Montecarlo Matlab

Bounds.m

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+classdef Bounds
+    %BOUNDS Summary of this class goes here
+    %   Detailed explanation goes here
+    
+    properties
+        x LinearBounds
+        y LinearBounds
+    end
+    
+    methods
+        function obj = Bounds(xIn,yIn)            %BOUNDS Construct an instance of this class
+            %   Detailed explanation goes here
+            obj.x = xIn;
+            obj.y = yIn;
+        end
+        
+        function outputArg = area(obj)
+            %METHOD1 Summary of this method goes here
+            %   Detailed explanation goes here
+            outputArg = obj.x.length * obj.y.length;
+        end
+        function outputArg = getRandomPoint(obj)
+            outputArg = Point(obj.x.getRandomValue, obj.y.getRandomValue);
+        end
+    end
+end
+

LinearBounds.m

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+classdef LinearBounds
+    %LINEARBOUNDS Summary of this class goes here
+    %   Detailed explanation goes here
+    
+    properties
+        lower double
+        higher double
+    end
+    
+    methods
+        function obj = LinearBounds(lowerIn,higherIn)
+            obj.lower = lowerIn;
+            obj.higher = higherIn;
+        end
+        
+        function outputArg = length(obj)
+            outputArg = abs(obj.higher-obj.lower);
+        end
+        
+        function outputArg = getRandomValue(obj)
+            outputArg = obj.lower + (rand() * obj.length);
+        end
+    end
+end
+

MonteCarloMatlab.m

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+tic;
+samples = 10000000;
+xBounds = LinearBounds(0,20);
+yBounds = LinearBounds(-10,150000);
+bounds = Bounds(xBounds,yBounds);
+pointsInside = 0;
+realValue = realIntegral(bounds.x);
+
+for i = 0:samples
+    toTestPoint = bounds.getRandomPoint;
+    if getIsInside(toTestPoint)
+        pointsInside = pointsInside+1;
+    end
+end
+
+
+format longG
+integral = (pointsInside/samples)*bounds.area
+realValue
+error = abs(realValue-integral)
+samples
+toc
+
+
+
+function out = mainFunction(x)
+    out = x^4-4*x^3+18*x^2-12*x-69;
+end
+
+function out = indefiniteIntegral(x)
+    out = (1/5)* x^5 - x^4 + 6* x^3 - 6*x^2 - 69*x;
+end
+
+function out = getIsInside(p)
+    arguments
+        p Point
+    end
+    y_0 = mainFunction(p.x);
+    out = abs(y_0) > abs(p.y) && y_0 * p.y >= 0;
+end
+
+function out = realIntegral(bounds)
+    arguments
+        bounds LinearBounds
+    end
+    out = indefiniteIntegral(bounds.higher) - indefiniteIntegral(bounds.lower);
+end

Point.m

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+classdef Point
+    properties
+        x double
+        y double
+    end
+    methods
+        function obj = Point(xIn, yIn)
+            obj.x = xIn;
+            obj.y = yIn;
+        end
+    end
+end