forked from kscience/kmath
419 lines
9.7 KiB
Plaintext
419 lines
9.7 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "code",
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"source": [
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"%use kmath(0.3.1-dev-5)\n",
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"%use plotly(0.5.0)\n",
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"@file:DependsOn(\"space.kscience:kmath-commons:0.3.1-dev-5\")"
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],
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"execution_count": null,
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"outputs": [],
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"metadata": {
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"datalore": {
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"node_id": "lQbSB87rNAn9lV6poArVWW",
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"type": "CODE",
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"hide_input_from_viewers": false,
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"hide_output_from_viewers": false
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}
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}
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},
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{
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"cell_type": "code",
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"source": [
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"//Uncomment to work in Jupyter classic or DataLore\n",
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"//Plotly.jupyter.notebook()"
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],
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"execution_count": null,
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"outputs": [],
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"metadata": {
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"datalore": {
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"node_id": "0UP158hfccGgjQtHz0wAi6",
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"type": "CODE",
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"hide_input_from_viewers": false,
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"hide_output_from_viewers": false
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}
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}
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},
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{
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"cell_type": "markdown",
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"source": [
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"# The model\n",
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"\n",
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"Defining the input data format, the statistic abstraction and the statistic implementation based on a weighted sum of elements."
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],
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"metadata": {
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"collapsed": false
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}
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},
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{
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"cell_type": "code",
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"source": [
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"class XYValues(val xValues: DoubleArray, val yValues: DoubleArray) {\n",
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" init {\n",
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" require(xValues.size == yValues.size)\n",
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" }\n",
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"}\n",
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"\n",
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"fun interface XYStatistic {\n",
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" operator fun invoke(values: XYValues): Double\n",
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"}\n",
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"\n",
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"class ConvolutionalXYStatistic(val weights: DoubleArray) : XYStatistic {\n",
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" override fun invoke(values: XYValues): Double {\n",
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" require(weights.size == values.yValues.size)\n",
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" val norm = values.yValues.sum()\n",
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" return values.yValues.zip(weights) { value, weight -> value * weight }.sum()/norm\n",
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" }\n",
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"}"
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],
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"execution_count": null,
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"outputs": [],
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"metadata": {
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"datalore": {
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"node_id": "Zhgz1Ui91PWz0meJiQpHol",
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"type": "CODE",
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"hide_input_from_viewers": false,
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"hide_output_from_viewers": false
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}
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}
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},
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{
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"cell_type": "markdown",
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"source": [
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"# Generator\n",
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"Generate sample data for parabolas and hyperbolas"
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],
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"metadata": {
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"collapsed": false
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}
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"outputs": [],
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"source": [
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"fun generateParabolas(xValues: DoubleArray, a: Double, b: Double, c: Double): XYValues {\n",
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" val yValues = xValues.map { x -> a * x * x + b * x + c }.toDoubleArray()\n",
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" return XYValues(xValues, yValues)\n",
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"}\n",
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"\n",
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"fun generateHyperbols(xValues: DoubleArray, gamma: Double, x0: Double, y0: Double): XYValues {\n",
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" val yValues = xValues.map { x -> y0 + gamma / (x - x0) }.toDoubleArray()\n",
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" return XYValues(xValues, yValues)\n",
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"}"
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],
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"metadata": {
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"collapsed": false
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}
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},
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{
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"cell_type": "code",
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"source": [
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"val xValues = (1.0..10.0).step(1.0).toDoubleArray()\n",
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"\n",
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"val xy = generateHyperbols(xValues, 1.0, 0.0, 0.0)\n",
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"\n",
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"Plotly.plot {\n",
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" scatter {\n",
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" this.x.doubles = xValues\n",
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" this.y.doubles = xy.yValues\n",
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" }\n",
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"}"
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],
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"execution_count": null,
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"outputs": [],
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"metadata": {
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"datalore": {
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"node_id": "ZE2atNvFzQsCvpAF8KK4ch",
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"type": "CODE",
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"hide_input_from_viewers": false,
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"hide_output_from_viewers": false
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}
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}
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},
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{
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"cell_type": "markdown",
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"source": [
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"Create a default statistic with uniform weights"
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],
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"metadata": {
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"collapsed": false
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}
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},
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{
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"cell_type": "code",
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"source": [
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"val statistic = ConvolutionalXYStatistic(DoubleArray(xValues.size){1.0})\n",
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"statistic(xy)"
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],
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"execution_count": null,
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"outputs": [],
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"metadata": {
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"datalore": {
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"node_id": "EA5HaydTddRKYrtAUwd29h",
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"type": "CODE",
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"hide_input_from_viewers": false,
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"hide_output_from_viewers": false
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}
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}
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},
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{
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"cell_type": "code",
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"source": [
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"import kotlin.random.Random\n",
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"\n",
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"val random = Random(1288)\n",
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"\n",
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"val parabolas = buildList{\n",
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" repeat(500){\n",
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" add(\n",
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" generateParabolas(\n",
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" xValues, \n",
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" random.nextDouble(), \n",
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" random.nextDouble(), \n",
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" random.nextDouble()\n",
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" )\n",
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" )\n",
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" }\n",
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"}\n",
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"\n",
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"val hyperbolas: List<XYValues> = buildList{\n",
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" repeat(500){\n",
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" add(\n",
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" generateHyperbols(\n",
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" xValues, \n",
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" random.nextDouble()*10, \n",
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" random.nextDouble(), \n",
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" random.nextDouble()\n",
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" )\n",
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" )\n",
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" }\n",
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"}"
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],
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"execution_count": null,
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"outputs": [],
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"metadata": {
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"datalore": {
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"node_id": "t5t6IYmD7Q1ykeo9uijFfQ",
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"type": "CODE",
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"hide_input_from_viewers": false,
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"hide_output_from_viewers": false
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}
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}
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},
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{
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"cell_type": "code",
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"source": [
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"Plotly.plot { \n",
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" scatter { \n",
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" x.doubles = xValues\n",
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" y.doubles = parabolas[257].yValues\n",
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" }\n",
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" scatter { \n",
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" x.doubles = xValues\n",
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" y.doubles = hyperbolas[252].yValues\n",
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" }\n",
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" }"
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],
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"execution_count": null,
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"outputs": [],
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"metadata": {
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"datalore": {
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"node_id": "oXB8lmju7YVYjMRXITKnhO",
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"type": "CODE",
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"hide_input_from_viewers": false,
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"hide_output_from_viewers": false
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}
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}
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},
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{
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"cell_type": "code",
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"source": [
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"Plotly.plot { \n",
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" histogram { \n",
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" name = \"parabolae\"\n",
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" x.numbers = parabolas.map { statistic(it) }\n",
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" }\n",
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" histogram { \n",
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" name = \"hyperbolae\"\n",
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" x.numbers = hyperbolas.map { statistic(it) }\n",
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" }\n",
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"}"
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],
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"execution_count": null,
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"outputs": [],
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"metadata": {
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"datalore": {
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"node_id": "8EIIecUZrt2NNrOkhxG5P0",
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"type": "CODE",
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"hide_input_from_viewers": false,
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"hide_output_from_viewers": false
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}
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}
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},
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{
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"cell_type": "code",
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"source": [
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"val lossFunction: (XYStatistic) -> Double = { statistic ->\n",
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" - abs(parabolas.sumOf { statistic(it) } - hyperbolas.sumOf { statistic(it) })\n",
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"}"
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],
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"execution_count": null,
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"outputs": [],
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"metadata": {
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"datalore": {
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"node_id": "h7UmglJW5zXkAfKHK40oIL",
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"type": "CODE",
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"hide_input_from_viewers": false,
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"hide_output_from_viewers": false
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}
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}
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},
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{
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"cell_type": "markdown",
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"source": [
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"Using commons-math optimizer to optimize weights"
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],
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"metadata": {
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"collapsed": false
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}
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},
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{
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"cell_type": "code",
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"source": [
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"import org.apache.commons.math3.optim.*\n",
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"import org.apache.commons.math3.optim.nonlinear.scalar.*\n",
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"import org.apache.commons.math3.optim.nonlinear.scalar.noderiv.*\n",
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"\n",
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"val optimizer = SimplexOptimizer(1e-1, Double.MAX_VALUE)\n",
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"\n",
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"val result = optimizer.optimize(\n",
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" ObjectiveFunction { point ->\n",
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" lossFunction(ConvolutionalXYStatistic(point))\n",
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" },\n",
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" NelderMeadSimplex(xValues.size),\n",
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" InitialGuess(DoubleArray(xValues.size){ 1.0 }),\n",
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" GoalType.MINIMIZE,\n",
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" MaxEval(100000)\n",
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")"
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],
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"execution_count": null,
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"outputs": [],
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"metadata": {
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"datalore": {
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"node_id": "0EG3K4aCUciMlgGQKPvJ57",
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"type": "CODE",
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"hide_input_from_viewers": false,
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"hide_output_from_viewers": false
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}
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}
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},
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{
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"cell_type": "markdown",
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"source": [
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"Print resulting weights of optimization"
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],
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"metadata": {
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"collapsed": false
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}
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},
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{
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"cell_type": "code",
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"source": [
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"result.point"
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],
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"execution_count": null,
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"outputs": [],
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"metadata": {
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"datalore": {
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"node_id": "LelUlY0ZSlJEO9yC6SLk5B",
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"type": "CODE",
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"hide_input_from_viewers": false,
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"hide_output_from_viewers": false
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}
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}
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},
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{
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"cell_type": "code",
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"source": [
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"Plotly.plot { \n",
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" scatter { \n",
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" y.doubles = result.point\n",
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" }\n",
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"}"
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],
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"execution_count": null,
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"outputs": [],
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"metadata": {
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"datalore": {
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"node_id": "AuFOq5t9KpOIkGrOLsVXNf",
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"type": "CODE",
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"hide_input_from_viewers": false,
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"hide_output_from_viewers": false
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}
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}
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},
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{
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"cell_type": "markdown",
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"source": [
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"# The resulting statistic distribution"
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],
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"metadata": {
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"collapsed": false
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}
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},
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{
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"cell_type": "code",
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"source": [
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"val resultStatistic = ConvolutionalXYStatistic(result.point)\n",
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"Plotly.plot { \n",
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" histogram { \n",
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" name = \"parabolae\"\n",
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" x.numbers = parabolas.map { resultStatistic(it) }\n",
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" }\n",
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" histogram { \n",
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" name = \"hyperbolae\"\n",
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" x.numbers = hyperbolas.map { resultStatistic(it) }\n",
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" }\n",
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"}"
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],
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"execution_count": null,
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"outputs": [],
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"metadata": {
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"datalore": {
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"node_id": "zvmq42DRdM5mZ3SpzviHwI",
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"type": "CODE",
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"hide_input_from_viewers": false,
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"hide_output_from_viewers": false
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}
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}
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"outputs": [],
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"source": [],
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"metadata": {
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"collapsed": false
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}
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Kotlin",
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"language": "kotlin",
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"name": "kotlin"
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},
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"datalore": {
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"version": 1,
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"computation_mode": "JUPYTER",
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"package_manager": "pip",
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"base_environment": "default",
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"packages": []
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}
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},
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"nbformat": 4,
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"nbformat_minor": 4
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}
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