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 1.137 2008/06/14 16:34:54 www 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:
30: #init some globals
31: $hidden::RANDOMINIT=0;
32: $pi=atan2(1,1)*4;
33: $rad2deg=180.0/$pi;
34: $deg2rad=$pi/180.0;
35: $"=' ';
36: use strict;
37: {
38: my $n = 0;
39: my $total = 0;
40: my $num_left = 0;
41: my @order;
42: my $type;
43:
44: sub init_permutation {
45: my ($size,$requested_type) = @_;
46: @order = (0..$size-1);
47: $n = $size;
48: $type = $requested_type;
49: if ($type eq 'ordered') {
50: $total = $num_left = 1;
51: } elsif ($type eq 'unordered') {
52: $total = $num_left = &factorial($size);
53: } else {
54: die("Unkown type: $type");
55: }
56: }
57:
58: sub get_next_permutation {
59: if ($num_left == $total) {
60: $num_left--;
61: return \@order;
62: }
63:
64: # Find largest index j with a[j] < a[j+1]
65:
66: my $j = scalar(@order) - 2;
67: while ($order[$j] > $order[$j+1]) {
68: $j--;
69: }
70:
71: # Find index k such that a[k] is smallest integer
72: # greater than a[j] to the right of a[j]
73:
74: my $k = scalar(@order) - 1;
75: while ($order[$j] > $order[$k]) {
76: $k--;
77: }
78:
79: # Interchange a[j] and a[k]
80:
81: @order[($k,$j)] = @order[($j,$k)];
82:
83: # Put tail end of permutation after jth position in increasing order
84:
85: my $r = scalar(@order) - 1;
86: my $s = $j + 1;
87:
88: while ($r > $s) {
89: @order[($s,$r)]=@order[($r,$s)];
90: $r--;
91: $s++;
92: }
93:
94: $num_left--;
95: return(\@order);
96: }
97:
98: sub get_permutations_left {
99: return $num_left;
100: }
101: }
102:
103: sub check_commas {
104: my ($response)=@_;
105: #print("$response ");
106: my @numbers=split(',',$response);
107: #print(" numbers ".join('-',@numbers)." ");
108: if (scalar(@numbers) > 1) {
109: #print(" numbers[0] ".$numbers[0]." ");
110: if (length($numbers[0]) > 3 || length($numbers[0]) == 0) { return -1; }
111: shift(@numbers);
112: #print(" numbers ".scalar(@numbers)." ");
113: while (scalar(@numbers) > 1) {
114: #print(" numbers ".join('-',@numbers)." ");
115: if (length($numbers[0]) != 3) { return -2; }
116: shift(@numbers);
117: }
118: my ($number)=split('\.',$numbers[0]);
119: #print(" number ".$number." ");
120: #print(" numbers[0] ".$numbers[0]." ");
121: if (length($number) != 3) { return -3; }
122: } else {
123: my ($number)=split('\.',$numbers[0]);
124: if (length($number) > 3) { return -4; }
125: }
126: return 1;
127: }
128:
129:
130: sub caparesponse_check {
131: my ($answer,$response)=@_;
132: #not properly used yet: calc
133: #not to be used: $ans_fmt
134: my $type=$LONCAPA::CAPAresponse_args{'type'};
135: my $tol=$LONCAPA::CAPAresponse_args{'tol'};
136: my $sig=$LONCAPA::CAPAresponse_args{'sig'};
137: my $ans_fmt=$LONCAPA::CAPAresponse_args{'format'};
138: my $unit=$LONCAPA::CAPAresponse_args{'unit'};
139: my $calc=$LONCAPA::CAPAresponse_args{'calc'};
140: my $samples=$LONCAPA::CAPAresponse_args{'samples'};
141:
142: my $tol_type=''; # gets it's value from whether tol has a % or not done
143: my $sig_lbound=''; #done
144: my $sig_ubound=''; #done
145:
146:
147: #type's definitons come from capaParser.h
148:
149: #remove leading and trailing whitespace
150: if (!defined($response)) {
151: $response='';
152: }
153: if ($response=~ /^\s|\s$/) {
154: $response=~ s:^\s+|\s+$::g;
155: &LONCAPA_INTERNAL_DEBUG("Removed ws now :$response:");
156: }
157:
158: #&LONCAPA_INTERNAL_DEBUG(" type is $type ");
159: if ($type eq 'cs' || $type eq 'ci') {
160: #for string answers make sure all places spaces occur, there is
161: #really only 1 space, in both the answer and the response
162: $answer=~s/ +/ /g;
163: $response=~s/ +/ /g;
164: } elsif ($type eq 'mc') {
165: $answer=~s/[\s,]//g;
166: $response=~s/[\s,]//g;
167: }
168: if ($type eq 'float' && $unit=~/\$/) {
169: if ($response!~/^\$|\$$/) { return ('NO_UNIT', undef); }
170: $response=~s/\$//g;
171: }
172: if ($type eq 'float' && $unit=~/\,/ && (&check_commas($response)<0)) {
173: return "COMMA_FAIL:";
174: }
175: $ans_fmt=~s/\W//g;
176: $unit=~s/[\$,]//g;
177: if ($type eq 'float') { $response=~s/,//g; }
178:
179: if (length($response) > 500) { return ('TOO_LONG',undef); }
180:
181: if ($type eq '' ) {
182: &LONCAPA_INTERNAL_DEBUG("Didn't find a type :$type: defaulting");
183: if ( $answer eq ($answer *1.0)) { $type = 2;
184: } else { $type = 3; }
185: } else {
186: if ($type eq 'cs') { $type = 4; }
187: elsif ($type eq 'ci') { $type = 3 }
188: elsif ($type eq 'mc') { $type = 5; }
189: elsif ($type eq 'fml') { $type = 8; }
190: elsif ($type eq 'math') { $type = 9; }
191: elsif ($type eq 'subj') { $type = 7; }
192: elsif ($type eq 'float') { $type = 2; }
193: elsif ($type eq 'int') { $type = 1; }
194: else { return ('ERROR', "Unknown type of answer: $type") }
195: }
196:
197: my $points;
198: my $id_list;
199: #formula type setup the sample points
200: if ($type eq '8') {
201: ($id_list,$points)=split(/@/,$samples);
202: &LONCAPA_INTERNAL_DEBUG("Found :$id_list:$points: points in $samples");
203: }
204: if ($tol eq '') {
205: $tol=0.0;
206: $tol_type=1; #TOL_ABSOLUTE
207: } else {
208: if ($tol =~ /%$/) {
209: chop $tol;
210: $tol_type=2; #TOL_PERCENTAGE
211: } else {
212: $tol_type=1; #TOL_ABSOLUTE
213: }
214: }
215:
216: ($sig_ubound,$sig_lbound)=&LONCAPA_INTERNAL_get_sigrange($sig);
217:
218: my $reterror="";
219: my $result;
220: if ((($type eq '9') || ($type eq '8')) && ($response=~/\=/)) { return ('BAD_FORMULA','Please submit just an expression, not an equation.'); }
221: if ($type eq '9') {
222: $result = &maxima_check(&maxima_cas_formula_fix($response),&maxima_cas_formula_fix($answer),\$reterror);
223: } else {
224: if ($type eq '8') { # fml type
225: $response = &capa_formula_fix($response);
226: $answer = &capa_formula_fix($answer);
227: }
228: $result = &caparesponse_capa_check_answer($response,$answer,$type,
229: $tol_type,$tol,
230: $sig_lbound,$sig_ubound,
231: $ans_fmt,$unit,$calc,$id_list,
232: $points,$external::randomseed,
233: \$reterror);
234: }
235: if ($result == '1') { $result='EXACT_ANS'; }
236: elsif ($result == '2') { $result='APPROX_ANS'; }
237: elsif ($result == '3') { $result='SIG_FAIL'; }
238: elsif ($result == '4') { $result='UNIT_FAIL'; }
239: elsif ($result == '5') { $result='NO_UNIT'; }
240: elsif ($result == '6') { $result='UNIT_OK'; }
241: elsif ($result == '7') { $result='INCORRECT'; }
242: elsif ($result == '8') { $result='UNIT_NOTNEEDED'; }
243: elsif ($result == '9') { $result='ANS_CNT_NOT_MATCH'; }
244: elsif ($result =='10') { $result='SUB_RECORDED'; }
245: elsif ($result =='11') { $result='BAD_FORMULA'; }
246: elsif ($result =='12' && !$response) { $result='MISSING_ANSWER'; }
247: elsif ($result =='12') { $result='WANTED_NUMERIC'; }
248: elsif ($result =='13') { $result='UNIT_INVALID_INSTRUCTOR'; }
249: elsif ($result =='141') { $result='UNIT_INVALID_STUDENT'; }
250: elsif ($result =='142') { $result='UNIT_INVALID_STUDENT'; }
251: elsif ($result =='143') { $result='UNIT_INVALID_STUDENT'; }
252: elsif ($result =='15') { $result='UNIT_IRRECONCIBLE'; }
253: else {$result = "ERROR: Unknown Result:$result:$@:";}
254:
255: &LONCAPA_INTERNAL_DEBUG("RetError $reterror: Answer $answer: Response $response: type-$type|$tol|$tol_type|$sig:$sig_lbound:$sig_ubound|$unit|");
256: &LONCAPA_INTERNAL_DEBUG(" $answer $response $result ");
257: return ($result,$reterror)
258: }
259:
260:
261: sub caparesponse_check_list {
262: my $responses=$LONCAPA::CAPAresponse_args{'response'};
263: &LONCAPA_INTERNAL_DEBUG("args ".join(':',%LONCAPA::CAPAresponse_args));
264: my $type = $LONCAPA::CAPAresponse_args{'type'};
265: my $answerunit=$LONCAPA::CAPAresponse_args{'unit'};
266: &LONCAPA_INTERNAL_DEBUG("Got type :$type: answer unit :$answerunit:\n");
267:
268: my $num_input_lines =
269: scalar(@{$LONCAPA::CAPAresponse_answer->{'answers'}});
270:
271: if ($type ne '' ) {
272: if (scalar(@$responses) < $num_input_lines) {
273: return 'MISSING_ANSWER';
274: }
275: if (scalar(@$responses) > $num_input_lines) {
276: return 'EXTRA_ANSWER';
277: }
278:
279: }
280:
281: foreach my $which (0..($num_input_lines-1)) {
282: my $answer_size =
283: scalar(@{$LONCAPA::CAPAresponse_answer->{'answers'}[$which]});
284: if ($type ne ''
285: && $answer_size > 1) {
286: $responses->[$which]=[split(/,/,$responses->[$which])];
287: } else {
288: $responses->[$which]=[$responses->[$which]];
289: }
290: }
291: foreach my $which (0..($num_input_lines-1)) {
292: my $answer_size =
293: scalar(@{$LONCAPA::CAPAresponse_answer->{'answers'}[$which]});
294: my $response_size =
295: scalar(@{$responses->[$which]});
296: if ($answer_size > $response_size) {
297: return 'MISSING_ANSWER';
298: }
299: if ($answer_size < $response_size) {
300: return 'EXTRA_ANSWER';
301: }
302: }
303:
304: &LONCAPA_INTERNAL_DEBUG("Initial final response :$responses->[0][-1]:");
305: my $unit;
306: if ($type eq '' || $type eq 'float') {
307: #for numerical problems split off the unit
308: # if ( $responses->[0][-1]=~ /(.*[^\s])\s+([^\s]+)/ ) {
309: if ( $responses->[0][-1]=~ /^([\d\.\,\s\$]*(?:(?:[xX\*]10[\^\*]*|[eE]*)[\+\-]*\d*)*(?:^|\S)\d+)([\$\s\w\^\*\/\(\)\+\-]*[^\d\.\s\,][\$\s\w\^\*\/\(\)\+\-]*)$/ ) {
310: $responses->[0][-1]=$1;
311: $unit=&capa_formula_fix($2);
312: &LONCAPA_INTERNAL_DEBUG("Found unit :$unit:");
313: }
314: }
315: &LONCAPA_INTERNAL_DEBUG("Final final response :$responses->[0][-1]:$unit:");
316: $unit=~s/\s//;
317: foreach my $response (@$responses) {
318: foreach my $element (@$response) {
319: $element =~ s/\s//g;
320: my $appendunit=$unit;
321: if ($unit=~/\%/) {
322: $element=$element/100;
323: $appendunit=~s/\%//;
324: }
325: if (($element==0) && ($unit!~/\w/) && ($answerunit=~/\w/)) {
326: $appendunit=$answerunit;
327: }
328: $element .= " $appendunit";
329: &LONCAPA_INTERNAL_DEBUG("Made response element :$element:");
330: }
331: }
332:
333: foreach my $thisanswer (@{ $LONCAPA::CAPAresponse_answer->{'answers'} }) {
334: if (!defined($thisanswer)) {
335: return ('ERROR','answer was undefined');
336: }
337: }
338:
339:
340: # &LONCAPA_INTERNAL_DEBUG(&LONCAPA_INTERNAL_Dumper($responses));
341: my %memoized;
342: if ($LONCAPA::CAPAresponse_answer->{'type'} eq 'ordered') {
343: for (my $i=0; $i<scalar(@$responses);$i++) {
344: my $answer = $LONCAPA::CAPAresponse_answer->{'answers'}[$i];
345: my $response = $responses->[$i];
346: my $key = "$answer\0$response";
347: my (@awards,@msgs);
348: for (my $j=0; $j<scalar(@$response); $j++) {
349: my ($award,$msg) = &caparesponse_check($answer->[$j],
350: $response->[$j]);
351: push(@awards,$award);
352: push(@msgs, $msg);
353: }
354: my ($award,$msg) =
355: &LONCAPA_INTERNAL_FINALIZEAWARDS(\@awards,\@msgs);
356: $memoized{$key} = [$award,$msg];
357: }
358: } else {
359: #FIXME broken with unorder responses where one is a <value>
360: # and the other is a <vector> (need to delay parse til
361: # inside the loop?)
362: foreach my $response (@$responses) {
363: my $response_size = scalar(@{$response});
364: foreach my $answer (@{ $LONCAPA::CAPAresponse_answer->{'answers'} }) {
365: my $key = "$answer\0$response";
366: my $answer_size = scalar(@{$answer});
367: my ($award,$msg);
368: if ($answer_size > $response_size) {
369: $award = 'MISSING_ANSWER';
370: } elsif ($answer_size < $response_size) {
371: $award = 'EXTRA_ANSWER';
372: } else {
373: my (@awards,@msgs);
374: for (my $j=0; $j<scalar(@$response); $j++) {
375: my ($award,$msg) = &caparesponse_check($answer->[$j],
376: $response->[$j]);
377: push(@awards,$award);
378: push(@msgs, $msg);
379: }
380: ($award,$msg) =
381: &LONCAPA_INTERNAL_FINALIZEAWARDS(\@awards,\@msgs);
382: }
383: $memoized{$key} = [$award,$msg];
384: }
385: }
386: }
387:
388: my ($final_award,$final_msg);
389: &init_permutation(scalar(@$responses),
390: $LONCAPA::CAPAresponse_answer->{'type'});
391:
392: # possible FIXMEs
393: # - significant time is spent calling non-safe space routine
394: # from safe space
395: # - early outs could be possible with classifying awards is to stratas
396: # and stopping as so as hitting the top strata
397: # - some early outs also might be possible with check ing the
398: # memoized hash of results (is correct even possible? etc.)
399:
400: my (@final_awards,@final_msg);
401: while( &get_permutations_left() ) {
402: my $order = &get_next_permutation();
403: my (@awards, @msgs, $i);
404: foreach my $thisanswer (@{ $LONCAPA::CAPAresponse_answer->{'answers'} }) {
405: my $key = "$thisanswer\0".$responses->[$order->[$i]];
406: push(@awards,$memoized{$key}[0]);
407: push(@msgs,$memoized{$key}[1]);
408: $i++;
409:
410: }
411: &LONCAPA_INTERNAL_DEBUG(" all awards ".join(':',@awards));
412:
413: my ($possible_award,$possible_msg) =
414: &LONCAPA_INTERNAL_FINALIZEAWARDS(\@awards,\@msgs);
415: &LONCAPA_INTERNAL_DEBUG(" pos awards ".$possible_award);
416: push(@final_awards,$possible_award);
417: push(@final_msg,$possible_msg);
418: }
419:
420: &LONCAPA_INTERNAL_DEBUG(" all final_awards ".join(':',@final_awards));
421: my ($final_award,$final_msg) =
422: &LONCAPA_INTERNAL_FINALIZEAWARDS(\@final_awards,\@final_msg,undef,1);
423: return ($final_award,$final_msg);
424: }
425:
426: sub cas {
427: my ($system,$input,$library)=@_;
428: my $output;
429: if ($system eq 'maxima') {
430: $output=&maxima_eval($input,$library);
431: } else {
432: $output='Error: unrecognized CAS';
433: }
434: return $output;
435: }
436:
437: sub tex {
438: if ( $external::target eq "tex" ) {
439: return $_[0];
440: } else {
441: return $_[1];
442: }
443: }
444:
445: sub var_in_tex {
446: if ( $external::target eq "tex" ) {
447: return $_[0];
448: } else {
449: return "";
450: }
451: }
452:
453: sub web {
454: if ( $external::target eq "tex" ) {
455: return $_[1];
456: } else {
457: if ( $external::target eq "web" || $external::target eq "answer") {
458: return $_[2];
459: } else {
460: return $_[0];
461: }
462: }
463: }
464:
465: sub html {
466: if ( $external::target eq "web" ) {
467: return shift;
468: }
469: }
470:
471: sub hinton {
472: return 0;
473: }
474:
475: sub random {
476: my ($start,$end,$step)=@_;
477: if ( ! $hidden::RANDOMINIT ) {
478: if ($external::randomseed == 0) { $external::randomseed=1; }
479: if ($external::randomseed =~/,/) {
480: my ($num1,$num2)=split(/,/,$external::randomseed);
481: &random_set_seed(1,abs($num1));
482: } elsif ($external::randomseed =~/:/) {
483: my ($num1,$num2)=split(/:/,$external::randomseed);
484: &random_set_seed(abs($num1),abs($num2));
485: } else {
486: &random_set_seed(1,int(abs($external::randomseed)));
487: }
488: &math_random_uniform();
489: $hidden::RANDOMINIT=1;
490: }
491: if (!defined($step)) { $step=1; }
492: my $num=1+int(($end-$start)/$step);
493: my $result=$start + int(&math_random_uniform() * $num)*$step;
494: return $result;
495: }
496:
497: sub random_normal {
498: my ($item_cnt,$seed,$av,$std_dev) = @_;
499: my @oldseed=&random_get_seed();
500: my @retArray;
501: &random_set_seed_from_phrase($seed);
502: @retArray=&math_random_normal($item_cnt,$av,$std_dev);
503: &random_set_seed(@oldseed);
504: return @retArray;
505: }
506:
507: sub random_beta {
508: my ($item_cnt,$seed,$aa,$bb) = @_;
509: my @oldseed=&random_get_seed();
510: my @retArray;
511: &random_set_seed_from_phrase($seed);
512: @retArray=&math_random_beta($item_cnt,$aa,$bb);
513: &random_set_seed(@oldseed);
514: return @retArray;
515: }
516:
517: sub random_gamma {
518: my ($item_cnt,$seed,$a,$r) = @_;
519: my @oldseed=&random_get_seed();
520: my @retArray;
521: &random_set_seed_from_phrase($seed);
522: @retArray=&math_random_gamma($item_cnt,$a,$r);
523: &random_set_seed(@oldseed);
524: return @retArray;
525: }
526:
527: sub random_exponential {
528: my ($item_cnt,$seed,$av) = @_;
529: my @oldseed=&random_get_seed();
530: my @retArray;
531: &random_set_seed_from_phrase($seed);
532: @retArray=&math_random_exponential($item_cnt,$av);
533: &random_set_seed(@oldseed);
534: return @retArray;
535: }
536:
537: sub random_poisson {
538: my ($item_cnt,$seed,$mu) = @_;
539: my @oldseed=&random_get_seed();
540: my @retArray;
541: &random_set_seed_from_phrase($seed);
542: @retArray=&math_random_poisson($item_cnt,$mu);
543: &random_set_seed(@oldseed);
544: return @retArray;
545: }
546:
547: sub random_chi {
548: my ($item_cnt,$seed,$df) = @_;
549: my @oldseed=&random_get_seed();
550: my @retArray;
551: &random_set_seed_from_phrase($seed);
552: @retArray=&math_random_chi_square($item_cnt,$df);
553: &random_set_seed(@oldseed);
554: return @retArray;
555: }
556:
557: sub random_noncentral_chi {
558: my ($item_cnt,$seed,$df,$nonc) = @_;
559: my @oldseed=&random_get_seed();
560: my @retArray;
561: &random_set_seed_from_phrase($seed);
562: @retArray=&math_random_noncentral_chi_square($item_cnt,$df,$nonc);
563: &random_set_seed(@oldseed);
564: return @retArray;
565: }
566:
567: sub random_f {
568: my ($item_cnt,$seed,$dfn,$dfd) = @_;
569: my @oldseed=&random_get_seed();
570: my @retArray;
571: &random_set_seed_from_phrase($seed);
572: @retArray=&math_random_f($item_cnt,$dfn,$dfd);
573: &random_set_seed(@oldseed);
574: return @retArray;
575: }
576:
577: sub random_noncentral_f {
578: my ($item_cnt,$seed,$dfn,$dfd,$nonc) = @_;
579: my @oldseed=&random_get_seed();
580: my @retArray;
581: &random_set_seed_from_phrase($seed);
582: @retArray=&math_random_noncentral_f($item_cnt,$dfn,$dfd,$nonc);
583: &random_set_seed(@oldseed);
584: return @retArray;
585: }
586:
587: sub random_multivariate_normal {
588: my ($item_cnt,$seed,$mean,$covar) = @_;
589: my @oldseed=&random_get_seed();
590: &random_set_seed_from_phrase($seed);
591: my @retArray=&math_random_multivariate_normal($item_cnt,@$mean,@$covar);
592: &random_set_seed(@oldseed);
593: return @retArray;
594: }
595:
596: sub random_multinomial {
597: my ($item_cnt,$seed,@p) = @_;
598: my @oldseed=&random_get_seed();
599: my @retArray;
600: &random_set_seed_from_phrase($seed);
601: my @retArray=&math_random_multinomial($item_cnt,@p);
602: &random_set_seed(@oldseed);
603: return @retArray;
604: }
605:
606: sub random_permutation {
607: my ($seed,@inArray) = @_;
608: my @oldseed=&random_get_seed();
609: my @retArray;
610: &random_set_seed_from_phrase($seed);
611: @retArray=&math_random_permutation(@inArray);
612: &random_set_seed(@oldseed);
613: return @retArray;
614: }
615:
616: sub random_uniform {
617: my ($item_cnt,$seed,$low,$high) = @_;
618: my @oldseed=&random_get_seed();
619: my @retArray;
620: &random_set_seed_from_phrase($seed);
621: @retArray=&math_random_uniform($item_cnt,$low,$high);
622: &random_set_seed(@oldseed);
623: return @retArray;
624: }
625:
626: sub random_uniform_integer {
627: my ($item_cnt,$seed,$low,$high) = @_;
628: my @oldseed=&random_get_seed();
629: my @retArray;
630: &random_set_seed_from_phrase($seed);
631: @retArray=&math_random_uniform_integer($item_cnt,$low,$high);
632: &random_set_seed(@oldseed);
633: return @retArray;
634: }
635:
636: sub random_binomial {
637: my ($item_cnt,$seed,$nt,$p) = @_;
638: my @oldseed=&random_get_seed();
639: my @retArray;
640: &random_set_seed_from_phrase($seed);
641: @retArray=&math_random_binomial($item_cnt,$nt,$p);
642: &random_set_seed(@oldseed);
643: return @retArray;
644: }
645:
646: sub random_negative_binomial {
647: my ($item_cnt,$seed,$ne,$p) = @_;
648: my @oldseed=&random_get_seed();
649: my @retArray;
650: &random_set_seed_from_phrase($seed);
651: @retArray=&math_random_negative_binomial($item_cnt,$ne,$p);
652: &random_set_seed(@oldseed);
653: return @retArray;
654: }
655:
656: sub abs { CORE::abs(shift) }
657: sub sin { CORE::sin(shift) }
658: sub cos { CORE::cos(shift) }
659: sub exp { CORE::exp(shift) }
660: sub int { CORE::int(shift) }
661: sub log { CORE::log(shift) }
662: sub atan2 { CORE::atan2($_[0],$_[1]) }
663: sub sqrt { CORE::sqrt(shift) }
664:
665: sub tan { CORE::sin($_[0]) / CORE::cos($_[0]) }
666: #sub atan { atan2($_[0], 1); }
667: #sub acos { atan2(sqrt(1 - $_[0] * $_[0]), $_[0] ); }
668: #sub asin { atan2($_[0], sqrt(1- $_[0] * $_[0]) ); }
669:
670: sub log10 { CORE::log($_[0])/CORE::log(10); }
671:
672: sub factorial {
673: my $input = CORE::int(shift);
674: return "Error - unable to take factorial of an negative number ($input)" if $input < 0;
675: return "Error - factorial result is greater than system limit ($input)" if $input > 170;
676: return 1 if $input == 0;
677: my $result = 1;
678: for (my $i=2; $i<=$input; $i++) { $result *= $i }
679: return $result;
680: }
681:
682: sub sgn {
683: return -1 if $_[0] < 0;
684: return 0 if $_[0] == 0;
685: return 1 if $_[0] > 0;
686: }
687:
688: sub min {
689: my @sorted = sort { $a <=> $b || $a cmp $b } @_;
690: return shift @sorted;
691: }
692:
693: sub max {
694: my @sorted = sort { $a <=> $b || $a cmp $b } @_;
695: return pop @sorted;
696: }
697:
698: sub roundto {
699: my ($input,$n) = @_;
700: return sprintf('%.'.$n.'f',$input);
701: }
702:
703: sub to_string {
704: my ($input,$n) = @_;
705: return sprintf($input) if $n eq "";
706: $n = '.'.$n if $n !~ /^\./;
707: return sprintf('%'.$n,$input) if $n ne "";
708: }
709:
710: sub sub_string {
711: my ($str,$start,$len) = @_;
712: return substr($str,$start-1,$len);
713: }
714:
715: sub pow {return $_[0] ** $_[1]; }
716: sub ceil {return (($_[0]-CORE::int($_[0]))== 0.0) ? $_[0] : (($_[0] > 0) ? (CORE::int($_[0])+ 1) : CORE::int($_[0])); }
717: sub floor {return (($_[0]-CORE::int($_[0]))== 0.0) ? $_[0] : (($_[0] > 0) ? CORE::int($_[0]) : (CORE::int($_[0])-1)); }
718: #sub floor {return int($_[0]); }
719:
720: sub format {
721: my ($value,$fmt)=@_;
722: my ($dollarmode,$commamode,$alwaysperiod,$options);
723: if ($fmt =~ /^([^\d]*)(.*)/) { $options=$1; $fmt=$2; }
724: #if ($options =~ /\$/) { $dollamode=1; }
725: #if ($options =~ /,/) { $commamode=1; }
726: if ($options =~ /\./) { $alwaysperiod=1; }
727: my $result;
728: if ($fmt=~/s$/i) {
729: $result=&format_significant_figures($value,$fmt);
730: } else {
731: $fmt=~s/e/E/g;
732: $result=sprintf('%.'.$fmt,$value);
733: if ($alwaysperiod && $fmt eq '0f') { $result .='.'; }
734: $result=~s/(E[+-]*)0/$1/;
735: }
736: #if ($dollarmode) {$result=&dollarformat($result);}
737: #if ($commamode) {$result=&commaformat($result);}
738: return $result;
739: }
740:
741: sub chemparse {
742: my ($reaction) = @_;
743: my @tokens = split(/(\s\+|\->|<=>|<\-|\.)/,$reaction);
744: my $formula = '';
745: foreach my $token (@tokens) {
746: if ($token eq '->' ) {
747: $formula .= '<m>\ensuremath{\rightarrow}</m> ';
748: next;
749: }
750: if ($token eq '<-' ) {
751: $formula .= '<m>\ensuremath{\leftarrow}</m> ';
752: next;
753: }
754: if ($token eq '<=>') {
755: if ($external::target eq 'web' &&
756: &EXT('request.browser.unicode')) {
757: $formula .= '⇌ ';
758: } else {
759: $formula .= &web('<=> ','<m>\ensuremath{\rightleftharpoons}</m> ',
760: '<=> ');
761: }
762: next;
763: }
764: if ($token eq '.') {
765: $formula =~ s/(\ \;| )$//;
766: $formula .= '·';
767: next;
768: }
769: $token =~ /^\s*([\d|\/]*(?:&frac\d\d)?)(.*)/;
770: $formula .= $1 if ($1 ne '1'); # stoichiometric coefficient
771:
772: my $molecule = $2;
773: # subscripts
774: $molecule =~ s|(?<=[a-zA-Z\)\]\s])(\d+)|<sub>$1</sub>|g;
775: # superscripts
776: $molecule =~ s|\^(\d*[+\-]*)|<sup>$1</sup>|g;
777: # strip whitespace
778: $molecule =~ s/\s*//g;
779: # forced space
780: $molecule =~ s/_/ /g;
781: $molecule =~ s/-/−/g;
782: $formula .= $molecule.' ';
783: }
784: # get rid of trailing space
785: $formula =~ s/(\ \;| )$//;
786: return &xmlparse($formula);
787: }
788:
789: sub prettyprint {
790: my ($value,$fmt,$target)=@_;
791: my $result;
792: if (!$target) { $target = $external::target; }
793: if ($fmt =~ /chem/i) { return(&chemparse($value)); }
794: my ($dollarmode,$commamode,$alwaysperiod,$options);
795: if ($fmt =~ /^([^\d]*)(.*)/) { $options=$1; $fmt=$2; }
796: if ($options =~ /\$/) { $dollarmode=1; }
797: if ($options =~ /,/) { $commamode=1; }
798: if ($options =~ /\./) { $alwaysperiod=1; }
799: if ($fmt=~/s$/i) {
800: $value=&format_significant_figures($value,$fmt);
801: } elsif ($fmt) {
802: $value=sprintf('%.'.$fmt,$value);
803: }
804: if ($alwaysperiod && $fmt eq '0f') {
805: if ($target eq 'tex') {
806: $value .='\\ensuremath{.}';
807: } else {
808: $value .='.';
809: }
810: }
811: if ($value =~ /([0-9\.\-\+]+)E([0-9\-\+]+)/i ) {
812: my $frac=$1;
813: if ($dollarmode) { $frac=&dollarformat($frac); }
814: if ($commamode) { $frac=&commaformat($frac); }
815: my $exponent=$2;
816: $exponent=~s/^\+0*//;
817: $exponent=~s/^-0*/-/;
818: $exponent=~s/^-0*/-/;
819: if ($exponent eq '-') { undef($exponent); }
820: if ($exponent) {
821: if ($target eq 'web') {
822: $result=$frac.'×10<sup>'.$exponent.'</sup>';
823: } elsif ($target eq 'tex') {
824: $result='\ensuremath{'.$frac.'\times 10^{'.$exponent.'}}';
825: } else {
826: $result=$value;
827: }
828: } else {
829: $result=$frac;
830: }
831: } else {
832: $result=$value;
833: if ($dollarmode) { $result=&dollarformat($result,$target); }
834: elsif ($commamode) { $result=&commaformat($result,$target); }
835: }
836: return $result;
837: }
838:
839: sub commaformat {
840: my ($number,$target) = @_;
841: if ($number =~ /\./) {
842: while ($number =~ /([^0-9]*)([0-9]+)([^\.,][^\.,][^\.,])([,0-9]*\.[0-9]*)$/) {
843: $number = $1.$2.','.$3.$4;
844: }
845: } else {
846: while ($number =~ /^([^0-9]*)([0-9]+)([^,][^,][^,])([,0-9]*)$/) {
847: $number = $1.$2.','.$3.$4;
848: }
849: }
850: return $number;
851: }
852:
853: sub dollarformat {
854: my ($number,$target) = @_;
855: if (!$target) { $target = $external::target; }
856: $number=&commaformat($number,$target);
857: if ($target eq 'tex') {
858: $number='\$'.$number; #' stupid emacs
859: } else {
860: $number='$'.$number; #' stupid emacs
861: }
862: return $number;
863: }
864:
865: # format of form ns or nS where n is an integer
866: sub format_significant_figures {
867: my ($number,$format) = @_;
868: return '0' if ($number == 0);
869: # extract number of significant figures needed
870: my ($sig) = ($format =~ /(\d+)s/i);
871: # arbitrary choice - suggestions ?? or throw error message?
872: $sig = 3 if ($sig eq '');
873: # save the minus sign
874: my $sign = ($number < 0) ? '-' : '';
875: $number = abs($number);
876: # needed to correct for a number greater than 1 (or
877: my $power = ($number < 1) ? 0 : 1;
878: # could round up. Take the integer part of log10.
879: my $x10 = int(log($number)/log(10));
880: # find number with values left of decimal pt = # of sign figs.
881: my $xsig = $number*10**($sig-$x10-$power);
882: # get just digits left of decimal pt - also rounds off correctly
883: my $xint = sprintf('%.0f',$xsig);
884: # save any trailing zero's
885: my ($zeros) = ($xint =~ /(0+)$/);
886: # return number to original magnitude
887: my $numSig = $xint*10**($x10-$sig+$power);
888: # insert trailing zero's if have decimal point
889: $numSig =~ s/^(\d+)\.(\d+)(\e?(.*)?)$/$1\.$2$zeros$3/;
890: # put a decimal pt for number ending with 0 and length = # of sig fig
891: $numSig.='.' if (length($numSig) == $sig && $numSig =~ /0$/);
892: if (length($numSig) < $sig) {
893: $numSig.='.'.substr($zeros,0,($sig-length($numSig)));
894: }
895: # return number with sign
896: return $sign.$numSig;
897:
898: }
899:
900: sub map {
901: my ($phrase,$dest,$source)=@_;
902: my @oldseed=&random_get_seed();
903: my @seed = &random_seed_from_phrase($phrase);
904: &random_set_seed(@seed);
905: my $destct = scalar(@$dest);
906: if (!$source) {
907: my @output;
908: my @idx = &math_random_permuted_index($destct);
909: my $ctr = 0;
910: while ($ctr < $destct) {
911: $output[$ctr] = $$dest[$idx[$ctr]];
912: $ctr++;
913: }
914: &random_set_seed(@oldseed);
915: return @output;
916: } else {
917: my $num = scalar(@$source);
918: my @idx = &math_random_permuted_index($num);
919: my $ctr = 0;
920: my $tot = $num;
921: $tot = $destct if $destct < $num;
922: if (ref($$dest[0])) {
923: while ($ctr < $tot) {
924: ${$$dest[$ctr]} = $$source[$idx[$ctr]];
925: $ctr++;
926: }
927: } else {
928: while ($ctr < $tot) {
929: $$dest[$ctr] = $$source[$idx[$ctr]];
930: $ctr++;
931: }
932: }
933: }
934: &random_set_seed(@oldseed);
935: return '';
936: }
937:
938: sub rmap {
939: my ($phrase,$dest,$source)=@_;
940: my @oldseed=&random_get_seed();
941: my @seed = &random_seed_from_phrase($phrase);
942: &random_set_seed(@seed);
943: my $destct = scalar(@$dest);
944: if (!$source) {
945: my @idx = &math_random_permuted_index($destct);
946: my $ctr = 0;
947: my @r_idx;
948: while ($ctr < $destct) {
949: $r_idx[$idx[$ctr]] = $ctr;
950: $ctr++;
951: }
952: my @output;
953: $ctr = 0;
954: while ($ctr < $destct) {
955: $output[$ctr] = $$dest[$r_idx[$ctr]];
956: $ctr++;
957: }
958: &random_set_seed(@oldseed);
959: return @output;
960: } else {
961: my $num = scalar(@$source);
962: my @idx = &math_random_permuted_index($num);
963: my $ctr = 0;
964: my $tot = $num;
965: $tot = $destct if $destct < $num;
966: my @r_idx;
967: while ($ctr < $tot) {
968: $r_idx[$idx[$ctr]] = $ctr;
969: $ctr++;
970: }
971: $ctr = 0;
972: if (ref($$dest[0])) {
973: while ($ctr < $tot) {
974: ${$$dest[$ctr]} = $$source[$r_idx[$ctr]];
975: $ctr++;
976: }
977: } else {
978: while ($ctr < $tot) {
979: $$dest[$ctr] = $$source[$r_idx[$ctr]];
980: $ctr++;
981: }
982: }
983: }
984: &random_set_seed(@oldseed);
985: return '';
986: }
987:
988: sub capa_id { return }
989:
990: sub problem { return }
991:
992: sub name{
993: my $fullname = &EXT('environment.lastname').', '.&EXT('environment.firstname').' '.&EXT('environment.middlename');
994: $fullname = "" if $fullname eq ", ";
995: $fullname =~ s/\%2d/-/g;
996: return $fullname;
997: }
998:
999: sub student_number {
1000: my $id = &EXT('environment.id');
1001: $id = '' if $id eq "";
1002: return $id;
1003: }
1004:
1005: sub class {
1006: my $course = &EXT('course.description');
1007: $course = '' if $course eq "";
1008: return $course;
1009: }
1010:
1011: sub firstname {
1012: my $firstname = &EXT('environment.firstname');
1013: $firstname = '' if $firstname eq "";
1014: return $firstname;
1015: }
1016:
1017: sub lastname {
1018: my $lastname = &EXT('environment.lastname');
1019: $lastname = '' if $lastname eq "";
1020: return $lastname;
1021: }
1022:
1023: sub sec {
1024: my $sec = &EXT('request.course.sec');
1025: $sec = '' if $sec eq "";
1026: return $sec;
1027: }
1028:
1029: sub submission {
1030: my ($partid,$responseid,$subnumber)=@_;
1031: my $sub='';
1032: if ($subnumber) { $sub=$subnumber.':'; }
1033: return &EXT('user.resource.'.$sub.'resource.'.$partid.'.'.$responseid.'.submission');
1034: }
1035:
1036: sub currentpart {
1037: return $external::part;
1038: }
1039:
1040: sub eval_time {
1041: my ($timestamp)=@_;
1042: unless ($timestamp) { return ''; }
1043: return &locallocaltime($timestamp);
1044: }
1045:
1046: sub open_date {
1047: my ($partid)=@_;
1048: unless ($partid) { $partid=0; }
1049: return &eval_time(&EXT('resource.'.$partid.'.opendate'));
1050: }
1051:
1052: sub due_date {
1053: my ($partid)=@_;
1054: unless ($partid) { $partid=0; }
1055: return &eval_time(&EXT('resource.'.$partid.'.duedate'));
1056: }
1057:
1058: sub answer_date {
1059: my ($partid)=@_;
1060: unless ($partid) { $partid=0; }
1061: return &eval_time(&EXT('resource.'.$partid.'.answerdate'));
1062: }
1063:
1064: sub open_date_epoch {
1065: my ($partid)=@_;
1066: unless ($partid) { $partid=0; }
1067: return &EXT('resource.'.$partid.'.opendate');
1068: }
1069:
1070: sub due_date_epoch {
1071: my ($partid)=@_;
1072: unless ($partid) { $partid=0; }
1073: return &EXT('resource.'.$partid.'.duedate');
1074: }
1075:
1076: sub answer_date_epoch {
1077: my ($partid)=@_;
1078: unless ($partid) { $partid=0; }
1079: return &EXT('resource.'.$partid.'.answerdate');
1080: }
1081:
1082: sub array_moments {
1083: my @input=@_;
1084: my (@output,$N);
1085: $N=scalar (@input);
1086: $output[0]=$N;
1087: if ($N <= 1) {
1088: $output[1]=$input[0];
1089: $output[1]="Input array not defined" if ($N == 0);
1090: $output[2]="variance undefined for N<=1";
1091: $output[3]="skewness undefined for N<=1";
1092: $output[4]="kurtosis undefined for N<=1";
1093: return @output;
1094: }
1095: my $sum=0;
1096: foreach my $line (@input) {
1097: $sum+=$line;
1098: }
1099: $output[1] = $sum/$N;
1100: my ($x,$sdev,$var,$skew,$kurt) = 0;
1101: foreach my $line (@input) {
1102: $x=$line-$output[1];
1103: $var+=$x**2;
1104: $skew+=$x**3;
1105: $kurt+=$x**4;
1106: }
1107: $output[2]=$var/($N-1);
1108: $sdev=CORE::sqrt($output[2]);
1109: if ($sdev == 0) {
1110: $output[3]="inf-variance=0";
1111: $output[4]="inf-variance=0";
1112: return @output;
1113: }
1114: $output[3]=$skew/($sdev**3*$N);
1115: $output[4]=$kurt/($sdev**4*$N)-3;
1116: return @output;
1117: }
1118:
1119: sub choose {
1120: my $num = $_[0];
1121: return $_[$num];
1122: }
1123:
1124: #&sum1(1,$x,sub { &sum1($_[0],2*$_[0], sub { fact($_[0])**2 })});
1125: #sub sum1 {
1126: # my ($start,$end,$sub)=@_;
1127: # my $sum=0;
1128: # for (my $i=$start;$i<=$end;$i++) {
1129: # $sum+=&$sub($i);
1130: # }
1131: # return $sum
1132: #}
1133:
1134: #&sum2('a',1,$x,'&sum2(\'b\',$a,2*$a, \'&factorial($b)**2\')');
1135: #sub sum2 {
1136: # my ($varname,$start,$end,$line)=@_;
1137: # my $sum=0;
1138: # for (my $i=$start;$i<=$end;$i++) {
1139: # my $func=sub {
1140: # eval("\$".$varname."=$i");
1141: # eval($line);
1142: # };
1143: # $sum+=&$func($i);
1144: # }
1145: # return $sum
1146: #}
1147:
1148: # expiremental idea
1149: sub proper_path {
1150: my ($path)=@_;
1151: if ( $external::target eq "tex" ) {
1152: return '/home/httpd/html'.$path;
1153: } else {
1154: return $path;
1155: }
1156: }
1157:
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