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ileasile/example.ipynb

Last active July 10, 2023 12:57
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Curve fitting
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example.ipynb
{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
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"data": {
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"data": {
"text/html": [
" <div id=\"kotlin_out_0\"></div>\n",
" <script type=\"text/javascript\">\n",
" if(!window.kotlinQueues) {\n",
" window.kotlinQueues = {};\n",
" }\n",
" if(!window.kotlinQueues[\"kandyLetsPlot\"]) {\n",
" var resQueue = [];\n",
" window.kotlinQueues[\"kandyLetsPlot\"] = resQueue;\n",
" window[\"call_kandyLetsPlot\"] = function(f) {\n",
" resQueue.push(f);\n",
" }\n",
" }\n",
" (function (){\n",
" var modifiers = [(function(script) {\n",
" script.src = \"https://cdn.jsdelivr.net/gh/JetBrains/lets-plot@v3.1.0/js-package/distr/lets-plot.min.js\"\n",
" script.type = \"text/javascript\";\n",
"})];\n",
" var e = document.getElementById(\"kotlin_out_0\");\n",
" modifiers.forEach(function (gen) {\n",
" var script = document.createElement(\"script\");\n",
" gen(script)\n",
" script.addEventListener(\"load\", function() {\n",
" window[\"call_kandyLetsPlot\"] = function(f) {f();};\n",
" window.kotlinQueues[\"kandyLetsPlot\"].forEach(function(f) {f();});\n",
" window.kotlinQueues[\"kandyLetsPlot\"] = [];\n",
" }, false);\n",
" script.addEventListener(\"error\", function() {\n",
" window[\"call_kandyLetsPlot\"] = function(f) {};\n",
" window.kotlinQueues[\"kandyLetsPlot\"] = [];\n",
" var div = document.createElement(\"div\");\n",
" div.style.color = 'darkred';\n",
" div.textContent = 'Error loading resource kandyLetsPlot';\n",
" document.getElementById(\"kotlin_out_0\").appendChild(div);\n",
" }, false);\n",
" \n",
" e.appendChild(script);\n",
" });\n",
" })();\n",
" </script>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"%useLatestDescriptors\n",
"%use kandy"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"@file:DependsOn(\"org.apache.commons:commons-math3:3.6.1\")"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"import org.apache.commons.math3.fitting.PolynomialCurveFitter\n",
"import org.apache.commons.math3.fitting.WeightedObservedPoints"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Polynomial coefficients:\n",
"Coefficient 0: 12.714285714285442\n",
"Coefficient 1: -18.397186147185792\n",
"Coefficient 2: 10.874999999999847\n",
"Coefficient 3: -2.159090909090883\n",
"Coefficient 4: 0.14015151515151358\n"
]
}
],
"source": [
"val data = mapOf(\n",
" 1 to 3,\n",
" 2 to 5,\n",
" 3 to 8,\n",
" 4 to 10,\n",
" 5 to 12,\n",
" 6 to 8,\n",
" 7 to 13\n",
")\n",
"\n",
"// Prepare the observed data points\n",
"val obs = WeightedObservedPoints()\n",
"data.forEach { (x, y) ->\n",
" obs.add(x.toDouble(), y.toDouble())\n",
"}\n",
"\n",
"// Perform polynomial regression\n",
"val degree = 4 // Change the degree as per your requirement\n",
"val fitter = PolynomialCurveFitter.create(degree)\n",
"val coefficients = fitter.fit(obs.toList())\n",
"\n",
"// Print the coefficients\n",
"println(\"Polynomial coefficients:\")\n",
"coefficients.forEachIndexed { index, coefficient ->\n",
" println(\"Coefficient $index: $coefficient\")\n",
"}"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"fun buildPolynomialFunction(coefficients: DoubleArray): (Double) -> Double {\n",
" return { x ->\n",
" var result = 0.0\n",
" for (i in coefficients.indices.reversed()) {\n",
" result += result * x + coefficients[i]\n",
" }\n",
" result\n",
" }\n",
"}"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"val f = buildPolynomialFunction(coefficients)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"10.822510822510797"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
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"source": [
"f(3.0)"
]
},
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"cell_type": "code",
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"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"30.14285714285692"
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"source": [
"f(7.0)"
]
},
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"cell_type": "code",
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},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"val N = 200\n",
"val start = -1.0\n",
"val end = 10.0\n",
"\n",
"plot {\n",
" line {\n",
" x((0..N).map { start + it * (end - start)/N })\n",
" y((0..N).map { f(start + it * (end - start)/N) })\n",
" }\n",
" // doesn't work because of bug\n",
"// points {\n",
"// val d = data.entries.toList().sortedBy { it.key }\n",
"// x (d.map { it.key })\n",
"// y (d.map { it.value })\n",
"// }\n",
"}"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"data class Point(val x: Double, val y: Double)\n",
"\n",
"fun approximatePolynomial(points: List<Point>, degree: Int): (Double) -> Double {\n",
" val n = points.size\n",
" require(degree >= 0 && degree < n) { \"Degree must be between 0 and ${n - 1}\" }\n",
"\n",
" val xValues = points.map { it.x }\n",
" val yValues = points.map { it.y }\n",
"\n",
" val aMatrix = Array(degree + 1) { DoubleArray(degree + 1) }\n",
" val bVector = DoubleArray(degree + 1)\n",
"\n",
" for (i in 0..degree) {\n",
" for (j in 0..degree) {\n",
" aMatrix[i][j] = sumOfPowers(xValues, i + j)\n",
" }\n",
" bVector[i] = sumOfPowerXY(xValues, yValues, i)\n",
" }\n",
"\n",
" val coefficients = solveSystemOfEquations(aMatrix, bVector)\n",
"\n",
" return { x ->\n",
" var result = 0.0\n",
" for (i in 0..degree) {\n",
" result += coefficients[i] * Math.pow(x, i.toDouble())\n",
" }\n",
" result\n",
" }\n",
"}\n",
"\n",
"fun sumOfPowers(xValues: List<Double>, power: Int): Double {\n",
" var result = 0.0\n",
" for (x in xValues) {\n",
" result += Math.pow(x, power.toDouble())\n",
" }\n",
" return result\n",
"}\n",
"\n",
"fun sumOfPowerXY(xValues: List<Double>, yValues: List<Double>, power: Int): Double {\n",
" var result = 0.0\n",
" for (i in xValues.indices) {\n",
" result += Math.pow(xValues[i], power.toDouble()) * yValues[i]\n",
" }\n",
" return result\n",
"}\n",
"\n",
"fun solveSystemOfEquations(aMatrix: Array<DoubleArray>, bVector: DoubleArray): DoubleArray {\n",
" val n = aMatrix.size\n",
"\n",
" for (p in 0 until n) {\n",
" var maxRow = p\n",
" for (i in p + 1 until n) {\n",
" if (Math.abs(aMatrix[i][p]) > Math.abs(aMatrix[maxRow][p])) {\n",
" maxRow = i\n",
" }\n",
" }\n",
"\n",
" val tempRow = aMatrix[p]\n",
" aMatrix[p] = aMatrix[maxRow]\n",
" aMatrix[maxRow] = tempRow\n",
"\n",
" val tempB = bVector[p]\n",
" bVector[p] = bVector[maxRow]\n",
" bVector[maxRow] = tempB\n",
"\n",
" for (i in p + 1 until n) {\n",
" val factor = aMatrix[i][p] / aMatrix[p][p]\n",
" bVector[i] -= factor * bVector[p]\n",
" for (j in p until n) {\n",
" aMatrix[i][j] -= factor * aMatrix[p][j]\n",
" }\n",
" }\n",
" }\n",
"\n",
" val coefficients = DoubleArray(n)\n",
"\n",
" for (i in n - 1 downTo 0) {\n",
" var sum = 0.0\n",
" for (j in i + 1 until n) {\n",
" sum += aMatrix[i][j] * coefficients[j]\n",
" }\n",
" coefficients[i] = (bVector[i] - sum) / aMatrix[i][i]\n",
" }\n",
"\n",
" return coefficients\n",
"}"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"val h = approximatePolynomial(data.map {Point(it.key.toDouble(), it.value.toDouble())}, 4)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"8.454545454546231"
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},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"h(3.0)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"12.744588744590772"
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},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"h(7.0)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
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},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot {\n",
" line {\n",
" x((0..N).map { start + it * (end - start)/N })\n",
" y((0..N).map { h(start + it * (end - start)/N) })\n",
" }\n",
" // doesn't work because of bug\n",
"// points {\n",
"// val d = data.entries.toList().sortedBy { it.key }\n",
"// x (d.map { it.key })\n",
"// y (d.map { it.value })\n",
"// }\n",
"}"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
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"display_name": "Kotlin",
"language": "kotlin",
"name": "kotlin"
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"name": "kotlin",
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}
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