{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
" \n"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"Plots.PlotlyBackend()"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"using Plots\n",
"plotly()"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"F (generic function with 1 method)"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#Generated using the Calculus package\n",
"#Here are functions for the polynomial and its 5 next derivatives. \n",
"#They are combined into a function F that generates a vector of these functions.\n",
"#Because the root finder code uses all of these derivatvies, use F(x)[ind] to be the function your root-finding for.\n",
"f(x) = -(1/720)+x/36-(31 *x^2)/144+(29* x^3)/36-(29* x^4)/20+x^5\n",
"fp(x) = ((((0.027777777777777776 - (31 * (2x)) / 144) + (29 * (3 * x ^ 2)) / 36) - (29 * (4 * x ^ 3)) / 20) + 5 * x ^ 4)\n",
"fpp(x) = (((-0.4305555555555556 + (29 * (3 * (2x))) / 36) - (29 * (4 * (3 * x ^ 2))) / 20) + 5 * (4 * x ^ 3))\n",
"fppp(x) = ((4.833333333333333 - (29 * (4 * (3 * (2x)))) / 20) + 5 * (4 * (3 * x ^ 2)))\n",
"fpppp(x) = (-34.8 + 5 * (4 * (3 * (2x))))\n",
"fppppp(x) = 120\n",
"F(x) = [f(x), fp(x), fpp(x), fppp(x), fpppp(x), fppppp(x)]"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
" \n",
" \n"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#Here is a visual on the function\n",
"X = 0:0.0001:1\n",
"plot(X,f.(X), xaxis=[0,0.6], yaxis=[-0.001,0.001])"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Dekker (generic function with 1 method)"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Dekker Method\n",
"n = 100000 #maximum number of iterations permitted without finding a root.\n",
"epsilon_f = 1e-10 #epsilon of F value.\n",
"epsilon_x = 1e-10 #epsilon of X value\n",
"# Insert your code into this function. \n",
"# Use F(x)[ind] to call f (this format is required by the roots function later)\n",
"# l is the lower part of the range\n",
"# r is the upper part of the range\n",
"function Dekker(ind, l, r)\n",
" \n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"roots (generic function with 1 method)"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#Call: roots(6,0,1)\n",
"function roots(Level, Low, High)\n",
" if(Level==1)\n",
" #println(\"Range: \", Low,\" \",High)\n",
" end\n",
" if(Level==0)\n",
" return\n",
" end\n",
" root = Dekker(Level, Low, High) \n",
" #println(root, \" \", Level, \" \", Low, \" \", High)\n",
" if(Level == 1)\n",
" if(root==nothing || abs(root - High) < epsilon_x || abs(root-Low) < epsilon_x)\n",
" \n",
" else\n",
" println(root)\n",
" end\n",
" end\n",
" if(root == nothing || abs(root - High) < epsilon_x || abs(root-Low) < epsilon_x)\n",
" roots(Level-1, Low, High)\n",
" else\n",
" roots(Level-1, Low, root)\n",
" roots(Level-1, root, High)\n",
" end\n",
" \n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"#This function prints out the roots found by using your Dekker function.\n",
"roots(6,0,1)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"#This function returns a single root of the original polynomial in the range 0.1 and 0.8\n",
"Dekker(1,0.1,0.8)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
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"display_name": "Julia 0.6.2",
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