// script irGrade: interactive, real-time grading; html formatting; statistical functions, // linear algebra // copyright 1997, 1998, 1999, 2000, 2001. P.B. Stark, stark@stat.berkeley.edu // Version 1.0 // All rights reserved. // !!!!Beginning of the code!!!! var irGradeModTime = '2001/10/09/0150'; // modification date and time var today = (new Date()).toLocaleString(); var copyYr = '1997--2001. '; // copyright years var theChapters = [-1,0,1,2,3.1,3.2,3.3,4.1,4.2,4.3,5.1,5.2,5.3,6,7,8.1,8.2,9, 10,11,12,13,14.1,14.2,14.3,15,16.1,16.2,17.1,17.2,18,19.1,19.2, 20.1,20.2,20.3,21,22,23,24,25 ]; // list of the chapters var cookieExpireDays = 10; // days for the cookies to endure var theChapter; // current chapter var type = 'LA'; // default question type is 'literal answer' var newStyleAnswer = true; // flag for pop-up versus inline var ansText = ' '; // to display correct answer var pCtr = 1; // counter for problems var qCtr = 1; // counter for questions //var sCtr = 0; // counter for solved exercises var fCtr = 0; // counter for footnotes //var sEx = new Array(); // array for exercise numbers of solved exercises //var sEnum = 0; // counter for displaying solutions var footnotes = new Array(); // array of footnotes var key = new Array(); // key for self-graded exercises var boxList = new Array(); // list of images for self-graded exercises var longKey = new Array(); // long answers for exercises var solutionCode = new Array(); // javascript code to evaluate after writing solution var setNum; // current problem set number var isLab = false; // is this a problem set? var pbsURL = 'http://www.stat.berkeley.edu/~stark'; // P.B. Stark's URL var pbsRef = 'P.B. Stark'; // link to author var fudgeFactor = 0.01; // relative tolerance for imprecise numerical answers var absFudge = 1.e-20; // absolute tolerance for identically zero answers var wrongHtm = '

Sorry, wrong answer.

'; // message for wrong answer var rightHtm = '

Correct!

'; // message for right answer var dsmsHtm = '

'; // to go on when answer is right var startHtm = ' '; var showAnsHtm = '

' + '

'; // to go on or show answer when answer is wrong var inlinePrefix="Q#:a#:"; var bigPi = "3141592653"; var rmin = 2.3e-308; // for numerical analysis var eps = 2.3e-16; // ditto var maxIterations = 100; // default iteration limit for iterative algorithms var continueLab; var htmStuff; var randSeed; // seed of random number generator var CA = false; var sectionContext; // store chapter-specific initialization script var qImgSrc = '../Graphics/answer_unknown.gif'; var rightImgSrc = '../Graphics/answer_good.gif'; var wrongImgSrc = '../Graphics/answer_bad.gif'; var alphabet = ['a','b','c','d','e','f','g','h','i','j','k','l','m','n','o','p', 'q','r','s','t','u','v','w','x','y','z' ]; var ALPHABET = ['A','B','C','D','E','F','G','H','I','J','K','L','M','N','O','P', 'Q','R','S','T','U','V','W','X','Y','Z' ]; var Alphabet = ALPHABET; var cardinals = ['zero','one','two','three','four','five','six','seven','eight','nine','ten', 'eleven','twelve','thirteen','fourteen','fifteen','sixteen','seventeen','eighteen', 'nineteen','twenty','twenty-one','twenty-two','twenty-three','twenty-four', 'twenty-five','twenty-six','twenty-seven','twenty-eight','twenty-nine','thirty', 'thirty-one','thirty-two','thirty-three','thirty-four','thirty-five','thirty-six', 'thirty-seven','thirty-eight','thirty-nine','fourty','fourty-one','fourty-two', 'fourty-three','fourty-four','fourty-five','fourty-six','fourty-seven','fourty-eight', 'fourty-nine','fifty','fifty-one','fifty-two','fifty-three','fifty-four','fifty-five', 'fifty-six','fifty-seven','fifty-eight','fifty-nine','sixty','sixty-one','sixty-two', 'sixty-three','sixty-four','sixty-five','sixty-six','sixty-seven','sixty-eight', 'sixty-nine','seventy','seventy-one','seventy-two','seventy-three','seventy-four', 'seventy-five','seventy-six','seventy-seven','seventy-eight','seventy-nine', 'eighty','eighty-one','eighty-two','eighty-three','eighty-four','eighty-five', 'eighty-six','eighty-seven','eighty-eight','eighty-nine','ninety', 'ninety-one','ninety-two','ninety-three','ninety-four','ninety-five', 'ninety-six','ninety-seven','ninety-eight','ninety-nine','one hundred' ]; var Cardinals = ['Zero','One','Two','Three','Four','Five','Six','Seven','Eight','Nine','Ten', 'Eleven','Twelve','Thirteen','Fourteen','Fifteen','Sixteen','Seventeen','Eighteen', 'Nineteen','Twenty','Twenty-one','Twenty-two','Twenty-three','Twenty-four', 'Twenty-five','Twenty-six','Twenty-seven','Twenty-eight','Twenty-nine','Thirty', 'Thirty-one','Thirty-two','Thirty-three','Thirty-four','Thirty-five','Thirty-six', 'Thirty-seven','Thirty-eight','Thirty-nine','Fourty','Fourty-one','Fourty-two', 'Fourty-three','Fourty-four','Fourty-five','Fourty-six','Fourty-seven','Fourty-eight', 'Fourty-nine','Fifty','Fifty-one','Fifty-two','Fifty-three','Fifty-four','Fifty-five', 'Fifty-six','Fifty-seven','Fifty-eight','Fifty-nine','Sixty','Sixty-one','Sixty-two', 'Sixty-three','Sixty-four','Sixty-five','Sixty-six','Sixty-seven','Sixty-eight', 'Sixty-nine','Seventy','Seventy-one','Seventy-two','Seventy-three','Seventy-four', 'Seventy-five','Seventy-six','Seventy-seven','Seventy-eight','Seventy-nine', 'Eighty','Eighty-one','Eighty-two','Eighty-three','Eighty-four','Eighty-five', 'Eighty-six','Eighty-seven','Eighty-eight','Eighty-nine','Ninety', 'Ninety-one','Ninety-two','Ninety-three','Ninety-four','Ninety-five', 'Ninety-six','Ninety-seven','Ninety-eight','Ninety-nine','One hundred' ]; var ordinals = ['zeroth','first','second','third','fourth','fifth','sixth','seventh','eighth', 'ninth','tenth','eleventh','twelfth','thirteenth','fourteenth','fifteenth', 'sixteenth','seventeenth','eighteenth','ninteenth','twentieth','twenty-first', 'twenty-second','twenty-third','twenty-fourth','twenty-fifth','twenty-sixth', 'twenty-seventh','twenty-eighth','twenty-ninth','thirtieth','thirty-first', 'thirty-second','thirty-third','thirty-fourth','thirty-fifth','thirty-sixth', 'thirty-seventh','thirty-eighth','thirty-ninth','fourtieth','fourty-first', 'fourty-second','fourty-third','fourty-fourth','fourty-fifth','fourty-sixth', 'fourty-seventh','fourty-eighth','fourty-ninth','fiftieth','fifty-first', 'fifty-second','fifty-third','fifty-fourth','fifty-fifth','fifty-sixth', 'fifty-seventh','fifty-eighth','fifty-ninth','sixtieth','sixty-first', 'sixty-second','sixty-third','sixty-fourth','sixty-fifth','sixty-sixth', 'sixty-seventh','sixty-eighth','sixty-ninth','seventieth','seventy-first', 'seventy-second','seventy-third','seventy-fourth','seventy-fifth','seventy-sixth', 'seventy-seventh','seventy-eighth','seventy-ninth','eightieth','eighty-first', 'eighty-second','eighty-third','eighty-fourth','eighty-fifth', 'eighty-sixth','eighty-seventh','eighty-eightth','eighty-ninth','ninetieth', 'ninety-first','ninety-second','ninety-third','ninety-fourth','ninety-fifth', 'ninety-sixth','ninety-seventh','ninety-eighth','ninety-ninth','hundredth' ]; var iteratives = ['no times','once','twice','thrice']; for (var i=4; i < cardinals.length; i++) { iteratives[i] = cardinals[i] + ' times'; } var primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53]; var nPrimes = [0, 0, 1, 2, 2, 3, 3, 4, 4, 4, // 0-9 4, 5, 5, 6, 6, 6, 6, 7, 7, 8, // 10-19 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, // 20-29 10, 11, 11, 11, 11, 11, 11, 12, 12, 12, // 30-39 12, 13, 13, 14, 14, 14, 14, 15, 15, 15, // 40-49 15, 15, 15, 16]; // 50-53 var allTheChars = '~\`!1@2#3$4%5^6&7*8(9)0_-+=QqWwEeRrTtYyUuIiOoPp{[}]|\\AaSsDdFfGgHhJjKkLl:;' + '\"\'ZzXxCcVvBbNnMm<,>.?/'; var faces = ['Ace','two','three','four','five','six','seven','eight','nine','ten','Jack', 'Queen','King']; var suits = ['spades','hearts','diamonds','clubs']; var colors = ['red','orange','yellow','green','blue','indigo','violet', 'black','white','gray','silver','gold','brown','aqua','teal', 'fuschia','magenta','cyan','sage','turquoise','chartreuse', 'mauve','periwinkle','umber','brick','marigold','seafoam','coral', 'purple','grape','cherry','beige','copper','sienna','baby blue' ]; // ======================================================================== // FUNCTION LIBRARY // ======================================================================== // =============== STRING HANDLERS and HTML GENERATORS =================== function trimBlanks(s){ if (s == null || s.length == 0 ) { return(s); } while (s.charAt(s.length-1) == ' ' ) { // trim trailing blanks s = s.substring(0, s.length-1); } while (s.charAt(0) == ' ') { // trim leading blanks s = s.substring(1, s.length); } return(s); } function allBlanks(s) { if (s == null || trimBlanks(s).length == 0) { return(true); } else { return(false); } } function removeAllBlanks(s){ if (s == null || s.length == 0 ) { return(s); } while (s.indexOf(' ') > -1 ) { s = s.substring(0, s.indexOf(' ')) + s.substring(s.indexOf(' ')+1, s.length); } return(s); } function makeTopLevel(nameString,features) { // ensures the window is a top level window with name nameString if (window != top) { window.open(window.location,nameString,features); window.close(); parent.close(); } else { window.name=nameString; } return(true); } function makeTopLevel(nameString){ if (window != top) { window.open(window.location,nameString, 'toolbar=yes,location=yes,status=yes'); window.close(); parent.close(); } else window.name=nameString; return(true); } function makeTopLevel(){ if (window != top) { window.open(window.location,'', 'toolbar=yes,location=yes,status=yes'); window.close(); parent.close(); } return(true); } function sticiRef() { // pops up a window with the pronunciation of SticiGui sticiWin = window.open('','sticiWin', 'toolbar=no,location=no,directories=no,status=no,scrollbars=yes,'+ 'resizable=yes,width=200,height=30,top=5,left=5'); sticiWin.document.write('How do you say that?' + '

Pronounced

' + '

\"Sticky-Gooey\"

' + ''); sticiWin.document.close(); sticiWin.focus(); return(true); } function glossRef(lnk) { // opens a glossary window, if not already open, and displays the glossary entry // referred to in the link. window.open(lnk, target="glossWin"); return(true); } function trimToLowerCase(s) { // trim trailing blanks, convert to lower case if (s == null || s.length == 0 ) { return(s); } return(trimBlanks(s.toLowerCase())); } function allLetters(s){ // return true if all characters in string s are letters (or trailing blanks) var trimS = trimToLowerCase(s); var alpha=' -abcdefghijklmnopqrstuvwxyz'; var truth = true; for (var i = 0; i < trimS.length; i++) { if(alpha.indexOf(trimS.charAt(i)) < 0) { truth = false; } } return(truth); } function removeCommas(s) { // removes commas from a putative number return(removeString(',',s)); } function removeString(str,s) { // removes instances of the string str from s. // kluge to avoid regular expressions var sOut = s; var s1; var strLen = str.length; var inx = s.indexOf(str); while (inx > -1) { s1 = s.substring(0,inx); if (inx < (s.length - strLen) ) { s1 += s.substring(inx+strLen, s.length); } s = s1; inx = s.indexOf(str); } return(s); } function removeStrings(strArr,s) { for (var j=0; j < strArr.length; j++) { s = removeString(strArr[j], s); } return(s); } function parsePercent(s) { // parse a number that contains a % sign to turn it into a decimal fraction var value; if (s.indexOf('%') == -1) { value = parseFloat(trimBlanks(removeCommas(s))) } else { while (s.indexOf('%') != -1) { s = s.substring(0,s.indexOf('%')) + s.substring(s.indexOf('%')+1,s.length) } value = parseFloat(trimBlanks(removeCommas(s)))/100; } return(value); } function evalNum(s) { // try to evaluate a string as a numeric value var value; var dmy = s + ' '; dmy = dmy.replace(/\%/g,'\/100'); dmy = dmy.replace(/,/g,''); if ( typeof(s) == 'undefined' || s == null || !s.match(/[^ ]/) ) { value = 'NaN'; } else if ( dmy.match(/[^1234567890+*\/.ed() -]/i) ) { value = 'NaN'; } else if ( !dmy.match(/[1234567890]/) ) { value = 'NaN'; } else { eval('value = ' + dmy + ';'); } return(value); } function parseMultiple(option) { // pre-processes multiple selections so that checkAnswer can be used to grade them var response = ''; for (var i=0; i < option.length; i++) { if (option[i].selected) { response += trimToLowerCase(option[i].value) + ',' ; } } if (response.charAt(response.length - 1) == ',') { // trim trailing comma response = response.substring(0, response.length - 1); } return(response); } function getFormElementIndex(q) { // finds the form element named q and returns its index. for (var inx =0; inx < document.forms[0].elements.length; inx++) { if (document.forms[0].elements[inx].name == q) return(inx); } alert('Error #1 in irGrade.getFormElementIndex(): Form element ' + q + ' is missing!'); return('document.forms[0].length'); } function findNum(s) { // if s is an integer or its string representation, returns s. // if not, tries to remove characters to // leave an int, and returns that int. var i = parseInt(s); if ( !isNaN(i)) { return(i); } else { var q = ''; for (var j=0; j < s.length; j++) { var dum = q; if (!isNaN(parseInt(dum + s.charAt(j)))) { q += s.charAt(j); } } return(q); } } function vFindNum(s) { // finds numbers in a string array var a = new Array(s.length); for (var i=0; i < s.length; i++) { a[i] = findNum(s[i]);} return(a); } // ============================================================================ // ========================= COOKIE MANIPULATION ============================== function expireTimeString(ed) { var now = new Date(); var expire = new Date(); var cookDays; if (typeof(ed) == 'undefined' || ed == null) { cookDays = cookieExpireDays; } else { cookDays = ed; } expire.setTime(now.getTime() + cookDays*60*60*1000*24); return(expire.toGMTString()); } function getCookieVal(cook,key){ // gets the value of key within the cookie cook var searchStr = cook + '&'; var val = null; var pat = key + '='; var inx = searchStr.indexOf(pat); if (inx > -1){ searchStr = searchStr.substring(inx + pat.length, searchStr.length); val = unescape(searchStr.substring(0, searchStr.indexOf('&'))); } return(val); } function getCookieArray(cook,stem,len) { // gets an array from the cookie var ansArr = new Array(len); for (var i=0; i < len; i++) { ansArr[i] = getCookieVal(cook, stem + i.toString()); } return(ansArr); } function setCookieArray(arr,stem) { // make a cookie-like string from the array arr var ansStr = ''; for (var i=0; i < arr.length; i++) { ansStr += stem + i.toString() + '=' + arr[i] + '&'; } if (ansStr.substr(ansStr.length-1,1) == '&') { ansStr = ansStr.substring(0, ansStr.length - 1); } return(ansStr); } // ============================================================================ // ========================= PROBLEM AND GRADING SUBROUTINES ================== function numToMultiple(opt,ans) { // finds the multiple choice closest to ans var dif = Math.abs(parsePercent(opt[0]) - ans); var aVal = 'a'; for (var i=1; i < opt.length; i++) { var d2 = Math.abs(parsePercent(opt[i]) - ans); if (d2 < dif) { dif = d2; aVal = alphabet[i]; } } return(aVal); } function hiddenInput(string, val){ // hidden input with name="string" and value="val" var s = ""; return(s); } function textExercise(size,q,ca,checkFun) { // text input area of "size" size, name q, and appropriate onChange() var s = ""; return(s); } function startExercise(q) { // writes html to start an exercise, numbered q var s; if (HI) { s = "Problem " + q.toString() + "."; } else { s = "Exercise " + q.toString() + "."; } return(s); } function startProblem(q) { // writes html to start a problem, numbered q var s; if (HI) { s = "Problem " + q.toString() + "."; } else { s = "Exercise " + q.toString() + "."; } return(s); } function startSolution(q) { // html to start a solution, numbered q var s; if (HI) { s = "Solution to Problem " + q.toString() + "."; } else { s = "Solution to Exercise " + q.toString() + "."; } return(s); } function writeSelectExercise(mult, q, opt, ans) { document.writeln(selectExerciseString(mult, q, opt, ans)); return(true); } function selectExerciseString(mult, q, opt, ans) { var name = 'Q' + q.toString(); var s = selectExercise(mult, name, opt, CA); if (CA) { if (mult) { s += ''; } if (newStyleAnswer != null && newStyleAnswer) { boxList[q - 1] = document.images.length; s += '' + '

'; } } key[q - 1] = ans; return(s); } function writeTextExercise(size, q, ans) { // does all the printing for a textfield exercise document.writeln(textExercise(size, 'Q' + q, CA)); var cf = false; if (typeof(ans) == 'function') { // TO DO: allow functional checks of answers. cf = true; } if (CA) { if (newStyleAnswer != null && newStyleAnswer) { boxList[q - 1] = document.images.length; document.writeln('' + ' click to see the answer

click to see the answer

'); } } key[q - 1] = ans; return(true); } function writeRadioExercise(q, opt, ans) { // write a radio exercise document.writeln(radioExercise('Q'+q, opt, CA)); if (CA) { if (newStyleAnswer != null && newStyleAnswer) { boxList[q - 1] = document.images.length; document.writeln('' + '

'); } } key[q-1] = ans; return(true); } function radioExercise(q, opt, ca){ // makes a collection of radio inputs. var s = ""; var oplen = opt.length; for (var i = 0; i < oplen; i++) { s += '\n'; } return(s); } function selectExercise(mult, q, opt, ca) { // makes a select with multiple=mult, name q. // if mult, makes the size large enough to show all options. // otherwise size=1; opt is a 1 by array. var s; var size; var oplen = opt.length; if (mult) { // leave room for all the answers to be visible. size= oplen+1; } else { size = 1; } var s = ''; return(s); } function scoreProblem(truth,response){ var answer = parseKey(truth); response = trimToLowerCase(response); var rsp; var correctness; if (response == null) { correctness = false; } else if (type == 'WC') { rsp = trimBlanks(response); if (rsp.length > 0) {correctness = true}; } else if (type == 'LA') { // try to parse as number; if fail, take literal. rsp = evalNum(response); if (!isNaN(rsp)) { response = rsp; // if (response.indexOf('%') != -1) { // rsp = parsePercent(response); // if (!isNaN(rsp)) { // response = rsp; // } // } else if (!isNaN(parseFloat(trimBlanks(removeCommas(response))))) { // response = parseFloat(trimBlanks(removeCommas(response))); } if (answer.toString() == response.toString()) { correctness = true; } else { correctness = false; } } else if (type == 'RG') { var r = evalNum(response); if ((answer[0] <= r) && (r <= answer[1])) { correctness = true; } else {correctness = false;} } else if (type == 'MA') { correctness = false; for (var i=0; i < answer.length; i++) { if (response == answer[i]) { correctness = true; } } } else if (type == 'MR') { correctness = false; resArray = response.split(','); resArray.sort() if (resArray.length == answer.length) { correctness = true; for (var i=0; i < answer.length; i++ ) { if (answer[i] != trimToLowerCase(resArray[i])) { correctness = false; } } } } return(correctness); } function parseKey(s) { // parses the answer keys for interactive grading. See header. s = trimBlanks(s.toLowerCase()) // use only lower-case letters var answer; if (s.indexOf(':') != -1) { // solution is a range answer = s.split(':') if (answer.length != 2) { alert('Error #1 in irGrade.parseKey(): bad range syntax!') } type = 'RG' // answer is of type range (RG) for (var i=0; i < answer.length; i++) { answer[i] = parsePercent(answer[i]); if (isNaN(answer[i])){ alert('Error #2 in irGrade.parseKey(): unparsable number in range!'); } } ansText = answer[0] + ' to ' + answer[1]; } else if (s.indexOf('&') != -1 ){ // multiple required answers; assume all // are letters answer = s.split('&'); type = 'MR' // answer is of type multiple required (MR) for (var i=0; i < answer.length; i++ ) { answer[i] = trimBlanks(answer[i].toLowerCase()); answer.sort(); } ansText = answer[0]; for (var i=1; i < answer.length; i++) { ansText += ' and ' + answer[i]; } } else if (s.indexOf('|') != -1 ){ // multiple answers accepted; assume all // are letters answer = s.split('|'); type = 'MA'; // answer is of type multiple accepted (MA) for (var i=0; i < answer.length; i++ ) { answer[i] = trimBlanks(answer[i].toLowerCase()); } ansText = answer[0]; for (var i=1; i < answer.length; i++) { ansText += ' or ' + answer[i]; } } else if (s == '*') { type = 'WC'; // wildcard answer = '*'; ansText = 'any non-blank answer'; } else { // answer is literal type = 'LA' // literal answer (LA) answer = parsePercent(s); if (isNaN(answer)) { answer = trimBlanks(s.toLowerCase()); } ansText = answer; } return(answer); } function setCourse(inx) { setCourseSpecs(inx); document.applets[0].getSidFile(courses[inx][1] + sFileBase); return(document.applets[0].setBox(courses[inx][1] + dFileBase)); } function setCourseSpecs(inx) { course = courses[inx][1]; courseName = courses[inx][2]; teacher = courses[inx][3]; teacherName = courses[inx][4]; gPath = courses[inx][5]; dFile = cRoot + course + dFileBase; var sFile = cRoot + course + sFileBase; } function setDFile(inx) { setCourseSpecs(inx); document.forms[0].elements["dFile"].value = dFile; document.forms[0].elements["class"].value = courses[inx][1]; return(true); } function writeCourseOptions(fun) { document.writeln('Course:'); return(true); } function spawnGradePage(theForm) { if (validateLablet(theForm)) { var scorQStr = scoreBase + "class=" + course + "&gpath=" + gPath + "&teacher=" + teacher; var queryURL = queryBase + "class=" + course + "&gpath=" + gPath + "&teacher=" + teacher + "&sid=" + theForm.sid.value + "&passwd=" + escape(theForm.sid.value) + "&dFile=" + dFile + "&querylist=" + queryList; var histURL = '../Grades/scoreHist.htm'; gradePage = open('',"gradePage",'toolbar=yes,location=no,directories=no,status=yes,'+ 'scrollbars=yes,resizable=yes'); gradePage.document.open(); gradePage.scorQStr = scorQStr; gradePage.teacherName = teacherName; gradePage.courseName = courseName; gradePage.semester = semester; gradePage.document.writeln("SticiGui Grade Query"); gradePage.document.writeln(""); gradePage.document.writeln(""); gradePage.document.writeln(""); gradePage.document.writeln(""); gradePage.document.close(); return(true); } else { return(false); } } function spawnProblem(theForm,i) { if (validateLablet(theForm)) { var ck = document.cookie; var fname = formStemName + i.toString(); var assigned = document.applets[0].isAssigned(fname); if (!assigned) { alert('This problem set is not yet assigned.\n' + 'Try again later.'); return(false); } var sstr = crypt("sid" + theForm.sid.value, theForm.sid.value) + '='; if (ck.indexOf(sstr) < 0){ var rs = (theForm.sid.value).toString(); if (rs.length < 10){ rs += rs; } randSeed = parseInt(rs.substr(0,Math.min(10,rs.length))); setSubmitCookie("sid", theForm, true); ck = document.cookie; if (ck.indexOf(sstr) < 0){ alert('Error #1 in irGrade.spawnProblem()!\n' + 'Make sure your browser is configured to accept cookies.\n' + 'Clear existing cookies and try again.'); return(false); } } var ss = ck.substring(ck.indexOf(sstr) + sstr.length, ck.length); if (ss.indexOf(';') > -1) {ss = ss.substring(0,ss.indexOf(';'))}; var cl = crypt(ss, theForm.sid.value); var instr = '../Problems/set' + i.toString() + 'i.htm'; var appl = '../Problems/set' + i.toString() + 'j.htm'; lablet = open('',"lablet",'toolbar=no,location=no,directories=no,status=no,'+ 'scrollbars=yes,resizable=yes'); lablet.document.open(); lablet.continueLab = cl; var reveal = document.applets[0].revealKey(fname); var allowSubmit = document.applets[0].allowSubmit(fname); lablet.reveal = reveal; lablet.allowSubmit = allowSubmit; lablet.dFile = dFile; lablet.course = course; lablet.teacher = teacher; lablet.document.writeln("SticiGui Problem Set " + i +""); lablet.document.writeln(""); lablet.document.writeln(""); lablet.document.writeln(""); lablet.document.writeln(""); lablet.document.close(); return(true); } else { return(false); } } function checkAnswer(number, response) { // check response against key[number-1]. If number is not an integer, // calls findNum(number) to remove characters to try to leave an integer. var theQuestion = findNum(number); var truth = scoreProblem(key[theQuestion-1],response); if (truth) { document.images[boxList[theQuestion-1]].src = rightImgSrc; } else { document.images[boxList[theQuestion-1]].src = wrongImgSrc; } return(truth); } function isAnswered(qVal) { // checks whether the student answered a question var n = findNum(qVal) - 1; var iA = false; var inx; var el = document.forms[0].elements[qVal]; var qT = el.type; if (qT == 'select-one') { inx = el.selectedIndex; if (inx > 0) { iA = true; } } else if (qT == 'select-multiple') { resp = parseMultiple(el.options); if (resp != null && resp != '' && resp != '?') { iA = true; } } else if (qT == 'text') { resp = el.value; if (resp != null && resp != '' && removeAllBlanks(resp) != null && removeAllBlanks(resp).length > 0) { iA = true; } } else if (qT == 'radio') { // incomprehensible bugs with this for (var i=0; i < el.length; i++) { if (el[i].checked) { iA = true; } } } else if ( typeof(qT) == 'undefined' || qT == null ) { // assume it is a radio for (var i=0; i < el.length; i++) { if (el[i].checked) { iA = true; } } } else { alert('Error #1 in irGrade.js.isAnswered(): input type ' + qT + ' is not supported!'); } return(iA); } function giveAnswer(number) { // display the answer to question[number] in a new window, provided the student has // tried to answer the question answer = parseKey(key[findNum(number)-1]); ansWin = window.open('','ansWin', 'toolbar=no,location=no,directories=no,status=no,' + 'scrollbars=yes,resizable=yes,width=230,height=160'); ansWin.document.write(startHtm); if (isAnswered(number)) { ansWin.document.write('

The correct answer is
\n' + '' + ansText + '.

\n' + dsmsHtm + endHtm); } else { ansWin.document.write('

You must answer before you can ' + 'see the solution.' + dsmsHtm + endHtm); } return(true); } function validEmail(e) { // checks whether e appears to be a valid email address var okEmailChars="._-@:%0123456789abcdefghijklmnopqrstuvwxyz"; var truth = true; if (e == null || e.length == 0) { truth=false; } else { et = trimToLowerCase(e); if (et.indexOf('@') == -1 || ( (et.lastIndexOf('.') != et.length - 4 ) && (et.lastIndexOf('.') != et.length - 3 ) ) ) truth = false; else if (et.indexOf('@') != et.lastIndexOf('@')) { truth = false; } else { for (var i=0; i < et.length; i++) { if(okEmailChars.indexOf(et.charAt(i)) < 0) {truth = false;} } } } return(truth); } function validSID(s){ // check whether SID is valid var digits="0123456789"; var truth = false; if (s.length == 8 && s.charAt(0) == "1" || s.length == 9) { truth = true; for (var i=0; i < s.length; i++){ if (digits.indexOf(s.charAt(i)) < 0) {truth = false;} } } return(truth); } function validateLabletSubmit(theForm){ // check that various form entries are filled in correctly, submit or cancel if (validateLablet(theForm)){ return(labletSubmit(theForm)); } else { return(false); } } function labletSubmit(theForm) { theForm.submitTime = new Date(); confirmStr = 'Your assignment is ready to submit, ' + theForm.firstName.value + ' ' + theForm.lastName.value + '.\nPress \"OK\" to submit it now, or \"Cancel\" to return to the assignment.'; if (confirm(confirmStr)){ setExtraInputs(theForm); setSubmitCookie(setNum.toString(),theForm,false); document.forms[1].action = "http://www.stat.berkeley.edu/cgi-bin/grader"; var s = collectResponses(theForm,true,true); document.forms[1].elements['contents'].value = crypt(s,bigPi); document.forms[1].submit(); return(true); } else { alert("Your assignment has NOT been submitted."); return(false); } } function validateLablet(theForm) { if (theForm.lastName.value == null || theForm.lastName.value.length == 0 || allBlanks(theForm.lastName.value) ) { alert('Last Name is missing'); theForm.lastName.focus(); return(false); } else if (!allLetters(theForm.lastName.value) ) { alert('Illegal character(s) in Last Name'); theForm.lastName.focus(); return(false); } else if (theForm.firstName.value == null || theForm.firstName.value.length == 0 || allBlanks(theForm.firstName.value)) { alert('First Name is missing'); theForm.firstName.focus(); return(false); } else if (!allLetters(theForm.firstName.value) ) { alert('Illegal character(s) in First Name'); theForm.firstName.focus(); return(false); } else if ( !validEmail(theForm.email.value)) { alert('Email address is missing or invalid'); theForm.email.focus(); return(false); } else if (!document.applets[0].acceptSid(theForm.sid.value)) { alert('This SID is not enrolled.\nDid you set the course correctly?'); theForm.sid.focus(); return(false); } else if (!validSID(theForm.sid.value)) { alert('Invalid password'); theForm.sid.focus(); return(false); } else if (!document.applets[0].isOkPasswd(trimBlanks(theForm.sid.value), trimBlanks(theForm.email.value))) { alert('This email address is not enrolled, or does not match the SID.\n' + 'Did you set the course correctly?'); theForm.email.focus(); return(false); } else { theForm.lastName.value = trimBlanks(theForm.lastName.value); theForm.firstName.value = trimBlanks(theForm.firstName.value); theForm.email.value = trimBlanks(theForm.email.value); theForm.sid.value = trimBlanks(theForm.sid.value); return(true); } } function saveResponses(fname,theForm,saveAns) { if(setSubmitCookie(fname,theForm,false)) { confirm('Your answers have been saved as a cookie on your computer.\n' + 'Cookies are NOT RELIABLE storage--do not count on them!\n' + 'You should write your answers down, too.\n' + 'The cookie will be erased automatically in ' + cookieExpireDays.toString() + ' days.'); return(true); } else { alert('Error #1 in irGrade.saveResponses:\nYour answers have NOT been saved!\n' + 'Something went wrong.'); return(false); } } function setSubmitCookie(fff,theForm,idInfo){ var s = collectResponses(theForm,false,idInfo); document.cookie = crypt(fff + theForm.sid.value, theForm.sid.value) + "=" + crypt(s, theForm.sid.value) + ";EXPIRES=" + expireTimeString(); return(true); } function recoverResponses() { if (continueLab == null) { return(false); } else { var theSid = getCookieVal(continueLab,"sid"); var thePw = theSid; var tv = false; var theForm = document.forms[0]; var ascStr = crypt(setNum.toString() + theSid, thePw)+ "="; var searchStr = document.cookie; var startInx = searchStr.indexOf(ascStr); if (startInx < 0 ) { return(false); } searchStr = searchStr.substring(startInx+ascStr.length,searchStr.length); var endInx = searchStr.indexOf(";"); if (endInx > -1 ) { searchStr = searchStr.substring(0,endInx); } searchStr = crypt(searchStr,thePw) + "&"; var qName; var aText; var inx; var ampInx; var elem; for (var i=0; i < theForm.elements.length; i++) { qName = theForm.elements[i].name + '='; if (qName.indexOf("Q") == 0) { elem = theForm.elements[i]; if (elem.type == "select-multiple") { while (searchStr.indexOf(qName) > -1) { inx = searchStr.indexOf(qName); searchStr = searchStr.substring(inx+qName.length,searchStr.length); ampInx = searchStr.indexOf('&'); qText = unescape(searchStr.substring(0,ampInx)); // search for option to select var ag = false; for (var j=0; j < elem.length; j++) { if (elem[j].value == qText) { elem.options[j].selected = true; ag = true; } } } // if (CA && ag){ //tv = checkAnswer(qName.substr(0,qName.length - 1), // parseMultiple(theForm.elements[i].options)); //} } else if (elem.type == 'select-one') { inx = searchStr.indexOf(qName); if (inx > -1){ searchStr = searchStr.substring(inx+qName.length,searchStr.length); ampInx = searchStr.indexOf('&'); qText = unescape(searchStr.substring(0,ampInx)); // search for option to select for (var j=0; j < elem.length; j++) { if (elem[j].value == qText) { elem.options[j].selected = true; } } } // if (CA) { // var si = theForm.elements[i].options.selectedIndex; // if (si != null) { // tv = checkAnswer(qName.substr(0,qName.length - 1), // elem.options[si].value); // } //} } else if (elem.type == 'text') { inx = searchStr.indexOf(qName); if (inx > -1) { searchStr = searchStr.substring( inx+qName.length,searchStr.length); ampInx = searchStr.indexOf('&'); qText = unescape(searchStr.substring(0,ampInx)); elem.value = qText; } // if (CA) { // var dba = trimBlanks(elem.value); // if (dba.length > 0) { // tv = checkAnswer(qName.substr(0,qName.length - 1), // elem.value); // } //} } else if (elem.type == null || elem.type == 'radio' || elem.type == 'undefined') { inx = searchStr.indexOf(qName); if (inx > -1){ searchStr = searchStr.substring(inx+qName.length,searchStr.length); ampInx = searchStr.indexOf('&'); qText = unescape(searchStr.substring(0,ampInx)); if (elem.value == qText) { elem.checked = true; } } } else { alert('Error #1 in irGrade.recoverResponses(): unsupported problem type ' + elem.type + '!'); return(false); } } } } return(true); } function collectResponses(theForm,saveAs,saveId) { var typ; var nam; var s = ''; s += 'randSeed=' + escape(randSeed) + '&'; for (var i=0; i < theForm.elements.length; i++) { typ = theForm.elements[i].type; nam = theForm.elements[i].name; if (typ == "button" || typ == "submit" || typ == "reset") { } else if (!saveId && (nam == "lastName" || nam == "firstName" || nam == "sid" || nam == "sid2" || nam == "email" || nam == "passwd" || nam == "passwd2")) { } else if (typ == "select-one") { s += escape(nam) + "=" + escape(theForm.elements[i].options[ theForm.elements[i].options.selectedIndex].value)+ "&"; } else if (typ == "select-multiple") { for (var j=0; j < theForm.elements[i].options.length; j++) { if (theForm.elements[i].options[j].selected) { s += escape(nam) + "=" + escape(theForm.elements[i].options[j].value) + "&"; } } } else if (typ == "radio") { if (theForm.elements[i].checked) { s += escape(nam) + '=' + escape(theForm.elements[i].value) + '&'; } } else { s += escape(nam) + "=" + escape(theForm.elements[i].value) + "&"; } } if (saveAs) { for (var i=0; i < key.length; i++) { s += escape('a' + (i+1).toString()) + '=' + escape(key[i].toString()) + '&'; } } if (s[s.length-1] == "&") { s = s.substring(0,s.length - 1); } return(s); } function labSetUp(seed, sn) { isLab = true; sectionContext = 'function setSectionContext() { \n' window.name= 'seti'; setNum = sn; HI = true; if (typeof(parent.reveal) == 'undefined') { CA = 'invalid'; } else { CA = parent.reveal; } if (seed != "SeEd") { rand = new rng(parseInt(seed)); } else { continueLab = parent.continueLab; if (continueLab == null || CA == 'invalid') { alert('Error #1 in irGrade.labSetUp()!\n' + 'Problem Set not initialized correctly.\n' + 'You must use the Problem Set Form to go to this page.\n' + 'If you did, make sure your browser is configured to accept cookies, ' + ' and try again.\n '); document.close(); window.close(); return(false); } else { var searchStr = continueLab + '&'; var pat = "randSeed="; var inx = searchStr.indexOf(pat); if (inx < 0) { alert('Error #2 in irGrade.labSetUp()!\n' + 'Problem Set not recovered correctly.\n' + 'Questions may have changed!'); rand = new rng(); } else { searchStr = searchStr.substring( inx + pat.length, searchStr.length); randSeed = unescape(searchStr.substring(0,searchStr.indexOf('&'))); rand = new rng(randSeed); } } } randSeed = rand.getSeed(); writeProblemSetHeader(setNum); return(true); } function setRequiredInputs(theForm) { theForm.elements['lastName'].value = getCookieVal(continueLab,"lastName"); theForm.elements['firstName'].value = getCookieVal(continueLab,"firstName"); theForm.elements['email'].value = getCookieVal(continueLab,"email"); theForm.elements['sid'].value = getCookieVal(continueLab,"sid"); theForm.elements['sid2'].value = getCookieVal(continueLab,"sid"); theForm.elements['passwd'].value = getCookieVal(continueLab,"sid"); theForm.elements['passwd2'].value = getCookieVal(continueLab,"sid"); return(true); } function setExtraInputs(theForm) { theForm.elements['inlinekey'].value = inlinePrefix + (qCtr-1).toString(); theForm.elements['dFile'].value = parent.dFile; theForm.elements['teacher'].value = parent.teacher; theForm.elements['class'].value = parent.course; theForm.elements['extrainfo'].value = escape("seed=" + randSeed.toString() + "&irGradeVersion=" + irGradeModTime.toString()); var nRight = 0; var qVal; var resp; var qType; for (var i=1; i < qCtr; i++) { qVal = 'Q' + i.toString(); qType = theForm.elements[qVal].type; if (qType == 'select-one') { resp = theForm.elements[qVal].options[ theForm.elements[qVal].options.selectedIndex].value; } else if (qType == 'select-multiple') { resp = parseMultiple(theForm.elements[qVal].options); } else if (qType == 'text') { resp = theForm.elements[qVal].value; } else if (qType == 'radio') { if (theForm.elements[qVal].checked) { resp = theForm.elements[qVal].value; } } else if (qType == null || qType == 'undefined') { // radio too! if (theForm.elements[qVal].checked) { resp = theForm.elements[qVal].value; } } else { alert('Error #1 in irGrade.setExtraInputs(): Input type ' + qType + ' in question ' + qVal + ' is not supported!'); } if (scoreProblem(key[i-1],resp)) nRight++; } theForm.elements['score'].value = roundToDig(100*nRight/(qCtr - 1),2).toString(); return(true); } function killApplets() { // dispose of applets when leaving the page for (var i = 0; i < document.applets.length; i++) { document.applets[i].stop(); document.applets[i].destroy(); } return(true); } // ============================================================================ // ============================ SPECIAL HTML GENERATORS ======================= function chapterSetUp(seed, chNum, titStr) { theChapter = null; for (var i=0; i < theChapters.length; i++) { if (theChapters[i].toString() == chNum.toString()) { theChapter = i; } } if (theChapter == null) { alert('Error in irGrade.chapterSetUp(): chapter ' + chNum + ' is not in the index!'); theChapter = 0; } var statStr; if (seed != "SeEd") { rand = new rng(parseInt(seed)); } else { rand = new rng(); } window.name = "bookWin"; if (typeof(titStr) == 'undefined' || titStr == null ) { statStr = "Chapter " + (theChapters[theChapter]).toString(); } else { statStr = titStr; } defaultStatus = "SticiGui " + statStr; document.writeln('' + defaultStatus + '' + ''); document.writeln("

SticiGui " + statStr + "

"); CA = (1==1); HI = false; randSeed = rand.getSeed(); sectionContext = 'function setSectionContext() { \n' return(true); } function examSetUp(seed, sName, sn) { isLab = false; sectionContext = 'function setSectionContext() { \n' window.name= 'seti'; examName = sName; examNum = sn; HI = true; if (seed != "SeEd") { rand = new rng(parseInt(seed)); } else { rand = new rng(); } randSeed = rand.getSeed(); writeExamHeader(examName, examNum.toString() + '.' + randSeed.toString() ); defaultStatus = 'SticiGui ' + examName + ' ' + examNum.toString(); return(true); } function writeExamHeader(exNam, exVer) { document.writeln("'); printFootnotes(); writeMiscFooter(false); return(true); } function writeSolution(p,text,evalStr) { longKey[p-1] = text; solutionCode[p-1] = evalStr; document.writeln('
Solution.'); return(true); } function writeFootnote(p,label,text) { footnotes[p] = text; document.writeln('^{' + label.toString() + '}'); return(true); } function printFootnotes() { if (footnotes.length > 0) { document.writeln('

' + 'Footnotes

'); for (var i=0; i < footnotes.length; i++ ) { if (typeof(footnotes[i]) != 'undefined') { document.writeln('

' + 'Footnote ' + (i+1).toString() + '. ' + footnotes[i] + '

'); } } } } function writeChapterFooter() { printFootnotes(); if (longKey.length > 0 ) { document.writeln('

' + 'Solutions to Selected Exercises

'); for (var i=0; i < longKey.length; i++ ) { if (typeof(longKey[i]) != 'undefined') { document.writeln('

' + 'Solution to exercise ' + (i+1).toString() + '. ' + longKey[i] + '

'); } if (typeof(solutionCode[i]) != 'undefined' && solutionCode[i] != null && solutionCode[i] != "") { eval(solutionCode[i]); } } } document.writeln('

'); if (theChapter > 1) { document.writeln('Chapter ' + (theChapters[theChapter-1]).toString() + ' (previous) | ') ; } document.writeln('Chapter ' + theChapters[theChapter] + ' (current) '); if (theChapter < theChapters.length - 1) { document.writeln(' | ' + 'Chapter ' + (theChapters[theChapter+1]).toString() + ' (next)
') ; } document.writeln('' + 'Text Table of Contents
' + '' + 'Problem Sets
' + '' + 'Glossary
' + '' + 'SticiGui Home

'); writeMiscFooter(false); return(true); } function writeMiscFooter(sr) { var stra = '

' + 'SticiGui Home

'; if (typeof(sr) == 'boolean') { if (sr) { document.writeln(stra + '..' + strb); } } else { document.writeln(stra + sr + strb); } document.write('

©' + copyYr + pbsRef + '. All rights reserved.
Last generated ' + today + '. '); if ( !(typeof(pageModDate) == 'undefined') && !(pageModDate == null) ) { document.write('Content last modified ' + pageModDate + '. '); } document.writeln('

'); return(true); } function writeProblemSetHeader(sn) { document.writeln("

"); var formName = "SticiGuiSet" + sn.toString(); document.writeln(""); continueLab = parent.continueLab; if (continueLab == null) { alert('Error #1 in irGrade.writeProblemSetHeader()!\n' + 'The problem set is not correctly initialized.\n' + 'Make sure your browser is set up to accept cookies and try again.'); document.close(); window.close(); return(false); } else { document.writeln("" + " " + " " + " " + " " + " " + " "); } document.writeln(""); document.writeln(""); document.writeln(""); document.writeln(""); document.writeln(""); document.writeln(""); setRequiredInputs(document.forms[0]); document.writeln("

" + "SticiGui Problem Set " + sn.toString() + "

"); return(true); } function makeOptions(ans, pert, dig, extra) { // make a set of numerical options as answers, // converted to strings with dig digits of // precision. each answer is perturbed by a // signed multiple of pert. // extra is appended to each answer if (typeof(dig) == "undefined" || dig == null) { dig = 0; } if (typeof(extra) == "undefined" || extra == null) { extra = ""; } var rs = listOfRandSigns(5); var rawOpt = new Array(5); for (var i=0; i < 5; i++) { rawOpt[i] = commify(roundToDig(ans + i*rs[i]*pert,dig)) + extra; } var optPerm = randPermutation(rawOpt,"inverse"); optPerm[1] = alphabet[optPerm[1][0]]; return(optPerm); } function makeRangeOptions(t, lo, hi, loLim, hiLim, dig, extra, iterLim) { // make multiple choice options // t is truth, lo is starting lower limit, hi is starting upper limit, // loLim is ultimate lower limit, hiLim is ultimate upper limit, // dig is digits of precision, extra is appended to each answer // steps up and down by 10% until t is within 0.3 of the space between // answers of one of the answers var pertFac = 0.07; // amount by which to move endpoints each iteration var closeFac = 0.35; // how much closer should answer be to one endpoint? var av; var altern = false; // alternate moving upper and lower endpoints if (typeof(extra) == 'undefined' || extra == null) { extra = ""; } if (typeof(dig) == 'undefined' || dig == null) { dig = 2; } var ok = false; var lim = 0; var maxIt; if (typeof(iterLim) == 'undefined' || iterLim == null) { maxIt = maxIterations; } else { maxIt = iterLim; } while(!ok && lim <= maxIt) { var ans = linspace(lo,hi,5); var d = closeFac*(ans[1]-ans[0]); // want to be significantly closer to one end if (t <= ans[0] ) { av = alphabet[0]; ok = true; } else if ( t >= ans[4]) { av = alphabet[4]; ok = true; } else { for (i=0; i < ans.length; i++) { if (Math.abs(t - ans[i]) <= d) { ok = true; av = alphabet[i]; } } if (altern) { lo = loLim + (1.0 - pertFac)*(lo-loLim); altern = !altern; } else { hi = hi + pertFac*(hiLim-hi); altern = !altern; } } if (lim++ == maxIt) { av = alphabet[0]; var ref = Math.abs(t-ans[0]); for (var i=1; i < ans.length; i++ ) { var nref = Math.abs(t-ans[i]); if (nref < ref) { ref = nref; av = alphabet[i]; } } ok = true; alert('Error #1 in irGrade.makeRangeOptions: maximum iterations exceeded in ' + 'problem ' + (pCtr-1).toString() + '.\nPlease report this to your ' + 'instructor.'); } } var opt = new Array(ans.length); for (i=0; i < ans.length; i++) { opt[i] = (roundToDig(ans[i],dig)).toString()+ extra; } var out = new Array(2); out[0] = opt; out[1] = av; return(out); } function makeProbOptions(t, lo, hi, dig, iter) { if (typeof(dig) == 'undefined' || dig == null) { dig = 0; } return(makeRangeOptions(100*t,100*lo,100*hi,0,100,dig,'%', iter)); } function truthTable(title, valArr) { // make a 2 by 2 truth table if (valArr.length < 4) { alert('Error #1 in irGrade.truthTable: number of truth values is ' + valArr.length); return(null); } else { return(truthTableHeader(title) + valArr[0] + '' + valArr[1] + 'F' + '' + valArr[2] + '' + valArr[3] + '

' ); } } function writeTruthTable(title, valArr) { document.writeln(truthTable(title, valArr)); return(true); } function truthTableHeader(title) { return( '

' + '' + '' + '' + '' + '' + '' + '' + '

Truth table for ' + title + '
	p	T	F
q
T		'); } function writeTruthTableProblem(title, ansArr) { // 2 by 2 truth table problem var opt = ['T','F']; document.writeln(truthTableHeader(title)); var solArr = new Array(ansArr.length); if ( (typeof(ansArr)).toLowerCase() == 'function') { trueArr = [true, false]; for (var i=0; i < 2; i++ ) { for (var j=0; j < 2; j++) { var inx = j + 2*i; if (ansArr(trueArr[j], trueArr[i])) { solArr[inx] = 'a'; } else { solArr[inx] = 'b'; } } } } else { for (var i=0; i < ansArr.length; i++) { if (ansArr[i]) { solArr[i] = 'a'; } else { solArr[i] = 'b'; } } } writeSelectExercise(false,qCtr++,opt,solArr[0]); document.writeln('	'); writeSelectExercise(false,qCtr++,opt,solArr[1]); document.writeln('
F		'); writeSelectExercise(false,qCtr++,opt,solArr[2]); document.writeln('	'); writeSelectExercise(false,qCtr++,opt,solArr[3]); document.writeln('

'); } // =============================================== // ===formatting functions and html generators==== // =============================================== function commify(num) { // punctuate number strings greater than 1,000 in magnitude var str; var strA = (removeAllBlanks(num.toString())).toLowerCase(); if ( (strA.indexOf('e') > -1) || (strA.indexOf('d') > -1) ) { str = strA; // don't mess with exponential notation } else { str = strA; var curLoc = str.length; if ( str.indexOf('.') > -1 ) { curLoc = str.indexOf('.'); } var negSign = str.indexOf('-'); for (var loc = curLoc-4; loc > negSign; loc -= 3) { str = str.substr(0,loc+1) + ',' + str.substr(loc+1, str.length); } } return(str); } function writeBlankLines(k) { // blank space if ( (typeof(k) == 'undefined') || (k == null) || (k < 0) ) { k = 1; } for (var i=0; i < k; i++) { document.writeln('

'); } } function roundToDig(num,dig) { // rounds a number to dig digits after the decimal place var powOfTen = Math.pow(10,dig); var fmt = Math.round(num*powOfTen)/powOfTen; return(fmt); } function doubleToStr(num,dig) { // returns a string representation of num, rounded to dig digits after the decimal return(removeAllBlanks(roundToDig(num,dig).toString())); } function doubleToRange(num,fudge) { // returns a string range of num +/- fudge, separated by a colon var dig = -Math.floor(Math.log(Math.abs(fudge))/Math.log(10)) + 1; var s = roundToDig(num,dig); var range = doubleToStr(s - Math.abs(fudge),dig) + ":" + doubleToStr(s+ Math.abs(fudge),dig); range = range.replace(/ /g,''); return(range); } function numToRange(num,fudge) { // returns a string range of num +/- fudge, separated by a colon if ( (typeof(fudge) == 'undefined') || (fudge == null) ) { fudge = fudgeFactor*num; } if (fudge == 0) { fudge = absFudge; } return(doubleToRange(num,Math.abs(fudge))); } function numToOrdinal(num) { // turns integer into string, appends appropriate suffix var st = (roundToDig(num,0)).toString(); var suffArray = ["th","st","nd","rd","th","th","th","th","th","th"]; var finalDig = parseInt(st.substr(st.length-1,st.length)); return(st + suffArray[finalDig]); } function listToTable(header,list,orientation,centering,print,ft) { // formats an array of arrays as an html table if (typeof(centering) == 'undefined' || centering == null) { centering = "right"; } if (typeof(print) == 'undefined') { print = true; } if (typeof(ft) == 'undefined' || ft == null) { ft = ""; eft = ""; } else { ft = ''; eft = ''; } var rows = list.length; var cols; if (typeof(list[0]) != 'object') { cols=null; } else { cols = list[0].length; } var str = "

"; if (cols == null || cols == 1) { str +=""; str +="\n"; if (orientation == "standard") { for (var j=0; j < rows; j++) { str +="\n"; } str +=""; } else if (orientation == "transpose") { str +=""; for (var j=0; j < rows; j++) { str +=""; str +="\n"; str +=""; } } else { alert("Error 1 in irGrade.listToTable: unsupported orientation " + orientation); } } else { if (orientation == "standard") { for (var j = 0; j < rows; j++) { str += ""; str += "\n"; for (var i=0; i < cols; i++) { str += ""; } str +=""; } } else if (orientation == "transpose") { str += ""; for (var i=0; i < header.length; i++) { str += "\n"; } str += ""; for (var j = 0; j < cols; j++) { str += ""; for (var i=0; i < rows; i++) { str += "\n"; } str +=""; } } else { alert("Error 2 in irGrade.listToTable: unsupported orientation " + orientation); } } str += "

" + ft + header +eft + "	" + ft + list[j] + eft + "
" + ft + list[j] + eft + "
" + ft + header[j] + eft + "	" + ft + list[j][i] + eft + "
" + ft + header[i] + eft + "
" + ft + list[i][j] + eft + "

"; if (print) { document.writeln(str); return(true); } else { return(str); } } function arrayToRow(v,alignment) { // makes a row of a table from the elements of the array v, with specified alignment document.writeln(""); for (var i=0; i < v.length; i++) { document.write(''); document.write(v[i].toString()); document.writeln(""); } document.writeln(""); return(true); } // ============================================================================ // ========================= STATISTICAL SUBROUTINES ========================== function mean(list) { // computes the mean of the list return(vSum(list)/list.length); } function vMult(a, list) { // multiply a vector times a scalar var list2 = new Array(list.length); for (var i=0; i < list.length; i++) { list2[i] = a*list[i]; } return(list2); } function vPointwiseMult(list1, list2) { // componentwise multiplication of two vectors var list3 = Math.NaN; if (list1.length != list2.length) { alert('Error #1 in irGrade.vPointwiseMult: vector lengths do not match!'); } else { list3 = new Array(list1.length); for (var i=0; i < list1.length; i++) { list3[i] = list1[i]*list2[i]; } } return(list3); } function vFloor(list) { // takes floor of all components var list2 = new Array(list.length); for (var i = 0; i < list.length; i++) { list2[i] = Math.floor(list[i]); } return(list2); } function vCeil(list) { // takes ceil of all components var list2 = new Array(list.length); for (var i = 0; i < list.length; i++) { list2[i] = Math.ceil(list[i]); } return(list2); } function vRoundToInts(list) { // round all components to the nearest int var list2 = new Array(list.length); var tmp; for (var i = 0; i < list.length; i++) { list2[i] = Math.floor(list[i]); if (list[i] - list2[i] >= 0.5) { list2[i]++; } } return(list2); } function vSum(list) { // computes the sum of the elements of list var tot = 0.0; for (var i = 0; i < list.length; i++) { tot += list[i]; } return(tot); } function vCum(list) { // vector of cumulative sum var list2 = list; for (var i = 1; i < list.length; i++ ) { list2[i] += list2[i-1]; } return(list2); } function vZero(n) { // returns a vector of zeros of length n var list = new Array(n); for (var i=0; i < n; i++) { list[i] = 0.0; } return(list); } function vOne(n) { // returns a vector of ones of length n var list = new Array(n); for (var i=0; i < n; i++) { list[i] = 1.0; } return(list); } function twoNorm(list) { // two norm of a vector var tn = 0.0; for (var i=0; i < list.length; i++) { tn += list[i]*list[i]; } return(Math.sqrt(tn)); } function convolve(a,b) { // convolve two lists var c = new Array(a.length + b.length - 1); var left; var right; for (var i=0; i < a.length + b.length - 1; i++) { c[i] = 0; right = Math.min(i+1, a.length); left = Math.max(0, i - b.length + 1); for (var j=left; j < right; j++) { c[i] += a[j]*b[b.length - i - 1 + j]; } } return(c); } function nFoldConvolve(a,n) { var b = a; for (var i=0; i < n; i++ ) { b = convolve(b,a); } return(b); } function numberLessThan(a,b) { // numerical ordering for javascript sort function var diff = parseFloat(a)-parseFloat(b); if (diff < 0) { return(-1); } else if (diff == 0) { return(0); } else { return(1); } } function numberGreaterThan(a,b) { // numerical ordering for javascript sort function var diff = parseFloat(a)-parseFloat(b); if (diff < 0) { return(1); } else if (diff == 0) { return(0); } else { return(-1); } } function sd(list) { // computes the SD of the list ave = mean(list); ssq = 0; for (var i = 0; i < list.length; i++) { ssq += (list[i] - ave)*(list[i] - ave); } ssq = Math.sqrt(ssq/list.length); return(ssq); } function sampleSd(list) { // computes the sample SD of the list ave = mean(list); ssq = 0; for (var i = 0; i < list.length; i++) { ssq += (list[i] - ave)*(list[i] - ave); } ssq = Math.sqrt(ssq/(list.length - 1.0)); return(ssq); } function corr(list1, list2) { // computes the correlation coefficient of list1 and list2 if (list1.length != list2.length) { alert("Error #1 in irGrade.corr(): lists have different lengths!"); return(Math.NaN); } else { var ave1 = mean(list1); var ave2 = mean(list2); var sd1 = sd(list1); var sd2 = sd(list2); var cc = 0.0; for (var i=0; i < list1.length; i++) { cc += (list1[i] - ave1)*(list2[i] - ave2); } cc /= sd1*sd2*list1.length; return(cc); } } function percentile(list,p) { // finds the pth percentile of list var n = list.length; var sList = new Array(n); for (var i=0; i < n; i++) sList[i] = list[i].valueOf(); sList.sort(numberLessThan); var ppt = Math.max(Math.ceil(p*n/100),1); return(sList[ppt-1]); } function listOfRandSigns(n) { // random +-1 vector var list = new Array(n); for (var i=0; i < n; i++) { var rn = rand.next(); if (rn < 0.5) { list[i] = -1; } else { list[i] = 1; } } return(list); } function listOfRandUniforms(n, lo, hi) { // n random variables uniform on (lo, hi) if ( (typeof(lo) == 'undefined') || (lo == null) ) { lo = 0.0; } if ( (typeof(hi) == 'undefined') || (hi == null) ) { hi = 1.0; } var list = new Array(n); for (var i=0; i < n; i++) { list[i] = lo + (hi-lo)*rand.next(); } return(list); } function listOfRandInts(n, lo, hi) { // n random integers between lo and hi var list = new Array(n); for (var i=0; i < n; i++) { list[i] = Math.floor((hi+1 - lo)*rand.next()) + lo; } return(list); } function listOfDistinctRandInts(n, lo, hi) { // n dintinct random integers between lo and hi var list = new Array(n); var trial; var i=0; var unique; while (i < n) { trial = Math.floor((hi+1 - lo)*rand.next()) + lo; unique = true; for (var j = 0; j < i; j++) { if (trial == list[j]) unique = false; } if (unique) { list[i] = trial; i++; } } return(list); } function randomSample(list, ssize, replace) { // sample from list, size ssize w/ or w/o replacement. // default is without replacement var sample = new Array(); var indices = new Array(); if (replace != null && replace ) { indices = listOfRandInts(ssize,0,list.length-1); } else { indices = listOfDistinctRandInts(ssize,0,list.length - 1); } for (var i=0; i < ssize; i++) { sample[i] = list[indices[i]]; } return(sample) ; } function multinomialSample(pVec, n) { // multinomial sample of size n with probabilities pVec pVec = vMult(1.0/vSum(pVec), pVec); // renormalize in case var pCum = vCum(pVec); var counts = vZero(pVec.length); var rv; var inx; for (var i=0; i < n; i++) { rv = rand.next(); inx = 0; while ( (rv > pCum[inx]) && (inx < n) ) { inx++; } counts[inx]++; } return(counts); } function normPoints(n, mu, s, dig) { // n normals with expected value mu, sd s, rounded to dig var round = true; if ( (typeof(dig) == 'undefined') || (dig == null) ) { var round = false; } var xVal = new Array(n); if (round) { for (var i=0; i < n; i++) { xVal[i] = roundToDig(mu + s*rNorm(),dig); } } else { for (var i=0; i < n; i++) { xVal[i] = mu + s*rNorm(),dig; } } return(xVal); } function cNormPoints(n, r) { // generate pseudorandom normal bivariate w/ specified realized correlation coefficient var xVal = new Array(n); var yVal = new Array(n); for (var i=0; i 4.0 var p = [3.05326634961232344e-1, 3.60344899949804439e-1, 1.25781726111229246e-1, 1.60837851487422766e-2, 6.58749161529837803e-4, 1.63153871373020978e-2]; var q = [2.56852019228982242e00, 1.87295284992346047e00, 5.27905102951428412e-1, 6.05183413124413191e-2, 2.33520497626869185e-3]; var y, z, xnum, xden, result, del; /* Translation of a FORTRAN program by W. J. Cody, Argonne National Laboratory, NETLIB/SPECFUN, March 19, 1990. The main computation evaluates near-minimax approximations from "Rational Chebyshev approximations for the error function" by W. J. Cody, Math. Comp., 1969, PP. 631-638. */ // evaluate erf for |x| <= 0.46875 if(Math.abs(x) <= xbreak) { y = Math.abs(x); z = y * y; xnum = a[4]*z; xden = z; for (var i = 0; i< 3; i++) { xnum = (xnum + a[i]) * z; xden = (xden + b[i]) * z; } result = 1.0 - x* (xnum + a[3])/ (xden + b[3]); } else if (Math.abs(x) <= 4.0) { y = Math.abs(x); xnum = c[8]*y; xden = y; for (var i = 0; i < 7; i++) { xnum = (xnum + c[i])* y; xden = (xden + d[i])* y; } result = (xnum + c[7])/(xden + d[7]); if (y > 0.0) { z = Math.floor(y*16)/16.0; } else { z = Math.ceil(y*16)/16.0; } del = (y-z)*(y+z); result = Math.exp(-z*z) * Math.exp(-del)* result; } else { y = Math.abs(x); z = 1.0 / (y*y); xnum = p[5]*z; xden = z; for (var i = 0; i < 4; i++) { xnum = (xnum + p[i])* z; xden = (xden + q[i])* z; } result = z * (xnum + p[4]) / (xden + q[4]); result = (1.0/Math.sqrt(Math.PI) - result)/y; if (y > 0.0) { z = Math.floor(y*16)/16.0; } else { z = Math.ceil(y*16)/16.0; } del = (y-z)*(y+z); result = Math.exp(-z*z) * Math.exp(-del) * result; } if (x < -xbreak) { result = 2.0 - result; } return(result); } function normInv(p) { if ( p == 0.0 ) { return(Math.NEGATIVE_INFINITY); } else if ( p >= 1.0 ) { return(Math.POSITIVE_INFINITY); } else { return(Math.sqrt(2.0) * erfInv(2*p - 1)); } } function erfInv(y) { var a = [ 0.886226899, -1.645349621, 0.914624893, -0.140543331]; var b = [-2.118377725, 1.442710462, -0.329097515, 0.012229801]; var c = [-1.970840454, -1.624906493, 3.429567803, 1.641345311]; var d = [ 3.543889200, 1.637067800]; var y0 = 0.7; var x = 0; var z = 0; if (Math.abs(y) <= y0) { z = y*y; x = y * (((a[3]*z+a[2])*z+a[1])*z+a[0])/ ((((b[3]*z+b[2])*z+b[1])*z+b[0])*z+1.0); } else if (y > y0 && y < 1.0) { z = Math.sqrt(-Math.log((1-y)/2)); x = (((c[3]*z+c[2])*z+c[1])*z+c[0]) / ((d[1]*z+d[0])*z+1); } else if (y < -y0 && y > -1) { z = Math.sqrt(-Math.log((1+y)/2)); x = -(((c[3]*z+c[2])*z+c[1])*z+c[0])/ ((d[1]*z+d[0])*z+1); } x = x - (1.0 - erfc(x) - y) / (2/Math.sqrt(Math.PI) * Math.exp(-x*x)); x = x - (1.0 - erfc(x) - y) / (2/Math.sqrt(Math.PI) * Math.exp(-x*x)); return(x); } // ends erfInv function betaCdf( x, a, b) { if (a <= 0 || b <= 0) { return(Math.NaN); } else if (x >= 1) { return(1.0); } else if ( x > 0.0) { return(Math.min(incBeta(x ,a ,b),1.0)); } else { return(0.0); } } function betaPdf( x, a, b) { if (a <= 0 || b <= 0 || x < 0 || x > 1) { return(Math.NaN); } else if ((x == 0 && a < 1) || (x == 2 && b < 1)) { return(Math.POSITIVE_INFINITY); } else if (!(a <= 0 || b <= 0 || x <= 0 || x >= 1)) { return(Math.exp((a - 1)*Math.log(x) + (b-1)*Math.log(1 - x) - lnBeta(a,b))); } else { return(0.0); } } function lnBeta( x, y) { return(lnGamma(x) + lnGamma(y) - lnGamma(x+y)); } function betaInv( p, a, b) { if (p < 0 || p > 1 || a <= 0 || b <= 0) { return(Math.NaN); } else if ( p == 0 ) { return(Math.NEGATIVE_INFINITY); } else if ( p == 1) { return(Math.POSITIVE_INFINITY); } else { var maxIt = 100; var it = 0; var tol = Math.sqrt(eps); var work = 1.0; var next; var x; if (a == 0.0 ) { x = Math.sqrt(eps); } else if ( b == 0.0) { x = 1 - Math.sqrt(eps); } else { x = a/(a+b); } while (Math.abs(work) > tol*Math.abs(x) && Math.abs(work) > tol && it < maxIt) { it++; work = (betaCdf(x,a,b) - p)/betaPdf(x,a,b); next = x - work; while (next < 0 || next > 1) { work = work/2; next = x - work; } x = next; } return(x); } } function lnGamma(x) { /* natural ln(gamma(x)) without computing gamma(x) P.B. Stark, stark@stat.berkeley.edu JavaScript subroutine is based on a MATLAB program by C. Moler, in turn based on a FORTRAN program by W. J. Cody, Argonne National Laboratory, NETLIB/SPECFUN, June 16, 1988. References: 1) W. J. Cody and K. E. Hillstrom, 'Chebyshev Approximations for the Natural Logarithm of the Gamma Function,' Math. Comp. 21, 1967, pp. 198-203. 2) K. E. Hillstrom, ANL/AMD Program ANLC366S, DGAMMA/DLGAMA, May, 1969. 3) Hart, Et. Al., Computer Approximations, Wiley and sons, New York, 1968. */ var d1 = -5.772156649015328605195174e-1; var p1 = [4.945235359296727046734888e0, 2.018112620856775083915565e2, 2.290838373831346393026739e3, 1.131967205903380828685045e4, 2.855724635671635335736389e4, 3.848496228443793359990269e4, 2.637748787624195437963534e4, 7.225813979700288197698961e3]; var q1 = [6.748212550303777196073036e1, 1.113332393857199323513008e3, 7.738757056935398733233834e3, 2.763987074403340708898585e4, 5.499310206226157329794414e4, 6.161122180066002127833352e4, 3.635127591501940507276287e4, 8.785536302431013170870835e3]; var d2 = 4.227843350984671393993777e-1; var p2 = [4.974607845568932035012064e0, 5.424138599891070494101986e2, 1.550693864978364947665077e4, 1.847932904445632425417223e5, 1.088204769468828767498470e6, 3.338152967987029735917223e6, 5.106661678927352456275255e6, 3.074109054850539556250927e6]; var q2 = [1.830328399370592604055942e2, 7.765049321445005871323047e3, 1.331903827966074194402448e5, 1.136705821321969608938755e6, 5.267964117437946917577538e6, 1.346701454311101692290052e7, 1.782736530353274213975932e7, 9.533095591844353613395747e6]; var d4 = 1.791759469228055000094023e0; var p4 = [1.474502166059939948905062e4, 2.426813369486704502836312e6, 1.214755574045093227939592e8, 2.663432449630976949898078e9, 2.940378956634553899906876e10, 1.702665737765398868392998e11, 4.926125793377430887588120e11, 5.606251856223951465078242e11]; var q4 = [2.690530175870899333379843e3, 6.393885654300092398984238e5, 4.135599930241388052042842e7, 1.120872109616147941376570e9, 1.488613728678813811542398e10, 1.016803586272438228077304e11, 3.417476345507377132798597e11, 4.463158187419713286462081e11]; var c = [-1.910444077728e-03, 8.4171387781295e-04, -5.952379913043012e-04, 7.93650793500350248e-04, -2.777777777777681622553e-03, 8.333333333333333331554247e-02, 5.7083835261e-03]; var lng = Math.NaN; var mach = 1.e-12; var den = 1.0; var num = 0; var xm1, xm2, xm4; if (x < 0) { return(lng); } else if (x <= mach) { return(-Math.log(x)); } else if (x <= 0.5) { for (var i = 0; i < 8; i++) { num = num * x + p1[i]; den = den * x + q1[i]; } lng = -Math.log(x) + (x * (d1 + x * (num/den))); } else if (x <= 0.6796875) { xm1 = x - 1.0; for (var i = 0; i < 8; i++) { num = num * xm1 + p2[i]; den = den * xm1 + q2[i]; } lng = -Math.log(x) + xm1 * (d2 + xm1*(num/den)); } else if (x <= 1.5) { xm1 = x - 1.0; for (var i = 0; i < 8; i++) { num = num*xm1 + p1[i]; den = den*xm1 + q1[i]; } lng = xm1 * (d1 + xm1*(num/den)); } else if (x <= 4.0) { xm2 = x - 2.0; for (var i = 0; i<8; i++) { num = num*xm2 + p2[i]; den = den*xm2 + q2[i]; } lng = xm2 * (d2 + xm2 * (num/den)); } else if (x <= 12) { xm4 = x - 4.0; den = -1.0; for (var i = 0; i < 8; i++) { num = num * xm4 + p4[i]; den = den * xm4 + q4[i]; } lng = d4 + xm4 * (num/den); } else { var r = c[6]; var xsq = x * x; for (var i = 0; i < 6; i++) { r = r / xsq + c[i]; } r = r / x; var lnx = Math.log(x); var spi = 0.9189385332046727417803297; lng = r + spi - 0.5*lnx + x*(lnx-1); } return(lng); } // ends lnGamma function normPdf( mu, sigma, x) { return(Math.exp(-(x-mu)*(x-mu)/(2*sigma*sigma))/ (Math.sqrt(2*Math.PI)*sigma)); } // ends normPdf function tCdf(df, x) { // cdf of Student's t distribution with df degrees of freedom var ans; if (df < 1) { ans = Math.NaN; } else if (x == 0.0) { ans = 0.5; } else if (df == 1) { ans = .5 + Math.atan(x)/Math.PI; } else if (x > 0) { ans = 1 - (incBeta(df/(df+x*x), df/2.0, 0.5))/2; } else if (x < 0) { ans = incBeta(df/(df+x*x), df/2.0, 0.5)/2; } return(ans); } function tInv(p, df ) { // inverse Student-t distribution with // df degrees of freedom var z; if (df < 0 || p < 0) { return(Math.NaN); } else if (p == 0) { return(Math.NEGATIVE_INFINITY); } else if (p == 1) { return(Math.POSITIVE_INFINITY); } else if (df == 1) { return(Math.tan(Math.PI*(p-0.5))); } else if ( p >= 0.5) { z = betaInv(2.0*(1-p),df/2.0,0.5); return(Math.sqrt(df/z - df)); } else { z = betaInv(2.0*p,df/2.0,0.5); return(-Math.sqrt(df/z - df)); } } function incBeta(x, a, b) { // incomplete beta function // I_x(z,w) = 1/beta(z,w) * integral from 0 to x of t^(z-1) * (1-t)^(w-1) dt // Ref: Abramowitz & Stegun, Handbook of Mathemtical Functions, sec. 26.5. var res; if (x < 0 || x > 1) { res = Math.NaN; } else { res = 0; var bt = Math.exp(lnGamma(a+b) - lnGamma(a) - lnGamma(b) + a*Math.log(x) + b*Math.log(1-x)); if (x < (a+1)/(a+b+2)) { res = bt * betaGuts(x, a, b) / a; } else { res = 1 - bt*betaGuts(1-x, b, a) / b; } } return(res); } function betaGuts( x, a, b) { // guts of the incomplete beta function var ap1 = a + 1; var am1 = a - 1; var apb = a + b; var am = 1; var bm = am; var y = am; var bz = 1 - apb*x/ap1; var d = 0; var app = d; var ap = d; var bpp = d; var bp = d; var yold = d; var m = 1; var t; while (y-yold > 4*eps*Math.abs(y)) { t = 2 * m; d = m * (b - m) * x / ((am1 + t) * (a + t)); ap = y + d * am; bp = bz + d * bm; d = -(a + m) * (apb + m) * x / ((a + t) * (ap1 + t)); app = ap + d * y; bpp = bp + d * bz; yold = y; am = ap / bpp; bm = bp / bpp; y = app / bpp; if (m == 1) bz = 1; m++; } return(y); } function chi2Cdf( x, df ) { return(gammaCdf(x,df/2,2)); } function chi2Inv( p, df ) { // kluge for chi-square quantile function. var guess = Math.NaN; if (p == 0.0) { guess = 0.0; } else if ( p == 1.0 ) { guess = Math.POSITIVE_INFINITY; } else if ( p < 0.0 ) { guess = Math.NaN; } else { var tolAbs = 1.0e-8; var tolRel = 1.0e-3; guess = Math.max(0.0, df + Math.sqrt(2*df)*normInv(p)); // guess from normal approx var currP = chi2Cdf( guess, df); var loP = currP; var hiP = currP; var guessLo = guess; var guessHi = guess; while (loP > p) { // step down guessLo = 0.8*guessLo; loP = chi2Cdf( guessLo, df); } while (hiP < p) { // step up guessHi = 1.2*guessHi; hiP = chi2Cdf( guessHi, df); } guess = (guessLo + guessHi)/2.0; currP = chi2Cdf( guess, df); while ( (Math.abs(currP - p) > tolAbs) || (Math.abs(currP - p)/p > tolRel) ) { // bisect if ( currP < p ) { guessLo = guess; } else { guessHi = guess; } guess = (guessLo + guessHi)/2.0; currP = chi2Cdf(guess, df); } } return(guess); } function gammaCdf( x, a, b) { // gamma distribution CDF. var p = Math.NaN; if (a <= 0 || b <= 0) { } else if (x <= 0) { p = 0.0; } else { p = Math.min(incGamma(x/b, a), 1.0); } return(p); } function incGamma( x, a) { var inc = 0; var gam = lnGamma(a+rmin); if (x == 0) { inc = 0; } else if (a == 0) { inc = 1; } else if (x < a+1) { var ap = a; var sum = 1.0/ap; var del = sum; while (Math.abs(del) >= 10*eps*Math.abs(sum)) { del *= x/(++ap); sum += del; } inc = sum * Math.exp(-x + a*Math.log(x) - gam); } else if (x >= a+1) { var a0 = 1; var a1 = x; var b0 = 0; var b1 = 1; var fac = 1; var n = 1; var g = 1; var gold = 0; var ana; var anf; while (Math.abs(g-gold) >= 10*eps*Math.abs(g)) { gold = g; ana = n - a; a0 = (a1 + a0 *ana) * fac; b0 = (b1 + b0 *ana) * fac; anf = n*fac; a1 = x * a0 + anf * a1; b1 = x * b0 + anf * b1; fac = 1.0 / a1; g = b1 * fac; n++; } inc = 1 - Math.exp(-x + a*Math.log(x) - gam) * g; } return(inc); } function poissonPmf( lambda, k) { var p = 0.0; if (k >= 0) { p = Math.exp(-lambda)*Math.pow(lambda,k)/factorial(k); } return(p); } function poissonCdf( lambda, k) { var p = 0; var b = 0; var m = 0; while (m <= k) { b += Math.pow(lambda, m++)/factorial(k); } p += Math.exp(-lambda)*b; return(p); } function poissonTail(lambda, k) { return(1.0-poissonCdf(lambda, k-1)); } function factorial(n) { // computes n! var fac=1; for (var i=n; i > 1; i--) {fac *= i;} return(fac); } function binomialCoef(n,k) { // computes n choose k if (n < k || n < 0) { return(0.0); } else if ( k == 0 || n == 0 || n == k) { return(1.0); } else { var minnk = Math.min(k, n-k); var coef = 1; for (var j = 0; j < minnk; j++) { coef *= (n-j)/(minnk-j); } return(coef); } } function binomialPmf(n, p, k) { // binomial pmf at k. var pmf = binomialCoef(n,k)*Math.pow(p,k)*Math.pow((1-p),(n-k)); return(pmf); } function binomialCdf(n, p, k) { // binomial CDF: Pr(X <= k), X~B(n,p) if (k < 0) { return(0.0); } else if (k >= n) { return(1.0); } else { var cdf = 0.0; for (var i = 0; i <= k; i++) { cdf += binomialPmf(n, p, i); } return(cdf); } } function binomialTail(n,p,k) { // binomial tail probability Pr(X >= k), X~B(n,p) if (k < 0) { return(1.0); } else if (k >= n) { return(0.0); } else { var tailP = 0.0; for (var i = k; i <= n; i++) { tailP += binomialPmf(n, p, i); } return(tailP); } } function binomialInv(n, p, pt) { // binomial percentile function var t = 0; if (pt < 0 || pt > 1) { t = NaN; } else if (pt == 0.0) { t = 0; } else if (pt == 1.0) { t = n; } else { var t = 0; var pc = 0.0; while ( pc < pt ) { pc += binomialPmf(n, p, t++); } t -= 1; } return(t); } function multinomialCoef(list, n) { // multinomial coefficient. // WARNING: not very stable algorithm; avoid for large n. var val = 0; var lmn = vMinMax(list); if (typeof(n) == 'undefined' || n == null) { n = vSum(list); } if (lmn[0] < 0.0) { alert('Error #1 in irGrade.multinomialCoef: a number of outcomes is negative!'); } else if (n == vSum(list)) { val = factorial(n); for (var i=0; i < list.length; i++) { val /= factorial(list[i]); } } return(val); } function multinomialPmf(olist, plist, n) { // multinomial pmf; not stable algorithm var val = 0.0; var pmn = vMinMax(plist); var omn = vMinMax(olist); if (typeof(n) == 'undefined' || n == null) { n = vSum(olist); } if (olist.length != plist.length) { alert('Error #1 in irGrade.multinomialPmf: length of outcome and probability vectors ' + 'do not match!'); } else if (pmn[0] < 0.0) { alert('Error #2 in irGrade.multinomialPmf: a probability is negative!'); } else if (omn[0] < 0.0) { alert('Error #3 in irGrade.multinomialPmf: a number of outcomes is negative!'); } else if (n == vSum(olist)) { var pl = vMult(1.0/vSum(plist), plist); // just in case val = factorial(n); for (var i=0; i< olist.length; i++) { val *= Math.pow(pl[i], olist[i])/factorial(olist[i]); } } return(val); } function geoPmf( p, k) { // chance it takes k trials to the first success in iid Bernoulli(p) trials // EX = 1/p; SD(X) = sqrt(1-p)/p if (k < 1 || p == 0.0) { return(0.0); } else { return(Math.pow((1-p),k-1)*p); } } function geoCdf( p, k) { // chance it takes k or fewer trials to the first success in iid Bernoulli(p) trials if (k < 1 || p == 0.0) { return(0.0); } else { return(1-Math.pow( 1-p, k)); } } function geoTail( p, k) { // chance of k or more trials to the first success in iid Bernoulli(p) trials return(1 - geoCdf(p, k-1)); } function geoInv(p, pt) { // geometric percentile function var t = 0; if (pt < 0 || pt > 1) { t = Math.NaN; } else if (pt == 0.0) { t = 0; } else if (pt == 1.0) { t = Math.POSITIVE_INFINITY; } else { var t = 0; var pc = 0.0; while ( pc < pt ) { pc += geoPmf(p, t++); } } return(t); } function hyperGeoPmf( N, M, n, m) { // chance of drawing m of M objects in a sample of size n from // N objects in all. p = (M C m)*(N-M C n-m)/(N C n) // EX = n*M/N; SD(X)= sqrt((N-n)/(N-1))*sqrt(np(1-p)); var p; if ( n < m || N < M || M < m || m < 0 || N < 0) { return(0.0); } else { p = binomialCoef(M,m)*binomialCoef(N-M,n-m)/binomialCoef(N,n); return(p); } } function hyperGeoCdf( N, M, n, m) { // chance of drawing m or fewer of M objects in a sample of size n from // N objects in all var p=0.0; var mMax = Math.min(m,M); mMax = Math.min(mMax,n); for (var i = 0; i <= mMax; i++) { p += hyperGeoPmf(N, M, n, i); } return(p); } function hyperGeoTail( N, M, n, m) { // chance of drawing m or more of M objects in a sample of size n from // N objects in all var p=0.0; for (var i = m; i <= M; i++) { p += hyperGeoPmf(N, M, n, i); } return(p); } function negBinomialPmf( p, s, t) { // chance that the sth success in iid Bernoulli trials is on the tth trial // EX = s/p; SD(X) = sqrt(s(1-p))/p if (s > t || s < 0) { return(0.0); } var prob = p*binomialPmf(t-1,p,s-1); return(prob); } function negBinomialCdf( p, s, t) { // chance the sth success in iid Bernoulli trials is on or before the tth trial var prob = 0.0; for (var i = s; i <= t; i++) { prob += negBinomialPmf(p, s, i); } return(prob); } function pDieRolls(rolls,spots) { // chance that the sum of 'rolls' rolls of a die = 'spots' if (rolls > 4) { alert("Error #1 in irGrade.pDiceRolls: too many rolls " + rolls + ". "); return(Math.NaN); } else { // BRUTE FORCE! var found = 0; if (spots < rolls || spots > 6*rolls) {return(0.0);} var possible = Math.pow(6,rolls); if (rolls == 1) { return(1/possible); } else if (rolls == 2) { for (var i=1; i <=6; i++ ) { for (var j=1; j <= 6; j++ ) { if (i+j == spots ) {found++;} } } } else if (rolls == 3 ) { for (var i=1; i <=6; i++ ) { for (var j=1; j<=6; j++ ) { for (var k=1; k<=6; k++ ) { if (i+j+k == spots ) {found++;} } } } } else if (rolls == 4 ) { for (var i=1; i <=6; i++ ) { for (var j=1; j<=6; j++ ) { for (var k=1; k<=6; k++ ) { for (var m=1; m <=6; m++ ) { if (i+j+k+m == spots ) {found++;} } } } } } return(found/possible); } return(false); } function permutations(n,k) { // number of permutations of k of n things if (n < k || n < 0) { return(0); } else if ( k==0 || n == 0) { return(1); } else { var coef=1; for (var j=0; j < k; j++) coef *= (n-j); } return(coef); } function sgn(x) { // signum function if (x >= 0) { return(1); } else if (x < 0) { return (-1); } } function linspace(lo,hi,n) { // n linearly spaced points between lo and hi var spaced = new Array(n); var dx =(hi-lo)/(n-1); for (var i=0; i < n; i++) { spaced[i] = lo + i*dx; } return(spaced); } function rms(list) { // rms var r = 0; for (var i=0; i < list.length; i++) r += list[i]*list[i]; r /= list.length; return(Math.sqrt(r)); } function vMinMax(list){ // returns min and max of list var mn = list[0]; var mx = list[0]; for (var i=1; i < list.length; i++) { if (mn > list[i]) mn = list[i]; if (mx < list[i]) mx = list[i]; } var vmnmx = new Array(mn,mx); return(vmnmx); } function vMinMaxIndices(list){ // returns min, max, index of min, index of max var mn = list[0]; var indMn = 0; var mx = list[0]; var indMx = 0; for (var i=1; i < list.length; i++) { if (mn > list[i]) { mn = list[i]; indMn = i; } if (mx < list[i]) { mx = list[i]; indMx = i; } } var vmnmx = new Array(mn,mx,indMn,indMx); return(vmnmx); } function vMinMaxAbs(list) { // returns min and max of absolute values of a list's elements var mn = Math.abs(list[0]); var mx = Math.abs(list[0]); var val; for (var i=1; i < list.length; i++) { val = Math.abs(list[i]); if (mn > val) mn = val; if (mx < val) mx = val; } var vmnmx = new Array(mn,mx); return(vmnmx); } function randBoolean(p){ // random boolean value, prob p that it is true if (typeof(p) == 'undefined' || p == null) { p = 0.5; } if (rand.next() <= p) { return(false); } else { return(true); } } function sortUnique(list,order) { // sort a list, remove duplicate entries var temp = list; if (typeof(order) != 'undefined' && order != null) { temp.sort(order); } else { temp.sort(); } var temp2 = new Array(temp.length); temp2[0] = temp[0]; var ix = 0; for (var i=1; i < temp.length; i++) { if (temp[i] != temp2[ix] ) { temp2[++ix] = temp[i]; } } return(temp2); } function randPermutation(list,index) { // returns a random permutation of list var randIndex = listOfDistinctRandInts(list.length,0,list.length-1); var thePermutation = new Array(list.length); for (var i=0; i < list.length; i++) { thePermutation[i] = list[randIndex[i]]; } if (typeof(index) != 'undefined' && index == 'forward') { // original indices var p = new Array(2); p[0] = thePermutation; p[1] = randIndex; thePermutation = p; } else if (typeof(index) != 'undefined' && index == 'inverse') { // inverse permutation var p = new Array(2); p[0] = thePermutation; p[1] = new Array(list.length); for (var i=0; i < list.length; i++) { p[1][randIndex[i]] = i; } thePermutation = p; } return(thePermutation); } function fakeBivariateData(nPoints, funArray, heteroFac, snr, loEnd, hiEnd) { // returns a 2-d array of synthetic data generated from a polynomial, // according to the contents of funArray. // if funArray[0] == "polynomial", uses the other elements of funArray as // the coefficients of a polynomial. // funArray[1] + funArray[2]*X + funArray[3]*X^2 + ... // 1/3 of the points have noise level heteroFac times larger than the rest. // Normalizes the errors to signal/noise ratio snr in 2-norm var data = new Array(2); data[0] = new Array(nPoints); data[1] = new Array(nPoints); var x; var fVal; var xPow; if (funArray[0] == "polynomial") { if (typeof(loEnd) == 'undefined' || loEnd == null) { // lower limit of X variable loEnd = -10; } if (typeof(hiEnd) == 'undefined' || hiEnd == null) { // upper limit of X variable hiEnd = 10; } var dX = (hiEnd - loEnd)/(nPoints - 1); for (var i=0; i < nPoints; i++) { x = loEnd + i*dX; data[0][i] = x; fVal = 0.0; xPow = 1.0; for (var j=1; j < funArray.length; j++) { fVal += xPow*funArray[j]; xPow *= x; } data[1][i] = fVal; } } else { alert('Error #1 in irGrade.fakeBivariateData()!\n' + 'Unsupported function type: ' + funArray[0].toString()); return(null); } // now add noise. var sigNorm = twoNorm(data[1]); var noise = new Array(nPoints); for (var i=0; i < nPoints; i++) { noise[i] = rNorm(); } // pick a random set to perturb for heteroscedastic noise var segLen = Math.floor(nPoints/3); var startPt = Math.floor(2*nPoints/3*rand.next()); for (var i=startPt; i < startPt+segLen; i++) { noise[i] = noise[i]*heteroFac; } var noiseNorm = twoNorm(noise); for (var i=0; i < nPoints; i++) { data[1][i] += noise[i]*sigNorm/noiseNorm/snr; } return(data) } function nextRand() { // generates next random number in a sequence var up = this.seed / this.Q; var lo = this.seed % this.Q; var trial = this.A * lo - this.R * up; if (trial > 0) { this.seed = trial; } else { this.seed = trial + this.M; } return (this.seed * this.oneOverM); } function rng(s) { if ( typeof(s)=='undefined' || s == null ){ var d = new Date(); this.seed = 2345678901 + (d.getSeconds() * 0xFFFFFF) + (d.getMinutes() * 0xFFFF); } else { this.seed = s; } this.A = 48271; this.M = 2147483647; this.Q = this.M / this.A; this.R = this.M % this.A; this.oneOverM = 1.0 / this.M; this.next = nextRand; this.getSeed = getRandSeed; return(this); } function getRandSeed() { // get seed of random number generator return(this.seed); } function crypt(s,t) { var slen = s.length; var tlen = t.length; var rad = 16; var r = 0; var i; var j = -1; var result = ''; if (s.substr(0,2) == "0x") { for (i=2; i < slen; i+=2) { if (++j >= tlen) {j = 0;} r = parseInt(s.substr(i,2),rad) ^ t.charCodeAt(j); result += String.fromCharCode(r); } } else { result +='0x'; for ( i=0; i < slen; i++) { if (++j >= tlen) {j = 0;} r = s.charCodeAt(i) ^ t.charCodeAt(j); result += (r < rad ? "0" : "") + r.toString(rad); } } return(result); }