Merge branch 'algorithm-archivists:master' into computus_in_javascript_typescript

Author: hugo-s29

.github/workflows/build.yml

@@ -0,0 +1,16 @@
+name: build
+on: pull_request
+
+jobs:
+  build:
+    runs-on: ubuntu-latest
+    steps:
+      - name: Checkout
+        uses: actions/checkout@v2
+        with:
+          persist-credentials: false
+
+      - name: Install and build
+        run: |
+          npm install
+          npx honkit build

.github/workflows/deploy.yml

@@ -0,0 +1,26 @@
+name: Build and Deploy
+on:
+  push:
+    branches:
+      - master
+
+jobs:
+  build-and-deploy:
+    runs-on: ubuntu-latest
+    if: github.repository == 'algorithm-archivists/algorithm-archive'
+    steps:
+      - name: Checkout
+        uses: actions/checkout@v2
+        with:
+          persist-credentials: false
+
+      - name: Install and build
+        run: |
+          npm install
+          npx honkit build
+
+      - name: Deploy
+        uses: JamesIves/github-pages-deploy-action@4.1.4
+        with:
+          branch: gh-pages
+          folder: _book

CONTRIBUTORS.md

@@ -55,3 +55,4 @@ This file lists everyone, who contributed to this repo and wanted to show up her
 - Jonathan Dönszelmann
 - Ishaan Verma
 - Delphi1024
+- ntindle

SUMMARY.md

@@ -6,6 +6,7 @@
 * [Plotting](contents/plotting/plotting.md)
     * [Domain Coloring](contents/domain_coloring/domain_coloring.md)
     * [Iterated Function Systems](contents/IFS/IFS.md)
+        * [The Barnsley Fern](contents/barnsley/barnsley.md)
 * [Data Structures](contents/data_structures/data_structures.md)
     * [Stacks and Queues](contents/stacks_and_queues/stacks_and_queues.md)
 * [Mathematical Background](contents/mathematical_background/mathematical_background.md)
@@ -43,3 +44,4 @@
     * [Flood Fill](contents/flood_fill/flood_fill.md)
 * [Quantum Information](contents/quantum_information/quantum_information.md)
 * [Computus](contents/computus/computus.md)
+* [Approximate Counting Algorithm](contents/approximate_counting/approximate_counting.md)

contents/IFS/IFS.md

@@ -36,7 +36,7 @@ int main() {
 
     chaos_game(shape_points, 3, out_points, 1000);
 
-    FILE *fp = fopen("out.dat", "w+");
+    FILE *fp = fopen("sierpinksi.dat", "w+");
 
     for (int i = 0; i < 1000; ++i) {
         fprintf(fp, "%f\t%f\n", out_points[i].x, out_points[i].y);

contents/IFS/code/c/IFS.c

@@ -0,0 +1,61 @@
+import java.io.FileWriter;
+import java.util.Random;
+
+public class IFS {
+
+    private static class Point {
+        double x, y;
+
+        public Point(double x, double y) {
+            this.x = x;
+            this.y = y;
+        }
+    }
+    
+    // This is a function to simulate a "chaos game"
+    public static Point[] chaosGame(int n, Point[] shapePoints) {
+        Random rng = new Random();
+
+        // Initialize output vector
+        Point[] outputPoints = new Point[n];
+
+        // Choose first point randomly
+        Point point = new Point(rng.nextDouble(), rng.nextDouble());
+
+        for (int i = 0; i < n; i++) {
+            outputPoints[i] = point;
+
+            // Clone point to get a new reference
+            point = new Point(point.x, point.y);
+
+            // Retrieve random shape point
+            Point temp = shapePoints[rng.nextInt(shapePoints.length)];
+            // Calculate midpoint
+            point.x = 0.5 * (point.x + temp.x);
+            point.y = 0.5 * (point.y + temp.y);
+        }
+
+        return outputPoints;
+    }
+
+    public static void main(String[] args) throws Exception {
+        // This will generate a Sierpinski triangle with a chaos game of n points for an
+        // initial triangle with three points on the vertices of an equilateral triangle:
+        //     A = (0.0, 0.0)
+        //     B = (0.5, sqrt(0.75))
+        //     C = (1.0, 0.0)
+        // It will output the file sierpinski.dat, which can be plotted after
+        Point[] shapePoints = new Point[]{
+                new Point(0.0, 0.0),
+                new Point(0.5, Math.sqrt(0.75)),
+                new Point(1.0, 0.0)
+        };
+        Point[] outputPoints = chaosGame(10000, shapePoints);
+
+        FileWriter fw = new FileWriter("sierpinski.dat");
+        for (Point p : outputPoints)
+            fw.write(p.x + "\t" + p.y + "\n");
+        fw.close();
+    }
+
+}

contents/IFS/code/java/IFS.java

@@ -26,4 +26,4 @@ shape_points = [[0.0, 0.0],
                 [0.5, sqrt(0.75)],
                 [1.0, 0.0]]
 output_points = chaos_game(10000, shape_points)
-writedlm("out.dat", output_points)
+writedlm("sierpinski.dat", output_points)

contents/IFS/code/julia/IFS.jl

@@ -0,0 +1,61 @@
+using Test 
+
+# This function takes 
+#     - v: value in register
+#     - a: a  scaling value for the logarithm based on Morris's paper
+# It returns n(v,a), the approximate count
+function n(v, a)
+    a*((1+1/a)^v-1)  
+end
+
+# This function takes
+#    - v: value in register
+#    - a: a scaling value for the logarithm based on Morris's paper
+# It returns a new value for v
+function increment(v, a)
+    # delta is the probability of incrementing our counter
+    delta = 1/(n(v+1, a)-n(v, a))
+
+    if rand() <= delta
+        return v += 1
+    else
+        return v
+    end
+end
+
+# This simulates counting and takes
+#     - n_items: number of items to count and loop over
+#     - a: a scaling value for the logarithm based on Morris's paper
+# It returns n(v,a), the approximate count
+function approximate_count(n_items, a)
+    v = 0
+    for i = 1:n_items
+        v = increment(v, a)
+    end
+
+    return n(v, a)
+end
+
+# This function takes
+#     - n_trials: the number of counting trials
+#     - n_items: the number of items to count to
+#     - a: a scaling value for the logarithm based on Morris's paper
+#     - threshold: the maximum percent error allowed
+# It returns a true / false test value
+function test_approximate_count(n_trials, n_items, a, threshold)
+    samples = [approximate_count(n_items, a) for i = 1:n_trials]
+
+    avg = sum(samples)/n_trials
+
+    @test ((avg - n_items) / n_items < threshold)
+end
+
+@testset "Counting Tests, 100 trials" begin
+    println("testing 1,000, a = 30, 1% error")
+        test_approximate_count(100, 1000, 30, 0.1)
+    println("testing 12,345, a = 10, 1% error")
+        test_approximate_count(100, 12345, 10, 0.1)
+    # Note: with a lower a, we need more trials, so a higher % error here.
+    println("testing 222,222, a = 0.5, 10% error")
+        test_approximate_count(100, 222222, 0.5, 0.2)
+end

contents/IFS/res/IFS_square_3.png

@@ -0,0 +1,123 @@
+using DelimitedFiles
+
+# n = number of events
+# prob = probability of incrementing counter
+function random_count(n, prob; a=30, prob_calc=false)
+    v = 0
+    base = 1+1/a
+    output = zeros(n)
+
+    if prob_calc
+        prob = 1
+        v = 1
+    end
+
+    if rand() < prob
+        output[1] = 1/prob
+    end
+
+    for i = 2:n
+        if prob_calc
+            prob = 1/((a*(base^(v+1)-1))-output[i-1])
+
+            if rand() <= prob
+                v += 1
+            end
+            output[i] = a*(base^v-1)
+        else
+            if rand() <= prob
+                output[i] = output[i-1]+1/prob
+            else
+                output[i] = output[i-1]
+            end
+        end
+    end
+
+    return output
+end
+
+# m = number of counting trials
+# l = number of saved trials
+function multi_count(n, m, l, prob; a=30, prob_calc=false, file_mod="",
+                     stops = [100000, 500000, 1000000])
+    out = zeros(n, l)
+    extremes = zeros(n, 2)
+
+    chosen_set = zeros(Int, l)
+    
+    for i = 1:l
+        chosen_number = rand(1:m)
+        while chosen_number in chosen_set
+            chosen_number = rand(1:m)
+        end
+        chosen_set[i] = chosen_number
+    end
+
+    histograms = zeros(Float64, m, length(stops))
+
+    out_count = 1
+    for i = 1:m
+        current_dist = random_count(n, prob; a, prob_calc)
+        if i == 1
+            extremes[:,1] .= current_dist
+            extremes[:,2] .= current_dist
+        else
+            for j = 1:n
+                if current_dist[j] < extremes[j,1]
+                    extremes[j,1] = current_dist[j]
+                end
+                if current_dist[j] > extremes[j,2]
+                    extremes[j,2] = current_dist[j]
+                end
+            
+            end
+        end
+
+        for j = 1:length(stops)
+            histograms[i,j] = current_dist[stops[j]]
+        end
+
+        if i in chosen_set
+            out[:,out_count] = current_dist
+            out_count += 1
+        end
+    end
+
+    output_file = open("out"*file_mod*".dat", "w")
+    writedlm(output_file, out)
+    close(output_file)
+
+    extreme_output_file = open("extremes"*file_mod*".dat", "w")
+    writedlm(extreme_output_file, extremes)
+    close(extreme_output_file)
+
+    formatted_histograms = [[],[],[]]
+    # Going through the histogram data to put it into the right format
+    for j = 1:length(stops)
+
+        max = floor(Int,maximum(histograms[:,j]))
+        min = floor(Int,minimum(histograms[:,j]))
+
+        println(min, '\t', max, '\t', sum(histograms[:,j])/m)
+
+        temp_array = zeros(max - min+1)
+
+        for i = 1:m
+
+            temp_array[floor(Int,histograms[i,j])-min+1] += 1
+
+        end
+
+        formatted_histograms[j] = temp_array
+    end
+
+    # output histograms into different files for each one
+
+    for i = 1:length(stops)
+        histogram_file = open("histogram_" * string(i)*file_mod* ".dat", "w")
+        writedlm(histogram_file, formatted_histograms[i])
+        close(histogram_file)
+    end
+    return formatted_histograms
+end
+

contents/approximate_counting/approximate_counting.md

@@ -0,0 +1,31 @@
+set terminal epslatex standalone color
+
+#set output "histexp_1.tex"
+#set output "histexp_2.tex"
+set output "histexp_3.tex"
+
+set size square
+
+#set title "True count of 10,000"
+#set title "True count of 500,000"
+set title "True count of 1,000,000"
+
+set xlabel ''
+#set xrange [-255:9745]
+#set xtics ("6000" -255, "10,000" 3745, "16,000" 9745)
+
+#set xrange [352000:644000]
+#set xrange[-1458:538542]
+#set xtics ("320,000" -1458, "500,000" 178542, "860,000" 538542)
+
+#set xrange [808000:1240000]
+set xrange[-19374:1100626]
+set xtics ("600,0000" -19374, "1,000,000" 380626, "1,720,000" 1100626)
+
+#set ylabel 'Approximate count $\left( \times 10^{5} \right)$'
+#set ytics ("0" 0, "2" 200000, "4" 400000, "6" 600000, "8" 800000, "10" 1000000)
+
+#plot "histogram_1exp.dat" w l lw 10 title ""
+#plot "histogram_2exp.dat" w l lw 10 title ""
+plot "histogram_3exp.dat" w l lw 10 title ""
+

contents/approximate_counting/code/julia/approximate_counting.jl

@@ -0,0 +1,31 @@
+set terminal epslatex standalone color
+
+#set output "hist_1.tex"
+#set output "hist_2.tex"
+set output "hist_3.tex"
+
+set size square
+
+#set title "True count of 10,000"
+#set title "True count of 500,000"
+set title "True count of 1,000,000"
+
+#set xlabel ''
+#set xrange [0:40000]
+#set xtics ("0" 0, "20,000" 20000, "40,000" 40000)
+
+#set xrange [352000:644000]
+#set xrange[10000:310000]
+#set xtics ("350,000" 10000, "500,000" 160000, "650,000" 310000)
+
+#set xrange [808000:1240000]
+set xrange[-10000:490000]
+set xtics ("750,0000" -10000, "1,000,000" 240000, "1,250,000" 490000)
+
+#set ylabel 'Approximate count $\left( \times 10^{5} \right)$'
+#set ytics ("0" 0, "2" 200000, "4" 400000, "6" 600000, "8" 800000, "10" 1000000)
+
+#plot "histogram_1.dat" w l lw 10 title ""
+#plot "histogram_2.dat" w l lw 10 title ""
+plot "histogram_3.dat" w l lw 10 title ""
+