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altavir/be-7.ipynb

Created May 26, 2020 11:21
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be-7.ipynb
{
"cells": [
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
" <div id=\"6Ch9fs\"></div>\n",
" <script type=\"text/javascript\">\n",
" if(!window.letsPlotCallQueue) {\n",
" window.letsPlotCallQueue = [];\n",
" }; \n",
" window.letsPlotCall = function(f) {\n",
" window.letsPlotCallQueue.push(f);\n",
" };\n",
" (function() {\n",
" var script = document.createElement(\"script\");\n",
" script.type = \"text/javascript\";\n",
" script.src = \"https://dl.bintray.com/jetbrains/lets-plot/lets-plot-1.0.0.min.js\";\n",
" script.onload = function() {\n",
" window.letsPlotCall = function(f) {f();};\n",
" window.letsPlotCallQueue.forEach(function(f) {f();});\n",
" window.letsPlotCallQueue = [];\n",
" \n",
" \n",
" };\n",
" script.onerror = function(event) {\n",
" window.letsPlotCall = function(f) {};\n",
" window.letsPlotCallQueue = [];\n",
" var div = document.createElement(\"div\");\n",
" div.style.color = 'darkred';\n",
" div.textContent = 'Error loading Lets-Plot JS';\n",
" document.getElementById(\"6Ch9fs\").appendChild(div);\n",
" };\n",
" var e = document.getElementById(\"6Ch9fs\");\n",
" e.appendChild(script);\n",
" })();\n",
" </script>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"%use lets-plot\n",
"%use kmath-commons"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"import org.apache.commons.math3.analysis.function.Gaussian\n",
"import org.apache.commons.math3.analysis.integration.SimpsonIntegrator\n",
"\n",
"//defined thedefault integrator\n",
"val integrator: SimpsonIntegrator = SimpsonIntegrator()\n",
"\n",
"// pre-define function to create a kernel\n",
"fun gauss(sigma: Double) = Gaussian(0.0, sigma)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Creating class hierarchy to work with peaks"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"import org.apache.commons.math3.analysis.UnivariateFunction\n",
"\n",
"/**\n",
" * Pre-define sealed hierarchi for two different types of peaks\n",
" */\n",
"sealed class Peak(val amplitude: Double){\n",
" class Delta(amplitude: Double, val position: Double): Peak(amplitude)\n",
" class Wide(amplitude: Double, val function: UnivariateFunction): Peak(amplitude)\n",
"}\n",
"\n",
"/**\n",
" * Define invoke operation for [UnivariateFunction]\n",
" */\n",
"operator fun UnivariateFunction.invoke(arg: Double) = value(arg)\n",
"\n",
"/**\n",
" * Additional function to scale function. Probably should be removed to avoid additional object creation\n",
" */\n",
"operator fun UnivariateFunction.times(d: Double): UnivariateFunction = UnivariateFunction{arg: Double -> [email protected](arg)*d }\n",
"\n",
"\n",
"/**\n",
" * An extension to performe actual convolution\n",
" */\n",
"fun UnivariateFunction.convolve(range: ClosedFloatingPointRange<Double>, function: UnivariateFunction): UnivariateFunction{\n",
" return UnivariateFunction{ x: Double ->\n",
" val integrand = UnivariateFunction{y: Double -> \n",
" this@convolve(x - y) * function(y)\n",
" }\n",
" integrator.integrate(100000, integrand, range.start, range.endInclusive)\n",
" }\n",
"}\n",
"\n",
"/**\n",
" * An extension to create convolution depending on a peak type\n",
" */\n",
"fun Peak.convolve(range: ClosedFloatingPointRange<Double>, kernel: UnivariateFunction): UnivariateFunction {\n",
" return when(this){\n",
" is Peak.Delta -> UnivariateFunction{arg -> kernel.value(arg - position) * amplitude}\n",
" is Peak.Wide -> function.convolve(range, kernel) * amplitude\n",
" }\n",
"}"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"import jetbrains.letsPlot.intern.Plot\n",
"\n",
"class Spectrum(val peaks: List<Peak>){\n",
" companion object{\n",
" fun of(vararg peaks: Peak) = Spectrum(peaks.toList())\n",
" }\n",
"}\n",
"\n",
"/**\n",
" * Convolve a spectrum with the [kernel] to produce a function. \n",
" * It is also possible to produce a spectrum with separate lines instead.\n",
" */\n",
"fun Spectrum.convolve(range: ClosedFloatingPointRange<Double>, kernel: UnivariateFunction) = UnivariateFunction{arg: Double ->\n",
" peaks.sumByDouble { peak ->\n",
" peak.convolve(range,kernel).value(arg)\n",
" }\n",
"}\n",
"\n",
"/**\n",
" * Display a plot\n",
" */\n",
"fun UnivariateFunction.show(range: ClosedFloatingPointRange<Double>, points: Int = 1000): Plot{\n",
" val x: List<Double> = List(points){i -> range.start + i*(range.endInclusive - range.start)/(points) - 1}\n",
" val y = x.map{value(it)}\n",
" \n",
" val data = mapOf<String, Any>(\n",
" \"x\" to x,\n",
" \"y\" to y\n",
" )\n",
" \n",
" var p = lets_plot(data)\n",
" p += geom_area{\n",
" this.x = \"x\"\n",
" this.y = \"y\"\n",
" }\n",
" return p\n",
"}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Define actual spectrum"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"import kotlin.math.*\n",
"\n",
"val k_base_prob = 0.864\n",
"val k_base_energy = 112.0\n",
"val k_ext_prob = 0.096\n",
"val k_ext_energy = 83.0\n",
"val l_base_prob = 0.036\n",
"val l_base_energy = 55.0\n",
"val l_ext_prob = 0.004 \n",
"\n",
"val ext_width = 28.0\n",
"\n",
"val spectrum = Spectrum.of(\n",
" Peak.Delta(k_base_prob, k_base_energy),\n",
" Peak.Delta(l_base_prob,l_base_energy),\n",
" Peak.Wide(k_ext_prob){ x ->\n",
" if(abs(x - k_ext_energy) > ext_width){\n",
" 0.0\n",
" } else{\n",
" cos( (x - k_ext_energy)/ext_width * PI/2.0) /2.0 *k_ext_prob\n",
" }\n",
" }\n",
")"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
" <div id=\"oMx0yd\"></div>\n",
" <script type=\"text/javascript\">\n",
" (function() {\n",
" var plotSpec={\n",
"'mapping':{\n",
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"'data':{\n",
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"},\n",
"'kind':\"plot\",\n",
"'scales':[],\n",
"'layers':[{\n",
"'stat':\"identity\",\n",
"'mapping':{\n",
"'x':\"x\",\n",
"'y':\"y\"\n",
"},\n",
"'data':{\n",
"},\n",
"'position':\"stack\",\n",
"'geom':\"area\"\n",
"}]\n",
"};\n",
" var plotContainer = document.getElementById(\"oMx0yd\");\n",
" window.letsPlotCall(function() {{\n",
" LetsPlot.buildPlotFromProcessedSpecs(plotSpec, -1, -1, plotContainer);\n",
" }});\n",
" })(); \n",
" </script>"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"val width = 1.0\n",
"\n",
"val convolved = spectrum.convolve(-5*width..5*width, gauss(0.0, width))\n",
"\n",
"convolved.show(0.0..130.0)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Kotlin",
"language": "kotlin",
"name": "kotlin"
},
"language_info": {
"codemirror_mode": "text/x-kotlin",
"file_extension": ".kt",
"mimetype": "text/x-kotlin",
"name": "kotlin",
"pygments_lexer": "kotlin",
"version": "1.4.0-dev-7568"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
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