{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "# Custom solvers\n",
    "In this example, we show how to define custom solvers. Our system\n",
    "will again be silicon, because we are not very imaginative"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "using DFTK, LinearAlgebra\n",
    "\n",
    "a = 10.26\n",
    "lattice = a / 2 * [[0 1 1.];\n",
    "                   [1 0 1.];\n",
    "                   [1 1 0.]]\n",
    "Si = ElementPsp(:Si, psp=load_psp(\"hgh/lda/Si-q4\"))\n",
    "atoms = [Si => [ones(3)/8, -ones(3)/8]]\n",
    "\n",
    "# We take very (very) crude parameters\n",
    "model = model_LDA(lattice, atoms)\n",
    "kgrid = [1, 1, 1]\n",
    "Ecut = 5\n",
    "basis = PlaneWaveBasis(model, Ecut; kgrid=kgrid);"
   ],
   "metadata": {},
   "execution_count": 1
  },
  {
   "cell_type": "markdown",
   "source": [
    "We define our custom fix-point solver: simply a damped fixed-point"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "function my_fp_solver(f, x0, max_iter; tol)\n",
    "    mixing_factor = .7\n",
    "    x = x0\n",
    "    fx = f(x)\n",
    "    for n = 1:max_iter\n",
    "        inc = fx - x\n",
    "        if norm(inc) < tol\n",
    "            break\n",
    "        end\n",
    "        x = x + mixing_factor * inc\n",
    "        fx = f(x)\n",
    "    end\n",
    "    (fixpoint=x, converged=norm(fx-x) < tol)\n",
    "end;"
   ],
   "metadata": {},
   "execution_count": 2
  },
  {
   "cell_type": "markdown",
   "source": [
    "Our eigenvalue solver just forms the dense matrix and diagonalizes\n",
    "it explicitly (this only works for very small systems)"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "function my_eig_solver(A, X0; maxiter, tol, kwargs...)\n",
    "    n = size(X0, 2)\n",
    "    A = Array(A)\n",
    "    E = eigen(A)\n",
    "    λ = E.values[1:n]\n",
    "    X = E.vectors[:, 1:n]\n",
    "    (λ=λ, X=X, residual_norms=[], iterations=0, converged=true, n_matvec=0)\n",
    "end;"
   ],
   "metadata": {},
   "execution_count": 3
  },
  {
   "cell_type": "markdown",
   "source": [
    "Finally we also define our custom mixing scheme. It will be a mixture\n",
    "of simple mixing (for the first 2 steps) and than default to Kerker mixing.\n",
    "In the mixing interface `δF` is ``(ρ_\\text{out} - ρ_\\text{in})``, i.e.\n",
    "the difference in density between two subsequent SCF steps and the `mix`\n",
    "function returns ``δρ``, which is added to ``ρ_\\text{in}`` to yield ``ρ_\\text{next}``,\n",
    "the density for the next SCF step."
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "struct MyMixing\n",
    "    α  # Damping parameter\n",
    "end\n",
    "MyMixing() = MyMixing(0.7)\n",
    "\n",
    "function DFTK.mix(mixing::MyMixing, basis, δF::RealFourierArray, δF_spin=nothing; n_iter, kwargs...)\n",
    "    if n_iter <= 2\n",
    "        # Just do simple mixing on total density and spin density (if it exists)\n",
    "        (mixing.α * δF, isnothing(δF_spin) ? nothing : mixing.α * δF_spin)\n",
    "    else\n",
    "        # Use the KerkerMixing from DFTK\n",
    "        DFTK.mix(KerkerMixing(α=mixing.α), basis, δF, δF_spin; kwargs...)\n",
    "    end\n",
    "end"
   ],
   "metadata": {},
   "execution_count": 4
  },
  {
   "cell_type": "markdown",
   "source": [
    "That's it! Now we just run the SCF with these solvers"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n     Energy            Eₙ-Eₙ₋₁     ρout-ρin   Diag\n",
      "---   ---------------   ---------   --------   ----\n",
      "  1   -7.167898191354         NaN   3.60e-01    0.0 \n",
      "  2   -7.238878037160   -7.10e-02   1.81e-01    0.0 \n",
      "  3   -7.247815008582   -8.94e-03   7.67e-02    0.0 \n",
      "  4   -7.248786690411   -9.72e-04   4.19e-02    0.0 \n",
      "  5   -7.249085823311   -2.99e-04   2.31e-02    0.0 \n",
      "  6   -7.249176447552   -9.06e-05   1.29e-02    0.0 \n",
      "  7   -7.249204104384   -2.77e-05   7.38e-03    0.0 \n",
      "  8   -7.249212720950   -8.62e-06   4.27e-03    0.0 \n",
      "  9   -7.249215484163   -2.76e-06   2.52e-03    0.0 \n",
      " 10   -7.249216400614   -9.16e-07   1.50e-03    0.0 \n",
      " 11   -7.249216715552   -3.15e-07   9.11e-04    0.0 \n",
      " 12   -7.249216827621   -1.12e-07   5.58e-04    0.0 \n",
      " 13   -7.249216868807   -4.12e-08   3.45e-04    0.0 \n",
      " 14   -7.249216884379   -1.56e-08   2.15e-04    0.0 \n",
      " 15   -7.249216890409   -6.03e-09   1.35e-04    0.0 \n"
     ]
    }
   ],
   "cell_type": "code",
   "source": [
    "scfres = self_consistent_field(basis;\n",
    "                               tol=1e-8,\n",
    "                               solver=my_fp_solver,\n",
    "                               eigensolver=my_eig_solver,\n",
    "                               mixing=MyMixing());"
   ],
   "metadata": {},
   "execution_count": 5
  },
  {
   "cell_type": "markdown",
   "source": [
    "Note that the default convergence criterion is on the difference of\n",
    "energy from one step to the other; when this gets below `tol`, the\n",
    "\"driver\" `self_consistent_field` artificially makes the fixpoint\n",
    "solver think it's converged by forcing `f(x) = x`. You can customize\n",
    "this with the `is_converged` keyword argument to\n",
    "`self_consistent_field`."
   ],
   "metadata": {}
  }
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