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The Science of Success Davy Stevenson @davystevenson Cascadia Ruby 2014

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The Columbia River Gorge, Home by Paul Kline

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Astronaut by Alan

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Williams College by Ethan Kan

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White, Mt Greylock by kumsval

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In Search of the Abominable Snowman by Peter Lee

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Fish Bowl Embroidery by Jenny S

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light brain by Mario D’Amore

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Cao Xueqin, Dream of the Red Chamber by Ivan Walsh

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Modern Art in Prague by BrunoDelzant

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Greek Philosopher Mosaic by Holly Hayes

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Hacker by the Preiser Project

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Glass of Heart by Rahim Packir Saibo

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100 Planetary Nebulas by Judy Schmidt

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Professor John Frink, Jr. vs. Professor Hubert J. Farnsworth by JD Hancock

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Complexity

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Brockhaus and Efron Encyclopedic Dictionary

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Complexity O(n) O(log n) O(n log n) O(n2) O(2n) O(n!)

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Complexity O(log n) - Logarithmic - Sorted Data

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Complexity O(n) - Linear - Analyze each point

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Complexity O(n log n) - Loglinear Best Sorting Algorithms

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Complexity O(n2) - Quadratic Compare pairs of points

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Complexity O(2n) - Exponential - Try and avoid

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Complexity O(n!) - Factorial You’re gonna have a bad time

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Algorithms

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Silver and Gold - Charles Babbage’s Difference Engine by odditty

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jar by hillary.hc.chang

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Convex Hull by fdecomite

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Stonebalancing in Greece by t.klick

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Jarvis March

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Plejaden M45 by Carsten Frenzi

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Plejaden M45 by Carsten Frenzi

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Plejaden M45 by Carsten Frenzi

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Plejaden M45 by Carsten Frenzi

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Plejaden M45 by Carsten Frenzi

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Plejaden M45 by Carsten Frenzi

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Plejaden M45 by Carsten Frenzi

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Plejaden M45 by Carsten Frenzi

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Plejaden M45 by Carsten Frenzi

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Plejaden M45 by Carsten Frenzi

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Plejaden M45 by Carsten Frenzi

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Jarvis March • Find one edge: O(n) • Find right-most point: O(n) • Repeat for each point on hull: O(h) • O(n + n * h) => O(n h) • Worst case: O(n2)

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Monotone Chain

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Plejaden M45 by Carsten Frenzi

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1 2 3 4 5 6 7 8 9 Plejaden M45 by Carsten Frenzi

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1 2 3 4 5 6 7 8 9 Plejaden M45 by Carsten Frenzi

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4 5 6 7 8 9 Plejaden M45 by Carsten Frenzi

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5 6 7 8 9 Plejaden M45 by Carsten Frenzi

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5 6 7 8 9 Plejaden M45 by Carsten Frenzi

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5 6 7 8 9 Plejaden M45 by Carsten Frenzi

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6 7 8 9 Plejaden M45 by Carsten Frenzi

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7 8 9 Plejaden M45 by Carsten Frenzi

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7 8 9 Plejaden M45 by Carsten Frenzi

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7 8 9 Plejaden M45 by Carsten Frenzi

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7 8 9 Plejaden M45 by Carsten Frenzi

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8 9 Plejaden M45 by Carsten Frenzi

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9 Plejaden M45 by Carsten Frenzi

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9 Plejaden M45 by Carsten Frenzi

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Plejaden M45 by Carsten Frenzi

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Plejaden M45 by Carsten Frenzi

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Plejaden M45 by Carsten Frenzi

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Plejaden M45 by Carsten Frenzi

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Plejaden M45 by Carsten Frenzi

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Monotone Chain • Sort points: O(n log n) • Construct lower hull: O(n) • Construct upper hull: O(n) • O(n log n + (n + n)) => O(n log n) • O(n) if already sorted

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Pushpins in a map over the USA by Marc Levin

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Benchmark

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Fast by photophilde

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require 'benchmark' n = 100_000 size = 10000 array = (0...size).to_a.shuffle ! Benchmark.bm do |x| x.report("#at") { n.times { array.at rand(size)} } x.report("#index") { n.times { array.index rand(size) } } x.report("#index-miss") { n.times { array.index (size + rand(size)) } } end

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require 'benchmark' n = 100_000 size = 10000 array = (0...size).to_a.shuffle ! Benchmark.bm do |x| x.report("#at") { n.times { array.at rand(size)} } x.report("#index") { n.times { array.index rand(size) } } x.report("#index-miss") { n.times { array.index (size + rand(size)) } } end

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require 'benchmark' n = 100_000 size = 10000 array = (0...size).to_a.shuffle ! Benchmark.bm do |x| x.report("#at") { n.times { array.at rand(size)} } x.report("#index") { n.times { array.index rand(size) } } x.report("#index-miss") { n.times { array.index (size + rand(size)) } } end

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require 'benchmark' n = 100_000 size = 10000 array = (0...size).to_a.shuffle ! Benchmark.bm do |x| x.report("#at") { n.times { array.at rand(size)} } x.report("#index") { n.times { array.index rand(size) } } x.report("#index-miss") { n.times { array.index (size + rand(size)) } } end

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require 'benchmark' n = 100_000 size = 10000 array = (0...size).to_a.shuffle ! Benchmark.bm do |x| x.report("#at") { n.times { array.at rand(size)} } x.report("#index") { n.times { array.index rand(size) } } x.report("#index-miss") { n.times { array.index (size + rand(size)) } } end

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$ ruby examples/bm.rb user system total real #at 0.020000 0.000000 0.020000 ( 0.023444) #index 2.380000 0.000000 2.380000 ( 2.391208) #index-miss 4.770000 0.000000 4.770000 ( 4.786147)

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$ ruby examples/bm.rb user system total real #at 0.020000 0.000000 0.020000 ( 0.023444) #index 2.380000 0.000000 2.380000 ( 2.391208) #index-miss 4.770000 0.000000 4.770000 ( 4.786147)

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require 'benchmark' n = 100_000 size = 10000 array = (0...size).to_a.shuffle ! Benchmark.bm do |x| x.report("#at") { n.times { array.at rand(size)} } x.report("#index") { n.times { array.index rand(size) } } x.report("#index-miss") { n.times { array.index (size + rand(size)) } } end

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require 'benchmark/ips' ! size = 10000 array = (0...size).to_a.shuffle ! Benchmark.ips do |x| x.report("#at") { array.at rand(size) } x.report("#index") { array.index rand(size) } x.report("#index-miss") { array.index (size + rand(size)) } x.compare! end

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require 'benchmark/ips' ! size = 10000 array = (0...size).to_a.shuffle ! Benchmark.ips do |x| x.report("#at") { array.at rand(size) } x.report("#index") { array.index rand(size) } x.report("#index-miss") { array.index (size + rand(size)) } x.compare! end

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$ ruby examples/ips.rb ! ! ! Calculating ------------------------------------- #at 79155 i/100ms #index 4039 i/100ms #index-miss 2055 i/100ms ------------------------------------------------- #at 3165995.2 (±10.7%) i/s - 15593535 in 5.006746s #index 41873.8 (±6.3%) i/s - 210028 in 5.040799s #index-miss 20592.7 (±7.5%) i/s - 102750 in 5.022168s ! Comparison: #at: 3165995.2 i/s #index: 41873.8 i/s - 75.61x slower #index-miss: 20592.7 i/s - 153.74x slower

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$ ruby examples/ips.rb ! ! ! Calculating ------------------------------------- #at 79155 i/100ms #index 4039 i/100ms #index-miss 2055 i/100ms ------------------------------------------------- #at 3165995.2 (±10.7%) i/s - 15593535 in 5.006746s #index 41873.8 (±6.3%) i/s - 210028 in 5.040799s #index-miss 20592.7 (±7.5%) i/s - 102750 in 5.022168s ! Comparison: #at: 3165995.2 i/s #index: 41873.8 i/s - 75.61x slower #index-miss: 20592.7 i/s - 153.74x slower

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$ ruby examples/ips.rb ! ! ! Calculating ------------------------------------- #at 79155 i/100ms #index 4039 i/100ms #index-miss 2055 i/100ms ------------------------------------------------- #at 3165995.2 (±10.7%) i/s - 15593535 in 5.006746s #index 41873.8 (±6.3%) i/s - 210028 in 5.040799s #index-miss 20592.7 (±7.5%) i/s - 102750 in 5.022168s ! Comparison: #at: 3165995.2 i/s #index: 41873.8 i/s - 75.61x slower #index-miss: 20592.7 i/s - 153.74x slower

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$ ruby examples/ips.rb ! ! ! Calculating ------------------------------------- #at 79155 i/100ms #index 4039 i/100ms #index-miss 2055 i/100ms ------------------------------------------------- #at 3165995.2 (±10.7%) i/s - 15593535 in 5.006746s #index 41873.8 (±6.3%) i/s - 210028 in 5.040799s #index-miss 20592.7 (±7.5%) i/s - 102750 in 5.022168s ! Comparison: #at: 3165995.2 i/s #index: 41873.8 i/s - 75.61x slower #index-miss: 20592.7 i/s - 153.74x slower

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$ ruby examples/ips.rb ! ! ! Calculating ------------------------------------- #at 79155 i/100ms #index 4039 i/100ms #index-miss 2055 i/100ms ------------------------------------------------- #at 3165995.2 (±10.7%) i/s - 15593535 in 5.006746s #index 41873.8 (±6.3%) i/s - 210028 in 5.040799s #index-miss 20592.7 (±7.5%) i/s - 102750 in 5.022168s ! Comparison: #at: 3165995.2 i/s #index: 41873.8 i/s - 75.61x slower #index-miss: 20592.7 i/s - 153.74x slower

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$ ruby examples/ips.rb ! ! ! Calculating ------------------------------------- #at 79155 i/100ms #index 4039 i/100ms #index-miss 2055 i/100ms ------------------------------------------------- #at 3165995.2 (±10.7%) i/s - 15593535 in 5.006746s #index 41873.8 (±6.3%) i/s - 210028 in 5.040799s #index-miss 20592.7 (±7.5%) i/s - 102750 in 5.022168s ! Comparison: #at: 3165995.2 i/s #index: 41873.8 i/s - 75.61x slower #index-miss: 20592.7 i/s - 153.74x slower

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Benchmark BigO

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Benchmark Big O • github.com/davy/benchmark-bigo • Provides Big O notation benchmarking for Ruby

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require 'benchmark/ips' ! size = 10000 array = (0...size).to_a.shuffle ! Benchmark.ips do |x| x.report("#at") { array.at rand(size) } x.report("#index") { array.index rand(size) } x.report("#index-miss") { array.index (size + rand(size)) } x.compare! end

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require 'benchmark/bigo' ! Benchmark.bigo do |x| x.generate :array x.linear 2000 ! x.report("#at") {|array, size| array.at rand(size) } x.report("#index") {|array, size| array.index rand(size) } x.report("#index-miss") {|array, size| array.index (size + rand(size)) } x.chart! 'array.html' end

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require 'benchmark/bigo' ! Benchmark.bigo do |x| x.generate :array x.linear 2000 ! x.report("#at") {|array, size| array.at rand(size) } x.report("#index") {|array, size| array.index rand(size) } x.report("#index-miss") {|array, size| array.index (size + rand(size)) } x.chart! 'array.html' end

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require 'benchmark/bigo' ! Benchmark.bigo do |x| x.generate :array x.exponential ! x.report("#at") {|array, size| array.at rand(size) } x.report("#index") {|array, size| array.index rand(size) } x.report("#index-miss") {|array, size| array.index (size + rand(size)) } x.chart! 'array.html' end

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require 'benchmark/bigo' ! Benchmark.bigo do |x| x.generate :array x.exponential ! x.report("#at") {|array, size| array.at rand(size) } x.report("#index") {|array, size| array.index rand(size) } x.report("#index-miss") {|array, size| array.index (size + rand(size)) } x.chart! 'array.html' end

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require 'benchmark/bigo' ! Benchmark.bigo do |x| x.generate :array x.exponential ! x.report("#at") {|array, size| array.at rand(size) } x.report("#index") {|array, size| array.index rand(size) } x.report("#index-miss") {|array, size| array.index (size + rand(size)) } x.chart! 'array.html' end

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$ ruby examples/bigo-exp.rb ! Calculating ------------------------------------- #at 1 68448 i/100ms #at 10 63310 i/100ms #at 100 67388 i/100ms #at 1000 65912 i/100ms #at 10000 65518 i/100ms #index 1 66714 i/100ms #index 10 63736 i/100ms #index 100 50055 i/100ms #index 1000 18838 i/100ms #index 10000 3752 i/100ms #index-miss 1 61960 i/100ms #index-miss 10 58333 i/100ms #index-miss 100 45989 i/100ms #index-miss 1000 14698 i/100ms #index-miss 10000 1898 i/100ms ------------------------------------------------- #at 1 2084640.3 (±9.5%) i/s - 10335648 in 5.029076s #at 10 2006228.2 (±8.3%) i/s - 9939670 in 5.003949s #at 100 1871633.1 (±18.1%) i/s - 8962604 in 5.025712s #at 1000 2055675.6 (±8.7%) i/s - 10216360 in 5.029822s #at 10000 2000566.4 (±8.6%) i/s - 9893218 in 4.999732s #index 1 1992529.4 (±8.2%) i/s - 9940386 in 5.035758s #index 10 1810344.6 (±8.3%) i/s - 8986776 in 5.012351s #index 100 1304666.0 (±9.2%) i/s - 6457095 in 5.010804s #index 1000 347986.2 (±6.0%) i/s - 1733096 in 5.002854s #index 10000 40728.2 (±10.7%) i/s - 202608 in 5.059052s #index-miss 1 1984727.2 (±9.4%) i/s - 9851640 in 5.028868s #index-miss 10 1762957.2 (±7.6%) i/s - 8749950 in 5.004258s #index-miss 100 986260.8 (±10.2%) i/s - 4874834 in 5.010465s #index-miss 1000 187159.1 (±7.9%) i/s - 940672 in 5.063904s #index-miss 10000 19330.9 (±12.8%) i/s - 94900 in 5.001322s

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Map of Node coverage with Convex Hulls by Dario Villanueva

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Terraformer

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Terraformer Ruby • github.com/esripdx/terraformer-ruby • A geometric toolkit for dealing with geometry, geography, formats • Can calculate Convex Hull

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Jarvis Tortoise by Alexander Montuschi

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Run, bunny, run! by shadow planet Monotone

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module Terraformer::Benchmark # portland LON = -122.6764 LAT = 45.5165 ! # calculate convex hull with given implementation def self.convex_hull obj, impl Terraformer::ConvexHull.impl = impl obj.convex_hull end end ! class Float def perm self + rand(-100..100) / 10000.0 end end

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module Terraformer::Benchmark # portland LON = -122.6764 LAT = 45.5165 ! # calculate convex hull with given implementation def self.convex_hull obj, impl Terraformer::ConvexHull.impl = impl obj.convex_hull end end ! class Float def perm self + rand(-100..100) / 10000.0 end end

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module Terraformer::Benchmark # portland LON = -122.6764 LAT = 45.5165 ! # calculate convex hull with given implementation def self.convex_hull obj, impl Terraformer::ConvexHull.impl = impl obj.convex_hull end end ! class Float def perm self + rand(-100..100) / 10000.0 end end

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module Terraformer::Benchmark ! # generates a Line String representing a random walk def self.random_walk size walk = [[LON, LAT]] # start in pdx ! size.times do walk << walk.last.map{|i| i.perm } end ! # create line string from the random walk ls = Terraformer::LineString.new(walk) ! # convert to feature ls.to_feature end end

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module Terraformer::Benchmark ! # generates a Line String representing a random walk def self.random_walk size walk = [[LON, LAT]] # start in pdx ! size.times do walk << walk.last.map{|i| i.perm } end ! # create line string from the random walk ls = Terraformer::LineString.new(walk) ! # convert to feature ls.to_feature end end

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Benchmark.bigo do |x| x.generator {|size| Terraformer::Benchmark.random_walk size } ! x.time = 20 # sample each point for 20 seconds x.linear 200 x.increments = 5 # 200..1000 ! x.report("#rand-jarvis") {|f, _| Terraformer::Benchmark.convex_hull f, :jarvis_march } ! x.report("#rand-monotone") {|f, _| Terraformer::Benchmark.convex_hull f, :monotone} ! x.chart! 'data/chart_random_walk.html' x.compare! end

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Benchmark.bigo do |x| x.generator {|size| Terraformer::Benchmark.random_walk size } ! x.time = 20 # sample each point for 20 seconds x.linear 200 x.increments = 5 # 200..1000 ! x.report("#rand-jarvis") {|f, _| Terraformer::Benchmark.convex_hull f, :jarvis_march } ! x.report("#rand-monotone") {|f, _| Terraformer::Benchmark.convex_hull f, :monotone} ! x.chart! 'data/chart_random_walk.html' x.compare! end

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Benchmark.bigo do |x| x.generator {|size| Terraformer::Benchmark.random_walk size } ! x.time = 20 # sample each point for 20 seconds x.linear 200 x.increments = 5 # 200..1000 ! x.report("#rand-jarvis") {|f, _| Terraformer::Benchmark.convex_hull f, :jarvis_march } ! x.report("#rand-monotone") {|f, _| Terraformer::Benchmark.convex_hull f, :monotone} ! x.chart! 'data/chart_random_walk.html' x.compare! end

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Water Balloon by Amyn Kassam

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Water Balloon by Amyn Kassam

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module Terraformer::Benchmark ! # generates a circle feature with size points def self.circle size ! # minimum size is three size = 3 if size < 3 ! # expand the diameter as size increases diam = [100, size].max ! # generate circle c = Terraformer::Circle.new([LON, LAT], diam, size) ! # convert to feature c.to_feature end end

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module Terraformer::Benchmark ! # generates a circle feature with size points def self.circle size ! # minimum size is three size = 3 if size < 3 ! # expand the diameter as size increases diam = [100, size].max ! # generate circle c = Terraformer::Circle.new([LON, LAT], diam, size) ! # convert to feature c.to_feature end end

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Benchmark.bigo do |x| x.generator {|size| Terraformer::Benchmark.circle size } ! x.time = 20 # sample each point for 20 seconds x.linear 200 x.increments = 5 # 200..1000 ! x.report("#circ-jarvis") {|f, _| Terraformer::Benchmark.convex_hull f, :jarvis_march } ! x.report("#circ-monotone") {|f, _| Terraformer::Benchmark.convex_hull f, :monotone} ! x.chart! 'data/chart_circle.html' x.compare! end

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Benchmark Terraformer • github.com/davy/benchmark-terraformer • Helper code • Benchmark code • Map Viewer • Example charts, geojson & raw data • Array benchmark code

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My grandfather's microscope by Juan Eduardo Donoso

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Peer Review!

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Line Fitting

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Prettier Graphs

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Verify Math

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Science Driven Development

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QUESTION

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why is ____________ slow?

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why is ____________ broken?

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is ____________ a success?

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HYPOTHESIS

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it is slow because ___________

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it is broken because ___________

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it is successful because ___________

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PREDICTION

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if __________ is why it is slow then ____________

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if __________ is why it is broken then ____________

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if __________ is true then it is a success

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TESTING

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test the speed of ____________

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test the logic of ____________

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test if ____________ is true

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ANALYSIS

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what does the data say?

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Fix

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Sleeping Cat by Terence Lee

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Scientist Minifig by Maia Weinstock

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Thanks! Questions? Davy Stevenson @davystevenson Cascadia Ruby 2014

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Resources Benchmark IPS - github.com/evanphx/benchmark-ips Benchmark BigO - github.com/davy/benchmark-bigo Terraformer.rb - github.com/esripdx/terraformer-ruby ! Benchmark Terraformer Results- github.com/davy/ benchmark-terraformer ! Maps by Leaflet - github.com/Leaflet/Leaflet extended with Esri Leaflet - github.com/Esri/esri-leaflet and Leaflet Ajax - github.com/calvinmetcalf/leaflet-ajax

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Attributions From the Noun Project: ! “Erlenmeyer Flask” by Emily van den Heever “Stopwatch” by Irit Barzily “Diamond” by Ryan Beck “Question” by Brennan Novak “Check Mark” by Brennan Novak “Arrow” by José Campos

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Attributions Backgrounds: Clouds by Joshua Rappeneker First Stars by Paul Chaloner grassy by cometwendy Drops on Bright Orange Flower by A Guy Taking Pictures Lightning by Stuart Williams Beach Palm Trees by Grand Velas Riviera Maya ! !