Montecarlo Kotlin

.gitignore

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+### IntelliJ IDEA ###
+out/
+!**/src/main/**/out/
+!**/src/test/**/out/
+
+### Eclipse ###
+.apt_generated
+.classpath
+.factorypath
+.project
+.settings
+.springBeans
+.sts4-cache
+bin/
+!**/src/main/**/bin/
+!**/src/test/**/bin/
+
+### NetBeans ###
+/nbproject/private/
+/nbbuild/
+/dist/
+/nbdist/
+/.nb-gradle/
+
+### VS Code ###
+.vscode/
+
+### Mac OS ###
+.DS_Store

.idea/.gitignore

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+# Default ignored files
+/shelf/
+/workspace.xml
+# Editor-based HTTP Client requests
+/httpRequests/
+# Datasource local storage ignored files
+/dataSources/
+/dataSources.local.xml

.idea/codeStyles/Project.xml

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+<component name="ProjectCodeStyleConfiguration">
+  <code_scheme name="Project" version="173">
+    <JetCodeStyleSettings>
+      <option name="CODE_STYLE_DEFAULTS" value="KOTLIN_OFFICIAL" />
+    </JetCodeStyleSettings>
+    <codeStyleSettings language="kotlin">
+      <option name="CODE_STYLE_DEFAULTS" value="KOTLIN_OFFICIAL" />
+    </codeStyleSettings>
+  </code_scheme>
+</component>

.idea/codeStyles/codeStyleConfig.xml

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+<component name="ProjectCodeStyleConfiguration">
+  <state>
+    <option name="USE_PER_PROJECT_SETTINGS" value="true" />
+  </state>
+</component>

.idea/inspectionProfiles/Project_Default.xml

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+<component name="InspectionProjectProfileManager">
+  <profile version="1.0">
+    <option name="myName" value="Project Default" />
+    <inspection_tool class="ReplaceUntilWithRangeUntil" enabled="true" level="WEAK WARNING" enabled_by_default="true" />
+  </profile>
+</component>

.idea/kotlinc.xml

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+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="Kotlin2JvmCompilerArguments">
+    <option name="jvmTarget" value="1.8" />
+  </component>
+  <component name="KotlinCommonCompilerArguments">
+    <option name="apiVersion" value="1.9" />
+    <option name="languageVersion" value="1.9" />
+  </component>
+</project>

.idea/libraries/KotlinJavaRuntime.xml

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+<component name="libraryTable">
+  <library name="KotlinJavaRuntime" type="repository">
+    <properties maven-id="org.jetbrains.kotlin:kotlin-stdlib-jdk8:1.9.23" />
+    <CLASSES>
+      <root url="jar://$MAVEN_REPOSITORY$/org/jetbrains/kotlin/kotlin-stdlib-jdk8/1.9.23/kotlin-stdlib-jdk8-1.9.23.jar!/" />
+      <root url="jar://$MAVEN_REPOSITORY$/org/jetbrains/kotlin/kotlin-stdlib/1.9.23/kotlin-stdlib-1.9.23.jar!/" />
+      <root url="jar://$MAVEN_REPOSITORY$/org/jetbrains/annotations/13.0/annotations-13.0.jar!/" />
+      <root url="jar://$MAVEN_REPOSITORY$/org/jetbrains/kotlin/kotlin-stdlib-jdk7/1.9.23/kotlin-stdlib-jdk7-1.9.23.jar!/" />
+    </CLASSES>
+    <JAVADOC>
+      <root url="jar://$MAVEN_REPOSITORY$/org/jetbrains/kotlin/kotlin-stdlib-jdk8/1.9.23/kotlin-stdlib-jdk8-1.9.23-javadoc.jar!/" />
+      <root url="jar://$MAVEN_REPOSITORY$/org/jetbrains/kotlin/kotlin-stdlib/1.9.23/kotlin-stdlib-1.9.23-javadoc.jar!/" />
+      <root url="jar://$MAVEN_REPOSITORY$/org/jetbrains/annotations/13.0/annotations-13.0-javadoc.jar!/" />
+      <root url="jar://$MAVEN_REPOSITORY$/org/jetbrains/kotlin/kotlin-stdlib-jdk7/1.9.23/kotlin-stdlib-jdk7-1.9.23-javadoc.jar!/" />
+    </JAVADOC>
+    <SOURCES>
+      <root url="jar://$MAVEN_REPOSITORY$/org/jetbrains/kotlin/kotlin-stdlib-jdk8/1.9.23/kotlin-stdlib-jdk8-1.9.23-sources.jar!/" />
+      <root url="jar://$MAVEN_REPOSITORY$/org/jetbrains/kotlin/kotlin-stdlib/1.9.23/kotlin-stdlib-1.9.23-sources.jar!/" />
+      <root url="jar://$MAVEN_REPOSITORY$/org/jetbrains/annotations/13.0/annotations-13.0-sources.jar!/" />
+      <root url="jar://$MAVEN_REPOSITORY$/org/jetbrains/kotlin/kotlin-stdlib-jdk7/1.9.23/kotlin-stdlib-jdk7-1.9.23-sources.jar!/" />
+    </SOURCES>
+  </library>
+</component>

.idea/misc.xml

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+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="ProjectRootManager" version="2" languageLevel="JDK_21" default="true" project-jdk-name="21" project-jdk-type="JavaSDK">
+    <output url="file://$PROJECT_DIR$/out" />
+  </component>
+</project>

.idea/modules.xml

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+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="ProjectModuleManager">
+    <modules>
+      <module fileurl="file://$PROJECT_DIR$/MonteCarlo_Kotlin.iml" filepath="$PROJECT_DIR$/MonteCarlo_Kotlin.iml" />
+    </modules>
+  </component>
+</project>

MonteCarlo_Kotlin.iml

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+<?xml version="1.0" encoding="UTF-8"?>
+<module type="JAVA_MODULE" version="4">
+  <component name="NewModuleRootManager" inherit-compiler-output="true">
+    <exclude-output />
+    <content url="file://$MODULE_DIR$">
+      <sourceFolder url="file://$MODULE_DIR$/resources" type="java-resource" />
+      <sourceFolder url="file://$MODULE_DIR$/src" isTestSource="false" />
+      <sourceFolder url="file://$MODULE_DIR$/test" isTestSource="true" />
+      <sourceFolder url="file://$MODULE_DIR$/testResources" type="java-test-resource" />
+    </content>
+    <orderEntry type="jdk" jdkName="21" jdkType="JavaSDK" />
+    <orderEntry type="sourceFolder" forTests="false" />
+    <orderEntry type="library" name="KotlinJavaRuntime" level="project" />
+  </component>
+</module>

src/Main.kt

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+import java.text.DecimalFormat
+import kotlin.math.abs
+import kotlin.math.pow
+import kotlin.random.Random.Default.nextDouble
+import kotlin.system.measureTimeMillis
+
+var lowerX = 0.0
+var upperX = 20.0
+
+fun randomFloat(): Double {
+    return nextDouble()
+}
+
+class Point(private var x: Double, private var y: Double) {
+    fun getX() : Double {
+        return x
+    }
+    fun getY() : Double {
+        return y
+    }
+
+}
+
+class LinearBounds(private var lower: Float, private var higher: Float) {
+
+    fun length(): Double {
+        return abs(higher-lower).toDouble()
+    }
+    fun getRandomValue() : Double{
+        return lower + (randomFloat()*length())
+    }
+    fun getLower() : Float {
+        return lower
+    }
+    fun getHigher() : Float {
+        return higher
+    }
+}
+
+class Bounds(private var x : LinearBounds, private var y : LinearBounds) {
+    fun area() : Double {
+        return x.length() * y.length()
+    }
+
+    fun getRandomPoint() : Point {
+        return Point(x.getRandomValue(), y.getRandomValue())
+    }
+
+    fun getX() : LinearBounds {
+        return x
+    }
+}
+
+fun function(x : Double) : Double {
+    return x.pow(4.0) -4* x.pow(3.0) +18* x.pow(2.0) -12*x-69
+}
+fun indefiniteIntegral(x : Double) : Double {
+    return (1.0/5) * x.pow(5) - x.pow(4) + 6*x.pow(3) - 6 * x.pow(2) -69*x
+}
+
+fun getIsInside(p : Point) : Boolean {
+    var y0 = function(p.getX())
+    return abs(y0) > abs(p.getY()) && y0*p.getY() >= 0
+}
+
+fun getRealIntegral(bounds : LinearBounds) : Double{
+    return indefiniteIntegral(bounds.getHigher()-indefiniteIntegral(bounds.getLower().toDouble()))
+}
+
+fun getUpperLimit() : Float{
+    var upperLimit = 0.0f
+    var i = lowerX
+    while(i < upperX) {
+        i += 0.025
+        if(function(i) > upperLimit) {
+            upperLimit = (function(i) * 1.025).toFloat()
+        }
+    }
+    return upperLimit
+}
+
+fun getLowerLimit() : Float {
+    var lowerLimit = 0.0f
+    var i = lowerX
+    while(i < upperX) {
+        i += 0.025
+        if(function(i) < lowerLimit) {
+            lowerLimit = (function(i) * 1.025).toFloat()
+        }
+    }
+    return lowerLimit
+
+}
+
+fun main() {
+
+    val format = DecimalFormat("#,###.##")
+    var pointsInside = 0.0
+    val samples = 20_000_000
+    val bounds = Bounds(LinearBounds(lowerX.toFloat(), upperX.toFloat()), LinearBounds(getLowerLimit(), getUpperLimit()))
+
+    var integral = 0.0
+    var error = 0.0
+    var result = 0.0
+
+    val realValue = getRealIntegral(bounds.getX())
+    var toTestPoint : Point
+
+    val elapsed = measureTimeMillis {
+        for(i in 0..50){
+            for(ii in 0..samples) {
+                toTestPoint = bounds.getRandomPoint()
+                if(getIsInside(toTestPoint)){
+                    pointsInside++
+                }
+            }
+
+
+            integral = (pointsInside/samples) * bounds.area()
+            result += integral
+            integral = 0.0
+            pointsInside = 0.0
+        }
+        result /= 50.0
+        error = abs(realValue-result)
+    }
+    println("The approximated Integral of the function is: " + format.format(result))
+    println("The real Integral of the function is: " + format.format(realValue))
+    println("That's an error of " + format.format(error) + " or " + format.format((error/realValue)*100) + "%")
+    println("And the whole thing took " + format.format(elapsed/1000.0) + " Seconds for 50 times" + format.format(samples) + " Samples")
+}