Bspline_v1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From: CPC **188** 94-102 (2015)\n",
    "A mixed basis density functional approach for low dimensional systems with B-splines"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A B-spline of order $\\kappa$ is formed by positive polynomials of degree $\\kappa-1$ over $\\kappa$ adjacent subintervals. These polynomials vanish everywhere outside the subinterval $\\tau_{i} \\le z \\le \\tau_{i+\\kappa}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given the order $\\kappa$ and knot sequence $\\{\\tau_{i}\\}$, B-spline can be generated by the following relation:\n",
    "\n",
    "$$\n",
    "B_{i,\\kappa}(z) = \\frac{z-\\tau_{i}}{\\tau_{i+\\kappa-1} - \\tau_{i}} B_{i,\\kappa-1}(z) +\n",
    "\\frac{\\tau_{i+\\kappa} - z}{\\tau_{i+\\kappa} - \\tau_{i+1}} B_{i+1,\\kappa-1}(z)\n",
    "$$\n",
    "\n",
    "with\n",
    "\n",
    "$$\n",
    "B_{i,1}(z) = \\begin{cases}\n",
    "1, \\,\\,\\tau_{i} \\leq z \\leq \\tau_{i+1} \\\\\n",
    "0, \\,\\,\\text{otherwise}\n",
    "\\end{cases}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For example $\\kappa = 4$, we need at least xx subintervals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "κ = 5\n",
    "Npoints = 11"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [],
   "source": [
    "z_min = 0.0\n",
    "z_max = 10.0\n",
    "τ = PeriodicGrid( collect(range(z_min,z_max,length=Npoints)) );"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "eval_B_spline (generic function with 4 methods)"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function eval_B_spline(τ::PeriodicGrid, i::Int64, κ::Int64, z::Float64)\n",
    "    if κ == 1\n",
    "        if (z < τ[i+1]) && (z >= τ[i])\n",
    "            return 1.0\n",
    "        else\n",
    "            return 0.0\n",
    "        end\n",
    "    else\n",
    "        term1 = (z - τ[i])/(τ[i+κ-1] - τ[i])*eval_B_spline(τ,i,κ-1,z)\n",
    "        term2 = (τ[i+κ] - z)/(τ[i+κ] - τ[i+1])*eval_B_spline(τ,i+1,κ-1,z)\n",
    "        return term1 + term2\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eval_B_spline(τ,6,κ,0.9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [],
   "source": [
    "NptsPlot = 100\n",
    "z_grid = range(z_min,z_max,length=NptsPlot)\n",
    "B = zeros(NptsPlot,Npoints)\n",
    "for i = 1:Npoints\n",
    "    for i_z = 1:NptsPlot\n",
    "        B[i_z,i] = eval_B_spline(τ,i,κ,z_grid[i_z])\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "import PyPlot\n",
    "const plt = PyPlot\n",
    "plt.svg(true);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "PyPlot.Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.clf()\n",
    "for i = 1:Npoints\n",
    "    plt.plot(z_grid, B[:,i])\n",
    "end\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "getindex (generic function with 234 methods)"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "struct PeriodicGrid <: AbstractArray{Float64,1}\n",
    "    grid::Array{Float64,1}\n",
    "end\n",
    "\n",
    "Base.size( S::PeriodicGrid ) = (length(S.grid),)\n",
    "Base.IndexStyle(::Type{<:PeriodicGrid}) = IndexLinear()\n",
    "\n",
    "import Base: getindex\n",
    "function getindex( S::PeriodicGrid, i::Int )\n",
    "    N = length(S.grid)\n",
    "    ii = i%N\n",
    "    if ii == 0\n",
    "        return S.grid[N]\n",
    "    else\n",
    "        return S.grid[ii]\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "getindex (generic function with 233 methods)"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "struct IsolatedGrid <: AbstractArray{Float64,1}\n",
    "    grid::Array{Float64,1}\n",
    "end\n",
    "\n",
    "Base.size( S::IsolatedGrid ) = (length(S.grid),)\n",
    "Base.IndexStyle(::Type{<:IsolatedGrid}) = IndexLinear()\n",
    "\n",
    "import Base: getindex\n",
    "function getindex( S::IsolatedGrid, i::Int )\n",
    "    N = length(S.grid)\n",
    "    if i > N\n",
    "        return 0.0\n",
    "    else\n",
    "        return S.grid[i]\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5-element IsolatedGrid:\n",
       " 1.0 \n",
       " 1.25\n",
       " 1.5 \n",
       " 1.75\n",
       " 2.0 "
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s = IsolatedGrid(collect(range(1.0,2.0,length=5)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s[8]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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