1: # The LearningOnline Network with CAPA
2: # used by lonxml::xmlparse() as input variable $safeinit to Apache::run::run()
3: #
4: # $Id: default_homework.lcpm,v 1.47 2002/05/31 22:19:06 albertel Exp $
5: #
6: # Copyright Michigan State University Board of Trustees
7: #
8: # This file is part of the LearningOnline Network with CAPA (LON-CAPA).
9: #
10: # LON-CAPA is free software; you can redistribute it and/or modify
11: # it under the terms of the GNU General Public License as published by
12: # the Free Software Foundation; either version 2 of the License, or
13: # (at your option) any later version.
14: #
15: # LON-CAPA is distributed in the hope that it will be useful,
16: # but WITHOUT ANY WARRANTY; without even the implied warranty of
17: # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
18: # GNU General Public License for more details.
19: #
20: # You should have received a copy of the GNU General Public License
21: # along with LON-CAPA; if not, write to the Free Software
22: # Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
23: #
24: # /home/httpd/html/adm/gpl.txt
25: #
26: # http://www.lon-capa.org/
27: #
28: #
29: # Guy Albertelli
30: #
31: # 05/25/2001 H. K. Ng
32: # 05/31/2001 H. K. Ng
33: # 12/21/2001 Matthew
34: #
35: #init some globals
36: $hidden::RANDOMINIT=0;
37: $pi=atan2(1,1)*4;
38: $rad2deg=180.0/$pi;
39: $deg2rad=$pi/180.0;
40: $"=' ';
41:
42: sub caparesponse_check {
43: #not properly used yet: calc
44: #not to be used: $ans_fmt
45: my ($answer,$type,$tol,$sig,$ans_fmt,$unit,$calc,$samples) =
46: eval $_[1].
47: ';return ($answer,$type,$tol,$sig,$ans_fmt,$unit,$calc,$samples);';
48:
49: my $tol_type=''; # gets it's value from whether tol has a % or not done
50: my $sig_lbound=''; #done
51: my $sig_ubound=''; #done
52: my ($response,$expr)=@_;
53:
54:
55: #type's definitons come from capaParser.h
56: my $message='';
57: #remove leading and trailing whitespace
58: if ($response=~ /^\s|\s$/) {
59: $response=~ s:^\s+|\s+$::g;
60: $message .="Removed ws now :$response:<br />";
61: } else {
62: $message .="no ws in :$response:<br />";
63: }
64:
65: if ($type eq '' ) {
66: $message .= "Didn't find a type :$type:$expr: defaulting<br />";
67: if ( $answer eq ($answer *1.0)) { $type = 2;
68: } else { $type = 3; }
69: } else {
70: if ($type eq 'cs') { $type = 4;
71: } elsif ($type eq 'ci') { $type = 3;
72: } elsif ($type eq 'mc') { $type = 5;
73: } elsif ($type eq 'fml') { $type = 8;
74: } elsif ($type eq 'subj') { $type = 7;
75: } elsif ($type eq 'float') { $type = 2;
76: } elsif ($type eq 'int') { $type = 1;
77: } else { return "ERROR: Unknown type of answer: $type" }
78: }
79:
80: my $points;
81: my $id_list;
82: #formula type setup the sample points
83: if ($type eq '8') {
84: ($id_list,$points)=split(/@/,$samples);
85: $message.="Found :$points: points<br />";
86: }
87: if ($tol eq '') {
88: $tol=0.0;
89: $tol_type=1; #TOL_ABSOLUTE
90: } else {
91: if ($tol =~ /%$/) {
92: chop $tol;
93: $tol_type=2; #TOL_PERCENTAGE
94: } else {
95: $tol_type=1; #TOL_ABSOLUTE
96: }
97: }
98:
99: if ($sig eq '') {
100: $sig_lbound = 0; #SIG_LB_DEFAULT
101: $sig_ubound =15; #SIG_UB_DEFAULT
102: } else {
103: ($sig_lbound,$sig_ubound) = split /,/,$sig;
104: if (!$sig_lbound) {
105: $sig_lbound = 0; #SIG_LB_DEFAULT
106: $sig_ubound =15; #SIG_UB_DEFAULT
107: }
108: if (!$sig_ubound) { $sig_ubound=$sig_lbound; }
109: }
110: my $result = &caparesponse_capa_check_answer($response,$answer,$type,
111: $tol_type,$tol,
112: $sig_lbound,$sig_ubound,
113: $ans_fmt,$unit,$calc,$id_list,
114: $points,$external::randomseed);
115:
116: if ($result == '1') { $result='EXACT_ANS'; }
117: elsif ($result == '2') { $result='APPROX_ANS'; }
118: elsif ($result == '3') { $result='SIG_FAIL'; }
119: elsif ($result == '4') { $result='UNIT_FAIL'; }
120: elsif ($result == '5') { $result='NO_UNIT'; }
121: elsif ($result == '6') { $result='UNIT_OK'; }
122: elsif ($result == '7') { $result='INCORRECT'; }
123: elsif ($result == '8') { $result='UNIT_NOTNEEDED'; }
124: elsif ($result == '9') { $result='ANS_CNT_NOT_MATCH'; }
125: elsif ($result =='10') { $result='SUB_RECORDED'; }
126: elsif ($result =='11') { $result='BAD_FORMULA'; }
127: elsif ($result =='12') { $result='WANTED_NUMERIC'; }
128: else {$result = "ERROR: Unknown Result:$result:$@:";}
129:
130: return "$result:<br />Error $error:<br />Answer $answer:<br />Response $response:<br /> type-$type|$tol|$tol_type|$sig:$sig_lbound:$sig_ubound|$unit|<br />$message$expr";
131: }
132:
133: sub get_array_args {
134: my ($expr,$arg)=@_;
135: # do these first, because who knows what varname the instructor might have used
136: # but it probably isn't $CAPARESPONSE_CHECK_LIST_answer
137: my $CAPARESPONSE_CHECK_LIST_answer = eval $expr.';return $'.$arg; #'
138: my $GET_ARRAY_ARGS_result;
139: my @GET_ARRAY_ARGS_list;
140: if ($CAPARESPONSE_CHECK_LIST_answer =~ /^\s*[\$\@]/) {
141: (@GET_ARRAY_ARGS_list) = eval $CAPARESPONSE_CHECK_LIST_answer;
142: }
143: $GET_ARRAY_ARGS_result.="error:$@:<br />";
144: # if the eval fails just use what is in the answer exactly
145: if (!defined(@GET_ARRAY_ARGS_list) || !defined($GET_ARRAY_ARGS_list[0])) {
146: $GET_ARRAY_ARGS_result.="list zero is undefined<br />";
147: $GET_ARRAY_ARGS_list[0]=$CAPARESPONSE_CHECK_LIST_answer;
148: }
149: return $GET_ARRAY_ARGS_result,@GET_ARRAY_ARGS_list;
150: }
151:
152: sub caparesponse_check_list {
153: my ($response,$expr)=@_;
154: my $result;
155: my ($result,@list) = &get_array_args($expr,'answer');
156: my $aresult='';
157: my $current_answer;
158: my $answers=join(':',@list);
159: $result.="Got response :$answers:<br />";
160: my @responselist;
161: my $type =eval $expr.';return $answer;';
162: if ($type ne '' && $#list > 0) {
163: (@responselist)=split /,/,$response;
164: } else {
165: (@responselist)=($response);
166: }
167: my $unit='';
168: $result.="Initial final response :$responselist['-1']:<br />";
169: if ($type eq '') {
170: #for numerical problems split off the unit
171: if ( $responselist['-1']=~ /(.*[^\s])\s+([^\s]+)/ ) {
172: $responselist['-1']=$1;
173: $unit=$2;
174: }
175: }
176: $result.="Final final response :$responselist['-1']:<br />";
177: $result.=":$#list: answers<br />";
178: $unit=~s/\s//;
179: my $i=0;
180: my $awards='';
181: for ($i=0; $i<@list;$i++) {
182: $result.="trying answer :$list[$i]:<br />";
183: if ($unit eq '') {
184: $aresult=&caparesponse_check($responselist[$i],
185: $expr.';my $answer=\''.$list[$i].'\';');
186: } else {
187: $aresult=&caparesponse_check($responselist[$i]." $unit",
188: $expr.';my $answer=\''.$list[$i].'\';');
189: }
190: my ($temp)=split /:/, $aresult;
191: $awards.="$temp,";
192: $result.=$aresult;
193: }
194: chop $awards;
195: return "$awards:<br />$result";
196: }
197:
198: sub tex {
199: if ( $external::target eq "tex" ) {
200: return @_[0];
201: } else {
202: return @_[1];
203: }
204: }
205:
206: sub var_in_tex {
207: if ( $external::target eq "tex" ) {
208: return @_[0];
209: } else {
210: return "";
211: }
212: }
213:
214: sub web {
215: if ( $external::target eq "tex" ) {
216: return @_[1];
217: } else {
218: if ( $external::target eq "web" || $external::target eq "answer") {
219: return @_[2];
220: } else {
221: return @_[0];
222: }
223: }
224: }
225:
226: sub html {
227: if ( $external::target eq "web" ) {
228: return shift;
229: }
230: }
231:
232: sub problem {
233: return '1';
234: }
235:
236: sub hinton {
237: return 0;
238: }
239:
240: sub random {
241: my ($start,$end,$step)=@_;
242: if ( ! $hidden::RANDOMINIT ) {
243: srand($external::randomseed);
244: $hidden::RANDOMINIT=1;
245: }
246: if (!defined($step)) { $step=1; }
247: my $num=1+int(($end-$start)/$step);
248: my $result=$start + int(rand() * $num)*$step;
249: return $result;
250: }
251:
252: sub random_normal {
253: my ($item_cnt,$seed,$av,$std_dev) = @_;
254: my @retArray;
255: &random_set_seed_from_phrase($seed);
256: @retArray=&math_random_normal($item_cnt,$av,$std_dev);
257: return @retArray;
258: }
259:
260: sub random_beta {
261: my ($item_cnt,$seed,$aa,$bb) = @_;
262: my @retArray;
263: &random_set_seed_from_phrase($seed);
264: @retArray=&math_random_beta($item_cnt,$aa,$bb);
265: return @retArray;
266: }
267:
268: sub random_gamma {
269: my ($item_cnt,$seed,$a,$r) = @_;
270: my @retArray;
271: &random_set_seed_from_phrase($seed);
272: @retArray=&math_random_gamma($item_cnt,$a,$r);
273: return @retArray;
274: }
275:
276: sub random_exponential {
277: my ($item_cnt,$seed,$av) = @_;
278: my @retArray;
279: &random_set_seed_from_phrase($seed);
280: @retArray=&math_random_exponential($item_cnt,$av);
281: return @retArray;
282: }
283:
284: sub random_poisson {
285: my ($item_cnt,$seed,$mu) = @_;
286: my @retArray;
287: &random_set_seed_from_phrase($seed);
288: @retArray=&math_random_poisson($item_cnt,$mu);
289: return @retArray;
290: }
291:
292: sub random_chi {
293: my ($item_cnt,$seed,$df) = @_;
294: my @retArray;
295: &random_set_seed_from_phrase($seed);
296: @retArray=&math_random_chi_square($item_cnt,$df);
297: return @retArray;
298: }
299:
300: sub random_noncentral_chi {
301: my ($item_cnt,$seed,$df,$nonc) = @_;
302: my @retArray;
303: &random_set_seed_from_phrase($seed);
304: @retArray=&math_random_noncentral_chi_square($item_cnt,$df,$nonc);
305: return @retArray;
306: }
307:
308: sub random_f {
309: my ($item_cnt,$seed,$dfn,$dfd) = @_;
310: my @retArray;
311: &random_set_seed_from_phrase($seed);
312: @retArray=&math_random_f($item_cnt,$dfn,$dfd);
313: return @retArray;
314: }
315:
316: sub random_noncentral_f {
317: my ($item_cnt,$seed,$dfn,$dfd,$nonc) = @_;
318: my @retArray;
319: &random_set_seed_from_phrase($seed);
320: @retArray=&math_random_noncentral_f($item_cnt,$dfn,$dfd,$nonc);
321: return @retArray;
322: }
323:
324: sub random_multivariate_normal {
325: my ($item_cnt,$seed,$mean,$covar) = @_;
326: &random_set_seed_from_phrase($seed);
327: @retArray=&math_random_multivariate_normal($item_cnt,@$mean,@$covar);
328: return @retArray;
329: }
330:
331: sub random_multinomial {
332: my ($item_cnt,$seed,@p) = @_;
333: my @retArray;
334: &random_set_seed_from_phrase($seed);
335: @retArray=&math_random_multinomial($item_cnt,@p);
336: return @retArray;
337: }
338:
339: sub random_permutation {
340: my ($seed,@inArray) = @_;
341: my @retArray;
342: &random_set_seed_from_phrase($seed);
343: @retArray=&math_random_permutation(@inArray);
344: return @retArray;
345: }
346:
347: sub random_uniform {
348: my ($item_cnt,$seed,$low,$high) = @_;
349: my @retArray;
350: &random_set_seed_from_phrase($seed);
351: @retArray=&math_random_uniform($item_cnt,$low,$high);
352: return @retArray;
353: }
354:
355: sub random_uniform_integer {
356: my ($item_cnt,$seed,$low,$high) = @_;
357: my @retArray;
358: &random_set_seed_from_phrase($seed);
359: @retArray=&math_random_uniform_integer($item_cnt,$low,$high);
360: return @retArray;
361: }
362:
363: sub random_binomial {
364: my ($item_cnt,$seed,$nt,$p) = @_;
365: my @retArray;
366: &random_set_seed_from_phrase($seed);
367: @retArray=&math_random_binomial($item_cnt,$nt,$p);
368: return @retArray;
369: }
370:
371: sub random_negative_binomial {
372: my ($item_cnt,$seed,$ne,$p) = @_;
373: my @retArray;
374: &random_set_seed_from_phrase($seed);
375: @retArray=&math_random_negative_binomial($item_cnt,$ne,$p);
376: return @retArray;
377: }
378:
379: sub abs { abs(shift) }
380: sub sin { sin(shift) }
381: sub cos { cos(shift) }
382: sub exp { exp(shift) }
383: sub int { int(shift) }
384: sub log { log(shift) }
385: sub atan2 { atan2($_[0],$_[1]) }
386: sub sqrt { sqrt(shift) }
387:
388: sub tan { sin($_[0]) / cos($_[0]) }
389: #sub atan { atan2($_[0], 1); }
390: #sub acos { atan2(sqrt(1 - $_[0] * $_[0]), $_[0] ); }
391: #sub asin { atan2($_[0], sqrt(1- $_[0] * $_[0]) ); }
392:
393: sub log10 { log($_[0])/log(10); }
394:
395: sub factorial {
396: my $input = int(shift);
397: return "Error - unable to take factorial of an negative number ($input)" if $input < 0;
398: return "Error - factorial result is greater than system limit ($input)" if $input > 170;
399: return 1 if $input == 0;
400: my $result = 1;
401: for (my $i=2; $i<=$input; $i++) { $result *= $i }
402: return $result;
403: }
404:
405: sub sgn {
406: return -1 if $_[0] < 0;
407: return 0 if $_[0] == 0;
408: return 1 if $_[0] > 0;
409: }
410:
411: sub min {
412: my @sorted = sort { $a <=> $b || $a cmp $b } @_;
413: return shift @sorted;
414: }
415:
416: sub max {
417: my @sorted = sort { $a <=> $b || $a cmp $b } @_;
418: return pop @sorted;
419: }
420:
421: sub roundto {
422: my ($input,$n) = @_;
423: return sprintf('%.'.$n.'f',$input);
424: }
425:
426: sub to_string {
427: my ($input,$n) = @_;
428: return sprintf($input) if $n eq "";
429: $n = '.'.$n if $n !~ /^\./;
430: return sprintf('%'.$n,$input) if $n ne "";
431: }
432:
433: sub sub_string {
434: my ($str,$start,$len) = @_;
435: return substr($str,$start-1,$len);
436: }
437:
438: sub pow {return $_[0] ** $_[1]; }
439: sub ceil {return (($_[0]-int($_[0]))== 0.0) ? $_[0] : (($_[0] > 0) ? (int($_[0])+ 1) : int($_[0])); }
440: sub floor {return (($_[0]-int($_[0]))== 0.0) ? $_[0] : (($_[0] > 0) ? int($_[0]) : (int($_[0])-1)); }
441: #sub floor {return int($_[0]); }
442:
443: sub format {
444: my ($value,$fmt)=@_;
445: return sprintf('%.'.$fmt,$value);
446: }
447:
448: sub prettyprint {
449: my ($value,$fmt)=@_;
450: my $result;
451: if ($fmt) { $value=sprintf('%.'.$fmt,$value); }
452: if ($value =~ /([0-9\.\-\+]+)E([0-9\-\+]+)/ ) {
453: my $frac=$1;
454: my $exponent=$2;
455: $exponent=~s/^\+0*//;
456: if (!$exponent) { return $frac; }
457: if ($external::target eq 'web') {
458: $result=$frac.'×10<sup>'.$exponent.'</sup>';
459: } elsif ($external::target eq 'tex') {
460: $result='\ensuremath{'.$frac.'\times 10^{'.$exponent.'}}';
461: } else {
462: $result=$value;
463: }
464: } else {
465: $result=$value;
466: }
467: return $result;
468: }
469:
470: sub map {
471: my ($phrase,$dest,$source)=@_;
472: my @seed = &random_seed_from_phrase($phrase);
473: &random_set_seed(@seed);
474: my $destct = scalar(@$dest);
475: if (!$source) {
476: my @output;
477: my @idx = &math_random_permuted_index($destct);
478: my $ctr = 0;
479: while ($ctr < $destct) {
480: $output[$ctr] = $$dest[$idx[$ctr]];
481: $ctr++;
482: }
483: return @output;
484: } else {
485: my $num = scalar(@$source);
486: my @idx = &math_random_permuted_index($num);
487: my $ctr = 0;
488: my $tot = $num;
489: $tot = $destct if $destct < $num;
490: if (ref($$dest[0])) {
491: while ($ctr < $tot) {
492: ${$$dest[$ctr]} = $$source[$idx[$ctr]];
493: $ctr++;
494: }
495: } else {
496: while ($ctr < $tot) {
497: $$dest[$ctr] = $$source[$idx[$ctr]];
498: $ctr++;
499: }
500: }
501: }
502: }
503:
504: sub rmap {
505: my ($phrase,$dest,$source)=@_;
506: my @seed = &random_seed_from_phrase($phrase);
507: &random_set_seed(@seed);
508: my $destct = scalar(@$dest);
509: if (!$source) {
510: my @idx = &math_random_permuted_index($destct);
511: my $ctr = 0;
512: my @r_idx;
513: while ($ctr < $destct) {
514: $r_idx[$idx[$ctr]] = $ctr;
515: $ctr++;
516: }
517: my @output;
518: $ctr = 0;
519: while ($ctr < $destct) {
520: $output[$ctr] = $$dest[$r_idx[$ctr]];
521: $ctr++;
522: }
523: return @output;
524: } else {
525: my $num = scalar(@$source);
526: my @idx = &math_random_permuted_index($num);
527: my $ctr = 0;
528: my $tot = $num;
529: $tot = $destct if $destct < $num;
530: my @r_idx;
531: while ($ctr < $tot) {
532: $r_idx[$idx[$ctr]] = $ctr;
533: $ctr++;
534: }
535: $ctr = 0;
536: if (ref($$dest[0])) {
537: while ($ctr < $tot) {
538: ${$$dest[$ctr]} = $$source[$r_idx[$ctr]];
539: $ctr++;
540: }
541: } else {
542: while ($ctr < $tot) {
543: $$dest[$ctr] = $$source[$r_idx[$ctr]];
544: $ctr++;
545: }
546: }
547: }
548: }
549:
550: sub capa_id { return }
551:
552: sub problem { return }
553:
554: sub name{
555: my $fullname = &EXT('environment.lastname').', '.&EXT('environment.firstname').' '.&EXT('environment.middlename');
556: $fullname = "" if $fullname eq ", ";
557: $fullname =~ s/\%2d/-/g;
558: return $fullname;
559: }
560:
561: sub student_number {
562: my $id = &EXT('environment.id');
563: $id = '' if $id eq "";
564: return $id;
565: }
566:
567: sub class {
568: my $course = &EXT('course.description');
569: $course = '' if $course eq "";
570: return $course;
571: }
572:
573: sub sec {
574: my $sec = &EXT('request.course.sec');
575: $sec = '' if $sec eq "";
576: return $sec;
577: }
578:
579: sub open_date {
580: my @dc = split(/\s+/,localtime(&EXT('resource.0.opendate')));
581: return '' if ($dc[0] eq "Wed" and $dc[2] == 31 and $dc[4] == 1969);
582: my @hm = split(/:/,$dc[3]);
583: my $ampm = " am";
584: if ($hm[0] > 12) {
585: $hm[0]-=12;
586: $ampm = " pm";
587: }
588: return $dc[0].', '.$dc[1].' '.$dc[2].', '.$dc[4].' at '.$hm[0].':'.$hm[1].$ampm;
589: }
590:
591: sub due_date {
592: my @dc = split(/\s+/,localtime(&EXT('resource.0.duedate')));
593: return '' if ($dc[0] eq "Wed" and $dc[2] == 31 and $dc[4] == 1969);
594: my @hm = split(/:/,$dc[3]);
595: my $ampm = " am";
596: if ($hm[0] > 12) {
597: $hm[0]-=12;
598: $ampm = " pm";
599: }
600: return $dc[0].', '.$dc[1].' '.$dc[2].', '.$dc[4].' at '.$hm[0].':'.$hm[1].$ampm;
601: # return $dc[0].', '.$dc[1].' '.$dc[2].', '.$dc[4].' at '.$dc[3];
602: }
603:
604: sub answer_date {
605: my @dc = split(/\s+/,localtime(&EXT('resource.0.answerdate')));
606: return '' if ($dc[0] eq "Wed" and $dc[2] == 31 and $dc[4] == 1969);
607: my @hm = split(/:/,$dc[3]);
608: my $ampm = " am";
609: if ($hm[0] > 12) {
610: $hm[0]-=12;
611: $ampm = " pm";
612: }
613: return $dc[0].', '.$dc[1].' '.$dc[2].', '.$dc[4].' at '.$hm[0].':'.$hm[1].$ampm;
614: # return $dc[0].', '.$dc[1].' '.$dc[2].', '.$dc[4].' at '.$dc[3];
615: }
616:
617: sub array_moments {
618: my @input=@_;
619: my (@output,$N);
620: $N=scalar (@input);
621: $output[0]=$N;
622: if ($N <= 1) {
623: $output[1]=$input[0];
624: $output[1]="Input array not defined" if ($N == 0);
625: $output[2]="variance undefined for N<=1";
626: $output[3]="skewness undefined for N<=1";
627: $output[4]="kurtosis undefined for N<=1";
628: return @output;
629: }
630: my $sum=0;
631: foreach my $line (@input) {
632: $sum+=$line;
633: }
634: $output[1] = $sum/$N;
635: my ($x,$sdev,$var,$skew,$kurt) = 0;
636: foreach my $line (@input) {
637: $x=$line-$output[1];
638: $var+=$x**2;
639: $skew+=$x**3;
640: $kurt+=$x**4;
641: }
642: $output[2]=$var/($N-1);
643: $sdev=sqrt($output[2]);
644: if ($sdev == 0) {
645: $output[3]="inf-variance=0";
646: $output[4]="inf-variance=0";
647: return @output;
648: }
649: $output[3]=$skew/($sdev**3*$N);
650: $output[4]=$kurt/($sdev**4*$N)-3;
651: return @output;
652: }
653:
654: sub choose {
655: my $num = $_[0];
656: return $_[$num];
657: }
658:
659:
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