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 1.142 2008/11/26 18:11:52 raeburn 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') || ($type eq '8')) {
221: if ($response=~/\=/) {
222: return ('BAD_FORMULA','Please submit just an expression, not an equation.');
223: } elsif ($response =~ /\,/) {
224: return ('BAD_FORMULA');
225: }
226: }
227: if ($type eq '9') {
228: $result = &maxima_check(&maxima_cas_formula_fix($response),&maxima_cas_formula_fix($answer),\$reterror);
229: } else {
230: if ($type eq '8') { # fml type
231: $response = &capa_formula_fix($response);
232: $answer = &capa_formula_fix($answer);
233: }
234: $result = &caparesponse_capa_check_answer($response,$answer,$type,
235: $tol_type,$tol,
236: $sig_lbound,$sig_ubound,
237: $ans_fmt,$unit,$calc,$id_list,
238: $points,$external::randomseed,
239: \$reterror);
240: }
241: if ($result == '1') { $result='EXACT_ANS'; }
242: elsif ($result == '2') { $result='APPROX_ANS'; }
243: elsif ($result == '3') { $result='SIG_FAIL'; }
244: elsif ($result == '4') { $result='UNIT_FAIL'; }
245: elsif ($result == '5') { $result='NO_UNIT'; }
246: elsif ($result == '6') { $result='UNIT_OK'; }
247: elsif ($result == '7') { $result='INCORRECT'; }
248: elsif ($result == '8') { $result='UNIT_NOTNEEDED'; }
249: elsif ($result == '9') { $result='ANS_CNT_NOT_MATCH'; }
250: elsif ($result =='10') { $result='SUB_RECORDED'; }
251: elsif ($result =='11') { $result='BAD_FORMULA'; }
252: elsif ($result =='12' && !$response) { $result='MISSING_ANSWER'; }
253: elsif ($result =='12') { $result='WANTED_NUMERIC'; }
254: elsif ($result =='13') { $result='UNIT_INVALID_INSTRUCTOR'; }
255: elsif ($result =='141') { $result='UNIT_INVALID_STUDENT'; }
256: elsif ($result =='142') { $result='UNIT_INVALID_STUDENT'; }
257: elsif ($result =='143') { $result='UNIT_INVALID_STUDENT'; }
258: elsif ($result =='15') { $result='UNIT_IRRECONCIBLE'; }
259: else {$result = "ERROR: Unknown Result:$result:$@:";}
260:
261: &LONCAPA_INTERNAL_DEBUG("RetError $reterror: Answer $answer: Response $response: type-$type|$tol|$tol_type|$sig:$sig_lbound:$sig_ubound|$unit|");
262: &LONCAPA_INTERNAL_DEBUG(" $answer $response $result ");
263: return ($result,$reterror);
264: }
265:
266:
267: sub caparesponse_check_list {
268: my $responses=$LONCAPA::CAPAresponse_args{'response'};
269: &LONCAPA_INTERNAL_DEBUG("args ".join(':',%LONCAPA::CAPAresponse_args));
270: my $type = $LONCAPA::CAPAresponse_args{'type'};
271: my $answerunit=$LONCAPA::CAPAresponse_args{'unit'};
272: &LONCAPA_INTERNAL_DEBUG("Got type :$type: answer unit :$answerunit:\n");
273:
274: my $num_input_lines =
275: scalar(@{$LONCAPA::CAPAresponse_answer->{'answers'}});
276:
277: if ($type ne '' ) {
278: if (scalar(@$responses) < $num_input_lines) {
279: return 'MISSING_ANSWER';
280: }
281: if (scalar(@$responses) > $num_input_lines) {
282: return 'EXTRA_ANSWER';
283: }
284:
285: }
286:
287: foreach my $which (0..($num_input_lines-1)) {
288: my $answer_size =
289: scalar(@{$LONCAPA::CAPAresponse_answer->{'answers'}[$which]});
290: if ($type ne ''
291: && $answer_size > 1) {
292: $responses->[$which]=[split(/,/,$responses->[$which])];
293: } else {
294: $responses->[$which]=[$responses->[$which]];
295: }
296: }
297: foreach my $which (0..($num_input_lines-1)) {
298: my $answer_size =
299: scalar(@{$LONCAPA::CAPAresponse_answer->{'answers'}[$which]});
300: my $response_size =
301: scalar(@{$responses->[$which]});
302: if ($answer_size > $response_size) {
303: return 'MISSING_ANSWER';
304: }
305: if ($answer_size < $response_size) {
306: return 'EXTRA_ANSWER';
307: }
308: }
309:
310: &LONCAPA_INTERNAL_DEBUG("Initial final response :$responses->[0][-1]:");
311: my $unit;
312: if ($type eq 'float' || $type eq '') {
313: #for numerical problems split off the unit
314: # if ( $responses->[0][-1]=~ /(.*[^\s])\s+([^\s]+)/ ) {
315: if ( $responses->[0][-1]=~ /^([\d\.\,\s\$]*(?:(?:[xX\*]10[\^\*]*|[eE]*)[\+\-]*\d*)*(?:^|\S)\d+)([\$\s\w\^\*\/\(\)\+\-]*[^\d\.\s\,][\$\s\w\^\*\/\(\)\+\-]*)$/ ) {
316: $responses->[0][-1]=$1;
317: $unit=&capa_formula_fix($2);
318: &LONCAPA_INTERNAL_DEBUG("Found unit :$unit:");
319: }
320: }
321: &LONCAPA_INTERNAL_DEBUG("Final final response :$responses->[0][-1]:$unit:");
322: $unit=~s/\s//;
323: foreach my $response (@$responses) {
324: foreach my $element (@$response) {
325: if (($type eq 'float') || (($type eq '') && ($unit ne ''))) {
326: $element =~ s/\s//g;
327: }
328: my $appendunit=$unit;
329: if (($unit=~/\%/) && ($answerunit ne '%')) {
330: $element=$element/100;
331: $appendunit=~s/\%//;
332: }
333: if (($element==0) && ($unit!~/\w/) && ($answerunit=~/\w/)) {
334: $appendunit=$answerunit;
335: }
336: $element .= " $appendunit";
337: &LONCAPA_INTERNAL_DEBUG("Made response element :$element:");
338: }
339: }
340:
341: foreach my $thisanswer (@{ $LONCAPA::CAPAresponse_answer->{'answers'} }) {
342: if (!defined($thisanswer)) {
343: return ('ERROR','answer was undefined');
344: }
345: }
346:
347:
348: # &LONCAPA_INTERNAL_DEBUG(&LONCAPA_INTERNAL_Dumper($responses));
349: my %memoized;
350: if ($LONCAPA::CAPAresponse_answer->{'type'} eq 'ordered') {
351: for (my $i=0; $i<scalar(@$responses);$i++) {
352: my $answer = $LONCAPA::CAPAresponse_answer->{'answers'}[$i];
353: my $response = $responses->[$i];
354: my $key = "$answer\0$response";
355: my (@awards,@msgs);
356: for (my $j=0; $j<scalar(@$response); $j++) {
357: my ($award,$msg) = &caparesponse_check($answer->[$j],
358: $response->[$j]);
359: push(@awards,$award);
360: push(@msgs, $msg);
361: }
362: my ($award,$msg) =
363: &LONCAPA_INTERNAL_FINALIZEAWARDS(\@awards,\@msgs);
364: $memoized{$key} = [$award,$msg];
365: }
366: } else {
367: #FIXME broken with unorder responses where one is a <value>
368: # and the other is a <vector> (need to delay parse til
369: # inside the loop?)
370: foreach my $response (@$responses) {
371: my $response_size = scalar(@{$response});
372: foreach my $answer (@{ $LONCAPA::CAPAresponse_answer->{'answers'} }) {
373: my $key = "$answer\0$response";
374: my $answer_size = scalar(@{$answer});
375: my ($award,$msg);
376: if ($answer_size > $response_size) {
377: $award = 'MISSING_ANSWER';
378: } elsif ($answer_size < $response_size) {
379: $award = 'EXTRA_ANSWER';
380: } else {
381: my (@awards,@msgs);
382: for (my $j=0; $j<scalar(@$response); $j++) {
383: my ($award,$msg) = &caparesponse_check($answer->[$j],
384: $response->[$j]);
385: push(@awards,$award);
386: push(@msgs, $msg);
387: }
388: ($award,$msg) =
389: &LONCAPA_INTERNAL_FINALIZEAWARDS(\@awards,\@msgs);
390: }
391: $memoized{$key} = [$award,$msg];
392: }
393: }
394: }
395:
396: my ($final_award,$final_msg);
397: &init_permutation(scalar(@$responses),
398: $LONCAPA::CAPAresponse_answer->{'type'});
399:
400: # possible FIXMEs
401: # - significant time is spent calling non-safe space routine
402: # from safe space
403: # - early outs could be possible with classifying awards is to stratas
404: # and stopping as so as hitting the top strata
405: # - some early outs also might be possible with check ing the
406: # memoized hash of results (is correct even possible? etc.)
407:
408: my (@final_awards,@final_msg);
409: while( &get_permutations_left() ) {
410: my $order = &get_next_permutation();
411: my (@awards, @msgs, $i);
412: foreach my $thisanswer (@{ $LONCAPA::CAPAresponse_answer->{'answers'} }) {
413: my $key = "$thisanswer\0".$responses->[$order->[$i]];
414: push(@awards,$memoized{$key}[0]);
415: push(@msgs,$memoized{$key}[1]);
416: $i++;
417:
418: }
419: &LONCAPA_INTERNAL_DEBUG(" all awards ".join(':',@awards));
420:
421: my ($possible_award,$possible_msg) =
422: &LONCAPA_INTERNAL_FINALIZEAWARDS(\@awards,\@msgs);
423: &LONCAPA_INTERNAL_DEBUG(" pos awards ".$possible_award);
424: push(@final_awards,$possible_award);
425: push(@final_msg,$possible_msg);
426: }
427:
428: &LONCAPA_INTERNAL_DEBUG(" all final_awards ".join(':',@final_awards));
429: my ($final_award,$final_msg) =
430: &LONCAPA_INTERNAL_FINALIZEAWARDS(\@final_awards,\@final_msg,undef,1);
431: return ($final_award,$final_msg);
432: }
433:
434: sub cas {
435: my ($system,$input,$library)=@_;
436: my $output;
437: if ($system eq 'maxima') {
438: $output=&maxima_eval($input,$library);
439: } else {
440: $output='Error: unrecognized CAS';
441: }
442: return $output;
443: }
444:
445: sub tex {
446: if ( $external::target eq "tex" ) {
447: return $_[0];
448: } else {
449: return $_[1];
450: }
451: }
452:
453: sub var_in_tex {
454: if ( $external::target eq "tex" ) {
455: return $_[0];
456: } else {
457: return "";
458: }
459: }
460:
461: sub web {
462: if ( $external::target eq "tex" ) {
463: return $_[1];
464: } else {
465: if ( $external::target eq "web" || $external::target eq "answer") {
466: return $_[2];
467: } else {
468: return $_[0];
469: }
470: }
471: }
472:
473: sub html {
474: if ( $external::target eq "web" ) {
475: return shift;
476: }
477: }
478:
479: sub hinton {
480: return 0;
481: }
482:
483: sub random {
484: my ($start,$end,$step)=@_;
485: if ( ! $hidden::RANDOMINIT ) {
486: if ($external::randomseed == 0) { $external::randomseed=1; }
487: if ($external::randomseed =~/,/) {
488: my ($num1,$num2)=split(/,/,$external::randomseed);
489: &random_set_seed(1,abs($num1));
490: } elsif ($external::randomseed =~/:/) {
491: my ($num1,$num2)=split(/:/,$external::randomseed);
492: &random_set_seed(abs($num1),abs($num2));
493: } else {
494: &random_set_seed(1,int(abs($external::randomseed)));
495: }
496: &math_random_uniform();
497: $hidden::RANDOMINIT=1;
498: }
499: if (!defined($step)) { $step=1; }
500: my $num=1+int(($end-$start)/$step);
501: my $result=$start + int(&math_random_uniform() * $num)*$step;
502: return $result;
503: }
504:
505: sub random_normal {
506: my ($item_cnt,$seed,$av,$std_dev) = @_;
507: my @oldseed=&random_get_seed();
508: my @retArray;
509: &random_set_seed_from_phrase($seed);
510: @retArray=&math_random_normal($item_cnt,$av,$std_dev);
511: &random_set_seed(@oldseed);
512: return @retArray;
513: }
514:
515: sub random_beta {
516: my ($item_cnt,$seed,$aa,$bb) = @_;
517: my @oldseed=&random_get_seed();
518: my @retArray;
519: &random_set_seed_from_phrase($seed);
520: @retArray=&math_random_beta($item_cnt,$aa,$bb);
521: &random_set_seed(@oldseed);
522: return @retArray;
523: }
524:
525: sub random_gamma {
526: my ($item_cnt,$seed,$a,$r) = @_;
527: my @oldseed=&random_get_seed();
528: my @retArray;
529: &random_set_seed_from_phrase($seed);
530: @retArray=&math_random_gamma($item_cnt,$a,$r);
531: &random_set_seed(@oldseed);
532: return @retArray;
533: }
534:
535: sub random_exponential {
536: my ($item_cnt,$seed,$av) = @_;
537: my @oldseed=&random_get_seed();
538: my @retArray;
539: &random_set_seed_from_phrase($seed);
540: @retArray=&math_random_exponential($item_cnt,$av);
541: &random_set_seed(@oldseed);
542: return @retArray;
543: }
544:
545: sub random_poisson {
546: my ($item_cnt,$seed,$mu) = @_;
547: my @oldseed=&random_get_seed();
548: my @retArray;
549: &random_set_seed_from_phrase($seed);
550: @retArray=&math_random_poisson($item_cnt,$mu);
551: &random_set_seed(@oldseed);
552: return @retArray;
553: }
554:
555: sub random_chi {
556: my ($item_cnt,$seed,$df) = @_;
557: my @oldseed=&random_get_seed();
558: my @retArray;
559: &random_set_seed_from_phrase($seed);
560: @retArray=&math_random_chi_square($item_cnt,$df);
561: &random_set_seed(@oldseed);
562: return @retArray;
563: }
564:
565: sub random_noncentral_chi {
566: my ($item_cnt,$seed,$df,$nonc) = @_;
567: my @oldseed=&random_get_seed();
568: my @retArray;
569: &random_set_seed_from_phrase($seed);
570: @retArray=&math_random_noncentral_chi_square($item_cnt,$df,$nonc);
571: &random_set_seed(@oldseed);
572: return @retArray;
573: }
574:
575: sub random_f {
576: my ($item_cnt,$seed,$dfn,$dfd) = @_;
577: my @oldseed=&random_get_seed();
578: my @retArray;
579: &random_set_seed_from_phrase($seed);
580: @retArray=&math_random_f($item_cnt,$dfn,$dfd);
581: &random_set_seed(@oldseed);
582: return @retArray;
583: }
584:
585: sub random_noncentral_f {
586: my ($item_cnt,$seed,$dfn,$dfd,$nonc) = @_;
587: my @oldseed=&random_get_seed();
588: my @retArray;
589: &random_set_seed_from_phrase($seed);
590: @retArray=&math_random_noncentral_f($item_cnt,$dfn,$dfd,$nonc);
591: &random_set_seed(@oldseed);
592: return @retArray;
593: }
594:
595: sub random_multivariate_normal {
596: my ($item_cnt,$seed,$mean,$covar) = @_;
597: my @oldseed=&random_get_seed();
598: &random_set_seed_from_phrase($seed);
599: my @retArray=&math_random_multivariate_normal($item_cnt,@$mean,@$covar);
600: &random_set_seed(@oldseed);
601: return @retArray;
602: }
603:
604: sub random_multinomial {
605: my ($item_cnt,$seed,@p) = @_;
606: my @oldseed=&random_get_seed();
607: my @retArray;
608: &random_set_seed_from_phrase($seed);
609: my @retArray=&math_random_multinomial($item_cnt,@p);
610: &random_set_seed(@oldseed);
611: return @retArray;
612: }
613:
614: sub random_permutation {
615: my ($seed,@inArray) = @_;
616: my @oldseed=&random_get_seed();
617: my @retArray;
618: &random_set_seed_from_phrase($seed);
619: @retArray=&math_random_permutation(@inArray);
620: &random_set_seed(@oldseed);
621: return @retArray;
622: }
623:
624: sub random_uniform {
625: my ($item_cnt,$seed,$low,$high) = @_;
626: my @oldseed=&random_get_seed();
627: my @retArray;
628: &random_set_seed_from_phrase($seed);
629: @retArray=&math_random_uniform($item_cnt,$low,$high);
630: &random_set_seed(@oldseed);
631: return @retArray;
632: }
633:
634: sub random_uniform_integer {
635: my ($item_cnt,$seed,$low,$high) = @_;
636: my @oldseed=&random_get_seed();
637: my @retArray;
638: &random_set_seed_from_phrase($seed);
639: @retArray=&math_random_uniform_integer($item_cnt,$low,$high);
640: &random_set_seed(@oldseed);
641: return @retArray;
642: }
643:
644: sub random_binomial {
645: my ($item_cnt,$seed,$nt,$p) = @_;
646: my @oldseed=&random_get_seed();
647: my @retArray;
648: &random_set_seed_from_phrase($seed);
649: @retArray=&math_random_binomial($item_cnt,$nt,$p);
650: &random_set_seed(@oldseed);
651: return @retArray;
652: }
653:
654: sub random_negative_binomial {
655: my ($item_cnt,$seed,$ne,$p) = @_;
656: my @oldseed=&random_get_seed();
657: my @retArray;
658: &random_set_seed_from_phrase($seed);
659: @retArray=&math_random_negative_binomial($item_cnt,$ne,$p);
660: &random_set_seed(@oldseed);
661: return @retArray;
662: }
663:
664: sub abs { CORE::abs(shift) }
665: sub sin { CORE::sin(shift) }
666: sub cos { CORE::cos(shift) }
667: sub exp { CORE::exp(shift) }
668: sub int { CORE::int(shift) }
669: sub log { CORE::log(shift) }
670: sub atan2 { CORE::atan2($_[0],$_[1]) }
671: sub sqrt { CORE::sqrt(shift) }
672:
673: sub tan { CORE::sin($_[0]) / CORE::cos($_[0]) }
674: #sub atan { atan2($_[0], 1); }
675: #sub acos { atan2(sqrt(1 - $_[0] * $_[0]), $_[0] ); }
676: #sub asin { atan2($_[0], sqrt(1- $_[0] * $_[0]) ); }
677:
678: sub log10 { CORE::log($_[0])/CORE::log(10); }
679:
680: sub factorial {
681: my $input = CORE::int(shift);
682: return "Error - unable to take factorial of an negative number ($input)" if $input < 0;
683: return "Error - factorial result is greater than system limit ($input)" if $input > 170;
684: return 1 if $input == 0;
685: my $result = 1;
686: for (my $i=2; $i<=$input; $i++) { $result *= $i }
687: return $result;
688: }
689:
690: sub sgn {
691: return -1 if $_[0] < 0;
692: return 0 if $_[0] == 0;
693: return 1 if $_[0] > 0;
694: }
695:
696: sub min {
697: my @sorted = sort { $a <=> $b || $a cmp $b } @_;
698: return shift @sorted;
699: }
700:
701: sub max {
702: my @sorted = sort { $a <=> $b || $a cmp $b } @_;
703: return pop @sorted;
704: }
705:
706: sub roundto {
707: my ($input,$n) = @_;
708: return sprintf('%.'.$n.'f',$input);
709: }
710:
711: sub to_string {
712: my ($input,$n) = @_;
713: return sprintf($input) if $n eq "";
714: $n = '.'.$n if $n !~ /^\./;
715: return sprintf('%'.$n,$input) if $n ne "";
716: }
717:
718: sub sub_string {
719: my ($str,$start,$len) = @_;
720: return substr($str,$start-1,$len);
721: }
722:
723: sub pow {return $_[0] ** $_[1]; }
724: sub ceil {return (($_[0]-CORE::int($_[0]))== 0.0) ? $_[0] : (($_[0] > 0) ? (CORE::int($_[0])+ 1) : CORE::int($_[0])); }
725: sub floor {return (($_[0]-CORE::int($_[0]))== 0.0) ? $_[0] : (($_[0] > 0) ? CORE::int($_[0]) : (CORE::int($_[0])-1)); }
726: #sub floor {return int($_[0]); }
727:
728: sub format {
729: my ($value,$fmt)=@_;
730: my ($dollarmode,$commamode,$alwaysperiod,$options);
731: if ($fmt =~ /^([^\d]*)(.*)/) { $options=$1; $fmt=$2; }
732: #if ($options =~ /\$/) { $dollamode=1; }
733: #if ($options =~ /,/) { $commamode=1; }
734: if ($options =~ /\./) { $alwaysperiod=1; }
735: my $result;
736: if ($fmt=~/s$/i) {
737: $result=&format_significant_figures($value,$fmt);
738: } else {
739: $fmt=~s/e/E/g;
740: $result=sprintf('%.'.$fmt,$value);
741: if ($alwaysperiod && $fmt eq '0f') { $result .='.'; }
742: $result=~s/(E[+-]*)0/$1/;
743: }
744: #if ($dollarmode) {$result=&dollarformat($result);}
745: #if ($commamode) {$result=&commaformat($result);}
746: return $result;
747: }
748:
749: sub chemparse {
750: my ($reaction) = @_;
751: my @tokens = split(/(\s\+|\->|<=>|<\-|\.)/,$reaction);
752: my $formula = '';
753: foreach my $token (@tokens) {
754: if ($token eq '->' ) {
755: $formula .= '<m>\ensuremath{\rightarrow}</m> ';
756: next;
757: }
758: if ($token eq '<-' ) {
759: $formula .= '<m>\ensuremath{\leftarrow}</m> ';
760: next;
761: }
762: if ($token eq '<=>') {
763: if ($external::target eq 'web' &&
764: &EXT('request.browser.unicode')) {
765: $formula .= '⇌ ';
766: } else {
767: $formula .= &web('<=> ','<m>\ensuremath{\rightleftharpoons}</m> ',
768: '<=> ');
769: }
770: next;
771: }
772: if ($token eq '.') {
773: $formula =~ s/(\ \;| )$//;
774: $formula .= '·';
775: next;
776: }
777: $token =~ /^\s*([\d|\/]*(?:&frac\d\d)?)(.*)/;
778: $formula .= $1 if ($1 ne '1'); # stoichiometric coefficient
779:
780: my $molecule = $2;
781: # subscripts
782: $molecule =~ s|(?<=[a-zA-Z\)\]\s])(\d+)|<sub>$1</sub>|g;
783: # superscripts
784: $molecule =~ s|\^(\d*[+\-]*)|<sup>$1</sup>|g;
785: # strip whitespace
786: $molecule =~ s/\s*//g;
787: # forced space
788: $molecule =~ s/_/ /g;
789: $molecule =~ s/-/−/g;
790: $formula .= $molecule.' ';
791: }
792: # get rid of trailing space
793: $formula =~ s/(\ \;| )$//;
794: return &xmlparse($formula);
795: }
796:
797: sub prettyprint {
798: my ($value,$fmt,$target)=@_;
799: my $result;
800: if (!$target) { $target = $external::target; }
801: if ($fmt =~ /chem/i) { return(&chemparse($value)); }
802: my ($dollarmode,$commamode,$alwaysperiod,$options);
803: if ($fmt =~ /^([^\d]*)(.*)/) { $options=$1; $fmt=$2; }
804: if ($options =~ /\$/) { $dollarmode=1; }
805: if ($options =~ /,/) { $commamode=1; }
806: if ($options =~ /\./) { $alwaysperiod=1; }
807: if ($fmt=~/s$/i) {
808: $value=&format_significant_figures($value,$fmt);
809: } elsif ($fmt) {
810: $value=sprintf('%.'.$fmt,$value);
811: }
812: if ($alwaysperiod && $fmt eq '0f') {
813: if ($target eq 'tex') {
814: $value .='\\ensuremath{.}';
815: } else {
816: $value .='.';
817: }
818: }
819: if ($value =~ /([0-9\.\-\+]+)E([0-9\-\+]+)/i ) {
820: my $frac=$1;
821: if ($dollarmode) { $frac=&dollarformat($frac); }
822: if ($commamode) { $frac=&commaformat($frac); }
823: my $exponent=$2;
824: $exponent=~s/^\+0*//;
825: $exponent=~s/^-0*/-/;
826: $exponent=~s/^-0*/-/;
827: if ($exponent eq '-') { undef($exponent); }
828: if ($exponent) {
829: if ($target eq 'web') {
830: $result=$frac.'×10<sup>'.$exponent.'</sup>';
831: } elsif ($target eq 'tex') {
832: $result='\ensuremath{'.$frac.'\times 10^{'.$exponent.'}}';
833: } else {
834: $result=$value;
835: }
836: } else {
837: $result=$frac;
838: }
839: } else {
840: $result=$value;
841: if ($dollarmode) { $result=&dollarformat($result,$target); }
842: elsif ($commamode) { $result=&commaformat($result,$target); }
843: }
844: return $result;
845: }
846:
847: sub commaformat {
848: my ($number,$target) = @_;
849: if ($number =~ /\./) {
850: while ($number =~ /([^0-9]*)([0-9]+)([^\.,][^\.,][^\.,])([,0-9]*\.[0-9]*)$/) {
851: $number = $1.$2.','.$3.$4;
852: }
853: } else {
854: while ($number =~ /^([^0-9]*)([0-9]+)([^,][^,][^,])([,0-9]*)$/) {
855: $number = $1.$2.','.$3.$4;
856: }
857: }
858: return $number;
859: }
860:
861: sub dollarformat {
862: my ($number,$target) = @_;
863: if (!$target) { $target = $external::target; }
864: $number=&commaformat($number,$target);
865: if ($target eq 'tex') {
866: $number='\$'.$number; #' stupid emacs
867: } else {
868: $number='$'.$number; #' stupid emacs
869: }
870: return $number;
871: }
872:
873: # format of form ns or nS where n is an integer
874: sub format_significant_figures {
875: my ($number,$format) = @_;
876: return '0' if ($number == 0);
877: # extract number of significant figures needed
878: my ($sig) = ($format =~ /(\d+)s/i);
879: # arbitrary choice - suggestions ?? or throw error message?
880: $sig = 3 if ($sig eq '');
881: # save the minus sign
882: my $sign = ($number < 0) ? '-' : '';
883: $number = abs($number);
884: # needed to correct for a number greater than 1 (or
885: my $power = ($number < 1) ? 0 : 1;
886: # could round up. Take the integer part of log10.
887: my $x10 = int(log($number)/log(10));
888: # find number with values left of decimal pt = # of sign figs.
889: my $xsig = $number*10**($sig-$x10-$power);
890: # get just digits left of decimal pt - also rounds off correctly
891: my $xint = sprintf('%.0f',$xsig);
892: # save any trailing zero's
893: my ($zeros) = ($xint =~ /(0+)$/);
894: # return number to original magnitude
895: my $numSig = $xint*10**($x10-$sig+$power);
896: # insert trailing zero's if have decimal point
897: $numSig =~ s/^(\d+)\.(\d+)(\e?(.*)?)$/$1\.$2$zeros$3/;
898: # put a decimal pt for number ending with 0 and length = # of sig fig
899: $numSig.='.' if (length($numSig) == $sig && $numSig =~ /0$/);
900: if (length($numSig) < $sig) {
901: $numSig.='.'.substr($zeros,0,($sig-length($numSig)));
902: }
903: # return number with sign
904: return $sign.$numSig;
905:
906: }
907:
908: sub map {
909: my ($phrase,$dest,$source)=@_;
910: my @oldseed=&random_get_seed();
911: my @seed = &random_seed_from_phrase($phrase);
912: &random_set_seed(@seed);
913: my $destct = scalar(@$dest);
914: if (!$source) {
915: my @output;
916: my @idx = &math_random_permuted_index($destct);
917: my $ctr = 0;
918: while ($ctr < $destct) {
919: $output[$ctr] = $$dest[$idx[$ctr]];
920: $ctr++;
921: }
922: &random_set_seed(@oldseed);
923: return @output;
924: } else {
925: my $num = scalar(@$source);
926: my @idx = &math_random_permuted_index($num);
927: my $ctr = 0;
928: my $tot = $num;
929: $tot = $destct if $destct < $num;
930: if (ref($$dest[0])) {
931: while ($ctr < $tot) {
932: ${$$dest[$ctr]} = $$source[$idx[$ctr]];
933: $ctr++;
934: }
935: } else {
936: while ($ctr < $tot) {
937: $$dest[$ctr] = $$source[$idx[$ctr]];
938: $ctr++;
939: }
940: }
941: }
942: &random_set_seed(@oldseed);
943: return '';
944: }
945:
946: sub rmap {
947: my ($phrase,$dest,$source)=@_;
948: my @oldseed=&random_get_seed();
949: my @seed = &random_seed_from_phrase($phrase);
950: &random_set_seed(@seed);
951: my $destct = scalar(@$dest);
952: if (!$source) {
953: my @idx = &math_random_permuted_index($destct);
954: my $ctr = 0;
955: my @r_idx;
956: while ($ctr < $destct) {
957: $r_idx[$idx[$ctr]] = $ctr;
958: $ctr++;
959: }
960: my @output;
961: $ctr = 0;
962: while ($ctr < $destct) {
963: $output[$ctr] = $$dest[$r_idx[$ctr]];
964: $ctr++;
965: }
966: &random_set_seed(@oldseed);
967: return @output;
968: } else {
969: my $num = scalar(@$source);
970: my @idx = &math_random_permuted_index($num);
971: my $ctr = 0;
972: my $tot = $num;
973: $tot = $destct if $destct < $num;
974: my @r_idx;
975: while ($ctr < $tot) {
976: $r_idx[$idx[$ctr]] = $ctr;
977: $ctr++;
978: }
979: $ctr = 0;
980: if (ref($$dest[0])) {
981: while ($ctr < $tot) {
982: ${$$dest[$ctr]} = $$source[$r_idx[$ctr]];
983: $ctr++;
984: }
985: } else {
986: while ($ctr < $tot) {
987: $$dest[$ctr] = $$source[$r_idx[$ctr]];
988: $ctr++;
989: }
990: }
991: }
992: &random_set_seed(@oldseed);
993: return '';
994: }
995:
996: sub capa_id { return }
997:
998: sub problem { return }
999:
1000: sub name{
1001: my $fullname = &EXT('environment.lastname').', '.&EXT('environment.firstname').' '.&EXT('environment.middlename');
1002: $fullname = "" if $fullname eq ", ";
1003: $fullname =~ s/\%2d/-/g;
1004: return $fullname;
1005: }
1006:
1007: sub student_number {
1008: my $id = &EXT('environment.id');
1009: $id = '' if $id eq "";
1010: return $id;
1011: }
1012:
1013: sub class {
1014: my $course = &EXT('course.description');
1015: $course = '' if $course eq "";
1016: return $course;
1017: }
1018:
1019: sub firstname {
1020: my $firstname = &EXT('environment.firstname');
1021: $firstname = '' if $firstname eq "";
1022: return $firstname;
1023: }
1024:
1025: sub lastname {
1026: my $lastname = &EXT('environment.lastname');
1027: $lastname = '' if $lastname eq "";
1028: return $lastname;
1029: }
1030:
1031: sub sec {
1032: my $sec = &EXT('request.course.sec');
1033: $sec = '' if $sec eq "";
1034: return $sec;
1035: }
1036:
1037: sub submission {
1038: my ($partid,$responseid,$subnumber)=@_;
1039: my $sub='';
1040: if ($subnumber) { $sub=$subnumber.':'; }
1041: return &EXT('user.resource.'.$sub.'resource.'.$partid.'.'.$responseid.'.submission');
1042: }
1043:
1044: sub currentpart {
1045: return $external::part;
1046: }
1047:
1048: sub eval_time {
1049: my ($timestamp)=@_;
1050: unless ($timestamp) { return ''; }
1051: return &locallocaltime($timestamp);
1052: }
1053:
1054: sub open_date {
1055: my ($partid)=@_;
1056: unless ($partid) { $partid=0; }
1057: return &eval_time(&EXT('resource.'.$partid.'.opendate'));
1058: }
1059:
1060: sub due_date {
1061: my ($partid)=@_;
1062: unless ($partid) { $partid=0; }
1063: return &eval_time(&EXT('resource.'.$partid.'.duedate'));
1064: }
1065:
1066: sub answer_date {
1067: my ($partid)=@_;
1068: unless ($partid) { $partid=0; }
1069: return &eval_time(&EXT('resource.'.$partid.'.answerdate'));
1070: }
1071:
1072: sub open_date_epoch {
1073: my ($partid)=@_;
1074: unless ($partid) { $partid=0; }
1075: return &EXT('resource.'.$partid.'.opendate');
1076: }
1077:
1078: sub due_date_epoch {
1079: my ($partid)=@_;
1080: unless ($partid) { $partid=0; }
1081: return &EXT('resource.'.$partid.'.duedate');
1082: }
1083:
1084: sub answer_date_epoch {
1085: my ($partid)=@_;
1086: unless ($partid) { $partid=0; }
1087: return &EXT('resource.'.$partid.'.answerdate');
1088: }
1089:
1090: sub array_moments {
1091: my @input=@_;
1092: my (@output,$N);
1093: $N=scalar (@input);
1094: $output[0]=$N;
1095: if ($N <= 1) {
1096: $output[1]=$input[0];
1097: $output[1]="Input array not defined" if ($N == 0);
1098: $output[2]="variance undefined for N<=1";
1099: $output[3]="skewness undefined for N<=1";
1100: $output[4]="kurtosis undefined for N<=1";
1101: return @output;
1102: }
1103: my $sum=0;
1104: foreach my $line (@input) {
1105: $sum+=$line;
1106: }
1107: $output[1] = $sum/$N;
1108: my ($x,$sdev,$var,$skew,$kurt) = 0;
1109: foreach my $line (@input) {
1110: $x=$line-$output[1];
1111: $var+=$x**2;
1112: $skew+=$x**3;
1113: $kurt+=$x**4;
1114: }
1115: $output[2]=$var/($N-1);
1116: $sdev=CORE::sqrt($output[2]);
1117: if ($sdev == 0) {
1118: $output[3]="inf-variance=0";
1119: $output[4]="inf-variance=0";
1120: return @output;
1121: }
1122: $output[3]=$skew/($sdev**3*$N);
1123: $output[4]=$kurt/($sdev**4*$N)-3;
1124: return @output;
1125: }
1126:
1127: sub choose {
1128: my $num = $_[0];
1129: return $_[$num];
1130: }
1131:
1132: #&sum1(1,$x,sub { &sum1($_[0],2*$_[0], sub { fact($_[0])**2 })});
1133: #sub sum1 {
1134: # my ($start,$end,$sub)=@_;
1135: # my $sum=0;
1136: # for (my $i=$start;$i<=$end;$i++) {
1137: # $sum+=&$sub($i);
1138: # }
1139: # return $sum
1140: #}
1141:
1142: #&sum2('a',1,$x,'&sum2(\'b\',$a,2*$a, \'&factorial($b)**2\')');
1143: #sub sum2 {
1144: # my ($varname,$start,$end,$line)=@_;
1145: # my $sum=0;
1146: # for (my $i=$start;$i<=$end;$i++) {
1147: # my $func=sub {
1148: # eval("\$".$varname."=$i");
1149: # eval($line);
1150: # };
1151: # $sum+=&$func($i);
1152: # }
1153: # return $sum
1154: #}
1155:
1156: # expiremental idea
1157: sub proper_path {
1158: my ($path)=@_;
1159: if ( $external::target eq "tex" ) {
1160: return '/home/httpd/html'.$path;
1161: } else {
1162: return $path;
1163: }
1164: }
1165:
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