 L2018.31 183.444 L2018.31 178.05 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M2048.54 192.078 L2048.54 178.05 L2052.8 178.05 L2052.8 214.069 L2048.54 214.069 L2048.54 210.18 Q2047.2 212.495 2045.14 213.629 Q2043.1 214.74 2040.23 214.74 Q2035.53 214.74 2032.57 210.99 Q2029.63 207.24 2029.63 201.129 Q2029.63 195.018 2032.57 191.268 Q2035.53 187.518 2040.23 187.518 Q2043.1 187.518 2045.14 188.652 Q2047.2 189.763 2048.54 192.078 M2034.03 201.129 Q2034.03 205.828 2035.95 208.513 Q2037.9 211.175 2041.28 211.175 Q2044.65 211.175 2046.6 208.513 Q2048.54 205.828 2048.54 201.129 Q2048.54 196.43 2046.6 193.768 Q2044.65 191.083 2041.28 191.083 Q2037.9 191.083 2035.95 193.768 Q2034.03 196.43 2034.03 201.129 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M2083.75 200.041 L2083.75 202.124 L2064.17 202.124 Q2064.45 206.522 2066.81 208.837 Q2069.19 211.129 2073.43 211.129 Q2075.88 211.129 2078.17 210.527 Q2080.49 209.925 2082.76 208.721 L2082.76 212.749 Q2080.46 213.721 2078.06 214.231 Q2075.65 214.74 2073.17 214.74 Q2066.97 214.74 2063.34 211.129 Q2059.72 207.518 2059.72 201.36 Q2059.72 194.995 2063.15 191.268 Q2066.6 187.518 2072.43 187.518 Q2077.66 187.518 2080.7 190.897 Q2083.75 194.254 2083.75 200.041 M2079.49 198.791 Q2079.45 195.296 2077.53 193.212 Q2075.63 191.129 2072.48 191.129 Q2068.91 191.129 2066.76 193.143 Q2064.63 195.157 2064.31 198.814 L2079.49 198.791 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M2116.04 178.097 Q2112.94 183.421 2111.44 188.629 Q2109.93 193.837 2109.93 199.184 Q2109.93 204.532 2111.44 209.786 Q2112.96 215.018 2116.04 220.319 L2112.34 220.319 Q2108.87 214.879 2107.13 209.624 Q2105.42 204.37 2105.42 199.184 Q2105.42 194.022 2107.13 188.791 Q2108.84 183.56 2112.34 178.097 L2116.04 178.097 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M2148.06 209.138 L2148.06 199.856 L2140.42 199.856 L2140.42 196.013 L2152.69 196.013 L2152.69 210.851 Q2149.98 212.772 2146.71 213.768 Q2143.45 214.74 2139.75 214.74 Q2131.65 214.74 2127.06 210.018 Q2122.5 205.272 2122.5 196.823 Q2122.5 188.351 2127.06 183.629 Q2131.65 178.884 2139.75 178.884 Q2143.13 178.884 2146.16 179.717 Q2149.21 180.55 2151.78 182.171 L2151.78 187.147 Q2149.19 184.948 2146.27 183.837 Q2143.36 182.726 2140.14 182.726 Q2133.8 182.726 2130.6 186.268 Q2127.43 189.809 2127.43 196.823 Q2127.43 203.814 2130.6 207.356 Q2133.8 210.897 2140.14 210.897 Q2142.62 210.897 2144.56 210.481 Q2146.51 210.041 2148.06 209.138 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M2172.83 201.036 Q2167.66 201.036 2165.67 202.217 Q2163.68 203.397 2163.68 206.245 Q2163.68 208.513 2165.16 209.856 Q2166.67 211.175 2169.24 211.175 Q2172.78 211.175 2174.91 208.675 Q2177.06 206.152 2177.06 201.985 L2177.06 201.036 L2172.83 201.036 M2181.32 199.277 L2181.32 214.069 L2177.06 214.069 L2177.06 210.133 Q2175.6 212.495 2173.43 213.629 Q2171.25 214.74 2168.1 214.74 Q2164.12 214.74 2161.76 212.518 Q2159.42 210.272 2159.42 206.522 Q2159.42 202.147 2162.34 199.925 Q2165.28 197.703 2171.09 197.703 L2177.06 197.703 L2177.06 197.286 Q2177.06 194.347 2175.12 192.749 Q2173.2 191.129 2169.7 191.129 Q2167.48 191.129 2165.37 191.661 Q2163.27 192.194 2161.32 193.259 L2161.32 189.323 Q2163.66 188.421 2165.86 187.981 Q2168.06 187.518 2170.14 187.518 Q2175.77 187.518 2178.54 190.434 Q2181.32 193.351 2181.32 199.277 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M2201.83 184.115 L2195.49 201.314 L2208.2 201.314 L2201.83 184.115 M2199.19 179.509 L2204.49 179.509 L2217.66 214.069 L2212.8 214.069 L2209.65 205.203 L2194.08 205.203 L2190.93 214.069 L2186 214.069 L2199.19 179.509 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M2239.05 188.907 L2239.05 192.934 Q2237.25 192.009 2235.3 191.546 Q2233.36 191.083 2231.27 191.083 Q2228.1 191.083 2226.51 192.055 Q2224.93 193.027 2224.93 194.971 Q2224.93 196.453 2226.07 197.309 Q2227.2 198.143 2230.63 198.907 L2232.08 199.231 Q2236.62 200.203 2238.52 201.985 Q2240.44 203.745 2240.44 206.916 Q2240.44 210.527 2237.57 212.633 Q2234.72 214.74 2229.72 214.74 Q2227.64 214.74 2225.37 214.323 Q2223.13 213.93 2220.63 213.12 L2220.63 208.721 Q2222.99 209.948 2225.28 210.573 Q2227.57 211.175 2229.82 211.175 Q2232.83 211.175 2234.45 210.157 Q2236.07 209.115 2236.07 207.24 Q2236.07 205.504 2234.89 204.578 Q2233.73 203.652 2229.77 202.796 L2228.29 202.448 Q2224.33 201.615 2222.57 199.902 Q2220.81 198.166 2220.81 195.157 Q2220.81 191.499 2223.4 189.509 Q2226 187.518 2230.76 187.518 Q2233.13 187.518 2235.21 187.865 Q2237.29 188.212 2239.05 188.907 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M2246.55 178.097 L2250.26 178.097 Q2253.73 183.56 2255.44 188.791 Q2257.18 194.022 2257.18 199.184 Q2257.18 204.37 2255.44 209.624 Q2253.73 214.879 2250.26 220.319 L2246.55 220.319 Q2249.63 215.018 2251.14 209.786 Q2252.66 204.532 2252.66 199.184 Q2252.66 193.837 2251.14 188.629 Q2249.63 183.421 2246.55 178.097 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><polyline clip-path=\"url(#clip760)\" style=\"stroke:#3da44d; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" stroke-dasharray=\"16, 8, 2, 8\" points=\"1526.79,248.629 1670.16,248.629 \"/>\n",
"<path clip-path=\"url(#clip760)\" d=\"M1712.48 240.747 L1712.48 244.774 Q1710.68 243.849 1708.73 243.386 Q1706.79 242.923 1704.7 242.923 Q1701.53 242.923 1699.93 243.895 Q1698.36 244.867 1698.36 246.811 Q1698.36 248.293 1699.49 249.149 Q1700.63 249.983 1704.05 250.747 L1705.51 251.071 Q1710.05 252.043 1711.95 253.825 Q1713.87 255.585 1713.87 258.756 Q1713.87 262.367 1711 264.473 Q1708.15 266.58 1703.15 266.58 Q1701.07 266.58 1698.8 266.163 Q1696.55 265.77 1694.05 264.96 L1694.05 260.561 Q1696.42 261.788 1698.71 262.413 Q1701 263.015 1703.24 263.015 Q1706.25 263.015 1707.87 261.997 Q1709.49 260.955 1709.49 259.08 Q1709.49 257.344 1708.31 256.418 Q1707.16 255.492 1703.2 254.636 L1701.72 254.288 Q1697.76 253.455 1696 251.742 Q1694.24 250.006 1694.24 246.997 Q1694.24 243.339 1696.83 241.349 Q1699.43 239.358 1704.19 239.358 Q1706.55 239.358 1708.64 239.705 Q1710.72 240.052 1712.48 240.747 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M1720.65 239.983 L1724.91 239.983 L1724.91 265.909 L1720.65 265.909 L1720.65 239.983 M1720.65 229.89 L1724.91 229.89 L1724.91 235.284 L1720.65 235.284 L1720.65 229.89 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M1733.82 229.89 L1738.08 229.89 L1738.08 265.909 L1733.82 265.909 L1733.82 229.89 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M1746.99 239.983 L1751.25 239.983 L1751.25 265.909 L1746.99 265.909 L1746.99 239.983 M1746.99 229.89 L1751.25 229.89 L1751.25 235.284 L1746.99 235.284 L1746.99 229.89 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M1778.82 240.978 L1778.82 244.96 Q1777.02 243.964 1775.19 243.478 Q1773.38 242.969 1771.53 242.969 Q1767.39 242.969 1765.1 245.608 Q1762.8 248.224 1762.8 252.969 Q1762.8 257.714 1765.1 260.353 Q1767.39 262.969 1771.53 262.969 Q1773.38 262.969 1775.19 262.483 Q1777.02 261.973 1778.82 260.978 L1778.82 264.913 Q1777.04 265.747 1775.12 266.163 Q1773.22 266.58 1771.07 266.58 Q1765.21 266.58 1761.76 262.899 Q1758.31 259.219 1758.31 252.969 Q1758.31 246.626 1761.79 242.992 Q1765.28 239.358 1771.35 239.358 Q1773.31 239.358 1775.19 239.775 Q1777.06 240.168 1778.82 240.978 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M1798.01 252.876 Q1792.85 252.876 1790.86 254.057 Q1788.87 255.237 1788.87 258.085 Q1788.87 260.353 1790.35 261.696 Q1791.86 263.015 1794.42 263.015 Q1797.97 263.015 1800.1 260.515 Q1802.25 257.992 1802.25 253.825 L1802.25 252.876 L1798.01 252.876 M1806.51 251.117 L1806.51 265.909 L1802.25 265.909 L1802.25 261.973 Q1800.79 264.335 1798.61 265.469 Q1796.44 266.58 1793.29 266.58 Q1789.31 266.58 1786.95 264.358 Q1784.61 262.112 1784.61 258.362 Q1784.61 253.987 1787.53 251.765 Q1790.47 249.543 1796.28 249.543 L1802.25 249.543 L1802.25 249.126 Q1802.25 246.187 1800.3 244.589 Q1798.38 242.969 1794.89 242.969 Q1792.67 242.969 1790.56 243.501 Q1788.45 244.034 1786.51 245.099 L1786.51 241.163 Q1788.85 240.261 1791.05 239.821 Q1793.24 239.358 1795.33 239.358 Q1800.95 239.358 1803.73 242.274 Q1806.51 245.191 1806.51 251.117 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M1840.58 229.937 Q1837.48 235.261 1835.98 240.469 Q1834.47 245.677 1834.47 251.024 Q1834.47 256.372 1835.98 261.626 Q1837.5 266.858 1840.58 272.159 L1836.88 272.159 Q1833.41 266.719 1831.67 261.464 Q1829.96 256.21 1829.96 251.024 Q1829.96 245.862 1831.67 240.631 Q1833.38 235.4 1836.88 229.937 L1840.58 229.937 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M1869.75 232.483 L1869.75 237.043 Q1867.09 235.77 1864.73 235.145 Q1862.36 234.52 1860.17 234.52 Q1856.35 234.52 1854.26 236.001 Q1852.2 237.483 1852.2 240.214 Q1852.2 242.506 1853.57 243.687 Q1854.96 244.844 1858.8 245.562 L1861.62 246.14 Q1866.85 247.136 1869.33 249.659 Q1871.83 252.159 1871.83 256.372 Q1871.83 261.395 1868.45 263.987 Q1865.1 266.58 1858.59 266.58 Q1856.14 266.58 1853.36 266.024 Q1850.6 265.469 1847.64 264.381 L1847.64 259.566 Q1850.49 261.163 1853.22 261.973 Q1855.95 262.784 1858.59 262.784 Q1862.6 262.784 1864.77 261.21 Q1866.95 259.636 1866.95 256.719 Q1866.95 254.173 1865.37 252.737 Q1863.82 251.302 1860.26 250.585 L1857.41 250.029 Q1852.18 248.987 1849.84 246.765 Q1847.5 244.543 1847.5 240.585 Q1847.5 236.001 1850.72 233.362 Q1853.96 230.724 1859.63 230.724 Q1862.06 230.724 1864.59 231.163 Q1867.11 231.603 1869.75 232.483 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M1878.94 239.983 L1883.2 239.983 L1883.2 265.909 L1878.94 265.909 L1878.94 239.983 M1878.94 229.89 L1883.2 229.89 L1883.2 235.284 L1878.94 235.284 L1878.94 229.89 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M1906.32 234.52 Q1901.23 234.52 1898.22 238.316 Q1895.23 242.112 1895.23 248.663 Q1895.23 255.191 1898.22 258.987 Q1901.23 262.784 1906.32 262.784 Q1911.41 262.784 1914.38 258.987 Q1917.36 255.191 1917.36 248.663 Q1917.36 242.112 1914.38 238.316 Q1911.41 234.52 1906.32 234.52 M1906.32 230.724 Q1913.59 230.724 1917.94 235.608 Q1922.29 240.469 1922.29 248.663 Q1922.29 256.835 1917.94 261.719 Q1913.59 266.58 1906.32 266.58 Q1899.03 266.58 1894.66 261.719 Q1890.3 256.858 1890.3 248.663 Q1890.3 240.469 1894.66 235.608 Q1899.03 230.724 1906.32 230.724 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M1931.16 263.27 L1940.97 263.27 L1940.97 265.909 L1927.13 265.909 L1927.13 263.362 Q1927.92 262.645 1929.38 261.348 Q1937.34 254.288 1937.34 252.112 Q1937.34 250.585 1936.14 249.659 Q1934.93 248.71 1932.97 248.71 Q1931.76 248.71 1930.35 249.126 Q1928.94 249.52 1927.27 250.33 L1927.27 247.483 Q1929.05 246.835 1930.58 246.511 Q1932.13 246.187 1933.45 246.187 Q1936.81 246.187 1938.82 247.714 Q1940.84 249.242 1940.84 251.742 Q1940.84 254.96 1933.17 261.534 Q1931.88 262.645 1931.16 263.27 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip760)\" d=\"M1947.76 229.937 L1951.46 229.937 Q1954.93 235.4 1956.65 240.631 Q1958.38 245.862 1958.38 251.024 Q1958.38 256.21 1956.65 261.464 Q1954.93 266.719 1951.46 272.159 L1947.76 272.159 Q1950.84 266.858 1952.34 261.626 Q1953.87 256.372 1953.87 251.024 Q1953.87 245.677 1952.34 240.469 Q1950.84 235.261 1947.76 229.937 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /></svg>\n"
]
},
"metadata": {},
"execution_count": 5
}
],
"cell_type": "code",
"source": [
"using Plots\n",
"\n",
"χ0_metal(q, kTF=1) = -kTF^2 / 4π\n",
"χ0_dielectric(q, εr, C₀=1-εr, kTF=1) = C₀*q^2 / (4π * (1 - C₀*q^2/kTF^2))\n",
"χ0_GaAs(q) = χ0_dielectric(q, 14.9)\n",
"χ0_SiO2(q) = χ0_dielectric(q, 1.5)\n",
"ε(χ0, q) = (1 - 4π/q^2 * χ0(q))\n",
"\n",
"p = plot(xlims=(1e-2, 1.5), ylims=(0, 16), xlabel=\"q\", ylabel=\"ε(q)\", lw=4)\n",
"plot!(p, x -> ε(χ0_metal, x), label=\"aluminium (Al)\")\n",
"plot!(p, x -> ε(χ0_GaAs, x), label=\"gallium arsenide (GaAs)\", ls=:dash)\n",
"plot!(p, x -> ε(χ0_SiO2, x), label=\"silica (SiO₂)\", ls=:dashdot)"
],
"metadata": {},
"execution_count": 5
},
{
"cell_type": "markdown",
"source": [
"As expected from this discussion, for insulators $P = I$ (no preconditioner) is sufficient, while for the two other cases, an appropriate preconditioner is needed to ensure good convergence properties for large systems.\n",
"\n",
"Here we show the results for three large bulk systems (40 unit cells) of the three materials:\n",
"\n",
"\n",
"| Aluminium (a metal) | Gallium arsenide (a semiconductor) | Silica (an insulator) |\n",
"| :-------------------------------------------------------: | :------------------------------------: | :-------: |\n",
"| <img src=\"Al_repeat_40.png\" width=300 /> | <img src=\"GaAs_repeat_40.png\" width=300 /> | <img src=\"SiO2_repeat_39.png\" width=300 /> |"
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"### Susceptibility models and LDOS preconditioner\n",
"\n",
"While the bulk preconditioning models mentioned above are a good step forward, they have two key disadvantages:\n",
"1. Since the preconditioner models (especially between metals and insulators) are rather distinct, the preconditioner needs to match the modelled material to ensure fast convergence for large systems. In other words one needs to know **a priori** what material one is modelling.\n",
"2. Being by nature bulk models, they miss important applications featuring inhomogeneous systems, such as catalytic surfaces, metal clusters etc.\n",
"\n",
"In order to overcome the second point it is important to realise that we need to give up on the translational independence of $\\chi_0$, i.e. we no longer are able to compute $P^{-1}(q)$ by $1/P(q)$. Our strategy will therefore be to construct more sophisticated approximations to $\\chi_0$, denoted by $\\widetilde{\\chi_0}$. The preconditioned density $x_n = P^{-1} \\rho_n = (1 - \\widetilde{\\chi_0} v_c)^{-1}$ is then obtained by solving\n",
"$$\n",
"(1 - \\widetilde{\\chi_0} v_c) x_n = \\rho_n\n",
"$$\n",
"iteratively for $x_n$ using GMRES.\n",
"\n",
"Note that $\\chi_0(r, r')$ has unit-cell internal fluctuations, but is overall diagonal dominant\n",
"\n",
"<img src=\"https://docs.dftk.org/stable/guide/chi0.png\" width=400 />\n",
"\n",
"Starting from the Adler-Wiser formula\n",
"$$\n",
"\\begin{align*}\n",
" \\chi_0(\\vec{r}, \\vec{r}')\n",
" &= \\sum_{n, m} \\frac{f_\\text{FD}(\\varepsilon_n) - f_\\text{FD}(\\varepsilon_m)}{\\varepsilon_n - \\varepsilon_m} \\psi_n(\\vec{r}) \\psi_m^\\ast(\\vec{r})\n",
" \\psi_m(\\vec{r}') \\psi_n^\\ast(\\vec{r}')%\\\\\n",
"\\end{align*}\n",
"$$\n",
"we want to capture the large-scale variations from $\\rho_n$ to $\\rho_{n+1}$ to counteract the charge-sloshing. Set $V = v_c \\rho_n$ and assume $\\vec{r} \\mapsto \\chi_0(\\vec{r}, \\vec{r}')$ to be more localised around $\\vec{r}'$ than $V(\\vec{r}')$. Then apply *row-sum mass lumping* to homogenise the operator:\n",
"$$\n",
"\\begin{align*}\n",
" \\int \\chi_0(\\vec{r}, \\vec{r}') V(\\vec{r}') d\\vec{r}'\n",
" &\\simeq V(\\vec{r})\\int \\chi_0(\\vec{r}, \\vec{r}') d\\vec{r}'\\\\\n",
" &= V(\\vec{r}) \\sum_{n, m} \\frac{f(\\varepsilon_n) - f(\\varepsilon_m)}\n",
" {\\varepsilon_n - \\varepsilon_m}\n",
" \\psi_n(\\vec{r}) \\psi_m^\\ast(\\vec{r}) \\delta_{mn}\\\\\n",
" &= V(\\vec{r}) \\sum_n f'(\\varepsilon_n) |\\psi_n(\\vec{r})|^2\\\\\n",
" &= V(\\vec{r}) \\cdot \\Big(- \\text{LDOS}(\\vec{r}) \\Big)\n",
"\\end{align*}\n",
"$$\n",
"Overall we thus approximate\n",
"$$\n",
"\\chi_0(r, r') \\simeq - \\text{LDOS}(r) \\, \\delta(r, r')\n",
"$$"
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"Note that this approach yields a generic framework, where further terms (capturing other physics of $\\chi_0$) could be easily employed on top of the $-\\text{LDOS}$ term.\n",
"\n",
"To conclude this chapter we show some results for mixed systems featuring various combinations of metals, insulators and semiconductors. In the table both the number of iterations as well as the condition number is shown. Cases where the condition number does not more than double as the system size is doubled are coloured.\n",
"\n",
"<img src=\"ldos_table.png\" width=\"700px\" />\n",
"\n",
"For the two metal-insulator systems, exemplary convergence curves are shown below:\n",
"\n",
"| Aluminium + Vacuum | Aluminium + Silica |\n",
"| :---------------------------------: | :----------------: |\n",
"| <img src=\"alvac.png\" width=400 /> | <img src=\"alsio2.png\" width=400 /> |\n",
"| <img src=\"AlVac_repeat_20.png\" width=400 /> | <img src=\"AlSiO2H_repeat_20.png\" width=400 /> |\n",
"\n",
"The LDOS preconditioning strategy is available in DFTK as `LdosMixing`. Since it is parameter-free and applicable to a wide range of systems (any mixture of insulator and metals), it is used by default in DFTK."
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"## Preconditioned SCF methods in practice\n",
"\n",
"We return to our aluminium setting produced by `aluminium_setup`.\n",
"In this case we are dealing with a prototypical\n",
"metal, such that `KerkerMixing` is indeed appropriate. We will thus employ it as\n",
"the preconditioner $P$ in the setting\n",
"$$\n",
"\\rho_{n+1} = \\rho_n + \\alpha P^{-1} (D(V(\\rho_n)) - \\rho_n),\n",
"$$\n",
"In DFTK this is done by running an SCF as follows:\n",
"```julia\n",
"self_consistent_field(basis; damping=0.8, mixing=KerkerMixing());\n",
"```\n",
"\n",
"If you wonder about the use of Anderson acceleration in this context:\n",
"It can simply be re-introduced by replacing the previous definition of $R$ by\n",
"$R(\\rho) = P^{-1} (F(\\rho_n) - \\rho_n)$. Again DFTK does exactly this by default\n",
"if no other `solver` is passed to `self_consistent_field`.\n",
"\n",
"> **Exercise 4**\n",
">\n",
"> Try the Anderson-accelerated and `KerkerMixing`-preconditioned setup for\n",
"> different values of `repeat` in `aluminium_setup`\n",
"> and check the number of iterations needed. Other mixings DFTK has to offer are `DielectricMixing` (best for semiconductors), `SimpleMixing` (which is $P = I$, i.e. no preconditioner at all, best for insulators) or `LdosMixing` (self-adapting, suitable for both metals *or* insulators *or* inhomogeneous mixtures). Note that `LdosMixing` is the default in DFTK (i.e. used if the `mixing` parameter is *not* supplied to `self_consistent_field`. Try these mixings (`SimpleMixing`, `DielectricMixing`, `LdosMixing` and `KerkerMixing`) and summarise your findings.\n",
"\n",
"You should notice that choosing a preconditioner matching the material under study aids a fast SCF convergence, but that sometimes being off does not seem to do much harm for our case. For larger values of `repeat` (beyond what you can probably effort on your laptop) this is no longer true and one needs to be very careful in selecting the right preconditioner. See for example the investigation in [^HL2021].\n",
"\n",
"[^HL2021]: M. Herbst, A. Levitt. *J. Phys.: Condens. Matter* **33** 085503 (2021) DOI: [10.1088/1361-648x/abcbdb](http://dx.doi.org/10.1088/1361-648x/abcbdb)\n",
"[^HL2022]: M. Herbst, A. Levitt *J. Comp. Phys.* **459** 111127 (2022). DOI [10.1016/j.jcp.2022.111127](http://dx.doi.org/10.1016/j.jcp.2022.111127)"
],
"metadata": {}
}
],
"nbformat_minor": 3,
"metadata": {
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.11.4"
},
"kernelspec": {
"name": "julia-1.11",
"display_name": "Julia 1.11.4",
"language": "julia"
}
},
"nbformat": 4
}