{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Piecewise polynomial interpolation\n",
"\n",
"Let us repeat the data from {doc}`interp-global` but use piecewise polynomials constructed using the `Interpolations` package."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"using FundamentalsNumericalComputation"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"\n",
"\n"
],
"text/plain": [
"Plot{Plots.GRBackend() n=1}"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"n = 12\n",
"t = LinRange(-1,1,n+1)\n",
"y = @. t^2 + t + 0.5*sin(20*t)\n",
"\n",
"scatter(t,y,label=\"data\",leg=:top)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here is an interpolant that is linear between each pair of consecutive nodes."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"\n",
"\n"
],
"text/plain": [
"Plot{Plots.GRBackend() n=2}"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"p = LinearInterpolation(t,y)\n",
"plot!(x->p(x),-1,1,label=\"piecewise linear\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We may instead request a smoother interpolant that is piecewise cubic."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"\n",
"\n"
],
"text/plain": [
"Plot{Plots.GRBackend() n=3}"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"p = CubicSplineInterpolation(t,y)\n",
"plot!(x->p(x),-1,1,label=\"piecewise cubic\")"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia (faststart)",
"language": "julia",
"name": "julia-fast"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.4.1"
}
},
"nbformat": 4,
"nbformat_minor": 4
}