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Curve fitting
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"%useLatestDescriptors\n", | |
"%use kandy" | |
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{ | |
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"metadata": {}, | |
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"@file:DependsOn(\"org.apache.commons:commons-math3:3.6.1\")" | |
] | |
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{ | |
"cell_type": "code", | |
"execution_count": 3, | |
"metadata": {}, | |
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"source": [ | |
"import org.apache.commons.math3.fitting.PolynomialCurveFitter\n", | |
"import org.apache.commons.math3.fitting.WeightedObservedPoints" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
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"metadata": {}, | |
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{ | |
"name": "stdout", | |
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"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", | |
"}" | |
] | |
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{ | |
"cell_type": "code", | |
"execution_count": 5, | |
"metadata": {}, | |
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"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", | |
"}" | |
] | |
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"val f = buildPolynomialFunction(coefficients)" | |
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"f(7.0)" | |
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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" | |
] | |
}, | |
"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" | |
] | |
}, | |
"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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"kernelspec": { | |
"display_name": "Kotlin", | |
"language": "kotlin", | |
"name": "kotlin" | |
}, | |
"language_info": { | |
"codemirror_mode": "text/x-kotlin", | |
"file_extension": ".kt", | |
"mimetype": "text/x-kotlin", | |
"name": "kotlin", | |
"nbconvert_exporter": "", | |
"pygments_lexer": "kotlin", | |
"version": "1.8.20" | |
} | |
}, | |
"nbformat": 4, | |
"nbformat_minor": 4 | |
} |
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