function mathphp($st, $varlist, $skipfactorial = false, $ignorestrings = true)
{
//translate a math formula to php function notation
// a^b --> pow(a,b)
// na --> n*a
// (...)d --> (...)*d
// n! --> factorial(n)
// sin^-1 --> asin etc.
//parenthesize variables with number endings, ie $c2^3 => ($c2)^3
//not needed since mathphp no longer used on php vars
//skipfactorial: legacy: not really used anymore. Originally intended
//to handle !something type ifcond. Might need to reexplore
$vars = explode('|', $varlist);
//security check variables (we might evaling with them later)
global $disallowedvar;
if (!isset($disallowedvar)) {
$disallowedvar = array('$link', '$qidx', '$qnidx', '$seed', '$qdata', '$toevalqtxt', '$la', '$GLOBALS', '$laparts', '$anstype', '$kidx', '$iidx', '$tips', '$options', '$partla', '$partnum', '$score', '$disallowedvar', '$allowedmacros');
}
foreach ($vars as $var) {
if (in_array('$' . $var, $disallowedvar) || substr($var, 0, 7) == 'GLOBALS') {
echo "disallowed variable name";
return "0;";
}
}
//take care of sin^-1 notation first
$st = mathphppre($st);
$st = preg_replace('/(\\+|\\-)\\s+(\\+|\\-)/', "\$1\$2", $st);
//$exp = str_replace(" ", "", $exp); //caused problems with "x > -3"
$st = str_replace("+-", "-", $st);
$st = str_replace("-+", "-", $st);
$st = str_replace("--", "+", $st);
return mathphpinterpretline($st . ' ', $vars, $ignorestrings);
}
function scorepart($anstype, $qn, $givenans, $options, $multi)
{
$defaultreltol = 0.0015;
global $mathfuncs;
if ($anstype == "number") {
if (is_array($options['answer'])) {
$answer = $options['answer'][$qn];
} else {
$answer = $options['answer'];
}
if (isset($options['reltolerance'])) {
if (is_array($options['reltolerance'])) {
$reltolerance = $options['reltolerance'][$qn];
} else {
$reltolerance = $options['reltolerance'];
}
}
if (isset($options['abstolerance'])) {
if (is_array($options['abstolerance'])) {
$abstolerance = $options['abstolerance'][$qn];
} else {
$abstolerance = $options['abstolerance'];
}
}
if (isset($options['answerformat'])) {
if (is_array($options['answerformat'])) {
$answerformat = $options['answerformat'][$qn];
} else {
$answerformat = $options['answerformat'];
}
}
if (isset($options['reqsigfigs'])) {
if (is_array($options['reqsigfigs'])) {
$reqsigfigs = $options['reqsigfigs'][$qn];
} else {
$reqsigfigs = $options['reqsigfigs'];
}
}
if (isset($options['requiretimes'])) {
if (is_array($options['requiretimes'])) {
$requiretimes = $options['requiretimes'][$qn];
} else {
$requiretimes = $options['requiretimes'];
}
}
if (isset($options['requiretimeslistpart'])) {
if (is_array($options['requiretimeslistpart'])) {
$requiretimeslistpart = $options['requiretimeslistpart'][$qn];
} else {
$requiretimeslistpart = $options['requiretimeslistpart'];
}
}
if (is_array($options['partialcredit'][$qn]) || $multi > 0 && is_array($options['partialcredit'])) {
$partialcredit = $options['partialcredit'][$qn];
} else {
$partialcredit = $options['partialcredit'];
}
$givenans = str_replace('∞', 'oo', $givenans);
$GLOBALS['partlastanswer'] = $givenans;
if (isset($requiretimes) && checkreqtimes($givenans, $requiretimes) == 0) {
return 0;
}
if (isset($partialcredit)) {
if (!is_array($partialcredit)) {
$partialcredit = explode(',', $partialcredit);
}
$altanswers = array();
$altweights = array();
for ($i = 0; $i < count($partialcredit); $i += 2) {
$altanswers[] = $partialcredit[$i];
$altweights[] = floatval($partialcredit[$i + 1]);
}
}
if (!isset($reltolerance) && !isset($abstolerance)) {
$reltolerance = $defaultreltol;
}
if (isset($reqsigfigs)) {
if ($reqsigfigs[0] == '=') {
$exactsigfig = true;
$reqsigfigs = substr($reqsigfigs, 1);
} else {
$exactsigfig = false;
}
}
if ($multi > 0) {
$qn = $multi * 1000 + $qn;
}
if ($answer === '') {
if (trim($givenans) === '') {
return 1;
} else {
return 0;
}
}
if ($answer === '0 or ') {
if (trim($givenans) === '' || trim($givenans) === '0') {
return 1;
} else {
return 0;
}
}
if ($givenans == null) {
return 0;
}
if ($answerformat == 'exactlist') {
$gaarr = explode(',', $givenans);
$gaarrcnt = count($gaarr);
$anarr = explode(',', $answer);
} else {
if ($answerformat == 'orderedlist') {
$gamasterarr = explode(',', $givenans);
$gaarr = $gamasterarr;
$anarr = explode(',', $answer);
} else {
if ($answerformat == 'list') {
$tmp = explode(',', $givenans);
sort($tmp);
$gaarr = array($tmp[0]);
for ($i = 1; $i < count($tmp); $i++) {
if ($tmp[$i] - $tmp[$i - 1] > 1.0E-12) {
$gaarr[] = $tmp[$i];
}
}
$gaarrcnt = count($gaarr);
$tmp = explode(',', $answer);
sort($tmp);
$anarr = array($tmp[0]);
for ($i = 1; $i < count($tmp); $i++) {
if ($tmp[$i] - $tmp[$i - 1] > 1.0E-12) {
$anarr[] = $tmp[$i];
}
}
} else {
$gaarr = array(str_replace(array('$', ',', ' ', '/', '^'), '', $givenans));
if (strpos($answer, '[') === false && strpos($answer, '(') === false) {
$anarr = array(str_replace(',', '', $answer));
} else {
$anarr = array($answer);
}
}
}
}
$extrapennum = count($gaarr) + count($anarr);
if ($answerformat == 'orderedlist') {
if (count($gamasterarr) != count($anarr)) {
return 0;
}
}
if ($answerformat == 'parenneg') {
foreach ($gaarr as $k => $v) {
if ($v[0] == '(') {
$gaarr[$k] = -1 * substr($v, 1, -1);
}
}
}
$correct = 0;
foreach ($anarr as $i => $answer) {
$foundloc = -1;
if ($answerformat == 'orderedlist') {
$gaarr = array($gamasterarr[$i]);
}
foreach ($gaarr as $j => $givenans) {
$givenans = trim($givenans);
if (isset($requiretimeslistpart) && checkreqtimes($givenans, $requiretimeslistpart) == 0) {
continue;
}
$anss = explode(' or ', $answer);
foreach ($anss as $anans) {
if (!is_numeric($anans)) {
if (preg_match('/(\\(|\\[)(-?[\\d\\.]+|-oo)\\,(-?[\\d\\.]+|oo)(\\)|\\])/', $anans, $matches)) {
if ($matches[2] == '-oo') {
$matches[2] = -1.0E+99;
}
if ($matches[3] == 'oo') {
$matches[3] = 1.0E+99;
}
if ($matches[1] == "(" && $givenans > $matches[2] || $matches[1] == "[" && $givenans >= $matches[2]) {
if ($matches[4] == ")" && $givenans < $matches[3] || $matches[4] == "]" && $givenans <= $matches[3]) {
$correct += 1;
$foundloc = $j;
break 2;
}
}
} else {
if ($anans == "DNE" && strtoupper($givenans) == "DNE") {
$correct += 1;
$foundloc = $j;
break 2;
} else {
if (($anans == "+oo" || $anans == "oo") && ($givenans == "+oo" || $givenans == "oo")) {
$correct += 1;
$foundloc = $j;
break 2;
} else {
if ($anans == "-oo" && $givenans == "-oo") {
$correct += 1;
$foundloc = $j;
break 2;
} else {
if (strtoupper($anans) == strtoupper($givenans)) {
$correct += 1;
$foundloc = $j;
break 2;
}
}
}
}
}
} else {
//{if (is_numeric($givenans)) {
//$givenans = preg_replace('/[^\-\d\.eE]/','',$givenans); //strip out units, dollar signs, whatever
$givenans = preg_replace('/^((-|\\+)?\\d*\\.?\\d*E?\\-?\\d*).*$/', '$1', trim($givenans));
//strip out units
if (is_numeric($givenans)) {
if (isset($reqsigfigs)) {
if ($givenans * $anans < 0) {
continue;
}
//move on if opposite signs
if ($anans != 0) {
$v = -1 * floor(-log10(abs($anans)) - 1.0E-12) - $reqsigfigs;
}
if (strpos($givenans, 'E') !== false) {
//handle computer-style scientific notation
preg_match('/^-?[1-9]\\.?(\\d*)E/', $givenans, $matches);
$gasigfig = 1 + strlen($matches[1]);
if ($exactsigfig) {
if ($gasigfig != $reqsigfigs) {
continue;
}
} else {
if ($gasigfig < $reqsigfigs) {
continue;
}
}
if (abs($anans - $givenans) < pow(10, $v) / 2 + 1.0E-12) {
$correct += 1;
$foundloc = $j;
break 2;
}
} else {
if (!$exactsigfig) {
//this line will reject 0.25 if the answer is 0.250 with 3 sigfigs
$gadploc = strpos($givenans, '.');
if ($gadploc === false) {
$gadploc = strlen($givenans);
}
if ($anans != 0 && $v < 0 && strlen($givenans) - $gadploc - 1 + $v < 0) {
continue;
}
//not enough decimal places
if (abs($anans - $givenans) < pow(10, $v) / 2 + 1.0E-12) {
$correct += 1;
$foundloc = $j;
break 2;
}
} else {
if (ltrim(prettysigfig($anans, $reqsigfigs, ''), '0') === ltrim($givenans, '0')) {
$correct += 1;
$foundloc = $j;
break 2;
}
}
}
} else {
if (isset($abstolerance)) {
if (abs($anans - $givenans) < $abstolerance + ($anans == 0 || abs($anans) > 1 ? 1.0E-12 : abs($anans) * 1.0E-12)) {
$correct += 1;
$foundloc = $j;
break 2;
}
} else {
if ($anans == 0) {
if (abs($anans - $givenans) < $reltolerance / 1000 + 1.0E-12) {
$correct += 1;
$foundloc = $j;
break 2;
}
} else {
if (abs($anans - $givenans) / (abs($anans) + (abs($anans) > 1 ? 1.0E-12 : abs($anans) * 1.0E-12)) < $reltolerance + 1.0E-12) {
$correct += 1;
$foundloc = $j;
break 2;
}
}
}
}
}
}
}
}
if ($foundloc > -1) {
array_splice($gaarr, $foundloc, 1);
//remove from list
if (count($gaarr) == 0 && $answerformat != 'orderedlist') {
break;
//stop if no student answers left
}
}
}
if ($answerformat != 'orderedlist') {
if ($gaarrcnt <= count($anarr)) {
$score = $correct / count($anarr);
} else {
$score = $correct / count($anarr) - ($gaarrcnt - count($anarr)) / $extrapennum;
//take off points for extranous stu answers
}
} else {
$score = $correct / count($anarr);
}
if ($score < 0) {
$score = 0;
}
if ($score == 0 && isset($partialcredit) && strpos($answerformat, 'list') === false && is_numeric($givenans)) {
foreach ($altanswers as $i => $anans) {
if (isset($reqsigfigs)) {
if ($givenans * $anans < 0) {
continue;
}
//move on if opposite signs
if (!$exactsigfig) {
if ($anans != 0) {
$v = -1 * floor(-log10(abs($anans)) - 1.0E-12) - $reqsigfigs;
}
//this line will reject 0.25 if the answer is 0.250 with 3 sigfigs
if ($anans != 0 && $v < 0 && strlen($givenans) - strpos($givenans, '.') - 1 + $v < 0) {
continue;
}
//not enough decimal places
if (abs($anans - $givenans) < pow(10, $v) / 2 + 1.0E-12) {
$score = $altweights[$i];
break;
}
} else {
if (ltrim(prettysigfig($anans, $reqsigfigs, ''), '0') === ltrim($givenans, '0')) {
$score = $altweights[$i];
break;
}
}
} else {
if (isset($abstolerance)) {
if (abs($anans - $givenans) < $abstolerance + 1.0E-12) {
$score = $altweights[$i];
break;
}
} else {
if (abs($anans - $givenans) / (abs($anans) + 0.0001) < $reltolerance + 1.0E-12) {
$score = $altweights[$i];
break;
}
}
}
}
}
return $score;
} else {
if ($anstype == "choices") {
if (is_array($options['questions'][$qn])) {
$questions = $options['questions'][$qn];
} else {
$questions = $options['questions'];
}
if (is_array($options['answer'])) {
$answer = $options['answer'][$qn];
} else {
$answer = $options['answer'];
}
if (isset($options['noshuffle'])) {
if (is_array($options['noshuffle'])) {
$noshuffle = $options['noshuffle'][$qn];
} else {
$noshuffle = $options['noshuffle'];
}
} else {
$noshuffle = "none";
}
if (is_array($options['partialcredit'][$qn]) || $multi > 0 && is_array($options['partialcredit'])) {
$partialcredit = $options['partialcredit'][$qn];
} else {
$partialcredit = $options['partialcredit'];
}
if (isset($partialcredit)) {
if (!is_array($partialcredit)) {
$partialcredit = explode(',', $partialcredit);
}
$creditweight = array();
for ($i = 0; $i < count($partialcredit); $i += 2) {
$creditweight[$partialcredit[$i]] = floatval($partialcredit[$i + 1]);
}
}
if (!is_array($questions)) {
echo _('Eeek! $questions is not defined or needs to be an array. Make sure $questions is defined in the Common Control section.');
return false;
}
if ($multi > 0) {
$qn = $multi * 1000 + $qn;
}
if ($noshuffle == "last") {
$randkeys = array_rand(array_slice($questions, 0, count($questions) - 1), count($questions) - 1);
shuffle($randkeys);
array_push($randkeys, count($questions) - 1);
} else {
if ($noshuffle == "all") {
$randkeys = array_keys($questions);
} else {
$randkeys = array_rand($questions, count($questions));
shuffle($randkeys);
}
}
if ($givenans === 'NA' || $givenans === null) {
$GLOBALS['partlastanswer'] = $givenans;
} else {
$GLOBALS['partlastanswer'] = $givenans . '$!$' . $randkeys[$givenans];
}
if ($givenans == null) {
return 0;
}
if ($givenans == 'NA') {
return 0;
}
$anss = explode(' or ', $answer);
foreach ($anss as $k => $v) {
$anss[$k] = intval($v);
}
//if ($randkeys[$givenans] == $answer) {return 1;} else { return 0;}
if (in_array($randkeys[$givenans], $anss)) {
return 1;
} else {
if (isset($partialcredit) && isset($creditweight[$randkeys[$givenans]])) {
return $creditweight[$randkeys[$givenans]];
} else {
return 0;
}
}
} else {
if ($anstype == "multans") {
if (is_array($options['questions'][$qn])) {
$questions = $options['questions'][$qn];
} else {
$questions = $options['questions'];
}
if (isset($options['answers'])) {
if (is_array($options['answers'])) {
$answers = $options['answers'][$qn];
} else {
$answers = $options['answers'];
}
} else {
if (isset($options['answer'])) {
if (is_array($options['answer'])) {
$answers = $options['answer'][$qn];
} else {
$answers = $options['answer'];
}
}
}
if (isset($options['noshuffle'])) {
if (is_array($options['noshuffle'])) {
$noshuffle = $options['noshuffle'][$qn];
} else {
$noshuffle = $options['noshuffle'];
}
}
if (isset($options['scoremethod'])) {
if (is_array($options['scoremethod'])) {
$scoremethod = $options['scoremethod'][$qn];
} else {
$scoremethod = $options['scoremethod'];
}
}
if (!is_array($questions)) {
echo _('Eeek! $questions is not defined or needs to be an array. Make sure $questions is defined in the Common Control section.');
return false;
}
if ($multi > 0) {
$qn = $multi * 1000 + $qn;
}
$score = 1.0;
if ($noshuffle == "last") {
$randqkeys = array_rand(array_slice($questions, 0, count($questions) - 1), count($questions) - 1);
shuffle($randqkeys);
array_push($randqkeys, count($questions) - 1);
} else {
if ($noshuffle == "all") {
$randqkeys = array_keys($questions);
} else {
$randqkeys = array_rand($questions, count($questions));
shuffle($randqkeys);
}
}
if (trim($answers) == '') {
$akeys = array();
} else {
$akeys = explode(",", $answers);
}
if (isset($scoremethod) && $scoremethod == 'answers') {
$deduct = 1.0 / count($akeys);
} else {
$deduct = 1.0 / count($questions);
}
$origla = array();
for ($i = 0; $i < count($questions); $i++) {
if ($i > 0) {
$GLOBALS['partlastanswer'] .= "|";
} else {
$GLOBALS['partlastanswer'] = '';
}
$GLOBALS['partlastanswer'] .= $_POST["qn{$qn}"][$i];
if (isset($_POST["qn{$qn}"][$i])) {
$origla[] = $randqkeys[$i];
}
if (isset($_POST["qn{$qn}"][$i]) !== in_array($randqkeys[$i], $akeys)) {
$score -= $deduct;
}
}
$GLOBALS['partlastanswer'] .= '$!$' . implode('|', $origla);
if (isset($scoremethod)) {
if ($scoremethod == 'allornothing' && $score < 1) {
$score = 0;
} else {
if ($scoremethod == 'takeanything') {
$score = 1;
}
}
}
if ($score < 0) {
$score = 0;
}
return $score;
} else {
if ($anstype == "matching") {
if (is_array($options['questions'][$qn])) {
$questions = $options['questions'][$qn];
} else {
$questions = $options['questions'];
}
if (isset($options['answers'])) {
if (is_array($options['answers'][$qn])) {
$answers = $options['answers'][$qn];
} else {
$answers = $options['answers'];
}
} else {
if (isset($options['answer'])) {
if (is_array($options['answer'][$qn])) {
$answers = $options['answer'][$qn];
} else {
$answers = $options['answer'];
}
}
}
if (is_array($options['matchlist'])) {
$matchlist = $options['matchlist'][$qn];
} else {
$matchlist = $options['matchlist'];
}
if (isset($options['noshuffle'])) {
if (is_array($options['noshuffle'])) {
$noshuffle = $options['noshuffle'][$qn];
} else {
$noshuffle = $options['noshuffle'];
}
}
if (!is_array($questions) || !is_array($answers)) {
echo _('Eeek! $questions or $answers is not defined or needs to be an array. Make sure both are defined in the Common Control section.');
return 0;
}
if ($multi > 0) {
$qn = $multi * 1000 + $qn;
}
$score = 1.0;
$deduct = 1.0 / count($questions);
if ($noshuffle == "questions" || $noshuffle == 'all') {
$randqkeys = array_keys($questions);
} else {
$randqkeys = array_rand($questions, count($questions));
shuffle($randqkeys);
}
if ($noshuffle == "answers" || $noshuffle == 'all') {
$randakeys = array_keys($answers);
} else {
$randakeys = array_rand($answers, count($answers));
shuffle($randakeys);
}
if (isset($matchlist)) {
$matchlist = explode(',', $matchlist);
}
$origla = array();
for ($i = 0; $i < count($questions); $i++) {
if ($i > 0) {
$GLOBALS['partlastanswer'] .= "|";
} else {
$GLOBALS['partlastanswer'] = '';
}
$GLOBALS['partlastanswer'] .= $_POST["qn{$qn}-{$i}"];
if ($_POST["qn{$qn}-{$i}"] != "" && $_POST["qn{$qn}-{$i}"] != "-") {
$qa = ord($_POST["qn{$qn}-{$i}"]);
if ($qa < 97) {
//if uppercase answer
$qa -= 65;
//shift A to 0
} else {
//if lower case
$qa -= 97;
//shift a to 0
}
$origla[$randqkeys[$i]] = $randakeys[$qa];
if (isset($matchlist)) {
if ($matchlist[$randqkeys[$i]] != $randakeys[$qa]) {
$score -= $deduct;
}
} else {
if ($randqkeys[$i] != $randakeys[$qa]) {
$score -= $deduct;
}
}
} else {
$origla[$randqkeys[$i]] = '';
$score -= $deduct;
}
}
ksort($origla);
$GLOBALS['partlastanswer'] .= '$!$' . implode('|', $origla);
return $score;
} else {
if ($anstype == "matrix") {
if (is_array($options['answer']) && isset($options['answer'][$qn])) {
$answer = $options['answer'][$qn];
} else {
$answer = $options['answer'];
}
if (isset($options['reltolerance'])) {
if (is_array($options['reltolerance'])) {
$reltolerance = $options['reltolerance'][$qn];
} else {
$reltolerance = $options['reltolerance'];
}
}
if (isset($options['abstolerance'])) {
if (is_array($options['abstolerance'])) {
$abstolerance = $options['abstolerance'][$qn];
} else {
$abstolerance = $options['abstolerance'];
}
}
if (!isset($reltolerance) && !isset($abstolerance)) {
$reltolerance = $defaultreltol;
}
if (isset($options['answersize'])) {
if (is_array($options['answersize'])) {
$answersize = $options['answersize'][$qn];
} else {
$answersize = $options['answersize'];
}
}
if ($multi > 0) {
$qn = $multi * 1000 + $qn;
}
$correct = true;
$ansr = substr($answer, 2, -2);
$ansr = preg_replace('/\\)\\s*\\,\\s*\\(/', ',', $ansr);
$answerlist = explode(',', $ansr);
foreach ($answerlist as $k => $v) {
$v = eval('return (' . mathphp($v, null) . ');');
$answerlist[$k] = preg_replace('/[^\\d\\.,\\-E]/', '', $v);
}
//$answer = preg_replace_callback('/([^\[\(\)\]\,]+)/',"preg_mathphp_callback",$answer);
//$answerlist = explode(",",preg_replace('/[^\d\.,\-]/','',$answer));
if (isset($answersize)) {
for ($i = 0; $i < count($answerlist); $i++) {
$givenanslist[$i] = $_POST["qn{$qn}-{$i}"];
}
$GLOBALS['partlastanswer'] = implode("|", $givenanslist);
} else {
$givenans = preg_replace('/\\)\\s*,\\s*\\(/', '),(', $givenans);
$GLOBALS['partlastanswer'] = $givenans;
$givenanslist = explode(",", preg_replace('/[^\\d,\\.\\-]/', '', $givenans));
if (substr_count($answer, '),(') != substr_count($_POST["qn{$qn}"], '),(')) {
$correct = false;
}
}
for ($i = 0; $i < count($answerlist); $i++) {
if (isset($abstolerance)) {
if (abs($answerlist[$i] - $givenanslist[$i]) > $abstolerance - 1.0E-12) {
$correct = false;
break;
}
} else {
if (abs($answerlist[$i] - $givenanslist[$i]) / (abs($answerlist[$i]) + 0.0001) > $reltolerance - 1.0E-12) {
$correct = false;
break;
}
}
}
if ($correct) {
return 1;
} else {
return 0;
}
} else {
if ($anstype == "calcmatrix") {
if (is_array($options['answer'])) {
$answer = $options['answer'][$qn];
} else {
$answer = $options['answer'];
}
if (isset($options['reltolerance'])) {
if (is_array($options['reltolerance'])) {
$reltolerance = $options['reltolerance'][$qn];
} else {
$reltolerance = $options['reltolerance'];
}
}
if (isset($options['abstolerance'])) {
if (is_array($options['abstolerance'])) {
$abstolerance = $options['abstolerance'][$qn];
} else {
$abstolerance = $options['abstolerance'];
}
}
if (!isset($reltolerance) && !isset($abstolerance)) {
$reltolerance = $defaultreltol;
}
if (isset($options['answersize'])) {
if (is_array($options['answersize'])) {
$answersize = $options['answersize'][$qn];
} else {
$answersize = $options['answersize'];
}
}
if (isset($options['answerformat'])) {
if (is_array($options['answerformat'])) {
$answerformat = $options['answerformat'][$qn];
} else {
$answerformat = $options['answerformat'];
}
}
if ($multi > 0) {
$qn = $multi * 1000 + $qn;
}
if (!isset($answerformat)) {
$answerformat = '';
}
$ansformats = explode(',', $answerformat);
$correct = true;
$ansr = substr($answer, 2, -2);
$ansr = preg_replace('/\\)\\s*\\,\\s*\\(/', ',', $ansr);
$answerlist = explode(',', $ansr);
foreach ($answerlist as $k => $v) {
$v = eval('return (' . mathphp($v, null) . ');');
$answerlist[$k] = preg_replace('/[^\\d\\.,\\-E]/', '', $v);
}
//$answer = preg_replace_callback('/([^\[\(\)\]\,]+)/',"preg_mathphp_callback",$answer);
//$answerlist = explode(",",preg_replace('/[^\d\.,\-E]/','',$answer));
if (isset($answersize)) {
for ($i = 0; $i < count($answerlist); $i++) {
$givenanslist[$i] = $_POST["qn{$qn}-{$i}"];
}
$GLOBALS['partlastanswer'] = implode("|", $givenanslist);
$GLOBALS['partlastanswer'] .= '$#$' . str_replace(',', '|', str_replace(array('(', ')', '[', ']'), '', $givenans));
for ($i = 0; $i < count($answerlist); $i++) {
if (!checkanswerformat($givenanslist[$i], $ansformats)) {
return 0;
//perhaps should just elim bad answer rather than all?
}
}
} else {
$_POST["tc{$qn}"] = preg_replace('/\\)\\s*,\\s*\\(/', '),(', $_POST["tc{$qn}"]);
$GLOBALS['partlastanswer'] = $_POST["tc{$qn}"] . '$#$' . $givenans;
if (substr_count($answer, '),(') != substr_count($_POST["tc{$qn}"], '),(')) {
$correct = false;
}
$tocheck = str_replace(' ', '', $_POST["tc{$qn}"]);
$tocheck = str_replace(array('],[', '),(', '>,<'), ',', $tocheck);
$tocheck = substr($tocheck, 2, strlen($tocheck) - 4);
$tocheck = explode(',', $tocheck);
foreach ($tocheck as $chkme) {
if (!checkanswerformat($chkme, $ansformats)) {
return 0;
//perhaps should just elim bad answer rather than all?
}
}
}
$givenanslist = explode(",", preg_replace('/[^\\d\\.,\\-]/', '', $givenans));
for ($i = 0; $i < count($answerlist); $i++) {
if (isset($abstolerance)) {
if (abs($answerlist[$i] - $givenanslist[$i]) > $abstolerance - 1.0E-12) {
$correct = false;
break;
}
} else {
if (abs($answerlist[$i] - $givenanslist[$i]) / (abs($answerlist[$i]) + 0.0001) > $reltolerance - 1.0E-12) {
$correct = false;
break;
}
}
}
if ($correct) {
return 1;
} else {
return 0;
}
} else {
if ($anstype == "ntuple" || $anstype == 'calcntuple') {
if (is_array($options['answer'])) {
$answer = $options['answer'][$qn];
} else {
$answer = $options['answer'];
}
if (isset($options['reltolerance'])) {
if (is_array($options['reltolerance'])) {
$reltolerance = $options['reltolerance'][$qn];
} else {
$reltolerance = $options['reltolerance'];
}
}
if (isset($options['abstolerance'])) {
if (is_array($options['abstolerance'])) {
$abstolerance = $options['abstolerance'][$qn];
} else {
$abstolerance = $options['abstolerance'];
}
}
if (isset($options['answerformat'])) {
if (is_array($options['answerformat'])) {
$answerformat = $options['answerformat'][$qn];
} else {
$answerformat = $options['answerformat'];
}
}
if (isset($options['requiretimes'])) {
if (is_array($options['requiretimes'])) {
$requiretimes = $options['requiretimes'][$qn];
} else {
$requiretimes = $options['requiretimes'];
}
}
if (!isset($reltolerance) && !isset($abstolerance)) {
$reltolerance = $defaultreltol;
}
if ($multi > 0) {
$qn = $multi * 1000 + $qn;
}
if (!isset($answerformat)) {
$answerformat = '';
}
$givenans = str_replace('∞', 'oo', $givenans);
$ansformats = explode(',', $answerformat);
$answer = str_replace(' ', '', $answer);
if ($anstype == 'ntuple') {
$GLOBALS['partlastanswer'] = $givenans;
} else {
if ($anstype == 'calcntuple') {
$GLOBALS['partlastanswer'] = $_POST["tc{$qn}"] . '$#$' . $givenans;
//test for correct format, if specified
if (checkreqtimes($_POST["tc{$qn}"], $requiretimes) == 0) {
return 0;
}
$tocheck = str_replace(' ', '', $_POST["tc{$qn}"]);
$tocheck = str_replace(array('],[', '),(', '>,<'), ',', $tocheck);
$tocheck = substr($tocheck, 1, strlen($tocheck) - 2);
$tocheck = explode(',', $tocheck);
if ($answer != 'DNE' && $answer != 'oo') {
foreach ($tocheck as $chkme) {
if (!checkanswerformat($chkme, $ansformats)) {
return 0;
//perhaps should just elim bad answer rather than all?
}
}
}
}
}
if ($givenans == null) {
return 0;
}
$givenans = str_replace(' ', '', $givenans);
if ($answer == 'DNE' && strtoupper($givenans) == 'DNE') {
return 1;
} else {
if ($answer == 'oo' && $givenans == 'oo') {
return 1;
}
}
preg_match_all('/([\\(\\[\\<\\{])(.*?)([\\)\\]\\>\\}])/', $givenans, $gaarr, PREG_SET_ORDER);
//preg_match_all('/([\(\[\<\{])(.*?)([\)\]\>\}])/', $answer, $anarr, PREG_SET_ORDER);
//replaced with string-based approach below. Allows eval as needed
$anarr = array();
$NCdepth = 0;
$lastcut = 0;
$answer = makepretty($answer);
for ($i = 0; $i < strlen($answer); $i++) {
$dec = false;
if ($answer[$i] == '(' || $answer[$i] == '[' || $answer[$i] == '<' || $answer[$i] == '{') {
if ($NCdepth == 0) {
$lastcut = $i;
}
$NCdepth++;
} else {
if ($answer[$i] == ')' || $answer[$i] == ']' || $answer[$i] == '>' || $answer[$i] == '}') {
$NCdepth--;
if ($NCdepth == 0) {
$anarr[] = array('', $answer[$lastcut], substr($answer, $lastcut + 1, $i - $lastcut - 1), $answer[$i]);
}
}
}
}
foreach ($anarr as $k => $v) {
$ansparts = explode(',', $v[2]);
foreach ($ansparts as $j => $v) {
if (!is_numeric($v)) {
$ansparts[$j] = eval('return(' . mathphp($v, null) . ');');
}
}
$anarr[$k][2] = $ansparts;
}
if (count($gaarr) == 0) {
return 0;
}
$extrapennum = count($gaarr) + count($anarr);
$correct = 0;
foreach ($anarr as $i => $answer) {
$foundloc = -1;
foreach ($gaarr as $j => $givenans) {
if ($answer[1] != $givenans[1] || $answer[3] != $givenans[3]) {
break;
}
//$ansparts = explode(',',$answer[2]);
$ansparts = $answer[2];
$gaparts = explode(',', $givenans[2]);
if (count($ansparts) != count($gaparts)) {
break;
}
for ($i = 0; $i < count($ansparts); $i++) {
if (is_numeric($ansparts[$i]) && is_numeric($gaparts[$i])) {
if (isset($abstolerance)) {
if (abs($ansparts[$i] - $gaparts[$i]) >= $abstolerance + 1.0E-12) {
break;
}
} else {
if (abs($ansparts[$i] - $gaparts[$i]) / (abs($ansparts[$i]) + 0.0001) >= $reltolerance + 1.0E-12) {
break;
}
}
} else {
break;
}
}
if ($i == count($ansparts)) {
$correct += 1;
$foundloc = $j;
break;
}
}
if ($foundloc > -1) {
array_splice($gaarr, $foundloc, 1);
// remove from list
if (count($gaarr) == 0) {
break;
}
}
}
$score = $correct / count($anarr) - count($gaarr) / $extrapennum;
if ($score < 0) {
$score = 0;
}
return $score;
} else {
if ($anstype == "complex" || $anstype == 'calccomplex') {
if (is_array($options['answer'])) {
$answer = $options['answer'][$qn];
} else {
$answer = $options['answer'];
}
if (isset($options['reltolerance'])) {
if (is_array($options['reltolerance'])) {
$reltolerance = $options['reltolerance'][$qn];
} else {
$reltolerance = $options['reltolerance'];
}
}
if (isset($options['abstolerance'])) {
if (is_array($options['abstolerance'])) {
$abstolerance = $options['abstolerance'][$qn];
} else {
$abstolerance = $options['abstolerance'];
}
}
if (isset($options['answerformat'])) {
if (is_array($options['answerformat'])) {
$answerformat = $options['answerformat'][$qn];
} else {
$answerformat = $options['answerformat'];
}
}
if (isset($options['requiretimes'])) {
if (is_array($options['requiretimes'])) {
$requiretimes = $options['requiretimes'][$qn];
} else {
$requiretimes = $options['requiretimes'];
}
}
if (isset($options['requiretimeslistpart'])) {
if (is_array($options['requiretimeslistpart'])) {
$requiretimeslistpart = $options['requiretimeslistpart'][$qn];
} else {
$requiretimeslistpart = $options['requiretimeslistpart'];
}
}
if (!isset($reltolerance) && !isset($abstolerance)) {
$reltolerance = $defaultreltol;
}
if ($multi > 0) {
$qn = $multi * 1000 + $qn;
}
if (!isset($answerformat)) {
$answerformat = '';
}
$ansformats = explode(',', $answerformat);
if ($anstype == 'complex') {
$GLOBALS['partlastanswer'] = $givenans;
} else {
if ($anstype == 'calccomplex') {
$GLOBALS['partlastanswer'] = $_POST["tc{$qn}"];
//test for correct format, if specified
if (checkreqtimes($_POST["tc{$qn}"], $requiretimes) == 0) {
return 0;
}
$tocheck = explode(',', $_POST["tc{$qn}"]);
foreach ($tocheck as $tchk) {
if (in_array('sloppycomplex', $ansformats)) {
$tchk = str_replace(array('sin', 'pi'), array('s$n', 'p$'), $tchk);
if (substr_count($tchk, 'i') > 1) {
return 0;
}
$tchk = str_replace(array('s$n', 'p$'), array('sin', 'pi'), $tchk);
} else {
$cpts = parsecomplex($tchk);
if (!is_array($cpts)) {
return 0;
}
if ($cpts[1][0] == '+') {
$cpts[1] = substr($cpts[1], 1);
}
//echo $cpts[0].','.$cpts[1].'<br/>';
if ($answer != 'DNE' && (!checkanswerformat($cpts[0], $ansformats) || !checkanswerformat($cpts[1], $ansformats))) {
return 0;
}
if ($answer != 'DNE' && isset($requiretimeslistpart) && checkreqtimes($tchk, $requiretimeslistpart) == 0) {
return 0;
}
}
}
}
}
if (!isset($answerformat)) {
$answerformat = '';
}
$ansformats = explode(',', $answerformat);
if ($givenans == null) {
return 0;
}
$answer = str_replace(' ', '', makepretty($answer));
$givenans = str_replace(' ', '', $givenans);
if ($answer == 'DNE' && strtoupper($givenans) == 'DNE') {
return 1;
}
$gaarr = explode(',', $givenans);
$anarr = explode(',', $answer);
if (count($gaarr) == 0) {
return 0;
}
$extrapennum = count($gaarr) + count($anarr);
$correct = 0;
foreach ($anarr as $i => $answer) {
$cparts = parsecomplex($answer);
if (!is_array($cparts)) {
$ansparts = parsesloppycomplex($answer);
} else {
$ansparts[0] = eval('return (' . mathphp($cparts[0], null) . ');');
$ansparts[1] = eval('return (' . mathphp($cparts[1], null) . ');');
}
$foundloc = -1;
foreach ($gaarr as $j => $givenans) {
$cparts = parsecomplex($givenans);
if (!is_array($cparts)) {
return 0;
} else {
$gaparts[0] = floatval($cparts[0]);
$gaparts[1] = floatval($cparts[1]);
}
if (count($ansparts) != count($gaparts)) {
break;
}
for ($i = 0; $i < count($ansparts); $i++) {
if (is_numeric($ansparts[$i]) && is_numeric($gaparts[$i])) {
if (isset($abstolerance)) {
if (abs($ansparts[$i] - $gaparts[$i]) >= $abstolerance + 1.0E-12) {
break;
}
} else {
if (abs($ansparts[$i] - $gaparts[$i]) / (abs($ansparts[$i]) + 0.0001) >= $reltolerance + 1.0E-12) {
break;
}
}
}
}
if ($i == count($ansparts)) {
$correct += 1;
$foundloc = $j;
break;
}
}
if ($foundloc > -1) {
array_splice($gaarr, $foundloc, 1);
// remove from list
if (count($gaarr) == 0) {
break;
}
}
}
$score = $correct / count($anarr) - count($gaarr) / $extrapennum;
if ($score < 0) {
$score = 0;
}
return $score;
} else {
if ($anstype == "calculated") {
if (is_array($options['answer'])) {
$answer = $options['answer'][$qn];
} else {
$answer = $options['answer'];
}
if (isset($options['reltolerance'])) {
if (is_array($options['reltolerance'])) {
$reltolerance = $options['reltolerance'][$qn];
} else {
$reltolerance = $options['reltolerance'];
}
}
if (isset($options['abstolerance'])) {
if (is_array($options['abstolerance'])) {
$abstolerance = $options['abstolerance'][$qn];
} else {
$abstolerance = $options['abstolerance'];
}
}
if (isset($options['answerformat'])) {
if (is_array($options['answerformat'])) {
$answerformat = $options['answerformat'][$qn];
} else {
$answerformat = $options['answerformat'];
}
}
if (isset($options['requiretimes'])) {
if (is_array($options['requiretimes'])) {
$requiretimes = $options['requiretimes'][$qn];
} else {
$requiretimes = $options['requiretimes'];
}
}
if (isset($options['requiretimeslistpart'])) {
if (is_array($options['requiretimeslistpart'])) {
$requiretimeslistpart = $options['requiretimeslistpart'][$qn];
} else {
$requiretimeslistpart = $options['requiretimeslistpart'];
}
}
if (!isset($reltolerance) && !isset($abstolerance)) {
$reltolerance = $defaultreltol;
}
if ($multi > 0) {
$qn = $multi * 1000 + $qn;
}
$givenans = str_replace(array('∞', '⁄ '), array('oo', '/'), $givenans);
$GLOBALS['partlastanswer'] = $_POST["tc{$qn}"] . '$#$' . $givenans;
$_POST["tc{$qn}"] = str_replace(array('∞', '⁄ '), array('oo', '/'), $_POST["tc{$qn}"]);
if ($answer === '') {
if (trim($_POST["tc{$qn}"]) === '') {
return 1;
} else {
return 0;
}
}
if ($givenans == null) {
return 0;
}
$formatok = "all";
if (checkreqtimes($_POST["tc{$qn}"], $requiretimes) == 0) {
//return 0;
$formatok = "nowhole";
}
$ansformats = explode(',', $answerformat);
if (in_array("scinot", $ansformats)) {
$answer = str_replace('xx', '*', $answer);
}
//pre-evaluate all instructor expressions - preg match all intervals. Return array of or options
if (in_array('exactlist', $ansformats) || in_array('orderedlist', $ansformats) || in_array('list', $ansformats)) {
$anarr = explode(',', $answer);
foreach ($anarr as $k => $ananswer) {
$aarr = explode(' or ', $ananswer);
foreach ($aarr as $j => $anans) {
if ($anans == '') {
if (isset($GLOBALS['teacherid'])) {
echo '<p>', _('Debug info: empty, missing or invalid $answer'), ' </p>';
}
return 0;
}
if (preg_match('/(\\(|\\[)([\\d\\.]+)\\,([\\d\\.]+)(\\)|\\])/', $anans, $matches)) {
$aarr[$j] = $matches;
} else {
if (!is_numeric($anans) && $anans != 'DNE' && $anans != 'oo' && $anans != '+oo' && $anans != '-oo') {
$aarr[$j] = eval('return(' . mathphp($anans, null) . ');');
}
}
}
$anarr[$k] = $aarr;
}
} else {
$aarr = explode(' or ', $answer);
foreach ($aarr as $j => $anans) {
if ($anans == '') {
if (isset($GLOBALS['teacherid'])) {
echo '<p>', _('Debug info: empty, missing, or invalid $answer'), ' </p>';
}
return 0;
}
if (preg_match('/(\\(|\\[)([\\d\\.]+)\\,([\\d\\.]+)(\\)|\\])/', $anans, $matches)) {
$aarr[$j] = $matches;
} else {
if (!is_numeric($anans) && $anans != 'DNE' && $anans != 'oo' && $anans != '+oo' && $anans != '-oo') {
if ((in_array("mixednumber", $ansformats) || in_array("sloppymixednumber", $ansformats) || in_array("mixednumberorimproper", $ansformats)) && preg_match('/^\\s*(\\-?\\s*\\d+)\\s*(_|\\s)\\s*(\\d+)\\s*\\/\\s*(\\d+)\\s*$/', $anans, $mnmatches)) {
$aarr[$j] = $mnmatches[1] + ($mnmatches[1] < 0 ? -1 : 1) * ($mnmatches[3] / $mnmatches[4]);
} else {
$aarr[$j] = eval('return(' . mathphp($anans, null) . ');');
}
}
}
}
$answer = $aarr;
}
if (in_array('exactlist', $ansformats)) {
$gaarr = explode(',', $givenans);
//$anarr = explode(',',$answer);
$orarr = explode(',', $_POST["tc{$qn}"]);
} else {
if (in_array('orderedlist', $ansformats)) {
$gamasterarr = explode(',', $givenans);
$gaarr = $gamasterarr;
//$anarr = explode(',',$answer);
$orarr = explode(',', $_POST["tc{$qn}"]);
} else {
if (in_array('list', $ansformats)) {
$tmp = explode(',', $givenans);
$tmpor = explode(',', $_POST["tc{$qn}"]);
asort($tmp);
$lastval = null;
foreach ($tmp as $i => $v) {
if ($lastval === null) {
$gaarr[] = $tmp[$i];
$orarr[] = $tmpor[$i];
} else {
if ($v - $lastval > 1.0E-12) {
$gaarr[] = $tmp[$i];
$orarr[] = $tmpor[$i];
}
}
$lastval = $v;
}
$tmp = $anarr;
sort($tmp);
$anarr = array($tmp[0]);
for ($i = 1; $i < count($tmp); $i++) {
if (!is_numeric($tmp[$i]) || !is_numeric($tmp[$i - 1]) || $tmp[$i] - $tmp[$i - 1] > 1.0E-12) {
$anarr[] = $tmp[$i];
}
}
} else {
$gaarr = array(str_replace(',', '', $givenans));
$anarr = array($answer);
$orarr = array($_POST["tc{$qn}"]);
}
}
}
$extrapennum = count($gaarr) + count($anarr);
$gaarrcnt = count($gaarr);
if (in_array('orderedlist', $ansformats)) {
if (count($gamasterarr) != count($anarr)) {
return 0;
}
}
$correct = 0;
foreach ($anarr as $i => $anss) {
$foundloc = -1;
if (in_array('orderedlist', $ansformats)) {
$gaarr = array($gamasterarr[$i]);
}
foreach ($gaarr as $j => $givenans) {
$partformatok = true;
if (!checkanswerformat($orarr[$j], $ansformats)) {
$formatok = "nopart";
$partformatok = false;
//continue;
}
if (isset($requiretimeslistpart) && checkreqtimes($orarr[$j], $requiretimeslistpart) == 0) {
$formatok = "nopart";
$partformatok = false;
//continue;
}
//removed - done above already
//$anss = explode(' or ',$answer);
foreach ($anss as $anans) {
if (!is_numeric($anans)) {
$givenans = trim($givenans);
/* moved to preprocessing
if (preg_match('/(\(|\[)([\d\.]+)\,([\d\.]+)(\)|\])/',$anans,$matches)) {
if (($matches[1]=="(" && $givenans>$matches[2]) || ($matches[1]=="[" && $givenans>=$matches[2])) {
if (($matches[4]==")" && $givenans<$matches[3]) || ($matches[4]=="]" && $givenans<=$matches[3])) {
$correct += 1; $foundloc = $j; break 2;
}
}
} */
if (is_array($anans)) {
if ($anans[1] == "(" && $givenans > $anans[2] || $anans[1] == "[" && $givenans >= $anans[2]) {
if ($anans[4] == ")" && $givenans < $anans[3] || $anans[4] == "]" && $givenans <= $anans[3]) {
if ($partformatok) {
$correct += 1;
}
$foundloc = $j;
break 2;
}
}
} else {
if ($anans == "DNE" && strtoupper($givenans) == "DNE") {
if ($partformatok) {
$correct += 1;
}
$foundloc = $j;
break 2;
} else {
if (($anans == "+oo" || $anans == "oo") && ($givenans == "+oo" || $givenans == "oo")) {
if ($partformatok) {
$correct += 1;
}
$foundloc = $j;
break 2;
} else {
if ($anans == "-oo" && $givenans == "-oo") {
if ($partformatok) {
$correct += 1;
}
$foundloc = $j;
break 2;
}
}
}
}
/* moved to preprocessing
else if (is_numeric($givenans)) {
//try evaling answer
$eanans = eval('return('.mathphp($anans,null).');');
if (isset($abstolerance)) {
if (abs($eanans-$givenans) < $abstolerance+1E-12) {$correct += 1; $foundloc = $j; break 2;}
} else {
if (abs($eanans - $givenans)/(abs($eanans)+.0001) < $reltolerance+1E-12) {$correct += 1; $foundloc = $j; break 2;}
}
}*/
} else {
if (is_numeric($givenans)) {
if (isset($abstolerance)) {
if (abs($anans - $givenans) < $abstolerance + ($anans == 0 || abs($anans) > 1 ? 1.0E-12 : abs($anans) * 1.0E-12)) {
if ($partformatok) {
$correct += 1;
}
$foundloc = $j;
break 2;
}
} else {
if ($anans == 0) {
if (abs($anans - $givenans) < $reltolerance / 1000 + 1.0E-12) {
if ($partformatok) {
$correct += 1;
}
$foundloc = $j;
break 2;
}
} else {
if (abs($anans - $givenans) / (abs($anans) + (abs($anans) > 1 ? 1.0E-12 : abs($anans) * 1.0E-12)) < $reltolerance + 1.0E-12) {
if ($partformatok) {
$correct += 1;
}
$foundloc = $j;
break 2;
}
}
}
}
}
}
}
if ($foundloc > -1) {
array_splice($gaarr, $foundloc, 1);
//remove from list
array_splice($orarr, $foundloc, 1);
if (count($gaarr) == 0 && !in_array('orderedlist', $ansformats)) {
break;
//stop if no student answers left
}
}
}
if (in_array('orderedlist', $ansformats)) {
$score = $correct / count($anarr);
} else {
//$score = $correct/count($anarr) - count($gaarr)/$extrapennum; //take off points for extranous stu answers
if ($gaarrcnt <= count($anarr)) {
$score = $correct / count($anarr);
} else {
$score = $correct / count($anarr) - ($gaarrcnt - count($anarr)) / $extrapennum;
//take off points for extranous stu answers
}
}
if ($score < 0) {
$score = 0;
}
if ($formatok != "all") {
$GLOBALS['partlastanswer'] .= '$f$1';
if ($formatok == 'nowhole') {
$score = 0;
}
}
return $score;
} else {
if ($anstype == "numfunc") {
if (is_array($options['answer'])) {
$answer = $options['answer'][$qn];
} else {
$answer = $options['answer'];
}
if (isset($options['reltolerance'])) {
if (is_array($options['reltolerance'])) {
$reltolerance = $options['reltolerance'][$qn];
} else {
$reltolerance = $options['reltolerance'];
}
}
if (isset($options['abstolerance'])) {
if (is_array($options['abstolerance'])) {
$abstolerance = $options['abstolerance'][$qn];
} else {
$abstolerance = $options['abstolerance'];
}
}
if (!isset($reltolerance) && !isset($abstolerance)) {
$reltolerance = $defaultreltol;
}
if (is_array($options['variables'])) {
$variables = $options['variables'][$qn];
} else {
$variables = $options['variables'];
}
if (isset($options['domain'])) {
if (is_array($options['domain'])) {
$domain = $options['domain'][$qn];
} else {
$domain = $options['domain'];
}
}
if (isset($options['requiretimes'])) {
if (is_array($options['requiretimes'])) {
$requiretimes = $options['requiretimes'][$qn];
} else {
$requiretimes = $options['requiretimes'];
}
}
if (isset($options['answerformat'])) {
if (is_array($options['answerformat'])) {
$answerformat = $options['answerformat'][$qn];
} else {
$answerformat = $options['answerformat'];
}
}
if ($multi > 0) {
$qn = $multi * 1000 + $qn;
}
$GLOBALS['partlastanswer'] = $_POST["tc{$qn}"];
$correct = true;
if (!isset($variables)) {
$variables = "x";
}
$variables = explode(",", $variables);
$ofunc = array();
for ($i = 0; $i < count($variables); $i++) {
$variables[$i] = trim($variables[$i]);
//find f() function variables
if (strpos($variables[$i], '(') !== false) {
$ofunc[] = substr($variables[$i], 0, strpos($variables[$i], '('));
$variables[$i] = substr($variables[$i], 0, strpos($variables[$i], '('));
}
}
if (count($ofunc) > 0) {
$flist = implode("|", $ofunc);
$answer = preg_replace('/(' . $flist . ')\\(/', "\$1*sin(\$1+", $answer);
}
if (($v = array_search('E', $variables)) !== false) {
$variables[$v] = 'varE';
$answer = str_replace('E', 'varE', $answer);
}
$vlist = implode("|", $variables);
if (isset($domain)) {
$fromto = explode(",", $domain);
} else {
$fromto[0] = -10;
$fromto[1] = 10;
}
for ($i = 0; $i < 20; $i++) {
for ($j = 0; $j < count($variables); $j++) {
if (isset($fromto[2]) && $fromto[2] == "integers") {
$tps[$i][$j] = rand($fromto[0], $fromto[1]);
} else {
if (isset($fromto[2 * $j + 1])) {
$tps[$i][$j] = $fromto[2 * $j] + ($fromto[2 * $j + 1] - $fromto[2 * $j]) * rand(0, 499) / 500.0 + 0.001;
} else {
$tps[$i][$j] = $fromto[0] + ($fromto[1] - $fromto[0]) * rand(0, 499) / 500.0 + 0.001;
}
}
}
}
if ($answerformat != "equation" && strpos($answer, '=') !== false) {
echo 'Your $answer contains an equal sign, but you do not have $answerformat="equation" set. This question probably will not work right.';
}
$ansarr = explode(' or ', $answer);
foreach ($ansarr as $answer) {
$correct = true;
$answer = preg_replace('/[^\\w\\*\\/\\+\\=\\-\\(\\)\\[\\]\\{\\}\\,\\.\\^\\$\\!\\s]+/', '', $answer);
if ($answerformat == "equation") {
if (substr_count($_POST["tc{$qn}"], '=') != 1) {
return 0;
}
$answer = preg_replace('/(.*)=(.*)/', '$1-($2)', $answer);
unset($ratios);
} else {
if ($answerformat == "toconst") {
unset($diffs);
unset($realanss);
}
}
if ($answer == '') {
return 0;
}
$answer = mathphppre($answer);
$answer = makepretty($answer);
$answer = mathphp($answer, $vlist);
for ($i = 0; $i < count($variables); $i++) {
$answer = str_replace("(" . $variables[$i] . ")", '($tp[' . $i . '])', $answer);
}
$myans = explode(",", $_POST["qn{$qn}-vals"]);
$cntnan = 0;
$cntzero = 0;
$cntbothzero = 0;
$stunan = 0;
$ysqrtot = 0;
$reldifftot = 0;
for ($i = 0; $i < 20; $i++) {
for ($j = 0; $j < count($variables); $j++) {
//causing problems on multipart - breaking messed up rand order
/* if (isset($fromto[2]) && $fromto[2]=="integers") {
$tp[$j] = rand($fromto[0],$fromto[1]);
} else {
$tp[$j] = $fromto[0] + ($fromto[1]-$fromto[0])*rand(0,32000)/32000.0;
}
*/
$tp[$j] = $tps[$i][$j];
}
$realans = eval("return ({$answer});");
//echo "$answer, real: $realans, my: {$myans[$i]},rel: ". (abs($myans[$i]-$realans)/abs($realans)) ."<br/>";
if (isNaN($realans)) {
$cntnan++;
continue;
}
//avoid NaN problems
if ($answerformat == "equation") {
//if equation, store ratios
if (abs($realans) > 1.0E-6 && is_numeric($myans[$i])) {
$ratios[] = $myans[$i] / $realans;
if (abs($myans[$i]) <= 1.0E-8 && $realans != 0) {
$cntzero++;
}
} else {
if (abs($realans) <= 1.0E-6 && is_numeric($myans[$i]) && abs($myans[$i]) <= 1.0E-8) {
$cntbothzero++;
}
}
} else {
if ($answerformat == "toconst") {
$diffs[] = $myans[$i] - $realans;
$realanss[] = $realans;
$ysqr = $realans * $realans;
$ysqrtot += 1 / ($ysqr + 0.0001);
$reldifftot += ($myans[$i] - $realans) / ($ysqr + 0.0001);
} else {
//otherwise, compare points
if (isNaN($myans[$i])) {
$stunan++;
} else {
if (isset($abstolerance)) {
if (abs($myans[$i] - $realans) > $abstolerance - 1.0E-12) {
$correct = false;
break;
}
} else {
if (abs($myans[$i] - $realans) / (abs($realans) + 0.0001) > $reltolerance - 1.0E-12) {
$correct = false;
break;
}
}
}
}
}
}
if ($cntnan == 20 && isset($GLOBALS['teacherid'])) {
echo "<p>", _('Debug info: function evaled to Not-a-number at all test points. Check $domain'), "</p>";
}
if ($stunan > 1) {
//if more than 1 student NaN response
return 0;
}
if ($answerformat == "equation") {
if ($cntbothzero > 18) {
$correct = true;
} else {
if (count($ratios) > 1) {
if (count($ratios) == $cntzero) {
$correct = false;
return 0;
} else {
$meanratio = array_sum($ratios) / count($ratios);
for ($i = 0; $i < count($ratios); $i++) {
if (isset($abstolerance)) {
if (abs($ratios[$i] - $meanratio) > $abstolerance - 1.0E-12) {
$correct = false;
break;
}
} else {
if (abs($ratios[$i] - $meanratio) / (abs($meanratio) + 0.0001) > $reltolerance - 1.0E-12) {
$correct = false;
break;
}
}
}
}
} else {
$correct = false;
}
}
} else {
if ($answerformat == "toconst") {
if (isset($abstolerance)) {
//if abs, use mean diff - will minimize error in abs diffs
$meandiff = array_sum($diffs) / count($diffs);
} else {
//if relative tol, use meandiff to minimize relative error
$meandiff = $reldifftot / $ysqrtot;
}
if (is_nan($meandiff)) {
$correct = false;
return 0;
}
for ($i = 0; $i < count($diffs); $i++) {
if (isset($abstolerance)) {
if (abs($diffs[$i] - $meandiff) > $abstolerance - 1.0E-12) {
$correct = false;
break;
}
} else {
//if ((abs($diffs[$i]-$meandiff)/(abs($meandiff)+0.0001) > $reltolerance-1E-12)) {$correct = false; break;}
if (abs($diffs[$i] - $meandiff) / (abs($realanss[$i]) + 0.0001) > $reltolerance - 1.0E-12) {
$correct = false;
break;
}
}
}
}
}
if ($correct == true) {
//test for correct format, if specified
if (checkreqtimes(str_replace(',', '', $_POST["tc{$qn}"]), $requiretimes) == 0) {
$GLOBALS['partlastanswer'] .= '$f$1';
return 0;
//$correct = false;
}
return 1;
}
}
return 0;
} else {
if ($anstype == "string") {
if (is_array($options['answer'])) {
$answer = $options['answer'][$qn];
} else {
$answer = $options['answer'];
}
if (is_array($options['strflags'])) {
$strflags = $options['strflags'][$qn];
} else {
$strflags = $options['strflags'];
}
if (isset($options['scoremethod'])) {
if (is_array($options['scoremethod'])) {
$scoremethod = $options['scoremethod'][$qn];
} else {
$scoremethod = $options['scoremethod'];
}
}
if (isset($options['answerformat'])) {
if (is_array($options['answerformat'])) {
$answerformat = $options['answerformat'][$qn];
} else {
$answerformat = $options['answerformat'];
}
}
if ($multi > 0) {
$qn = $multi * 1000 + $qn;
}
$GLOBALS['partlastanswer'] = $givenans;
if (isset($scoremethod) && $scoremethod == 'takeanything' && trim($givenans) != '') {
return 1;
}
$givenans = stripslashes($givenans);
if (!isset($answerformat)) {
$answerformat = "normal";
}
if ($answerformat == 'list') {
$gaarr = explode(',', $givenans);
$anarr = explode(',', $answer);
} else {
$gaarr = array($givenans);
$anarr = array($answer);
}
$strflags = str_replace(' ', '', $strflags);
$strflags = explode(",", $strflags);
$torem = array();
foreach ($strflags as $flag) {
$pc = explode('=', $flag);
if ($pc[0] == 'ignore_symbol') {
$torem[] = $pc[1];
continue;
}
if ($pc[1] === 'true' || $pc[1] === '1' || $pc[1] === 1) {
$pc[1] = true;
}
$flags[$pc[0]] = $pc[1];
}
if (!isset($flags['compress_whitespace'])) {
$flags['compress_whitespace'] = true;
}
if (!isset($flags['ignore_case'])) {
$flags['ignore_case'] = true;
}
$correct = 0;
foreach ($anarr as $i => $answer) {
$foundloc = -1;
if (count($torem) > 0) {
$answer = str_replace($torem, ' ', $answer);
}
foreach ($gaarr as $j => $givenans) {
$givenans = trim($givenans);
if (count($torem) > 0) {
$givenans = str_replace($torem, ' ', $givenans);
}
if ($flags['ignore_commas'] === true) {
$givenans = str_replace(',', '', $givenans);
$answer = str_replace(',', '', $answer);
}
if ($flags['compress_whitespace'] === true) {
$givenans = preg_replace('/\\s+/', ' ', $givenans);
$answer = preg_replace('/\\s+/', ' ', $answer);
}
if ($flags['trim_whitespace'] === true || $flags['compress_whitespace'] === true) {
$givenans = trim($givenans);
$answer = trim($answer);
}
if ($flags['remove_whitespace'] === true) {
$givenans = trim(preg_replace('/\\s+/', '', $givenans));
}
$specialor = false;
if ($flags['special_or'] === true) {
$specialor = true;
}
if ($flags['ignore_case'] === true) {
$givenans = strtoupper($givenans);
$answer = strtoupper($answer);
if ($specialor) {
$anss = explode(' *OR* ', $answer);
} else {
$anss = explode(' OR ', $answer);
}
} else {
if ($specialor) {
$anss = explode(' *or* ', $answer);
} else {
$anss = explode(' or ', $answer);
}
}
if ($flags['ignore_order']) {
$givenans = explode("\n", chunk_split($givenans, 1, "\n"));
sort($givenans, SORT_STRING);
$givenans = implode('', $givenans);
}
foreach ($anss as $anans) {
if ($flags['ignore_order'] === true) {
$anans = explode("\n", chunk_split($anans, 1, "\n"));
sort($anans, SORT_STRING);
$anans = implode('', $anans);
}
if ($flags['trim_whitespace'] === true || $flags['compress_whitespace'] === true) {
$anans = trim($anans);
}
if ($flags['remove_whitespace'] === true) {
$anans = trim(preg_replace('/\\s+/', '', $anans));
}
if ($flags['partial_credit'] === true && $answerformat != 'list') {
$poss = strlen($anans);
$dist = levenshtein($anans, $givenans);
$score = ($poss - $dist) / $poss;
if ($score > $correct) {
$correct = $score;
}
} else {
if (isset($flags['allow_diff'])) {
if (levenshtein($anans, $givenans) <= 1 * $flags['allow_diff']) {
$correct += 1;
$foundloc = $j;
break 2;
}
} else {
if (isset($flags['in_answer'])) {
if (strpos($givenans, $anans) !== false) {
$correct += 1;
$foundloc = $j;
break 2;
}
} else {
if (!strcmp($anans, $givenans)) {
$correct += 1;
$foundloc = $j;
break 2;
}
}
}
}
}
}
if ($foundloc > -1) {
array_splice($gaarr, $foundloc, 1);
//remove from list
if (count($gaarr) == 0) {
break;
//stop if no student answers left
}
}
}
$score = $correct / count($anarr);
if ($score < 0) {
$score = 0;
}
return $score;
//return $correct;
} else {
if ($anstype == "essay") {
require_once "../includes/htmLawed.php";
$htmlawedconfig = array('elements' => '*-script-form');
$givenans = addslashes(htmLawed(stripslashes($givenans), $htmlawedconfig));
$givenans = preg_replace('/&(\\w+;)/', "%\$1", $givenans);
$GLOBALS['partlastanswer'] = $givenans;
if (isset($options['scoremethod'])) {
if (is_array($options['scoremethod'])) {
$scoremethod = $options['scoremethod'][$qn];
} else {
$scoremethod = $options['scoremethod'];
}
}
if (isset($scoremethod) && $scoremethod == 'takeanything' && trim($givenans) != '') {
return 1;
} else {
if (trim($givenans) == '') {
return 0;
} else {
return -2;
}
}
} else {
if ($anstype == 'interval' || $anstype == 'calcinterval') {
if (is_array($options['answer'])) {
$answer = $options['answer'][$qn];
} else {
$answer = $options['answer'];
}
if (isset($options['reltolerance'])) {
if (is_array($options['reltolerance'])) {
$reltolerance = $options['reltolerance'][$qn];
} else {
$reltolerance = $options['reltolerance'];
}
}
if (isset($options['abstolerance'])) {
if (is_array($options['abstolerance'])) {
$abstolerance = $options['abstolerance'][$qn];
} else {
$abstolerance = $options['abstolerance'];
}
}
if (isset($options['answerformat'])) {
if (is_array($options['answerformat'])) {
$answerformat = $options['answerformat'][$qn];
} else {
$answerformat = $options['answerformat'];
}
}
if (isset($options['requiretimes'])) {
if (is_array($options['requiretimes'])) {
$requiretimes = $options['requiretimes'][$qn];
} else {
$requiretimes = $options['requiretimes'];
}
}
if (isset($options['variables'])) {
if (is_array($options['variables'])) {
$variables = $options['variables'][$qn];
} else {
$variables = $options['variables'];
}
}
if (!isset($variables)) {
$variables = 'x';
}
if (!isset($reltolerance) && !isset($abstolerance)) {
$reltolerance = $defaultreltol;
}
if ($multi > 0) {
$qn = $multi * 1000 + $qn;
}
$ansformats = explode(',', $answerformat);
$givenans = str_replace('∞', 'oo', $givenans);
$givenans = str_replace(array('（', '）'), array('(', ')'), $givenans);
if ($anstype == 'interval') {
$GLOBALS['partlastanswer'] = $givenans;
} else {
if ($anstype == 'calcinterval') {
$GLOBALS['partlastanswer'] = $_POST["tc{$qn}"];
//test for correct format, if specified
if (checkreqtimes($_POST["tc{$qn}"], $requiretimes) == 0) {
return 0;
}
if (in_array('inequality', $ansformats)) {
$_POST["tc{$qn}"] = str_replace('or', ' or ', $_POST["tc{$qn}"]);
preg_match_all('/([a-zA-Z]\\(\\s*[a-zA-Z]\\s*\\)|[a-zA-Z]+)/', $_POST["tc{$qn}"], $matches);
foreach ($matches[0] as $var) {
$var = str_replace(' ', '', $var);
if (in_array($var, $mathfuncs)) {
continue;
}
if ($var != 'or' && $var != 'and' && $var != $variables && $_POST["qn{$qn}"] != "(-oo,oo)") {
return 0;
}
}
$orarr = explode(' or ', $_POST["tc{$qn}"]);
foreach ($orarr as $opt) {
$opt = trim($opt);
if ($opt == 'DNE' || $givenans == '(-oo,oo)') {
continue;
}
//DNE or all real numbers
$opts = preg_split('/(<=?|>=?)/', $opt);
foreach ($opts as $optp) {
$optp = trim($optp);
if ($optp == $variables) {
continue;
}
if (!checkanswerformat($optp, $ansformats)) {
return 0;
}
}
}
} else {
if (in_array('list', $ansformats)) {
$orarr = preg_split('/(?<=[\\)\\]]),(?=[\\(\\[])/', $_POST["tc{$qn}"]);
} else {
$orarr = explode('U', $_POST["tc{$qn}"]);
}
foreach ($orarr as $opt) {
$opt = trim($opt);
if ($opt == 'DNE') {
continue;
}
$opts = explode(',', substr($opt, 1, strlen($opt) - 2));
if (strpos($opts[0], 'oo') === false && !checkanswerformat($opts[0], $ansformats)) {
return 0;
}
if (strpos($opts[1], 'oo') === false && !checkanswerformat($opts[1], $ansformats)) {
return 0;
}
}
}
}
}
if ($givenans == null) {
return 0;
}
$correct = 0;
$ansar = explode(' or ', $answer);
$givenans = str_replace(' ', '', $givenans);
foreach ($ansar as $anans) {
$answer = str_replace(' ', '', $anans);
if ($anans === 'DNE') {
if ($givenans === 'DNE') {
$correct = 1;
break;
} else {
continue;
}
}
if (in_array('list', $ansformats)) {
$aarr = preg_split('/(?<=[\\)\\]]),(?=[\\(\\[])/', $anans);
$gaarr = preg_split('/(?<=[\\)\\]]),(?=[\\(\\[])/', $givenans);
} else {
$aarr = explode('U', $anans);
$gaarr = explode('U', $givenans);
}
if (count($aarr) != count($gaarr)) {
continue;
}
foreach ($aarr as $ansint) {
$ansint = trim($ansint);
$anssm = substr($ansint, 0, 1);
$ansem = substr($ansint, -1);
$ansint = substr($ansint, 1, strlen($ansint) - 2);
list($anssn, $ansen) = explode(',', $ansint);
if (!is_numeric($anssn) && strpos($anssn, 'oo') === false) {
$anssn = eval('return(' . mathphp($anssn, null) . ');');
}
if (!is_numeric($ansen) && strpos($ansen, 'oo') === false) {
$ansen = eval('return(' . mathphp($ansen, null) . ');');
}
$foundloc = -1;
foreach ($gaarr as $k => $gansint) {
$gansint = trim($gansint);
$ganssm = substr($gansint, 0, 1);
$gansem = substr($gansint, -1);
$gansint = substr($gansint, 1, strlen($gansint) - 2);
list($ganssn, $gansen) = explode(',', $gansint);
if ($anssm != $ganssm || $ansem != $gansem) {
continue;
}
if (strpos($anssn, 'oo') !== false) {
$anssn = trim($anssn);
if (($anssn == 'oo' || $anssn == '+oo') && ($ganssn == 'oo' || $ganssn == '+oo')) {
} else {
if ($anssn == '-oo' && $ganssn == '-oo') {
} else {
continue;
}
}
//if ($anssn===$ganssn) {} else {continue;}
} else {
if (isset($abstolerance)) {
if (abs($anssn - $ganssn) < $abstolerance + 1.0E-12) {
} else {
continue;
}
} else {
if (abs($anssn - $ganssn) / (abs($anssn) + 0.0001) < $reltolerance + 1.0E-12) {
} else {
continue;
}
}
}
if (strpos($ansen, 'oo') !== false) {
$ansen = trim($ansen);
if (($ansen == 'oo' || $ansen == '+oo') && ($gansen == 'oo' || $gansen == '+oo')) {
} else {
if ($ansen == '-oo' && $gansen == '-oo') {
} else {
continue;
}
}
//if ($ansen===$gansen) {} else {continue;}
} else {
if (isset($abstolerance)) {
if (abs($ansen - $gansen) < $abstolerance + 1.0E-12) {
} else {
continue;
}
} else {
if (abs($ansen - $gansen) / (abs($ansen) + 0.0001) < $reltolerance + 1.0E-12) {
} else {
continue;
}
}
}
$foundloc = $k;
break;
}
if ($foundloc > -1) {
array_splice($gaarr, $foundloc, 1);
} else {
continue 2;
}
}
if (count($gaarr) > 0) {
//extraneous student intervals?
continue 2;
}
$correct = 1;
break;
}
return $correct;
} else {
if ($anstype == 'draw') {
if ($multi > 0) {
if (isset($options['grid'][$qn])) {
$grid = $options['grid'][$qn];
}
if (isset($options['snaptogrid'][$qn])) {
$snaptogrid = $options['snaptogrid'][$qn];
}
if (isset($options['answers'][$qn])) {
$answers = $options['answers'][$qn];
} else {
if (isset($options['answer'][$qn])) {
$answers = $options['answer'][$qn];
}
}
if (isset($options['partweights'][$qn])) {
$partweights = $options['partweights'][$qn];
}
} else {
if (isset($options['grid'])) {
$grid = $options['grid'];
}
if (isset($options['snaptogrid'])) {
$snaptogrid = $options['snaptogrid'];
}
if (isset($options['answers'])) {
$answers = $options['answers'];
} else {
if (isset($options['answer'])) {
$answers = $options['answer'];
}
}
if (isset($options['partweights'])) {
$partweights = $options['partweights'];
}
}
if (isset($options['reltolerance'])) {
if (is_array($options['reltolerance'])) {
$reltolerance = $options['reltolerance'][$qn];
} else {
$reltolerance = $options['reltolerance'];
}
}
if (isset($options['abstolerance'])) {
if (is_array($options['abstolerance'])) {
$abstolerance = $options['abstolerance'][$qn];
} else {
$abstolerance = $options['abstolerance'];
}
}
if (isset($options['answerformat'])) {
if (is_array($options['answerformat'])) {
$answerformat = $options['answerformat'][$qn];
} else {
$answerformat = $options['answerformat'];
}
}
if (!isset($reltolerance)) {
if (isset($GLOBALS['CFG']['AMS']['defaultdrawtol'])) {
$reltolerance = $GLOBALS['CFG']['AMS']['defaultdrawtol'];
} else {
$reltolerance = 1;
}
}
if ($multi > 0) {
$qn = $multi * 1000 + $qn;
}
$GLOBALS['partlastanswer'] = $givenans;
$imgborder = 5;
$step = 5;
if (!isset($answerformat)) {
$answerformat = array('line', 'dot', 'opendot');
} else {
if (!is_array($answerformat)) {
$answerformat = explode(',', $answerformat);
}
}
if ($answerformat[0] == 'numberline') {
$settings = array(-5, 5, -0.5, 0.5, 1, 0, 300, 50);
} else {
$settings = array(-5, 5, -5, 5, 1, 1, 300, 300);
}
if (isset($grid)) {
if (!is_array($grid)) {
$grid = explode(',', $grid);
}
for ($i = 0; $i < count($grid); $i++) {
if ($grid[$i] != '') {
$settings[$i] = evalbasic($grid[$i]);
}
}
}
if ($answerformat[0] == 'numberline') {
$settings[2] = -0.5;
$settings[3] = 0.5;
}
if ($snaptogrid > 0) {
list($newwidth, $newheight) = getsnapwidthheight($settings[0], $settings[1], $settings[2], $settings[3], $settings[6], $settings[7], $snaptogrid);
if (($newwidth - $settings[6]) / $settings[6] < 0.1) {
$settings[6] = $newwidth;
}
if (($newheight - $settings[7]) / $settings[7] < 0.1) {
$settings[7] = $newheight;
}
}
$pixelsperx = ($settings[6] - 2 * $imgborder) / ($settings[1] - $settings[0]);
$pixelspery = ($settings[7] - 2 * $imgborder) / ($settings[3] - $settings[2]);
$xtopix = create_function('$x', "return ((\$x - ({$settings[0]}))*({$pixelsperx}) + ({$imgborder}));");
$ytopix = create_function('$y', "return (({$settings[7]}) - (\$y- ({$settings[2]}))*({$pixelspery}) - ({$imgborder}));");
$anslines = array();
$ansdots = array();
$ansodots = array();
$anslineptcnt = array();
$types = array();
$extrastuffpenalty = 0;
$linepts = 0;
if (is_array($answers) && count($answers) == 0 || !is_array($answers) && $answers == '') {
if ($givenans == ';;;;;;;;') {
return 1;
} else {
return 0;
}
}
if (!is_array($answers)) {
settype($answers, "array");
}
if ($answerformat[0] == "polygon" || $answerformat[0] == 'closedpolygon') {
foreach ($answers as $key => $function) {
$function = explode(',', $function);
$pixx = ($function[0] - $settings[0]) * $pixelsperx + $imgborder;
$pixy = $settings[7] - ($function[1] - $settings[2]) * $pixelspery - $imgborder;
$ansdots[$key] = array($pixx, $pixy);
}
$isclosed = false;
if (abs($ansdots[0][0] - $ansdots[count($ansdots) - 1][0]) < 0.01 && abs($ansdots[0][1] - $ansdots[count($ansdots) - 1][1]) < 0.01) {
$isclosed = true;
array_pop($ansdots);
}
list($lines, $dots, $odots, $tplines, $ineqlines) = explode(';;', $givenans);
if ($lines == '') {
$line = array();
} else {
$lines = explode(';', $lines);
$line = $lines[0];
//only use first line
$line = explode('),(', substr($line, 1, strlen($line) - 2));
foreach ($line as $j => $pt) {
$line[$j] = explode(',', $pt);
}
if ($isclosed && ($line[0][0] - $line[count($line) - 1][0]) * ($line[0][0] - $line[count($line) - 1][0]) + ($line[0][1] - $line[count($line) - 1][1]) * ($line[0][1] - $line[count($line) - 1][1]) <= 25 * max(1, $reltolerance)) {
array_pop($line);
}
}
$matchstu = array();
for ($i = 0; $i < count($ansdots); $i++) {
for ($j = 0; $j < count($line); $j++) {
if (($ansdots[$i][0] - $line[$j][0]) * ($ansdots[$i][0] - $line[$j][0]) + ($ansdots[$i][1] - $line[$j][1]) * ($ansdots[$i][1] - $line[$j][1]) <= 25 * max(1, $reltolerance)) {
$matchstu[$i] = $j;
}
}
}
if ($isclosed && isset($matchstu[0])) {
$matchstu[count($ansdots)] = $matchstu[0];
}
$totaladj = 0;
$correctadj = 0;
for ($i = 0; $i < count($ansdots) - ($isclosed ? 0 : 1); $i++) {
$totaladj++;
/*if ($i==count($ansdots)-1) {
if (!isset($matchstu[$i]) || !isset($matchstu[0])) {
$diff = -1;
} else {
$diff = abs($matchstu[0]-$matchstu[$i]);
}
} else {
*/
if (!isset($matchstu[$i]) || !isset($matchstu[$i + 1])) {
$diff = -1;
} else {
$diff = abs($matchstu[$i] - $matchstu[$i + 1]);
}
//}
if ($diff == 1 || $isclosed && $diff == count($matchstu) - 2 && count($matchstu) != 0) {
$correctadj++;
}
}
//echo "Total adjacencies: $totaladj. Correct: $correctadj <br/>";
if ($isclosed && isset($matchstu[0])) {
$vals = (count($matchstu) - 1) / max(count($line), count($ansdots));
} else {
$vals = count($matchstu) / max(count($line), count($ansdots));
}
$adjv = $correctadj / $totaladj;
$totscore = ($vals + $adjv) / 2;
//echo "Vals score: $vals, adj score: $adjv. </p>";
if (isset($abstolerance)) {
if ($totscore < $abstolerance) {
return 0;
} else {
return 1;
}
} else {
return $totscore;
}
} else {
if ($answerformat[0] == "twopoint") {
$anscircs = array();
$ansparabs = array();
$ansabs = array();
$anssqrts = array();
$ansexps = array();
$anscoss = array();
$ansvecs = array();
$x0 = $settings[0];
$x1 = 1 / 4 * $settings[1] + 3 / 4 * $settings[0];
$x2 = 1 / 2 * $settings[1] + 1 / 2 * $settings[0];
$x3 = 3 / 4 * $settings[1] + 1 / 4 * $settings[0];
$x4 = $settings[1];
$x0p = $imgborder;
$x1p = $xtopix($x1);
//($x1 - $settings[0])*$pixelsperx + $imgborder;
$x2p = $xtopix($x2);
//($x2 - $settings[0])*$pixelsperx + $imgborder;
$x3p = $xtopix($x3);
//($x3 - $settings[0])*$pixelsperx + $imgborder;
$x4p = $xtopix($x4);
//($x4 - $settings[0])*$pixelsperx + $imgborder;
$ymid = ($settings[2] + $settings[3]) / 2;
$ymidp = $ytopix($ymid);
//$settings[7] - ($ymid-$settings[2])*$pixelspery - $imgborder;
foreach ($answers as $key => $function) {
if ($function == '') {
continue;
}
$function = explode(',', $function);
//curves: function
// function, xmin, xmax
//dot: x,y
// x,y,"closed" or "open"
//form: function, color, xmin, xmax, startmaker, endmarker
if (count($function) == 2 || count($function) == 3 && ($function[2] == 'open' || $function[2] == 'closed')) {
//is dot
$pixx = ($function[0] - $settings[0]) * $pixelsperx + $imgborder;
$pixy = $settings[7] - ($function[1] - $settings[2]) * $pixelspery - $imgborder;
if (count($function) == 2 || $function[2] == 'closed') {
$ansdots[$key] = array($pixx, $pixy);
} else {
$ansodots[$key] = array($pixx, $pixy);
}
continue;
} else {
if ($function[0] == 'vector') {
if (count($function) > 4) {
// form "vector, x_start, y_start, x_end, y_end"
$ansvecs[$key] = array('p', $xtopix($function[1]), $ytopix($function[2]), $xtopix($function[3]), $ytopix($function[4]));
} else {
if (count($function) > 2) {
//form "vector, dx, dy"
$ansvecs[$key] = array('d', $function[1] * $pixelsperx, -1 * $function[2] * $pixelspery);
}
}
} else {
if ($function[0] == 'circle') {
// form "circle,x_center,y_center,radius"
$anscircs[$key] = array(($function[1] - $settings[0]) * $pixelsperx + $imgborder, $settings[7] - ($function[2] - $settings[2]) * $pixelspery - $imgborder, $function[3] * $pixelsperx);
} else {
if (substr($function[0], 0, 2) == 'x=') {
$anslines[$key] = array('x', 10000, (substr($function[0], 2) - $settings[0]) * $pixelsperx + $imgborder);
} else {
if (count($function) == 3) {
//line segment or ray
$func = makepretty($function[0]);
$func = mathphp($func, 'x');
$func = str_replace("(x)", '($x)', $func);
$func = create_function('$x', 'return (' . $func . ');');
if ($function[1] == '-oo') {
//ray to left
$y1p = $ytopix($func(floatval($function[2]) - 1));
$y2p = $ytopix($func(floatval($function[2])));
$ansvecs[$key] = array('r', $xtopix($function[2]), $y2p, $xtopix(floatval($function[2]) - 1), $y1p);
} else {
if ($function[2] == 'oo') {
//ray to right
$y1p = $ytopix($func(floatval($function[1])));
$y2p = $ytopix($func(floatval($function[1]) + 1));
$ansvecs[$key] = array('r', $xtopix($function[1]), $y1p, $xtopix(floatval($function[1]) + 1), $y2p);
} else {
//line seg
$y1p = $ytopix($func(floatval($function[1])));
$y2p = $ytopix($func(floatval($function[2])));
$ansvecs[$key] = array('ls', $xtopix($function[1]), $y1p, $xtopix($function[2]), $y2p);
}
}
} else {
$func = makepretty($function[0]);
$func = mathphp($func, 'x');
$func = str_replace("(x)", '($x)', $func);
$func = create_function('$x', 'return (' . $func . ');');
$y1 = $func($x1);
$y2 = $func($x2);
$y3 = $func($x3);
$y1p = $settings[7] - ($y1 - $settings[2]) * $pixelspery - $imgborder;
$y2p = $settings[7] - ($y2 - $settings[2]) * $pixelspery - $imgborder;
$y3p = $settings[7] - ($y3 - $settings[2]) * $pixelspery - $imgborder;
$yop = $imgborder + $settings[3] * $pixelspery;
if ($settings[0] < 0 && $settings[1] > 0) {
$xop = $xtopix(0);
} else {
$xop = $x2p;
}
$settings[7] - ($y1 - $settings[2]) * $pixelspery - $imgborder;
if (strpos($function[0], 'abs') !== false) {
//is abs
$y0 = $func($x0);
$y4 = $func($x4);
$y0p = $settings[7] - ($y0 - $settings[2]) * $pixelspery - $imgborder;
$y4p = $settings[7] - ($y4 - $settings[2]) * $pixelspery - $imgborder;
if (abs($y2 - $y1 - ($y1 - $y0)) < 1.0E-9) {
//if first 3 points are colinear
$slope = ($y2p - $y1p) / ($x2p - $x1p);
} else {
if (abs($y4 - $y3 - ($y3 - $y2)) < 1.0E-9) {
//if last 3 points are colinear
$slope = -1 * ($y4p - $y3p) / ($x4p - $x3p);
//mult by -1 to get slope on left
}
}
if ($slope == 0) {
$anslines[$key] = array('y', $slope, $y2p);
} else {
$xip = ($slope * ($x4p + $x0p) + $y4p - $y0p) / (2 * $slope);
//x value of "vertex"
$ansabs[$key] = array($xip, $slope * ($xip - $x0p) + $y0p, $slope);
}
} else {
if (($p = strpos($function[0], 'sqrt(')) !== false) {
//is sqrt
$nested = 1;
for ($i = $p + 5; $i < strlen($function[0]); $i++) {
if ($function[0][$i] == '(') {
$nested++;
} else {
if ($function[0][$i] == ')') {
$nested--;
}
}
if ($nested == 0) {
break;
}
}
if ($nested == 0) {
$infunc = makepretty(substr($function[0], $p + 5, $i - $p - 5));
$infunc = mathphp($infunc, 'x');
$infunc = str_replace("(x)", '($x)', $infunc);
$infunc = create_function('$x', 'return (' . $infunc . ');');
$y0 = $infunc(0);
$y1 = $infunc(1);
$xint = -$y0 / ($y1 - $y0);
$xintp = ($xint - $settings[0]) * $pixelsperx + $imgborder;
$yint = $func($xint);
$yintp = $settings[7] - ($yint - $settings[2]) * $pixelspery - $imgborder;
$secx = $xint + ($x4 - $x0) / 5 * ($y1 > $y0 ? 1 : -1);
//over 1/5 of grid width
$secy = $func($secx);
$secyp = $settings[7] - ($secy - $settings[2]) * $pixelspery - $imgborder;
$anssqrts[$key] = array($xintp, $yintp, $secyp);
}
} else {
if (($p = strpos($function[0], 'cos')) !== false || ($q = strpos($function[0], 'sin')) !== false) {
//is sin/cos
if ($p === false) {
$p = $q;
}
$nested = 1;
for ($i = $p + 4; $i < strlen($function[0]); $i++) {
if ($function[0][$i] == '(') {
$nested++;
} else {
if ($function[0][$i] == ')') {
$nested--;
}
}
if ($nested == 0) {
break;
}
}
if ($nested == 0) {
$infunc = makepretty(substr($function[0], $p + 4, $i - $p - 4));
$infunc = mathphp($infunc, 'x');
$infunc = str_replace("(x)", '($x)', $infunc);
$infunc = create_function('$x', 'return (' . $infunc . ');');
$y0 = $infunc(0);
$y1 = $infunc(1);
$period = 2 * M_PI / ($y1 - $y0);
//slope of inside function
$xint = -$y0 / ($y1 - $y0);
if (strpos($function[0], 'sin') !== false) {
$xint += $period / 4;
}
$secx = $xint + $period / 2;
$xintp = ($xint - $settings[0]) * $pixelsperx + $imgborder;
$secxp = ($secx - $settings[0]) * $pixelsperx + $imgborder;
$yint = $func($xint);
$yintp = $settings[7] - ($yint - $settings[2]) * $pixelspery - $imgborder;
$secy = $func($secx);
$secyp = $settings[7] - ($secy - $settings[2]) * $pixelspery - $imgborder;
if ($yintp > $secyp) {
$anscoss[$key] = array($xintp, $secxp, $yintp, $secyp);
} else {
$anscoss[$key] = array($secxp, $xintp, $secyp, $yintp);
}
}
} else {
if (preg_match('/\\^[^2]/', $function[0])) {
//exponential
$base = safepow(($yop - $y3p) / ($yop - $y1p), 1 / ($x3p - $x1p));
$str = ($yop - $y3p) / safepow($base, $x3p - $xop);
$ansexps[$key] = array($str, $base);
} else {
if (abs($y3 - $y2 - ($y2 - $y1)) < 1.0E-9) {
//colinear
$slope = ($y2p - $y1p) / ($x2p - $x1p);
if (abs($slope) > 1.4) {
//use x value at ymid
$anslines[$key] = array('x', $slope, $x1p + ($ymidp - $y1p) / $slope);
} else {
//use y value at x2
$anslines[$key] = array('y', $slope, $y2p);
}
} else {
//assume parabolic for now
$denom = ($x1p - $x2p) * ($x1p - $x3p) * ($x2p - $x3p);
$A = ($x3p * ($y2p - $y1p) + $x2p * ($y1p - $y3p) + $x1p * ($y3p - $y2p)) / $denom;
$B = ($x3p * $x3p * ($y1p - $y2p) + $x2p * $x2p * ($y3p - $y1p) + $x1p * $x1p * ($y2p - $y3p)) / $denom;
$C = ($x2p * $x3p * ($x2p - $x3p) * $y1p + $x3p * $x1p * ($x3p - $x1p) * $y2p + $x1p * $x2p * ($x1p - $x2p) * $y3p) / $denom;
$xt = -$B / (2 * $A) + 20;
//use vertex and y value at x of vertex + 20 pixels
$ansparabs[$key] = array(-$B / (2 * $A), $C - $B * $B / (4 * $A), $A * $xt * $xt + $B * $xt + $C);
}
}
}
}
}
}
}
}
}
}
}
list($lines, $dots, $odots, $tplines, $ineqlines) = explode(';;', $givenans);
$lines = array();
$parabs = array();
$circs = array();
$abs = array();
$sqrts = array();
$coss = array();
$exps = array();
$vecs = array();
if ($tplines == '') {
$tplines = array();
} else {
$tplines = explode('),(', substr($tplines, 1, strlen($tplines) - 2));
foreach ($tplines as $k => $val) {
$pts = explode(',', $val);
if ($pts[0] == 5) {
//line
if ($pts[3] == $pts[1]) {
$lines[] = array('x', 10000, $pts[1]);
} else {
$slope = ($pts[4] - $pts[2]) / ($pts[3] - $pts[1]);
if (abs($slope) > 100) {
$slope = 10000;
}
if (abs($slope) > 1) {
$lines[] = array('x', $slope, $pts[1] + ($ymidp - $pts[2]) / $slope, $pts[2] + ($x2p - $pts[1]) * $slope);
} else {
$lines[] = array('y', $slope, $pts[2] + ($x2p - $pts[1]) * $slope);
}
}
} else {
if ($pts[0] == 5.2) {
$vecs[] = array($pts[1], $pts[2], $pts[3], $pts[4], 'r');
} else {
if ($pts[0] == 5.3) {
$vecs[] = array($pts[1], $pts[2], $pts[3], $pts[4], 'ls');
} else {
if ($pts[0] == 5.4) {
$vecs[] = array($pts[1], $pts[2], $pts[3], $pts[4], 'v');
} else {
if ($pts[0] == 6) {
//parab
if ($pts[4] == $pts[2]) {
$lines[] = array('y', 0, $pts[4]);
} else {
if ($pts[3] != $pts[1]) {
$a = ($pts[4] - $pts[2]) / (($pts[3] - $pts[1]) * ($pts[3] - $pts[1]));
$y = $pts[2] + $a * 400;
$parabs[] = array($pts[1], $pts[2], $y);
}
}
} else {
if ($pts[0] == 6.5) {
//sqrt
$flip = $pts[3] < $pts[1] ? -1 : 1;
$stretch = ($pts[4] - $pts[2]) / sqrt($flip * ($pts[3] - $pts[1]));
$secxp = $pts[1] + ($x4p - $x0p) / 5 * $flip;
//over 1/5 of grid width
$secyp = $stretch * sqrt($flip * ($secxp - $pts[1])) + $pts[2];
$sqrts[] = array($pts[1], $pts[2], $secyp);
} else {
if ($pts[0] == 7) {
//circle
$circs[] = array($pts[1], $pts[2], sqrt(($pts[3] - $pts[1]) * ($pts[3] - $pts[1]) + ($pts[4] - $pts[2]) * ($pts[4] - $pts[2])));
} else {
if ($pts[0] == 8) {
//abs
if ($pts[1] == $pts[3]) {
if ($pts[4] > $pts[2]) {
$slope = -10000000000.0;
} else {
$slope = 10000000000.0;
}
} else {
$slope = ($pts[4] - $pts[2]) / ($pts[3] - $pts[1]);
if ($pts[3] > $pts[1]) {
//we just found slope on right, so reverse for slope on left
$slope *= -1;
}
}
$abs[] = array($pts[1], $pts[2], $slope);
} else {
if ($pts[0] == 8.300000000000001) {
$adjy2 = $yop - $pts[4];
$adjy1 = $yop - $pts[2];
if ($adjy1 * $adjy2 > 0 && $pts[1] != $pts[3]) {
$base = safepow($adjy2 / $adjy1, 1 / ($pts[3] - $pts[1]));
if (abs($pts[1] - $xop) < abs($pts[3] - $xop)) {
$str = $adjy1 / safepow($base, $pts[1] - $xop);
} else {
$str = $adjy2 / safepow($base, $pts[3] - $xop);
}
//$exps[] = array($str,$base);
$exps[] = array($pts[1] - $xop, $adjy1, $pts[3] - $xop, $adjy2, $base);
}
} else {
if ($pts[0] == 9 || $pts[0] == 9.1) {
if ($pts[0] == 9.1) {
$pts[1] -= $pts[3] - $pts[1];
$pts[2] -= $pts[4] - $pts[2];
}
if ($pts[4] > $pts[2]) {
$coss[] = array($pts[3], $pts[1], $pts[4], $pts[2]);
} else {
$coss[] = array($pts[1], $pts[3], $pts[2], $pts[4]);
}
}
}
}
}
}
}
}
}
}
}
}
}
if ($dots == '') {
$dots = array();
} else {
$dots = explode('),(', substr($dots, 1, strlen($dots) - 2));
foreach ($dots as $k => $pt) {
$dots[$k] = explode(',', $pt);
}
}
if ($odots == '') {
$odots = array();
} else {
$odots = explode('),(', substr($odots, 1, strlen($odots) - 2));
foreach ($odots as $k => $pt) {
$odots[$k] = explode(',', $pt);
}
}
$scores = array();
if (count($dots) + count($odots) == 0) {
$extradots = 0;
} else {
$extradots = max((count($dots) + count($odots) - count($ansdots) - count($ansodots)) / (count($dots) + count($odots)), 0);
}
foreach ($ansdots as $key => $ansdot) {
$scores[$key] = 0;
for ($i = 0; $i < count($dots); $i++) {
if (($dots[$i][0] - $ansdot[0]) * ($dots[$i][0] - $ansdot[0]) + ($dots[$i][1] - $ansdot[1]) * ($dots[$i][1] - $ansdot[1]) <= 25 * max(1, $reltolerance)) {
$scores[$key] = 1 - $extradots;
break;
}
}
}
foreach ($ansodots as $key => $ansodot) {
$scores[$key] = 0;
for ($i = 0; $i < count($odots); $i++) {
if (($odots[$i][0] - $ansodot[0]) * ($odots[$i][0] - $ansodot[0]) + ($odots[$i][1] - $ansodot[1]) * ($odots[$i][1] - $ansodot[1]) <= 25 * max(1, $reltolerance)) {
$scores[$key] = 1 - $extradots;
break;
}
}
}
$deftol = 0.1;
$defpttol = 5;
foreach ($anslines as $key => $ansline) {
$scores[$key] = 0;
for ($i = 0; $i < count($lines); $i++) {
//check slope
$toladj = pow(10, -1 - 6 * abs($ansline[1]));
if (abs($ansline[1] - $lines[$i][1]) / (abs($ansline[1]) + $toladj) > $deftol * $reltolerance) {
continue;
}
if ($ansline[0] != $lines[$i][0]) {
if (abs(abs($ansline[1]) - 1) < 0.4) {
//check intercept
if (abs($ansline[2] - $lines[$i][3]) > $defpttol * $reltolerance) {
continue;
}
} else {
continue;
}
} else {
if (abs($ansline[2] - $lines[$i][2]) > $defpttol * $reltolerance) {
continue;
}
}
$scores[$key] = 1;
break;
}
}
foreach ($anscircs as $key => $anscirc) {
$scores[$key] = 0;
for ($i = 0; $i < count($circs); $i++) {
if (abs($anscirc[0] - $circs[$i][0]) > $defpttol * $reltolerance) {
continue;
}
if (abs($anscirc[1] - $circs[$i][1]) > $defpttol * $reltolerance) {
continue;
}
if (abs($anscirc[2] - $circs[$i][2]) > $defpttol * $reltolerance) {
continue;
}
$scores[$key] = 1;
break;
}
}
foreach ($ansvecs as $key => $ansvec) {
$scores[$key] = 0;
if ($ansvec[0] == 'p') {
//point
for ($i = 0; $i < count($vecs); $i++) {
if ($vecs[$i][4] != 'v') {
continue;
}
if (abs($ansvec[1] - $vecs[$i][0]) > $defpttol * $reltolerance) {
continue;
}
if (abs($ansvec[2] - $vecs[$i][1]) > $defpttol * $reltolerance) {
continue;
}
if (abs($ansvec[3] - $vecs[$i][2]) > $defpttol * $reltolerance) {
continue;
}
if (abs($ansvec[4] - $vecs[$i][3]) > $defpttol * $reltolerance) {
continue;
}
$scores[$key] = 1;
break;
}
} else {
if ($ansvec[0] == 'r') {
//ray
for ($i = 0; $i < count($vecs); $i++) {
if ($vecs[$i][4] != 'r') {
continue;
}
//make sure base point matches
if (abs($ansvec[1] - $vecs[$i][0]) > $defpttol * $reltolerance) {
continue;
}
if (abs($ansvec[2] - $vecs[$i][1]) > $defpttol * $reltolerance) {
continue;
}
//compare slopes
$correctdx = $ansvec[3] - $ansvec[1];
$correctdy = $ansvec[4] - $ansvec[2];
$studx = $vecs[$i][2] - $vecs[$i][0];
$study = $vecs[$i][3] - $vecs[$i][1];
//find angle between correct ray and stu ray
$cosang = ($studx * $correctdx + $study * $correctdy) / (sqrt($studx * $studx + $study * $study) * sqrt($correctdx * $correctdx + $correctdy * $correctdy));
$ang = acos($cosang) * 57.2957795;
if (abs($ang) > 1.4 * $reltolerance) {
continue;
}
/*
slope based grading
if (abs($correctdy)>abs($correctdx)) {
$m = $correctdx/$correctdy;
$stum = $studx/$study;
} else {
$m = $correctdy/$correctdx;
$stum =$study/$studx;
}
$toladj = pow(10,-1-6*abs($m));
if (abs($m-$stum)/abs($m+$toladj)>$deftol*$reltolerance) {
continue;
}
*/
$scores[$key] = 1;
break;
}
} else {
if ($ansvec[0] == 'ls') {
//line segment
for ($i = 0; $i < count($vecs); $i++) {
if ($vecs[$i][4] != 'ls') {
continue;
}
if (abs($ansvec[1] - $vecs[$i][0]) > $defpttol * $reltolerance && abs($ansvec[1] - $vecs[$i][2]) > $defpttol * $reltolerance) {
continue;
//ans x1 doesn't match either vec x
}
if (abs($ansvec[1] - $vecs[$i][0]) <= $defpttol * $reltolerance) {
//x1 of ans matched first vec x
if (abs($ansvec[2] - $vecs[$i][1]) > $defpttol * $reltolerance) {
continue;
}
if (abs($ansvec[3] - $vecs[$i][2]) > $defpttol * $reltolerance) {
continue;
}
if (abs($ansvec[4] - $vecs[$i][3]) > $defpttol * $reltolerance) {
continue;
}
} else {
if (abs($ansvec[2] - $vecs[$i][3]) > $defpttol * $reltolerance) {
continue;
}
if (abs($ansvec[3] - $vecs[$i][0]) > $defpttol * $reltolerance) {
continue;
}
if (abs($ansvec[4] - $vecs[$i][1]) > $defpttol * $reltolerance) {
continue;
}
}
$scores[$key] = 1;
break;
}
} else {
//direction vector
for ($i = 0; $i < count($vecs); $i++) {
if ($vecs[$i][4] != 'v') {
continue;
}
if (abs($ansvec[1] - ($vecs[$i][2] - $vecs[$i][0])) > $defpttol * $reltolerance) {
continue;
}
if (abs($ansvec[2] - ($vecs[$i][3] - $vecs[$i][1])) > $defpttol * $reltolerance) {
continue;
}
$scores[$key] = 1;
break;
}
}
}
}
}
foreach ($ansparabs as $key => $ansparab) {
$scores[$key] = 0;
for ($i = 0; $i < count($parabs); $i++) {
if (abs($ansparab[0] - $parabs[$i][0]) > $defpttol * $reltolerance) {
continue;
}
if (abs($ansparab[1] - $parabs[$i][1]) > $defpttol * $reltolerance) {
continue;
}
if (abs($ansparab[2] - $parabs[$i][2]) > $defpttol * $reltolerance) {
continue;
}
$scores[$key] = 1;
break;
}
}
foreach ($anssqrts as $key => $anssqrt) {
$scores[$key] = 0;
for ($i = 0; $i < count($sqrts); $i++) {
if (abs($anssqrt[0] - $sqrts[$i][0]) > $defpttol * $reltolerance) {
continue;
}
if (abs($anssqrt[1] - $sqrts[$i][1]) > $defpttol * $reltolerance) {
continue;
}
if (abs($anssqrt[2] - $sqrts[$i][2]) > $defpttol * $reltolerance) {
continue;
}
$scores[$key] = 1;
break;
}
}
foreach ($ansexps as $key => $ansexp) {
$scores[$key] = 0;
for ($i = 0; $i < count($exps); $i++) {
//if (abs($ansexp[0]-$exps[$i][0])>$defpttol*$reltolerance) {
// continue;
//}
if (abs($ansexp[1] - $exps[$i][4]) / (abs($ansexp[1] - 1) + 1.0E-18) > $deftol * $reltolerance) {
continue;
}
//check left point if base>1
if ($ansexp[1] > 1 && abs($ansexp[0] * safepow($ansexp[1], $exps[$i][0]) - $exps[$i][1]) > $defpttol * $reltolerance) {
continue;
}
//check right point if base<=
if ($ansexp[1] <= 1 && abs($ansexp[0] * safepow($ansexp[1], $exps[$i][2]) - $exps[$i][3]) > $defpttol * $reltolerance) {
continue;
}
$scores[$key] = 1;
break;
}
}
foreach ($anscoss as $key => $anscos) {
$scores[$key] = 0;
for ($i = 0; $i < count($coss); $i++) {
$per = abs($anscos[0] - $anscos[1]) * 2;
$adjdiff = abs($anscos[0] - $coss[$i][0]);
$adjdiff = abs($adjdiff - $per * round($adjdiff / $per));
if ($adjdiff > $defpttol * $reltolerance) {
continue;
}
$adjdiff = abs($anscos[1] - $coss[$i][1]);
$adjdiff = abs($adjdiff - $per * round($adjdiff / $per));
if ($adjdiff > $defpttol * $reltolerance) {
continue;
}
if (abs($anscos[2] - $coss[$i][2]) > $defpttol * $reltolerance) {
continue;
}
if (abs($anscos[3] - $coss[$i][3]) > $defpttol * $reltolerance) {
continue;
}
$scores[$key] = 1;
break;
}
}
foreach ($ansabs as $key => $aabs) {
$scores[$key] = 0;
for ($i = 0; $i < count($abs); $i++) {
if (abs($aabs[0] - $abs[$i][0]) > $defpttol * $reltolerance) {
continue;
}
if (abs($aabs[1] - $abs[$i][1]) > $defpttol * $reltolerance) {
continue;
}
//check slope
$toladj = pow(10, -1 - 6 * abs($aabs[2]));
if (abs($aabs[2] - $abs[$i][2]) / (abs($aabs[2]) + $toladj) > $deftol * $reltolerance) {
continue;
}
$scores[$key] = 1;
break;
}
}
$extrastuffpenalty = max((count($tplines) - count($answers)) / max(count($answers), count($tplines)), 0);
} else {
if ($answerformat[0] == "inequality") {
list($lines, $dots, $odots, $tplines, $ineqlines) = explode(';;', $givenans);
/*$x1 = 1/3*$settings[0] + 2/3*$settings[1];
$x2 = 2/3*$settings[0] + 1/3*$settings[1];
$x1p = ($x1 - $settings[0])*$pixelsperx + $imgborder;
$x2p = ($x2 - $settings[0])*$pixelsperx + $imgborder;
$ymid = ($settings[2]+$settings[3])/2;
$ymidp = $settings[7] - ($ymid-$settings[2])*$pixelspery - $imgborder;*/
$x1 = 1 / 4 * $settings[1] + 3 / 4 * $settings[0];
$x2 = 1 / 2 * $settings[1] + 1 / 2 * $settings[0];
$x3 = 3 / 4 * $settings[1] + 1 / 4 * $settings[0];
$x1p = ($x1 - $settings[0]) * $pixelsperx + $imgborder;
$x2p = ($x2 - $settings[0]) * $pixelsperx + $imgborder;
$x3p = ($x3 - $settings[0]) * $pixelsperx + $imgborder;
$ymid = ($settings[2] + $settings[3]) / 2;
$ymidp = $settings[7] - ($ymid - $settings[2]) * $pixelspery - $imgborder;
foreach ($answers as $key => $function) {
if ($function == '') {
continue;
}
$function = explode(',', $function);
if ($function[0][0] == 'x' && ($function[0][1] == '<' || $function[0][1] == '>')) {
$isxequals = true;
$function[0] = substr($function[0], 1);
} else {
$isxequals = false;
}
if ($function[0][1] == '=') {
$type = 10;
$c = 2;
} else {
$type = 10.2;
$c = 1;
}
$dir = $function[0][0];
if ($isxequals) {
$anslines[$key] = array('x', $dir, $type, -10000, (substr($function[0], $c) - $settings[0]) * $pixelsperx + $imgborder);
} else {
$func = makepretty(substr($function[0], $c));
$func = mathphp($func, 'x');
$func = str_replace("(x)", '($x)', $func);
$func = create_function('$x', 'return (' . $func . ');');
$y1 = $func($x1);
$y2 = $func($x2);
$y3 = $func($x3);
$y1p = $settings[7] - ($y1 - $settings[2]) * $pixelspery - $imgborder;
$y2p = $settings[7] - ($y2 - $settings[2]) * $pixelspery - $imgborder;
$y3p = $settings[7] - ($y3 - $settings[2]) * $pixelspery - $imgborder;
$denom = ($x1p - $x2p) * ($x1p - $x3p) * ($x2p - $x3p);
$A = ($x3p * ($y2p - $y1p) + $x2p * ($y1p - $y3p) + $x1p * ($y3p - $y2p)) / $denom;
if (abs($A) > 1.0E-5) {
//quadratic inequality: Contributed by Cam Joyce
if ($type == 10) {
//switch to quadratic
$type = 10.3;
} else {
$type = 10.4;
}
$B = ($x3p * $x3p * ($y1p - $y2p) + $x2p * $x2p * ($y3p - $y1p) + $x1p * $x1p * ($y2p - $y3p)) / $denom;
$C = ($x2p * $x3p * ($x2p - $x3p) * $y1p + $x3p * $x1p * ($x3p - $x1p) * $y2p + $x1p * $x2p * ($x1p - $x2p) * $y3p) / $denom;
$anslines[$key] = array('y', $dir, $type, $A, -$B / (2 * $A), $C - $B * $B / (4 * $A));
} else {
//linear inequality
$slope = ($y2p - $y1p) / ($x2p - $x1p);
if (abs($slope) > 1.4) {
//use x value at ymid
$anslines[$key] = array('x', $dir, $type, $slope, $x1p + ($ymidp - $y1p) / $slope);
} else {
//use y value at x2
$anslines[$key] = array('y', $dir, $type, $slope, $y2p);
}
}
}
}
if ($ineqlines == '') {
$ineqlines = array();
} else {
$ineqlines = explode('),(', substr($ineqlines, 1, strlen($ineqlines) - 2));
foreach ($ineqlines as $k => $val) {
$pts = explode(',', $val);
if ($pts[0] < 10.3) {
//linear
if ($pts[3] == $pts[1]) {
$slope = 10000;
} else {
$slope = ($pts[4] - $pts[2]) / ($pts[3] - $pts[1]);
}
if (abs($slope) > 50) {
if ($pts[5] > $pts[3]) {
$dir = '>';
} else {
$dir = '<';
}
$ineqlines[$k] = array('x', $dir, $pts[0], -10000, $pts[1]);
} else {
$yatpt5 = $slope * ($pts[5] - $pts[1]) + $pts[2];
if ($yatpt5 < $pts[6]) {
$dir = '<';
} else {
$dir = '>';
}
if (abs($slope) > 50) {
$slope = -10000;
}
if (abs($slope) > 1) {
$ineqlines[$k] = array('x', $dir, $pts[0], $slope, $pts[1] + ($ymidp - $pts[2]) / $slope, $pts[2] + ($x2p - $pts[1]) * $slope);
} else {
$ineqlines[$k] = array('y', $dir, $pts[0], $slope, $pts[2] + ($x2p - $pts[1]) * $slope);
}
}
} else {
//quadratic
$aUser = ($pts[4] - $pts[2]) / (($pts[3] - $pts[1]) * ($pts[3] - $pts[1]));
$yatpt5 = $aUser * ($pts[5] - $pts[1]) * ($pts[5] - $pts[1]) + $pts[2];
if ($yatpt5 < $pts[6]) {
$dir = '<';
} else {
$dir = '>';
}
$ineqlines[$k] = array('y', $dir, $pts[0], $aUser, $pts[1], $pts[2]);
}
}
}
$scores = array();
$deftol = 0.1;
$defpttol = 5;
foreach ($anslines as $key => $ansline) {
$scores[$key] = 0;
for ($i = 0; $i < count($ineqlines); $i++) {
if ($ansline[2] != $ineqlines[$i][2]) {
continue;
}
if ($ansline[1] != $ineqlines[$i][1]) {
continue;
}
if ($ansline[2] < 10.3) {
//linear inequality
//check slope
$toladj = pow(10, -1 - 6 * abs($ansline[3]));
$relerr = abs($ansline[3] - $ineqlines[$i][3]) / (abs($ansline[3]) + $toladj);
if ($relerr > $deftol * $reltolerance) {
continue;
}
if ($ansline[0] != $ineqlines[$i][0]) {
if (abs(abs($ansline[3]) - 1) < 0.4) {
//check intercept
if (abs($ansline[4] - $ineqlines[$i][5]) > $defpttol * $reltolerance) {
continue;
}
} else {
continue;
}
} else {
if (abs($ansline[4] - $ineqlines[$i][4]) > $defpttol * $reltolerance) {
continue;
}
}
$scores[$key] = 1;
break;
} else {
//quadratic inequality
//check values in y = a(x-p)+q
$toladj = pow(10, -1 - 6 * abs($ansline[3]));
$relerr = abs($ansline[3] - $ineqlines[$i][3]) / (abs($ansline[3]) + $toladj);
if ($relerr > $deftol * $reltolerance) {
continue;
}
if (abs($ansline[4] - $ineqlines[$i][4]) > $defpttol * $reltolerance) {
continue;
}
if (abs($ansline[5] - $ineqlines[$i][5]) > $defpttol * $reltolerance) {
continue;
}
$scores[$key] = 1;
break;
}
}
}
$extrastuffpenalty = max((count($ineqlines) - count($answers)) / max(count($answers), count($ineqlines)), 0);
} else {
//not polygon or twopoint, continue with regular grading
//evaluate all the functions in $answers
foreach ($answers as $key => $function) {
if ($function == '') {
continue;
}
$function = explode(',', $function);
//curves: function
// function, xmin, xmax
//dot: x,y
// x,y,"closed" or "open"
//form: function, color, xmin, xmax, startmaker, endmarker
if (count($function) == 2 || count($function) == 3 && ($function[2] == 'open' || $function[2] == 'closed')) {
//is dot
$pixx = ($function[0] - $settings[0]) * $pixelsperx + $imgborder;
$pixy = $settings[7] - ($function[1] - $settings[2]) * $pixelspery - $imgborder;
if (count($function) == 2 || $function[2] == 'closed') {
$ansdots[$key] = array($pixx, $pixy);
} else {
$ansodots[$key] = array($pixx, $pixy);
}
continue;
}
$anslines[$key] = array();
$func = makepretty($function[0]);
$func = mathphp($func, 'x');
$func = str_replace("(x)", '($x)', $func);
$func = create_function('$x', 'return (' . $func . ');');
if (!isset($function[1])) {
$function[1] = $settings[0];
}
if (!isset($function[2])) {
$function[2] = $settings[1];
}
$xminpix = max(2 * $imgborder, ($function[1] - $settings[0]) * $pixelsperx + $imgborder);
$xmaxpix = min($settings[6] - 2 * $imgborder, ($function[2] - $settings[0]) * $pixelsperx + $imgborder);
for ($k = ceil($xminpix / $step); $k * $step <= $xmaxpix; $k++) {
$x = $k * $step;
$coordx = ($x - $imgborder) / $pixelsperx + $settings[0] + 1.0E-10;
$coordy = $func($coordx);
if ($coordy > $settings[2] && $coordy < $settings[3]) {
$anslines[$key][$k] = $settings[7] - ($coordy - $settings[2]) * $pixelspery - $imgborder;
if (!isset($anslineptcnt[$k])) {
$anslineptcnt[$k] = 1;
} else {
$anslineptcnt[$k]++;
}
$linepts++;
}
}
$linecnt++;
}
//break apart student entry
list($lines, $dots, $odots, $tplines, $ineqlines) = explode(';;', $givenans);
if ($lines == '') {
$lines = array();
} else {
$lines = explode(';', $lines);
foreach ($lines as $k => $line) {
$lines[$k] = explode('),(', substr($line, 1, strlen($line) - 2));
foreach ($lines[$k] as $j => $pt) {
$lines[$k][$j] = explode(',', $pt);
}
}
}
if ($dots == '') {
$dots = array();
} else {
$dots = explode('),(', substr($dots, 1, strlen($dots) - 2));
foreach ($dots as $k => $pt) {
$dots[$k] = explode(',', $pt);
}
}
if ($odots == '') {
$odots = array();
} else {
$odots = explode('),(', substr($odots, 1, strlen($odots) - 2));
foreach ($odots as $k => $pt) {
$odots[$k] = explode(',', $pt);
}
}
//interp the lines
$linedata = array();
$totinterp = 0;
foreach ($lines as $k => $line) {
for ($i = 1; $i < count($line); $i++) {
$leftx = min($line[$i][0], $line[$i - 1][0]);
$rightx = max($line[$i][0], $line[$i - 1][0]);
if ($line[$i][0] == $line[$i - 1][0]) {
$m = 9999;
} else {
$m = ($line[$i][1] - $line[$i - 1][1]) / ($line[$i][0] - $line[$i - 1][0]);
}
for ($k = ceil($leftx / $step); $k * $step < $rightx; $k++) {
$x = $k * $step;
$y = $line[$i - 1][1] + $m * ($x - $line[$i - 1][0]);
if ($y > $imgborder && $y < $settings[7] - $imgborder) {
$linedata[$k][] = $y;
$totinterp++;
}
}
}
}
$stdevs = array();
$stcnts = array();
$scores = array();
$unmatchedanspts = array();
$unmatchedanskeys = array();
//compare lines
foreach ($anslines as $key => $answerline) {
$unmatchedptcnt = 0;
$stdevs[$key] = 0;
$stcnts[$key] = 0;
foreach ($answerline as $k => $ansy) {
//if there are more ans pts than drawn, want to match up better than this;
//mark it for coming back to
//if less ans pts than drawn, that's already accounted for in $percentoffpts
if ($anslineptcnt[$k] > count($linedata[$k])) {
$unmatchedanspts[$k] = 1;
continue;
}
$minerr = $settings[7];
for ($i = 0; $i < count($linedata[$k]); $i++) {
if (abs($ansy - $linedata[$k][$i]) < $minerr) {
$minerr = abs($ansy - $linedata[$k][$i]);
}
}
if ($minerr < $settings[7]) {
$stdevs[$key] += $minerr * $minerr;
$stcnts[$key]++;
}
}
}
//go back and match up drawn points with unmatched answer points
//we have more answer points than drawn points here
foreach (array_keys($unmatchedanspts) as $k) {
for ($i = 0; $i < count($linedata[$k]); $i++) {
$minerr = $settings[7];
$minerrkey = -1;
foreach ($anslines as $key => $answerline) {
if (abs($answerline[$k] - $linedata[$k][$i]) < $minerr) {
$minerr = abs($answerline[$k] - $linedata[$k][$i]);
$minerrkey = $key;
}
}
if ($minerrkey > -1) {
$stdevs[$minerrkey] += $minerr * $minerr;
$stcnts[$minerrkey]++;
}
}
}
//time to grade!
$percentunmatcheddrawn = 0;
//counts extra drawn points: percent of drawn that are extras
if ($totinterp > 0) {
$percentunmatcheddrawn = max(($totinterp - $linepts) / $totinterp - 0.05 * $reltolerance, 0);
}
//divide up over all the lines
$percentunmatcheddrawn = $percentunmatcheddrawn;
foreach ($anslines as $key => $answerline) {
if ($stcnts[$key] < 2) {
$stdevs[$key] = 0;
} else {
$stdevs[$key] = sqrt($stdevs[$key] / ($stcnts[$key] - 1));
}
$stdevpen = max(8 * ($stdevs[$key] - 5) / $settings[7], 0);
if (count($answerline) == 0) {
$percentunmatchedans = 1;
} else {
$percentunmatchedans = max((count($answerline) - $stcnts[$key]) / count($answerline), 0);
}
if ($percentunmatchedans < 0.05 * $reltolerance) {
$percentunmatchedans = 0;
}
$scores[$key] = 1 - ($stdevpen + $percentunmatcheddrawn + $percentunmatchedans) / $reltolerance;
//echo "Line: $key, stdev: {$stdevs[$key]}, unmatchedrawn: $percentunmatcheddrawn, unmatchedans: $percentunmatchedans <br/>";
if ($scores[$key] < 0) {
$scores[$key] = 0;
} else {
if ($scores[$key] > 1) {
$scores[$key] = 1;
}
}
}
//go through dots
//echo count($dots) .','.count($odots).','.count($ansdots).','.count($ansodots).'<br/>';
if (count($dots) + count($odots) == 0) {
$extradots = 0;
} else {
$extradots = max((count($dots) + count($odots) - count($ansdots) - count($ansodots)) / (count($dots) + count($odots)), 0);
}
foreach ($ansdots as $key => $ansdot) {
$scores[$key] = 0;
for ($i = 0; $i < count($dots); $i++) {
if (($dots[$i][0] - $ansdot[0]) * ($dots[$i][0] - $ansdot[0]) + ($dots[$i][1] - $ansdot[1]) * ($dots[$i][1] - $ansdot[1]) <= 25 * max(1, $reltolerance)) {
$scores[$key] = 1 - $extradots;
break;
}
}
}
//and open dots
foreach ($ansodots as $key => $ansdot) {
$scores[$key] = 0;
for ($i = 0; $i < count($odots); $i++) {
if (($odots[$i][0] - $ansdot[0]) * ($odots[$i][0] - $ansdot[0]) + ($odots[$i][1] - $ansdot[1]) * ($odots[$i][1] - $ansdot[1]) <= 25 * max(1, $reltolerance)) {
$scores[$key] = 1 - $extradots;
break;
}
}
}
}
}
}
if (!isset($partweights)) {
$partweights = array_fill(0, count($scores), 1 / count($scores));
} else {
if (!is_array($partweights)) {
$partweights = explode(',', $partweights);
}
}
$totscore = 0;
foreach ($scores as $key => $score) {
$totscore += $score * $partweights[$key];
}
if ($extrastuffpenalty > 0) {
$totscore = max($totscore * (1 - $extrastuffpenalty), 0);
}
if (isset($abstolerance)) {
if ($totscore < $abstolerance) {
return 0;
} else {
return 1;
}
} else {
return $totscore;
}
} else {
if ($anstype == "file") {
if (isset($options['scoremethod'])) {
if (is_array($options['scoremethod'])) {
$scoremethod = $options['scoremethod'][$qn];
} else {
$scoremethod = $options['scoremethod'];
}
}
if (isset($options['answer'])) {
if ($multi > 0) {
$answer = $options['answer'][$qn];
} else {
$answer = $options['answer'];
}
}
if (isset($options['answerformat'])) {
if (is_array($options['answerformat'])) {
$answerformat = $options['answerformat'][$qn];
} else {
$answerformat = $options['answerformat'];
}
}
if ($multi > 0) {
$qn = $multi * 1000 + $qn;
}
$filename = basename($_FILES["qn{$qn}"]['name']);
$filename = preg_replace('/[^\\w\\.]/', '', $filename);
$hasfile = false;
require_once "../includes/filehandler.php";
if (trim($filename) == '') {
$found = false;
if ($_POST["lf{$qn}"] != '') {
if ($multi > 0) {
if (strpos($GLOBALS['lastanswers'][$multi - 1], '@FILE:' . $_POST["lf{$qn}"] . '@') !== false) {
$found = true;
}
} else {
if (strpos($GLOBALS['lastanswers'][$qn], '@FILE:' . $_POST["lf{$qn}"] . '@') !== false) {
$found = true;
}
}
}
if ($found) {
$GLOBALS['partlastanswer'] = '@FILE:' . $_POST["lf{$qn}"] . '@';
if ($answerformat == 'excel') {
$zip = new ZipArchive();
if ($zip->open(getasidfilepath($_POST["lf{$qn}"]))) {
$doc = new DOMDocument();
$doc->loadXML($zip->getFromName('xl/worksheets/sheet1.xml'));
$zip->close();
} else {
$GLOBALS['scoremessages'] .= _(' Unable to open Excel file');
return 0;
}
}
$hasfile = true;
} else {
$GLOBALS['partlastanswer'] = '';
return 0;
}
}
if (!$hasfile) {
$extension = strtolower(strrchr($filename, "."));
$badextensions = array(".php", ".php3", ".php4", ".php5", ".bat", ".com", ".pl", ".p", ".exe");
if ($GLOBALS['scoremessages'] != '') {
$GLOBALS['scoremessages'] .= '<br/>';
}
$GLOBALS['scoremessages'] .= sprintf(_('Upload of %s: '), $filename);
if (in_array($extension, $badextensions)) {
$GLOBALS['partlastanswer'] = _('Error - Invalid file type');
$GLOBALS['scoremessages'] .= _('Error - Invalid file type');
return 0;
}
//if($GLOBALS['isreview']) {echo 'TRUE';}
if (isset($GLOBALS['asid'])) {
//going to use assessmentid/random
$randstr = '';
for ($i = 0; $i < 6; $i++) {
$n = rand(0, 61);
if ($n < 10) {
$randstr .= chr(48 + $n);
} else {
if ($n < 36) {
$randstr .= chr(65 + $n - 10);
} else {
$randstr .= chr(97 + $n - 36);
}
}
}
//in case "same random seed" is selected, students can overwrite their own
//files. Avoid this.
if (($GLOBALS['testsettings']['shuffle'] & 4) == 4 || ($GLOBALS['testsettings']['shuffle'] & 2) == 2) {
//if same random seed is set, need to check for duplicates
$n = 0;
do {
$n++;
$s3asid = $GLOBALS['testsettings']['id'] . "/{$n}";
} while (doesfileexist('assess', "adata/{$s3asid}/{$filename}"));
} else {
$s3asid = $GLOBALS['testsettings']['id'] . "/{$randstr}";
}
} else {
$GLOBALS['partlastanswer'] = _('Error - no asid');
$GLOBALS['scoremessages'] .= _('Error - no asid');
return 0;
}
if (is_numeric($s3asid) && $s3asid == 0) {
//set in testquestion for preview
$GLOBALS['partlastanswer'] = _('Error - File not uploaded in preview');
$GLOBALS['scoremessages'] .= _('Error - File not uploaded in preview');
return 0;
}
if (is_uploaded_file($_FILES["qn{$qn}"]['tmp_name'])) {
if ($answerformat == 'excel') {
$zip = new ZipArchive();
if ($zip->open($_FILES["qn{$qn}"]['tmp_name'])) {
echo "opened excel";
$doc = new DOMDocument();
if ($doc->loadXML($zip->getFromName('xl/worksheets/sheet1.xml'))) {
echo "read into doc";
}
$zip->close();
} else {
$GLOBALS['scoremessages'] .= _(' Unable to open Excel file');
return 0;
}
}
$s3object = "adata/{$s3asid}/{$filename}";
if (storeuploadedfile("qn{$qn}", $s3object)) {
$GLOBALS['partlastanswer'] = "@FILE:{$s3asid}/{$filename}@";
$GLOBALS['scoremessages'] .= _("Successful");
$hasfile = true;
} else {
//echo "Error storing file";
$GLOBALS['partlastanswer'] = _('Error storing file');
$GLOBALS['scoremessages'] .= _('Error storing file');
return 0;
}
} else {
//echo "Error uploading file";
if ($_FILES["qn{$qn}"]['error'] == 2 || $_FILES["qn{$qn}"]['error'] == 1) {
$GLOBALS['partlastanswer'] = _('Error uploading file - file too big');
$GLOBALS['scoremessages'] .= _('Error uploading file - file too big');
} else {
$GLOBALS['partlastanswer'] = _('Error uploading file');
$GLOBALS['scoremessages'] .= _('Error uploading file');
}
return 0;
}
}
if (isset($scoremethod) && $scoremethod == 'takeanything') {
return 1;
} else {
if ($answerformat == 'excel') {
$doccells = array();
$els = $doc->getElementsByTagName('c');
foreach ($els as $el) {
$doccells[$el->getAttribute('r')] = $el->getElementsByTagName('v')->item(0)->nodeValue;
}
$pts = 0;
foreach ($answer as $cell => $val) {
if (!isset($doccells[$cell])) {
continue;
}
if (is_numeric($val)) {
if (abs($val - $doccells[$cell]) < 0.01) {
$pts++;
} else {
$GLOBALS['scoremessages'] .= "<br/>Cell {$cell} incorrect";
echo "<br/>Cell {$cell} incorrect";
}
} else {
if (trim($val) == trim($doccells[$cell])) {
$pts++;
}
}
}
return $pts / count($answer);
} else {
return -2;
}
}
} else {
if ($anstype == "conditional") {
$answer = $options['answer'];
if (isset($options['abstolerance'])) {
$abstolerance = $options['abstolerance'];
}
if (isset($options['reltolerance'])) {
$reltolerance = $options['reltolerance'];
}
if (!isset($reltolerance) && !isset($abstolerance)) {
$reltolerance = $defaultreltol;
}
if (isset($options['domain'])) {
$domain = $options['domain'];
} else {
$domain = "-10,10";
}
if (isset($options['variables'])) {
$variables = $options['variables'];
} else {
$variables = "x";
}
$anstypes = $options['anstypes'];
if (!is_array($anstypes)) {
$anstypes = explode(',', $anstypes);
}
$la = array();
foreach ($anstypes as $i => $anst) {
$qnt = 1000 * ($qn + 1) + $i;
if (isset($_POST["tc{$qnt}"])) {
if ($anst == 'calculated') {
$la[$i] = $_POST["tc{$qnt}"] . '$#$' . $_POST["qn{$qnt}"];
} else {
$la[$i] = $_POST["tc{$qnt}"];
}
} else {
if (isset($_SESSION['choicemap'][$qnt]) && isset($_SESSION['choicemap'][$qnt][$_POST["qn{$qnt}"]])) {
$la[$i] = $_POST["qn{$qnt}"] . '$!$' . $_SESSION['choicemap'][$qnt][$_POST["qn{$qnt}"]];
} else {
$la[$i] = $_POST["qn{$qnt}"];
}
}
$la[$i] = str_replace('&', '', $la[$i]);
$la[$i] = preg_replace('/#+/', '#', $la[$i]);
}
$GLOBALS['partlastanswer'] = implode('&', $la);
if (isset($abstolerance)) {
$tol = '|' . $abstolerance;
} else {
$tol = $reltolerance;
}
$correct = true;
if (!is_array($answer)) {
//single boolean
if ($answer === true) {
return 1;
} else {
if ($answer === false) {
return 0;
} else {
return $answer;
}
}
}
if (is_array($answer) && is_string($answer[0])) {
//if single {'function',$f,$g) type, make array
$answer = array($answer);
}
foreach ($answer as $ans) {
if (is_array($ans)) {
if ($ans[0][0] == '!') {
$flip = true;
$ans[0] = substr($ans[0], 1);
} else {
$flip = false;
}
if ($ans[0] == 'number') {
$pt = comparenumbers($ans[1], $ans[2], $tol);
} else {
if ($ans[0] == 'function') {
$pt = comparefunctions($ans[1], $ans[2], $variables, $tol, $domain);
}
}
if ($flip) {
$pt = !$pt;
}
} else {
$pt = $ans;
}
if ($pt == false) {
return 0;
break;
}
}
return 1;
}
}
}
}
}
}
}
}
}
}
}
}
}
}
}
}
}
function comparefunctions($a, $b, $vars = 'x', $tol = '.001', $domain = '-10,10')
{
if ($a == '' || $b == '') {
return false;
}
//echo "comparing $a and $b";
if ($tol[0] == '|') {
$abstolerance = floatval(substr($tol, 1));
}
$type = "expression";
if (strpos($a, '=') !== false && strpos($b, '=') !== false) {
$type = "equation";
}
$fromto = explode(',', $domain);
$variables = explode(',', $vars);
$vlist = implode("|", $variables);
for ($i = 0; $i < 20; $i++) {
for ($j = 0; $j < count($variables); $j++) {
if (isset($fromto[2]) && $fromto[2] == "integers") {
$tps[$i][$j] = rand($fromto[0], $fromto[1]);
} else {
if (isset($fromto[2 * $j + 1])) {
$tps[$i][$j] = $fromto[2 * $j] + ($fromto[2 * $j + 1] - $fromto[2 * $j]) * rand(0, 499) / 500.0 + 0.001;
} else {
$tps[$i][$j] = $fromto[0] + ($fromto[1] - $fromto[0]) * rand(0, 499) / 500.0 + 0.001;
}
}
}
}
if ($type == 'equation') {
if (substr_count($a, '=') != 1) {
return false;
}
$a = preg_replace('/(.*)=(.*)/', '$1-($2)', $a);
if (substr_count($b, '=') != 1) {
return false;
}
$b = preg_replace('/(.*)=(.*)/', '$1-($2)', $b);
}
$a = mathphp(makepretty(mathphppre($a)), $vlist);
$b = mathphp(makepretty(mathphppre($b)), $vlist);
//echo "pretty: $a, $b";
for ($i = 0; $i < count($variables); $i++) {
$a = str_replace("(" . $variables[$i] . ")", '($tp[' . $i . '])', $a);
$b = str_replace("(" . $variables[$i] . ")", '($tp[' . $i . '])', $b);
}
$cntnana = 0;
$cntnanb = 0;
$correct = true;
$ratios = array();
for ($i = 0; $i < 20; $i++) {
for ($j = 0; $j < count($variables); $j++) {
$tp[$j] = $tps[$i][$j];
}
$ansa = @eval("return ({$a});");
$ansb = @eval("return ({$b});");
//echo "real: $ansa, my: $ansb <br/>";
if (isNaN($ansa)) {
$cntnana++;
if (isNaN($ansb)) {
$cntnanb++;
}
continue;
}
//avoid NaN problems
if (isNaN($ansb)) {
$cntnanb++;
continue;
}
if ($type == 'equation') {
if (abs($ansa) > 1.0E-6 && is_numeric($ansb)) {
$ratios[] = $ansb / $ansa;
if (abs($ansb) <= 1.0E-8 && $ansa != 0) {
$cntzero++;
}
} else {
if (abs($ansa) <= 1.0E-6 && is_numeric($ansb) && abs($ansb) <= 1.0E-8) {
$cntbothzero++;
}
}
} else {
if (isset($abstolerance)) {
if (abs($ansa - $ansb) > $abstolerance - 1.0E-12) {
$correct = false;
break;
}
} else {
if (abs($ansa - $ansb) / (abs($ansa) + 0.0001) > $tol - 1.0E-12) {
$correct = false;
break;
}
}
}
}
//echo "$i, $ansa, $ansb, $cntnana, $cntnanb";
if (($cntnana == 20 || $cntnanb == 20) && isset($GLOBALS['teacherid'])) {
echo "<p>Debug info: one function evaled to Not-a-number at all test points. Check \$domain</p>";
echo "<p>Funcs: {$a} and {$b}</p>";
return false;
}
if (abs($cntnana - $cntnanb) > 1) {
return false;
}
if ($type == "equation") {
if ($cntbothzero > 18) {
$correct = true;
} else {
if (count($ratios) > 0) {
if (count($ratios) == $cntzero) {
$correct = false;
} else {
$meanratio = array_sum($ratios) / count($ratios);
for ($i = 0; $i < count($ratios); $i++) {
if (isset($abstolerance)) {
if (abs($ratios[$i] - $meanratio) > $abstolerance - 1.0E-12) {
$correct = false;
break;
}
} else {
if (abs($ratios[$i] - $meanratio) / (abs($meanratio) + 0.0001) > $tol - 1.0E-12) {
$correct = false;
break;
}
}
}
}
} else {
$correct = false;
}
}
}
if ($correct) {
return true;
} else {
return false;
}
}