{"id":1352,"date":"2023-07-11T09:37:29","date_gmt":"2023-07-11T13:37:29","guid":{"rendered":"https:\/\/blogs.mathworks.com\/matlab\/?p=1352"},"modified":"2023-07-11T09:37:55","modified_gmt":"2023-07-11T13:37:55","slug":"partial-sorting-in-matlab","status":"publish","type":"post","link":"https:\/\/blogs.mathworks.com\/matlab\/2023\/07\/11\/partial-sorting-in-matlab\/","title":{"rendered":"Partial sorting in MATLAB"},"content":{"rendered":"<div class = rtcContent><div  style = 'margin: 2px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: rgb(33, 33, 33); font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left; '><span>I was recently working with a researcher who had to sort arrays of double precision numbers thousands of times.  In his application, however, he didn't need the full sorted list.  He only wanted the lowest <\/span><span style=' font-family: monospace;'>N\/2<\/span><span> elements of the array sorted.  As such, he had two questions.<\/span><\/div><ul  style = 'margin: 10px 0px 20px; padding-left: 0px; font-family: Helvetica, Arial, sans-serif; font-size: 14px; '><li  style = 'margin-left: 56px; line-height: 21px; min-height: 0px; text-align: left; white-space: pre-wrap; '><span>Does MATLAB have partial sort functions?  <\/span><\/li><li  style = 'margin-left: 56px; line-height: 21px; min-height: 0px; text-align: left; white-space: pre-wrap; '><span>Will they be faster for his application?<\/span><\/li><\/ul><div  style = 'margin: 2px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: rgb(33, 33, 33); font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left; '><span>The answer to the first question is easy.  MATLAB has <\/span><a href = \"https:\/\/www.mathworks.com\/help\/matlab\/ref\/mink.html\"><span style=' font-family: monospace;'>mink(x,k)<\/span><\/a><span> and <\/span><a href = \"https:\/\/www.mathworks.com\/help\/matlab\/ref\/maxk.html\"><span style=' font-family: monospace;'>maxk(x,k)<\/span><\/a><span> which find the lowest or highest sorted <\/span><span style=' font-family: monospace;'>k<\/span><span> elements from the array <\/span><span style=' font-family: monospace;'>x<\/span><span> respectively.  <\/span><\/div><div  style = 'margin: 2px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: rgb(33, 33, 33); font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left; '><span>The answer to the second question \"Will partial sorting be faster?\" depends on <\/span><span style=' font-family: monospace;'>k<\/span><span> as you might expect. Let's investigate how<\/span><\/div><h2  style = 'margin: 20px 10px 5px 4px; padding: 0px; line-height: 20px; min-height: 0px; white-space: pre-wrap; color: rgb(33, 33, 33); font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 20px; font-weight: 700; text-align: left; '><span>How long does a full sort take compared to a partial sort requesting the smallest 10 entries?<\/span><\/h2><div  style = 'margin: 2px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: rgb(33, 33, 33); font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left; '><span>We create a 100,000 element array of doubles<\/span><\/div><div style=\"background-color: #F5F5F5; margin: 10px 0 10px 0;\"><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 1px solid rgb(217, 217, 217); border-bottom: 1px solid rgb(217, 217, 217); border-radius: 4px; padding: 6px 45px 4px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >x = rand(100000,1);<\/span><\/span><\/div><\/div><\/div><div  style = 'margin: 10px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: rgb(33, 33, 33); font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left; '><span>I'm going to sort this array 300 times to match how it's used in the user's application.  Of course, in the real application, x varies every iteration but I want to isolate just the sort <\/span><\/div><div style=\"background-color: #F5F5F5; margin: 10px 0 10px 0;\"><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 1px solid rgb(217, 217, 217); border-bottom: 0px none rgb(33, 33, 33); border-radius: 4px 4px 0px 0px; padding: 6px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >tic<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span style=\"color: #0e00ff;\">for <\/span><span >i=1:300<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >    y = sort(x);<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >    res = y(1:10);   <\/span><span style=\"color: #008013;\">% We only want the lowest 10<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span style=\"color: #0e00ff;\">end<\/span><\/span><\/div><\/div><div class=\"inlineWrapper outputs\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 1px solid rgb(217, 217, 217); border-radius: 0px; padding: 0px 45px 4px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >sortTime=toc<\/span><\/span><\/div><div  style = 'color: rgb(33, 33, 33); padding: 10px 0px 6px 17px; background: rgb(255, 255, 255) none repeat scroll 0% 0% \/ auto padding-box border-box; font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; overflow-x: hidden; line-height: 17.234px; '><div class='variableElement' style='font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 12px; '>sortTime = 0.5181<\/div><\/div><\/div><\/div><div  style = 'margin: 10px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: rgb(33, 33, 33); font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left; '><span>If all we want is the 10 smallest numbers in x sorted, we can alternatively use <\/span><a href = \"https:\/\/www.mathworks.com\/help\/matlab\/ref\/mink.html\"><span style=' font-family: monospace;'>mink<\/span><\/a><\/div><div style=\"background-color: #F5F5F5; margin: 10px 0 10px 0;\"><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 1px solid rgb(217, 217, 217); border-bottom: 0px none rgb(33, 33, 33); border-radius: 4px 4px 0px 0px; padding: 6px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >tic<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span style=\"color: #0e00ff;\">for <\/span><span >i=1:300<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >    res = mink(x,10);<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span style=\"color: #0e00ff;\">end<\/span><\/span><\/div><\/div><div class=\"inlineWrapper outputs\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 1px solid rgb(217, 217, 217); border-radius: 0px; padding: 0px 45px 4px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >partialsortTime=toc<\/span><\/span><\/div><div  style = 'color: rgb(33, 33, 33); padding: 10px 0px 6px 17px; background: rgb(255, 255, 255) none repeat scroll 0% 0% \/ auto padding-box border-box; font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; overflow-x: hidden; line-height: 17.234px; '><div class='variableElement' style='font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 12px; '>partialsortTime = 0.0361<\/div><\/div><\/div><div class=\"inlineWrapper outputs\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 1px solid rgb(217, 217, 217); border-bottom: 1px solid rgb(217, 217, 217); border-radius: 0px; padding: 6px 45px 4px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >fprintf(<\/span><span style=\"color: #a709f5;\">\"Partial sort is %fx faster than full sort for k=10\"<\/span><span >,sortTime\/partialsortTime)<\/span><\/span><\/div><div  style = 'color: rgb(33, 33, 33); padding: 10px 0px 6px 17px; background: rgb(255, 255, 255) none repeat scroll 0% 0% \/ auto padding-box border-box; font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; overflow-x: hidden; line-height: 17.234px; '><div class=\"inlineElement eoOutputWrapper disableDefaultGestureHandling embeddedOutputsTextElement\" uid=\"755BDE87\" prevent-scroll=\"true\" data-testid=\"output_2\" tabindex=\"-1\" style=\"width: 1145px; white-space: pre; font-style: normal; color: rgb(33, 33, 33); font-size: 12px;\"><div class=\"textElement eoOutputContent\" tabindex=\"-1\" data-previous-available-width=\"1108\" data-previous-scroll-height=\"17\" data-hashorizontaloverflow=\"false\" style=\"max-height: 261px; white-space: pre; font-style: normal; color: rgb(33, 33, 33); font-size: 12px;\">Partial sort is 14.354572x faster than full sort for k=10<\/div><\/div><\/div><\/div><\/div><div  style = 'margin: 10px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: rgb(33, 33, 33); font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left; '><span>So, as you might expect, partial sorting is very useful when you only want a small number of sorted elements from a large array <\/span><\/div><h2  style = 'margin: 3px 10px 5px 4px; padding: 0px; line-height: 20px; min-height: 0px; white-space: pre-wrap; color: rgb(33, 33, 33); font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 20px; font-weight: 700; text-align: left; '><span>Is partial sorting always faster than full sorting?<\/span><\/h2><div  style = 'margin: 2px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: rgb(33, 33, 33); font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left; '><span>Next, I use the <\/span><span style=' font-family: monospace;'>mink<\/span><span> function to request the lowest k numbers where k varies from 100 to 15000, As before, I repeat each sort operation 300 times.<\/span><\/div><div style=\"background-color: #F5F5F5; margin: 10px 0 10px 0;\"><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 1px solid rgb(217, 217, 217); border-bottom: 0px none rgb(33, 33, 33); border-radius: 4px 4px 0px 0px; padding: 6px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >minkResults = zeros(150,1);<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >minkSize = zeros(150,1);<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span style=\"color: #0e00ff;\">for <\/span><span >j=1:150<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >    tic<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >    <\/span><span style=\"color: #0e00ff;\">for <\/span><span >i=1:300<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >        y=mink(x,j*100);<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >    <\/span><span style=\"color: #0e00ff;\">end<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >    minkResults(j)=toc;<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >    minkSize(j)=j*100;<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 1px solid rgb(217, 217, 217); border-radius: 0px 0px 4px 4px; padding: 0px 45px 4px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span style=\"color: #0e00ff;\">end<\/span><\/span><\/div><\/div><\/div><div  style = 'margin: 2px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: rgb(33, 33, 33); font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left; '><span>Plotting the results, we see that a partial sort is only faster than a full sort if we are requesting fewer than 4200 elements -- that's less than 5% of the full vector.  <\/span><\/div><div style=\"background-color: #F5F5F5; margin: 10px 0 10px 0;\"><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 1px solid rgb(217, 217, 217); border-bottom: 0px none rgb(33, 33, 33); border-radius: 4px 4px 0px 0px; padding: 6px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >plot(minkSize,minkResults,<\/span><span style=\"color: #a709f5;\">'.'<\/span><span >)<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >yline(sortTime)<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >legend(<\/span><span style=\"color: #a709f5;\">\"Partial sort\"<\/span><span >, <\/span><span style=\"color: #a709f5;\">\"full sort\"<\/span><span >)<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >xlabel(<\/span><span style=\"color: #a709f5;\">\"Number requested in partial sort\"<\/span><span >)<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >ylabel(<\/span><span style=\"color: #a709f5;\">\"Time (s)\"<\/span><span >)<\/span><\/span><\/div><\/div><div class=\"inlineWrapper outputs\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 1px solid rgb(217, 217, 217); border-radius: 0px; padding: 0px 45px 4px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >title(<\/span><span style=\"color: #a709f5;\">\"Time taken to sort \" <\/span><span >+ numel(x) + <\/span><span style=\"color: #a709f5;\">\" elements 300 times\"<\/span><span >)<\/span><\/span><\/div><div  style = 'color: rgb(33, 33, 33); padding: 10px 0px 6px 17px; background: rgb(255, 255, 255) none repeat scroll 0% 0% \/ auto padding-box border-box; font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; overflow-x: hidden; line-height: 17.234px; '><div class=\"inlineElement eoOutputWrapper disableDefaultGestureHandling embeddedOutputsFigure\" uid=\"34D2E9BD\" prevent-scroll=\"true\" data-testid=\"output_3\" tabindex=\"-1\" style=\"width: 1145px;\"><div class=\"figureElement eoOutputContent\"><img decoding=\"async\" class=\"figureImage figureContainingNode\" src=\"http:\/\/blogs.mathworks.com\/matlab\/files\/2023\/07\/partialsort_1.png\" style=\"width: 560px; padding-bottom: 0px;\"><\/div><div class=\"outputLayer selectedOutputDecorationLayer doNotExport\"><\/div><div class=\"outputLayer activeOutputDecorationLayer doNotExport\"><\/div><div class=\"outputLayer scrollableOutputDecorationLayer doNotExport\"><\/div><div class=\"outputLayer navigationFocusLayer doNotExport\" tabindex=\"-1\"><\/div><\/div><\/div><\/div><\/div><div style=\"background-color: #F5F5F5; margin: 10px 0 10px 0;\"><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 1px solid rgb(217, 217, 217); border-bottom: 0px none rgb(33, 33, 33); border-radius: 4px 4px 0px 0px; padding: 6px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >crossing = minkSize(find(minkResults&gt;sortTime,1,<\/span><span style=\"color: #a709f5;\">\"first\"<\/span><span >));<\/span><\/span><\/div><\/div><div class=\"inlineWrapper outputs\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 1px solid rgb(217, 217, 217); border-radius: 0px; padding: 0px 45px 4px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >fprintf(<\/span><span style=\"color: #a709f5;\">\"For x of size %d, mink(x,k) is faster than sort(x) only if k &lt; %d}\"<\/span><span >,numel(x),crossing)<\/span><\/span><\/div><div  style = 'color: rgb(33, 33, 33); padding: 10px 0px 6px 17px; background: rgb(255, 255, 255) none repeat scroll 0% 0% \/ auto padding-box border-box; font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; overflow-x: hidden; line-height: 17.234px; '><div class=\"inlineElement eoOutputWrapper disableDefaultGestureHandling embeddedOutputsTextElement\" uid=\"886F7B26\" prevent-scroll=\"true\" data-testid=\"output_4\" tabindex=\"-1\" style=\"width: 1145px; white-space: pre; font-style: normal; color: rgb(33, 33, 33); font-size: 12px;\"><div class=\"textElement eoOutputContent\" tabindex=\"-1\" data-previous-available-width=\"1108\" data-previous-scroll-height=\"17\" data-hashorizontaloverflow=\"false\" style=\"max-height: 261px; white-space: pre; font-style: normal; color: rgb(33, 33, 33); font-size: 12px;\">For x of size 100000, mink(x,k) is faster than sort(x) only if k &lt; 4200}<\/div><\/div><\/div><\/div><\/div><h2  style = 'margin: 3px 10px 5px 4px; padding: 0px; line-height: 20px; min-height: 0px; white-space: pre-wrap; color: rgb(33, 33, 33); font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 20px; font-weight: 700; text-align: left; '><span>Why isn't partial sorting better?<\/span><\/h2><div  style = 'margin: 2px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: rgb(33, 33, 33); font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left; '><span>You may be disappointed with this result because, for this example at least, partial sorting is only the better option if you want fewer than 5% of the total number of elements sorted. The primary reason for this is that <\/span><span style=' font-weight: bold;'>MATLAB's sort function is both fast and multithreaded.  <\/span><span>It's pretty hard to beat!<\/span><\/div><div  style = 'margin: 2px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: rgb(33, 33, 33); font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left; '><span>Let's take a look at how <\/span><span style=' font-weight: bold;'>sort scales with 100,000 elements<\/span><span>. I'll repeat the computation 300 times to get a stable average.<\/span><\/div><div style=\"background-color: #F5F5F5; margin: 10px 0 10px 0;\"><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 1px solid rgb(217, 217, 217); border-bottom: 0px none rgb(33, 33, 33); border-radius: 4px 4px 0px 0px; padding: 6px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span style=\"color: #008013;\">% Scaling of sort with respect to threads<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >arraySize = 100000;<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >repeats = 300;<\/span><\/span><\/div><\/div><div class=\"inlineWrapper outputs\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 1px solid rgb(217, 217, 217); border-radius: 0px; padding: 0px 45px 4px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >sortSpeedTest(arraySize,repeats)<\/span><\/span><\/div><div  style = 'color: rgb(33, 33, 33); padding: 10px 0px 6px 17px; background: rgb(255, 255, 255) none repeat scroll 0% 0% \/ auto padding-box border-box; font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; overflow-x: hidden; line-height: 17.234px; '><div class=\"inlineElement eoOutputWrapper disableDefaultGestureHandling embeddedOutputsVariableTableElement\" uid=\"30941361\" prevent-scroll=\"true\" data-testid=\"output_5\" tabindex=\"-1\" style=\"width: calc(100% - 5px);\"><div class=\"ClientDocument veSpecifier table DataFitToViewport\" id=\"variableeditor_client_Document_0\" widgetid=\"variableeditor_client_Document_0\" tabindex=\"0\" aria-labelledby=\"variableeditor_views_SummaryBar_0\"><div class=\"summaryBar\" style=\"font-size: 12px; font-family: Consolas, Inconsolata, Menlo, monospace;\"><span>ans = <\/span><span style=\"color: rgb(179, 179, 179); font-style: normal;\">4\u00d73 table <\/span><\/div><div id=\"variableeditor_TableViewModel_0\" widgetid=\"variableeditor_TableViewModel_0\" class=\"table ClientViewDiv hasSummaryBar\" data-viewid=\"__1\" style=\"width: 100%; overflow: auto;\"><table cellspacing=\"0\" style=\"border-spacing: 0px; border-collapse: collapse;\"><thead><tr><th rowspan=\"1\" style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 6px 3px 3px; width: 34px; border: 1px solid rgb(191, 191, 191); text-align: left; background-color: rgb(245, 245, 245); color: rgba(0, 0, 0, 0.75); font-weight: 700; box-sizing: border-box;\"><span>&nbsp;<\/span><\/th><th style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 6px 3px 3px; width: 118px; min-width: 118px; max-width: 118px; border: 1px solid rgb(191, 191, 191); text-align: center; background-color: rgb(245, 245, 245); color: rgba(0, 0, 0, 0.75); font-weight: 700; box-sizing: border-box;\"><span>numThreads<\/span><\/th><th style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 6px 3px 3px; width: 126px; min-width: 126px; max-width: 126px; border: 1px solid rgb(191, 191, 191); text-align: center; background-color: rgb(245, 245, 245); color: rgba(0, 0, 0, 0.75); font-weight: 700; box-sizing: border-box;\"><span>averageTime<\/span><\/th><th style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 6px 3px 3px; width: 94px; min-width: 94px; max-width: 94px; border: 1px solid rgb(191, 191, 191); text-align: center; background-color: rgb(245, 245, 245); color: rgba(0, 0, 0, 0.75); font-weight: 700; box-sizing: border-box;\"><span>SpeedUp<\/span><\/th><\/tr><\/thead><tbody><tr><th style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 6px 3px 3px; width: 34px; border-width: 0px 1px 1px; border-style: solid; border-color: rgb(191, 191, 191); border-image: initial; text-align: left; background-color: rgb(245, 245, 245); color: rgba(0, 0, 0, 0.75); font-weight: 700; box-sizing: border-box;\"><span>1<\/span><\/th><td style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 3px; width: 118px; min-width: 118px; max-width: 118px; border-width: 0px 1px 1px; border-style: solid; border-color: rgb(191, 191, 191); border-image: initial; text-align: right;\"><span>1<\/span><\/td><td style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 3px; width: 126px; min-width: 126px; max-width: 126px; border-width: 0px 1px 1px; border-style: solid; border-color: rgb(191, 191, 191); border-image: initial; text-align: right;\"><span>0.0052<\/span><\/td><td style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 3px; width: 94px; min-width: 94px; max-width: 94px; border-width: 0px 1px 1px; border-style: solid; border-color: rgb(191, 191, 191); border-image: initial; text-align: right;\"><span>1<\/span><\/td><\/tr><tr><th style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 6px 3px 3px; width: 34px; border-width: 0px 1px 1px; border-style: solid; border-color: rgb(191, 191, 191); border-image: initial; text-align: left; background-color: rgb(245, 245, 245); color: rgba(0, 0, 0, 0.75); font-weight: 700; box-sizing: border-box;\"><span>2<\/span><\/th><td style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 3px; width: 118px; min-width: 118px; max-width: 118px; border-width: 0px 1px 1px; border-style: solid; border-color: rgb(191, 191, 191); border-image: initial; text-align: right;\"><span>2<\/span><\/td><td style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 3px; width: 126px; min-width: 126px; max-width: 126px; border-width: 0px 1px 1px; border-style: solid; border-color: rgb(191, 191, 191); border-image: initial; text-align: right;\"><span>0.0028<\/span><\/td><td style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 3px; width: 94px; min-width: 94px; max-width: 94px; border-width: 0px 1px 1px; border-style: solid; border-color: rgb(191, 191, 191); border-image: initial; text-align: right;\"><span>1.8151<\/span><\/td><\/tr><tr><th style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 6px 3px 3px; width: 34px; border-width: 0px 1px 1px; border-style: solid; border-color: rgb(191, 191, 191); border-image: initial; text-align: left; background-color: rgb(245, 245, 245); color: rgba(0, 0, 0, 0.75); font-weight: 700; box-sizing: border-box;\"><span>3<\/span><\/th><td style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 3px; width: 118px; min-width: 118px; max-width: 118px; border-width: 0px 1px 1px; border-style: solid; border-color: rgb(191, 191, 191); border-image: initial; text-align: right;\"><span>4<\/span><\/td><td style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 3px; width: 126px; min-width: 126px; max-width: 126px; border-width: 0px 1px 1px; border-style: solid; border-color: rgb(191, 191, 191); border-image: initial; text-align: right;\"><span>0.0018<\/span><\/td><td style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 3px; width: 94px; min-width: 94px; max-width: 94px; border-width: 0px 1px 1px; border-style: solid; border-color: rgb(191, 191, 191); border-image: initial; text-align: right;\"><span>2.8250<\/span><\/td><\/tr><tr><th style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 6px 3px 3px; width: 34px; border-width: 0px 1px 1px; border-style: solid; border-color: rgb(191, 191, 191); border-image: initial; text-align: left; background-color: rgb(245, 245, 245); color: rgba(0, 0, 0, 0.75); font-weight: 700; box-sizing: border-box;\"><span>4<\/span><\/th><td style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 3px; width: 118px; min-width: 118px; max-width: 118px; border-width: 0px 1px 1px; border-style: solid; border-color: rgb(191, 191, 191); border-image: initial; text-align: right;\"><span>8<\/span><\/td><td style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 3px; width: 126px; min-width: 126px; max-width: 126px; border-width: 0px 1px 1px; border-style: solid; border-color: rgb(191, 191, 191); border-image: initial; text-align: right;\"><span>0.0015<\/span><\/td><td style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 3px; width: 94px; min-width: 94px; max-width: 94px; border-width: 0px 1px 1px; border-style: solid; border-color: rgb(191, 191, 191); border-image: initial; text-align: right;\"><span>3.5265<\/span><\/td><\/tr><\/tbody><\/table><\/div><\/div><div class=\"outputLayer selectedOutputDecorationLayer doNotExport\"><\/div><div class=\"outputLayer activeOutputDecorationLayer doNotExport\"><\/div><div class=\"outputLayer scrollableOutputDecorationLayer doNotExport\"><\/div><div class=\"outputLayer navigationFocusLayer doNotExport\" tabindex=\"-1\"><\/div><\/div><\/div><\/div><\/div><div  style = 'margin: 10px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: rgb(33, 33, 33); font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left; '><span>The algorithm used in the  <\/span><span style=' font-family: monospace;'>mink<\/span><span> function, on the other hand, does not lend itself to multithreading.  As such, it is completely single threaded.  Let's see this explicity using the same sized input matrix, requesting the lowest 10,000 numbers be sorted. <\/span><\/div><div style=\"background-color: #F5F5F5; margin: 10px 0 10px 0;\"><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 1px solid rgb(217, 217, 217); border-bottom: 0px none rgb(33, 33, 33); border-radius: 4px 4px 0px 0px; padding: 6px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span style=\"color: #008013;\">%Scaling of mink with respect to threads<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >k=10000;<\/span><\/span><\/div><\/div><div class=\"inlineWrapper outputs\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 1px solid rgb(217, 217, 217); border-radius: 0px; padding: 0px 45px 4px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >minkSpeedTest(arraySize,repeats,k)<\/span><\/span><\/div><div  style = 'color: rgb(33, 33, 33); padding: 10px 0px 6px 17px; background: rgb(255, 255, 255) none repeat scroll 0% 0% \/ auto padding-box border-box; font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; overflow-x: hidden; line-height: 17.234px; '><div class=\"inlineElement eoOutputWrapper disableDefaultGestureHandling embeddedOutputsVariableTableElement\" uid=\"1CAFF441\" prevent-scroll=\"true\" data-testid=\"output_6\" tabindex=\"-1\" style=\"width: calc(100% - 5px);\"><div class=\"ClientDocument veSpecifier table DataFitToViewport\" id=\"variableeditor_client_Document_1\" widgetid=\"variableeditor_client_Document_1\" tabindex=\"0\" aria-labelledby=\"variableeditor_views_SummaryBar_1\"><div class=\"summaryBar\" style=\"font-size: 12px; font-family: Consolas, Inconsolata, Menlo, monospace;\"><span>ans = <\/span><span style=\"color: rgb(179, 179, 179); font-style: normal;\">4\u00d73 table <\/span><\/div><div id=\"variableeditor_TableViewModel_1\" widgetid=\"variableeditor_TableViewModel_1\" class=\"table ClientViewDiv hasSummaryBar\" data-viewid=\"__1\" style=\"width: 100%; overflow: auto;\"><table cellspacing=\"0\" style=\"border-spacing: 0px; border-collapse: collapse;\"><thead><tr><th rowspan=\"1\" style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 6px 3px 3px; width: 34px; border: 1px solid rgb(191, 191, 191); text-align: left; background-color: rgb(245, 245, 245); color: rgba(0, 0, 0, 0.75); font-weight: 700; box-sizing: border-box;\"><span>&nbsp;<\/span><\/th><th style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 6px 3px 3px; width: 118px; min-width: 118px; max-width: 118px; border: 1px solid rgb(191, 191, 191); text-align: center; background-color: rgb(245, 245, 245); color: rgba(0, 0, 0, 0.75); font-weight: 700; box-sizing: border-box;\"><span>numThreads<\/span><\/th><th style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 6px 3px 3px; width: 126px; min-width: 126px; max-width: 126px; border: 1px solid rgb(191, 191, 191); text-align: center; background-color: rgb(245, 245, 245); color: rgba(0, 0, 0, 0.75); font-weight: 700; box-sizing: border-box;\"><span>averageTime<\/span><\/th><th style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 6px 3px 3px; width: 94px; min-width: 94px; max-width: 94px; border: 1px solid rgb(191, 191, 191); text-align: center; background-color: rgb(245, 245, 245); color: rgba(0, 0, 0, 0.75); font-weight: 700; box-sizing: border-box;\"><span>SpeedUp<\/span><\/th><\/tr><\/thead><tbody><tr><th style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 6px 3px 3px; width: 34px; border-width: 0px 1px 1px; border-style: solid; border-color: rgb(191, 191, 191); border-image: initial; text-align: left; background-color: rgb(245, 245, 245); color: rgba(0, 0, 0, 0.75); font-weight: 700; box-sizing: border-box;\"><span>1<\/span><\/th><td style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 3px; width: 118px; min-width: 118px; max-width: 118px; border-width: 0px 1px 1px; border-style: solid; border-color: rgb(191, 191, 191); border-image: initial; text-align: right;\"><span>1<\/span><\/td><td style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 3px; width: 126px; min-width: 126px; max-width: 126px; border-width: 0px 1px 1px; border-style: solid; border-color: rgb(191, 191, 191); border-image: initial; text-align: right;\"><span>0.0037<\/span><\/td><td style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 3px; width: 94px; min-width: 94px; max-width: 94px; border-width: 0px 1px 1px; border-style: solid; border-color: rgb(191, 191, 191); border-image: initial; text-align: right;\"><span>1<\/span><\/td><\/tr><tr><th style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 6px 3px 3px; width: 34px; border-width: 0px 1px 1px; border-style: solid; border-color: rgb(191, 191, 191); border-image: initial; text-align: left; background-color: rgb(245, 245, 245); color: rgba(0, 0, 0, 0.75); font-weight: 700; box-sizing: border-box;\"><span>2<\/span><\/th><td style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 3px; width: 118px; min-width: 118px; max-width: 118px; border-width: 0px 1px 1px; border-style: solid; border-color: rgb(191, 191, 191); border-image: initial; text-align: right;\"><span>2<\/span><\/td><td style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 3px; width: 126px; min-width: 126px; max-width: 126px; border-width: 0px 1px 1px; border-style: solid; border-color: rgb(191, 191, 191); border-image: initial; text-align: right;\"><span>0.0037<\/span><\/td><td style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 3px; width: 94px; min-width: 94px; max-width: 94px; border-width: 0px 1px 1px; border-style: solid; border-color: rgb(191, 191, 191); border-image: initial; text-align: right;\"><span>0.9967<\/span><\/td><\/tr><tr><th style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 6px 3px 3px; width: 34px; border-width: 0px 1px 1px; border-style: solid; border-color: rgb(191, 191, 191); border-image: initial; text-align: left; background-color: rgb(245, 245, 245); color: rgba(0, 0, 0, 0.75); font-weight: 700; box-sizing: border-box;\"><span>3<\/span><\/th><td style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 3px; width: 118px; min-width: 118px; max-width: 118px; border-width: 0px 1px 1px; border-style: solid; border-color: rgb(191, 191, 191); border-image: initial; text-align: right;\"><span>4<\/span><\/td><td style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 3px; width: 126px; min-width: 126px; max-width: 126px; border-width: 0px 1px 1px; border-style: solid; border-color: rgb(191, 191, 191); border-image: initial; text-align: right;\"><span>0.0037<\/span><\/td><td style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 3px; width: 94px; min-width: 94px; max-width: 94px; border-width: 0px 1px 1px; border-style: solid; border-color: rgb(191, 191, 191); border-image: initial; text-align: right;\"><span>1.0018<\/span><\/td><\/tr><tr><th style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 6px 3px 3px; width: 34px; border-width: 0px 1px 1px; border-style: solid; border-color: rgb(191, 191, 191); border-image: initial; text-align: left; background-color: rgb(245, 245, 245); color: rgba(0, 0, 0, 0.75); font-weight: 700; box-sizing: border-box;\"><span>4<\/span><\/th><td style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 3px; width: 118px; min-width: 118px; max-width: 118px; border-width: 0px 1px 1px; border-style: solid; border-color: rgb(191, 191, 191); border-image: initial; text-align: right;\"><span>8<\/span><\/td><td style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 3px; width: 126px; min-width: 126px; max-width: 126px; border-width: 0px 1px 1px; border-style: solid; border-color: rgb(191, 191, 191); border-image: initial; text-align: right;\"><span>0.0036<\/span><\/td><td style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 3px; width: 94px; min-width: 94px; max-width: 94px; border-width: 0px 1px 1px; border-style: solid; border-color: rgb(191, 191, 191); border-image: initial; text-align: right;\"><span>1.0197<\/span><\/td><\/tr><\/tbody><\/table><\/div><\/div><div class=\"outputLayer selectedOutputDecorationLayer doNotExport\"><\/div><div class=\"outputLayer activeOutputDecorationLayer doNotExport\"><\/div><div class=\"outputLayer scrollableOutputDecorationLayer doNotExport\"><\/div><div class=\"outputLayer navigationFocusLayer doNotExport\" tabindex=\"-1\"><\/div><\/div><\/div><\/div><\/div><div  style = 'margin: 10px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: rgb(33, 33, 33); font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left; '><span>It's pretty clear that mink doesn't benefit from differing numbers of threads. Any differences we see are just measurement noise.  If <\/span><span style=' font-family: monospace;'>sort(x)<\/span><span> were not mulithreaded, <\/span><span style=' font-family: monospace;'>mink(x,k)<\/span><span> would be faster here but multithreading helps a lot. <\/span><\/div><div  style = 'margin: 2px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: rgb(33, 33, 33); font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left; '><span>As we increase k, there will eventually come a point where even comparing single threaded <\/span><span style=' font-family: monospace;'>sort<\/span><span> with <\/span><span style=' font-family: monospace;'>mink<\/span><span> results in <\/span><span style=' font-family: monospace;'>mink<\/span><span> losing.  On my machine, k=16000 does it<\/span><\/div><div style=\"background-color: #F5F5F5; margin: 10px 0 10px 0;\"><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 1px solid rgb(217, 217, 217); border-bottom: 0px none rgb(33, 33, 33); border-radius: 4px 4px 0px 0px; padding: 6px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span style=\"color: #008013;\">%Scaling of mink with respect to threads<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >k=16000;<\/span><\/span><\/div><\/div><div class=\"inlineWrapper outputs\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 1px solid rgb(217, 217, 217); border-radius: 0px; padding: 0px 45px 4px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >minkSpeedTest(arraySize,repeats,k)<\/span><\/span><\/div><div  style = 'color: rgb(33, 33, 33); padding: 10px 0px 6px 17px; background: rgb(255, 255, 255) none repeat scroll 0% 0% \/ auto padding-box border-box; font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; overflow-x: hidden; line-height: 17.234px; '><div class=\"inlineElement eoOutputWrapper disableDefaultGestureHandling embeddedOutputsVariableTableElement\" uid=\"B7C17E73\" prevent-scroll=\"true\" data-testid=\"output_7\" tabindex=\"-1\" style=\"width: calc(100% - 5px);\"><div class=\"ClientDocument veSpecifier table DataFitToViewport\" id=\"variableeditor_client_Document_2\" widgetid=\"variableeditor_client_Document_2\" tabindex=\"0\" aria-labelledby=\"variableeditor_views_SummaryBar_2\"><div class=\"summaryBar\" style=\"font-size: 12px; font-family: Consolas, Inconsolata, Menlo, monospace;\"><span>ans = <\/span><span style=\"color: rgb(179, 179, 179); font-style: normal;\">4\u00d73 table <\/span><\/div><div id=\"variableeditor_TableViewModel_2\" widgetid=\"variableeditor_TableViewModel_2\" class=\"table ClientViewDiv hasSummaryBar\" data-viewid=\"__1\" style=\"width: 100%; overflow: auto;\"><table cellspacing=\"0\" style=\"border-spacing: 0px; border-collapse: collapse;\"><thead><tr><th rowspan=\"1\" style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 6px 3px 3px; width: 34px; border: 1px solid rgb(191, 191, 191); text-align: left; background-color: rgb(245, 245, 245); color: rgba(0, 0, 0, 0.75); font-weight: 700; box-sizing: border-box;\"><span>&nbsp;<\/span><\/th><th style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 6px 3px 3px; width: 118px; min-width: 118px; max-width: 118px; border: 1px solid rgb(191, 191, 191); text-align: center; background-color: rgb(245, 245, 245); color: rgba(0, 0, 0, 0.75); font-weight: 700; box-sizing: border-box;\"><span>numThreads<\/span><\/th><th style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 6px 3px 3px; width: 126px; min-width: 126px; max-width: 126px; border: 1px solid rgb(191, 191, 191); text-align: center; background-color: rgb(245, 245, 245); color: rgba(0, 0, 0, 0.75); font-weight: 700; box-sizing: border-box;\"><span>averageTime<\/span><\/th><th style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 6px 3px 3px; width: 94px; min-width: 94px; max-width: 94px; border: 1px solid rgb(191, 191, 191); text-align: center; background-color: rgb(245, 245, 245); color: rgba(0, 0, 0, 0.75); font-weight: 700; box-sizing: border-box;\"><span>SpeedUp<\/span><\/th><\/tr><\/thead><tbody><tr><th style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 6px 3px 3px; width: 34px; border-width: 0px 1px 1px; border-style: solid; border-color: rgb(191, 191, 191); border-image: initial; text-align: left; background-color: rgb(245, 245, 245); color: rgba(0, 0, 0, 0.75); font-weight: 700; box-sizing: border-box;\"><span>1<\/span><\/th><td style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 3px; width: 118px; min-width: 118px; max-width: 118px; border-width: 0px 1px 1px; border-style: solid; border-color: rgb(191, 191, 191); border-image: initial; text-align: right;\"><span>1<\/span><\/td><td style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 3px; width: 126px; min-width: 126px; max-width: 126px; border-width: 0px 1px 1px; border-style: solid; border-color: rgb(191, 191, 191); border-image: initial; text-align: right;\"><span>0.0053<\/span><\/td><td style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 3px; width: 94px; min-width: 94px; max-width: 94px; border-width: 0px 1px 1px; border-style: solid; border-color: rgb(191, 191, 191); border-image: initial; text-align: right;\"><span>1<\/span><\/td><\/tr><tr><th style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 6px 3px 3px; width: 34px; border-width: 0px 1px 1px; border-style: solid; border-color: rgb(191, 191, 191); border-image: initial; text-align: left; background-color: rgb(245, 245, 245); color: rgba(0, 0, 0, 0.75); font-weight: 700; box-sizing: border-box;\"><span>2<\/span><\/th><td style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 3px; width: 118px; min-width: 118px; max-width: 118px; border-width: 0px 1px 1px; border-style: solid; border-color: rgb(191, 191, 191); border-image: initial; text-align: right;\"><span>2<\/span><\/td><td style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 3px; width: 126px; min-width: 126px; max-width: 126px; border-width: 0px 1px 1px; border-style: solid; border-color: rgb(191, 191, 191); border-image: initial; text-align: right;\"><span>0.0053<\/span><\/td><td style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 3px; width: 94px; min-width: 94px; max-width: 94px; border-width: 0px 1px 1px; border-style: solid; border-color: rgb(191, 191, 191); border-image: initial; text-align: right;\"><span>1.0141<\/span><\/td><\/tr><tr><th style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 6px 3px 3px; width: 34px; border-width: 0px 1px 1px; border-style: solid; border-color: rgb(191, 191, 191); border-image: initial; text-align: left; background-color: rgb(245, 245, 245); color: rgba(0, 0, 0, 0.75); font-weight: 700; box-sizing: border-box;\"><span>3<\/span><\/th><td style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 3px; width: 118px; min-width: 118px; max-width: 118px; border-width: 0px 1px 1px; border-style: solid; border-color: rgb(191, 191, 191); border-image: initial; text-align: right;\"><span>4<\/span><\/td><td style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 3px; width: 126px; min-width: 126px; max-width: 126px; border-width: 0px 1px 1px; border-style: solid; border-color: rgb(191, 191, 191); border-image: initial; text-align: right;\"><span>0.0054<\/span><\/td><td style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 3px; width: 94px; min-width: 94px; max-width: 94px; border-width: 0px 1px 1px; border-style: solid; border-color: rgb(191, 191, 191); border-image: initial; text-align: right;\"><span>0.9917<\/span><\/td><\/tr><tr><th style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 6px 3px 3px; width: 34px; border-width: 0px 1px 1px; border-style: solid; border-color: rgb(191, 191, 191); border-image: initial; text-align: left; background-color: rgb(245, 245, 245); color: rgba(0, 0, 0, 0.75); font-weight: 700; box-sizing: border-box;\"><span>4<\/span><\/th><td style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 3px; width: 118px; min-width: 118px; max-width: 118px; border-width: 0px 1px 1px; border-style: solid; border-color: rgb(191, 191, 191); border-image: initial; text-align: right;\"><span>8<\/span><\/td><td style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 3px; width: 126px; min-width: 126px; max-width: 126px; border-width: 0px 1px 1px; border-style: solid; border-color: rgb(191, 191, 191); border-image: initial; text-align: right;\"><span>0.0053<\/span><\/td><td style=\"text-overflow: ellipsis; font-family: Arial, sans-serif; font-size: 12px; overflow: hidden; padding: 3px; width: 94px; min-width: 94px; max-width: 94px; border-width: 0px 1px 1px; border-style: solid; border-color: rgb(191, 191, 191); border-image: initial; text-align: right;\"><span>1.0129<\/span><\/td><\/tr><\/tbody><\/table><\/div><\/div><div class=\"outputLayer selectedOutputDecorationLayer doNotExport\"><\/div><div class=\"outputLayer activeOutputDecorationLayer doNotExport\"><\/div><div class=\"outputLayer scrollableOutputDecorationLayer doNotExport\"><\/div><div class=\"outputLayer navigationFocusLayer doNotExport\" tabindex=\"-1\"><\/div><\/div><\/div><\/div><\/div><div  style = 'margin: 10px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: rgb(33, 33, 33); font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left; '><span>Slightly slower than a single threaded full <\/span><span style=' font-family: monospace;'>sort<\/span><span>! A possible future enhacement to MATLAB's <\/span><span style=' font-family: monospace;'>mink<\/span><span> function would be to switch to using <\/span><span style=' font-family: monospace;'>sort<\/span><span> internally for large <\/span><span style=' font-family: monospace;'>k<\/span><span> since, sooner or later, <\/span><span style=' font-family: monospace;'>mink<\/span><span>'s algorithm just isn't the right choice.<\/span><\/div><h3  style = 'margin: 3px 10px 5px 4px; padding: 0px; line-height: 18px; min-height: 0px; white-space: pre-wrap; color: rgb(33, 33, 33); font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 17px; font-weight: 700; text-align: left; '><span>Information about my machine<\/span><\/h3><div  style = 'margin: 2px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: rgb(33, 33, 33); font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left; '><span>You will probably have different results from me if you run these tests on your machine.  As such, some information about my machine may be useful. Here, I use the excellent <\/span><a href = \"https:\/\/www.mathworks.com\/matlabcentral\/fileexchange\/33155-cpu-info?s_tid=srchtitle_cpuinfo_1\"><span>cpuinfo function by Ben Tordoff<\/span><\/a><span>, available on the MATLAB File Exchange.<\/span><\/div><div style=\"background-color: #F5F5F5; margin: 10px 0 10px 0;\"><div class=\"inlineWrapper outputs\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 1px solid rgb(217, 217, 217); border-bottom: 1px solid rgb(217, 217, 217); border-radius: 4px 4px 0px 0px; padding: 6px 45px 4px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >cpuinfo<\/span><\/span><\/div><div  style = 'color: rgb(33, 33, 33); padding: 10px 0px 6px 17px; background: rgb(255, 255, 255) none repeat scroll 0% 0% \/ auto padding-box border-box; font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; overflow-x: hidden; line-height: 17.234px; '><div class=\"inlineElement eoOutputWrapper disableDefaultGestureHandling embeddedOutputsVariableStringElement\" uid=\"79B8C26A\" prevent-scroll=\"true\" data-testid=\"output_8\" tabindex=\"-1\" style=\"width: 1145px; white-space: pre; font-style: normal; color: rgb(33, 33, 33); font-size: 12px;\"><div class=\"textElement eoOutputContent\" tabindex=\"-1\" data-previous-available-width=\"1108\" data-previous-scroll-height=\"153\" data-hashorizontaloverflow=\"false\" style=\"max-height: 261px; white-space: pre; font-style: normal; color: rgb(33, 33, 33); font-size: 12px;\"><div style=\"white-space: pre; font-style: normal; color: rgb(33, 33, 33); font-size: 12px;\"><span class=\"variableNameElement\" style=\"white-space: pre; font-style: normal; color: rgb(33, 33, 33); font-size: 12px;\">ans = <span class=\"headerElement\" style=\"white-space: pre; font-style: normal; color: rgb(33, 33, 33); font-size: 12px;\">struct with fields:<\/span><\/span><\/div><div style=\"white-space: pre; font-style: normal; color: rgb(33, 33, 33); font-size: 12px;\">        CPUName: '11th Gen Intel(R) Core(TM) i7-11700 @ 2.50GHz'\r\n          Clock: '2501 MHz'\r\n          Cache: 4194304\r\n    TotalMemory: 3.4010e+10\r\n        NumCPUs: 1\r\n     TotalCores: 8\r\n         OSType: 'Windows'\r\n      OSVersion: 'Microsoft Windows 11 Pro'\r\n       Hostname: 'DESKTOP-N3C7C6Q'\r\n<\/div><\/div><\/div><\/div><\/div><\/div><h2  style = 'margin: 20px 10px 5px 4px; padding: 0px; line-height: 20px; min-height: 0px; white-space: pre-wrap; color: rgb(33, 33, 33); font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 20px; font-weight: 700; text-align: left; '><span>Over to you<\/span><\/h2><div  style = 'margin: 2px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: rgb(33, 33, 33); font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left; '><span>In summary, partial sorting in MATLAB can be useful but only when used appropriately. Have you used <\/span><a href = \"https:\/\/www.mathworks.com\/help\/matlab\/ref\/mink.html\"><span>mink<\/span><\/a><span> or <\/span><a href = \"https:\/\/www.mathworks.com\/help\/matlab\/ref\/maxk.html\"><span>maxk<\/span><\/a><span> in your work...or have you just discovered them now?  What additional sorting functionality do you think MATLAB should have?<\/span><\/div><h3  style = 'margin: 3px 10px 5px 4px; padding: 0px; line-height: 18px; min-height: 0px; white-space: pre-wrap; color: rgb(33, 33, 33); font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 17px; font-weight: 700; text-align: left; '><span>Helper functions<\/span><\/h3><div style=\"background-color: #F5F5F5; margin: 10px 0 10px 0;\"><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 1px solid rgb(217, 217, 217); border-bottom: 0px none rgb(33, 33, 33); border-radius: 4px 4px 0px 0px; padding: 6px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span style=\"color: #0e00ff;\">function <\/span><span >result = sortSpeedTest(arraySize,repeats)<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span style=\"color: #008013;\">% Runs sort on an array of size arraySize using differing numbers of threads<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >format <\/span><span style=\"color: #a709f5;\">short<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >averageTime = zeros(4,1);<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >SpeedUp = zeros(4,1);<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >numThreads = [1;2;4;8];<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >x = rand(1,arraySize);<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span style=\"color: #0e00ff;\">for <\/span><span >testNum = 1:4<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >    threads = numThreads(testNum);<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >    maxNumCompThreads(threads);<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >    tic<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >    <\/span><span style=\"color: #0e00ff;\">for <\/span><span >i=1:repeats<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >        y = sort(x);<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >    <\/span><span style=\"color: #0e00ff;\">end<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >    averageTime(testNum) = toc\/repeats;<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >    SpeedUp(testNum) = averageTime(1)\/averageTime(testNum);<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span style=\"color: #0e00ff;\">end<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >result = table(numThreads,averageTime,SpeedUp);<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span style=\"color: #0e00ff;\">end<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '>&nbsp;<\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span style=\"color: #0e00ff;\">function <\/span><span >result = minkSpeedTest(arraySize,repeats,k)<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span style=\"color: #008013;\">% Runs mink on an array of size arraySize using differing numbers of threads<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >format <\/span><span style=\"color: #a709f5;\">short<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >averageTime = zeros(4,1);<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >SpeedUp = zeros(4,1);<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >numThreads = [1;2;4;8];<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >x = rand(1,arraySize);<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span style=\"color: #0e00ff;\">for <\/span><span >testNum = 1:4<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >    threads = numThreads(testNum);<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >    maxNumCompThreads(threads);<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >    tic<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >    <\/span><span style=\"color: #0e00ff;\">for <\/span><span >i=1:repeats<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >        y = mink(x,k);<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >    <\/span><span style=\"color: #0e00ff;\">end<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >    averageTime(testNum) = toc\/repeats;<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >    SpeedUp(testNum) = averageTime(1)\/averageTime(testNum);<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span style=\"color: #0e00ff;\">end<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 0px none rgb(33, 33, 33); border-radius: 0px; padding: 0px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span >result = table(numThreads,averageTime,SpeedUp);<\/span><\/span><\/div><\/div><div class=\"inlineWrapper\"><div  style = 'border-left: 1px solid rgb(217, 217, 217); border-right: 1px solid rgb(217, 217, 217); border-top: 0px none rgb(33, 33, 33); border-bottom: 1px solid rgb(217, 217, 217); border-radius: 0px 0px 4px 4px; padding: 0px 45px 4px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, \"Courier New\", monospace; font-size: 14px; '><span style=\"white-space: pre\"><span style=\"color: #0e00ff;\">end<\/span><\/span><\/div><\/div><\/div>\r\n<\/div><script type=\"text\/javascript\">var css = '\/* Styling that is common to warnings and errors is in diagnosticOutput.css *\/.embeddedOutputsErrorElement {    min-height: 18px; 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