OffserArrays and evalpoly

OffserArrays and evalpoly.ipynb

{
  "cells": [
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "using OffsetArrays\n\nA = OffsetArray([0.1, 2.3, 4.5, 6.7, 8.9], -2:2)\n\n@show A[-2]\n@show A[-1]\n@show A[0]\n@show A[1]\n@show A[2];",
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "text": "A[-2] = 0.1\nA[-1] = 2.3\nA[0] = 4.5\nA[1] = 6.7\nA[2] = 8.9\n",
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "@show A[begin]\n@show A[end];",
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "text": "A[begin] = 0.1\nA[end] = 8.9\n",
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "binom(x, k) = iszero(k) ? one(x) : prod((x-j+1)/j for j in k:-1:1)\n@show a = 0.5\n@show L = 1000\nc = OffsetArray(binom.(a, 0:L), 0:L) # binomial coefficients for the exponent a\n@show c[0]\n@show c[1]\n@show c[2]\n@show c[3]\n@show c[4]\n@show c[5]\n@show c[L];",
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "text": "a = 0.5 = 0.5\nL = 1000 = 1000\nc[0] = 1.0\nc[1] = 0.5\nc[2] = -0.125\nc[3] = 0.0625\nc[4] = -0.0390625\nc[5] = 0.02734375\nc[L] = -8.923967556705516e-6\n",
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "f(x; c=c) = sum(c[k]*(x-1)^k for k in eachindex(c)) # Taylor expansion of √x at x = 1\nf(1.9), √1.9",
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 4,
          "data": {
            "text/plain": "(1.3784048752090234, 1.378404875209022)"
          },
          "metadata": {}
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "evalpoly(1.9 - 1, parent(c))",
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 5,
          "data": {
            "text/plain": "1.378404875209022"
          },
          "metadata": {}
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "using BenchmarkTools",
      "execution_count": 6,
      "outputs": []
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "@benchmark evalpoly(1.9 - 1, $(parent(c)))",
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 7,
          "data": {
            "text/plain": "BenchmarkTools.Trial: \n  memory estimate:  0 bytes\n  allocs estimate:  0\n  --------------\n  minimum time:     1.493 μs (0.00% GC)\n  median time:      1.540 μs (0.00% GC)\n  mean time:        1.561 μs (0.00% GC)\n  maximum time:     15.256 μs (0.00% GC)\n  --------------\n  samples:          10000\n  evals/sample:     10"
          },
          "metadata": {}
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "@benchmark f(1.9; c=$c)",
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 8,
          "data": {
            "text/plain": "BenchmarkTools.Trial: \n  memory estimate:  48 bytes\n  allocs estimate:  2\n  --------------\n  minimum time:     89.107 μs (0.00% GC)\n  median time:      89.574 μs (0.00% GC)\n  mean time:        92.975 μs (0.00% GC)\n  maximum time:     247.729 μs (0.00% GC)\n  --------------\n  samples:          10000\n  evals/sample:     1"
          },
          "metadata": {}
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "",
      "execution_count": null,
      "outputs": []
    }
  ],
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        "description": "OffserArrays and evalpoly",
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