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 1.135 2008/06/10 16:20:29 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)=@_;
428: my $output;
429: if ($system eq 'maxima') {
430: $output=&maxima_eval($input);
431: }
432: return $output;
433: }
434:
435: sub tex {
436: if ( $external::target eq "tex" ) {
437: return $_[0];
438: } else {
439: return $_[1];
440: }
441: }
442:
443: sub var_in_tex {
444: if ( $external::target eq "tex" ) {
445: return $_[0];
446: } else {
447: return "";
448: }
449: }
450:
451: sub web {
452: if ( $external::target eq "tex" ) {
453: return $_[1];
454: } else {
455: if ( $external::target eq "web" || $external::target eq "answer") {
456: return $_[2];
457: } else {
458: return $_[0];
459: }
460: }
461: }
462:
463: sub html {
464: if ( $external::target eq "web" ) {
465: return shift;
466: }
467: }
468:
469: sub hinton {
470: return 0;
471: }
472:
473: sub random {
474: my ($start,$end,$step)=@_;
475: if ( ! $hidden::RANDOMINIT ) {
476: if ($external::randomseed == 0) { $external::randomseed=1; }
477: if ($external::randomseed =~/,/) {
478: my ($num1,$num2)=split(/,/,$external::randomseed);
479: &random_set_seed(1,abs($num1));
480: } elsif ($external::randomseed =~/:/) {
481: my ($num1,$num2)=split(/:/,$external::randomseed);
482: &random_set_seed(abs($num1),abs($num2));
483: } else {
484: &random_set_seed(1,int(abs($external::randomseed)));
485: }
486: &math_random_uniform();
487: $hidden::RANDOMINIT=1;
488: }
489: if (!defined($step)) { $step=1; }
490: my $num=1+int(($end-$start)/$step);
491: my $result=$start + int(&math_random_uniform() * $num)*$step;
492: return $result;
493: }
494:
495: sub random_normal {
496: my ($item_cnt,$seed,$av,$std_dev) = @_;
497: my @oldseed=&random_get_seed();
498: my @retArray;
499: &random_set_seed_from_phrase($seed);
500: @retArray=&math_random_normal($item_cnt,$av,$std_dev);
501: &random_set_seed(@oldseed);
502: return @retArray;
503: }
504:
505: sub random_beta {
506: my ($item_cnt,$seed,$aa,$bb) = @_;
507: my @oldseed=&random_get_seed();
508: my @retArray;
509: &random_set_seed_from_phrase($seed);
510: @retArray=&math_random_beta($item_cnt,$aa,$bb);
511: &random_set_seed(@oldseed);
512: return @retArray;
513: }
514:
515: sub random_gamma {
516: my ($item_cnt,$seed,$a,$r) = @_;
517: my @oldseed=&random_get_seed();
518: my @retArray;
519: &random_set_seed_from_phrase($seed);
520: @retArray=&math_random_gamma($item_cnt,$a,$r);
521: &random_set_seed(@oldseed);
522: return @retArray;
523: }
524:
525: sub random_exponential {
526: my ($item_cnt,$seed,$av) = @_;
527: my @oldseed=&random_get_seed();
528: my @retArray;
529: &random_set_seed_from_phrase($seed);
530: @retArray=&math_random_exponential($item_cnt,$av);
531: &random_set_seed(@oldseed);
532: return @retArray;
533: }
534:
535: sub random_poisson {
536: my ($item_cnt,$seed,$mu) = @_;
537: my @oldseed=&random_get_seed();
538: my @retArray;
539: &random_set_seed_from_phrase($seed);
540: @retArray=&math_random_poisson($item_cnt,$mu);
541: &random_set_seed(@oldseed);
542: return @retArray;
543: }
544:
545: sub random_chi {
546: my ($item_cnt,$seed,$df) = @_;
547: my @oldseed=&random_get_seed();
548: my @retArray;
549: &random_set_seed_from_phrase($seed);
550: @retArray=&math_random_chi_square($item_cnt,$df);
551: &random_set_seed(@oldseed);
552: return @retArray;
553: }
554:
555: sub random_noncentral_chi {
556: my ($item_cnt,$seed,$df,$nonc) = @_;
557: my @oldseed=&random_get_seed();
558: my @retArray;
559: &random_set_seed_from_phrase($seed);
560: @retArray=&math_random_noncentral_chi_square($item_cnt,$df,$nonc);
561: &random_set_seed(@oldseed);
562: return @retArray;
563: }
564:
565: sub random_f {
566: my ($item_cnt,$seed,$dfn,$dfd) = @_;
567: my @oldseed=&random_get_seed();
568: my @retArray;
569: &random_set_seed_from_phrase($seed);
570: @retArray=&math_random_f($item_cnt,$dfn,$dfd);
571: &random_set_seed(@oldseed);
572: return @retArray;
573: }
574:
575: sub random_noncentral_f {
576: my ($item_cnt,$seed,$dfn,$dfd,$nonc) = @_;
577: my @oldseed=&random_get_seed();
578: my @retArray;
579: &random_set_seed_from_phrase($seed);
580: @retArray=&math_random_noncentral_f($item_cnt,$dfn,$dfd,$nonc);
581: &random_set_seed(@oldseed);
582: return @retArray;
583: }
584:
585: sub random_multivariate_normal {
586: my ($item_cnt,$seed,$mean,$covar) = @_;
587: my @oldseed=&random_get_seed();
588: &random_set_seed_from_phrase($seed);
589: my @retArray=&math_random_multivariate_normal($item_cnt,@$mean,@$covar);
590: &random_set_seed(@oldseed);
591: return @retArray;
592: }
593:
594: sub random_multinomial {
595: my ($item_cnt,$seed,@p) = @_;
596: my @oldseed=&random_get_seed();
597: my @retArray;
598: &random_set_seed_from_phrase($seed);
599: my @retArray=&math_random_multinomial($item_cnt,@p);
600: &random_set_seed(@oldseed);
601: return @retArray;
602: }
603:
604: sub random_permutation {
605: my ($seed,@inArray) = @_;
606: my @oldseed=&random_get_seed();
607: my @retArray;
608: &random_set_seed_from_phrase($seed);
609: @retArray=&math_random_permutation(@inArray);
610: &random_set_seed(@oldseed);
611: return @retArray;
612: }
613:
614: sub random_uniform {
615: my ($item_cnt,$seed,$low,$high) = @_;
616: my @oldseed=&random_get_seed();
617: my @retArray;
618: &random_set_seed_from_phrase($seed);
619: @retArray=&math_random_uniform($item_cnt,$low,$high);
620: &random_set_seed(@oldseed);
621: return @retArray;
622: }
623:
624: sub random_uniform_integer {
625: my ($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_integer($item_cnt,$low,$high);
630: &random_set_seed(@oldseed);
631: return @retArray;
632: }
633:
634: sub random_binomial {
635: my ($item_cnt,$seed,$nt,$p) = @_;
636: my @oldseed=&random_get_seed();
637: my @retArray;
638: &random_set_seed_from_phrase($seed);
639: @retArray=&math_random_binomial($item_cnt,$nt,$p);
640: &random_set_seed(@oldseed);
641: return @retArray;
642: }
643:
644: sub random_negative_binomial {
645: my ($item_cnt,$seed,$ne,$p) = @_;
646: my @oldseed=&random_get_seed();
647: my @retArray;
648: &random_set_seed_from_phrase($seed);
649: @retArray=&math_random_negative_binomial($item_cnt,$ne,$p);
650: &random_set_seed(@oldseed);
651: return @retArray;
652: }
653:
654: sub abs { CORE::abs(shift) }
655: sub sin { CORE::sin(shift) }
656: sub cos { CORE::cos(shift) }
657: sub exp { CORE::exp(shift) }
658: sub int { CORE::int(shift) }
659: sub log { CORE::log(shift) }
660: sub atan2 { CORE::atan2($_[0],$_[1]) }
661: sub sqrt { CORE::sqrt(shift) }
662:
663: sub tan { CORE::sin($_[0]) / CORE::cos($_[0]) }
664: #sub atan { atan2($_[0], 1); }
665: #sub acos { atan2(sqrt(1 - $_[0] * $_[0]), $_[0] ); }
666: #sub asin { atan2($_[0], sqrt(1- $_[0] * $_[0]) ); }
667:
668: sub log10 { CORE::log($_[0])/CORE::log(10); }
669:
670: sub factorial {
671: my $input = CORE::int(shift);
672: return "Error - unable to take factorial of an negative number ($input)" if $input < 0;
673: return "Error - factorial result is greater than system limit ($input)" if $input > 170;
674: return 1 if $input == 0;
675: my $result = 1;
676: for (my $i=2; $i<=$input; $i++) { $result *= $i }
677: return $result;
678: }
679:
680: sub sgn {
681: return -1 if $_[0] < 0;
682: return 0 if $_[0] == 0;
683: return 1 if $_[0] > 0;
684: }
685:
686: sub min {
687: my @sorted = sort { $a <=> $b || $a cmp $b } @_;
688: return shift @sorted;
689: }
690:
691: sub max {
692: my @sorted = sort { $a <=> $b || $a cmp $b } @_;
693: return pop @sorted;
694: }
695:
696: sub roundto {
697: my ($input,$n) = @_;
698: return sprintf('%.'.$n.'f',$input);
699: }
700:
701: sub to_string {
702: my ($input,$n) = @_;
703: return sprintf($input) if $n eq "";
704: $n = '.'.$n if $n !~ /^\./;
705: return sprintf('%'.$n,$input) if $n ne "";
706: }
707:
708: sub sub_string {
709: my ($str,$start,$len) = @_;
710: return substr($str,$start-1,$len);
711: }
712:
713: sub pow {return $_[0] ** $_[1]; }
714: sub ceil {return (($_[0]-CORE::int($_[0]))== 0.0) ? $_[0] : (($_[0] > 0) ? (CORE::int($_[0])+ 1) : CORE::int($_[0])); }
715: sub floor {return (($_[0]-CORE::int($_[0]))== 0.0) ? $_[0] : (($_[0] > 0) ? CORE::int($_[0]) : (CORE::int($_[0])-1)); }
716: #sub floor {return int($_[0]); }
717:
718: sub format {
719: my ($value,$fmt)=@_;
720: my ($dollarmode,$commamode,$alwaysperiod,$options);
721: if ($fmt =~ /^([^\d]*)(.*)/) { $options=$1; $fmt=$2; }
722: #if ($options =~ /\$/) { $dollamode=1; }
723: #if ($options =~ /,/) { $commamode=1; }
724: if ($options =~ /\./) { $alwaysperiod=1; }
725: my $result;
726: if ($fmt=~/s$/i) {
727: $result=&format_significant_figures($value,$fmt);
728: } else {
729: $fmt=~s/e/E/g;
730: $result=sprintf('%.'.$fmt,$value);
731: if ($alwaysperiod && $fmt eq '0f') { $result .='.'; }
732: $result=~s/(E[+-]*)0/$1/;
733: }
734: #if ($dollarmode) {$result=&dollarformat($result);}
735: #if ($commamode) {$result=&commaformat($result);}
736: return $result;
737: }
738:
739: sub chemparse {
740: my ($reaction) = @_;
741: my @tokens = split(/(\s\+|\->|<=>|<\-|\.)/,$reaction);
742: my $formula = '';
743: foreach my $token (@tokens) {
744: if ($token eq '->' ) {
745: $formula .= '<m>\ensuremath{\rightarrow}</m> ';
746: next;
747: }
748: if ($token eq '<-' ) {
749: $formula .= '<m>\ensuremath{\leftarrow}</m> ';
750: next;
751: }
752: if ($token eq '<=>') {
753: if ($external::target eq 'web' &&
754: &EXT('request.browser.unicode')) {
755: $formula .= '⇌ ';
756: } else {
757: $formula .= &web('<=> ','<m>\ensuremath{\rightleftharpoons}</m> ',
758: '<=> ');
759: }
760: next;
761: }
762: if ($token eq '.') {
763: $formula =~ s/(\ \;| )$//;
764: $formula .= '·';
765: next;
766: }
767: $token =~ /^\s*([\d|\/]*(?:&frac\d\d)?)(.*)/;
768: $formula .= $1 if ($1 ne '1'); # stoichiometric coefficient
769:
770: my $molecule = $2;
771: # subscripts
772: $molecule =~ s|(?<=[a-zA-Z\)\]\s])(\d+)|<sub>$1</sub>|g;
773: # superscripts
774: $molecule =~ s|\^(\d*[+\-]*)|<sup>$1</sup>|g;
775: # strip whitespace
776: $molecule =~ s/\s*//g;
777: # forced space
778: $molecule =~ s/_/ /g;
779: $molecule =~ s/-/−/g;
780: $formula .= $molecule.' ';
781: }
782: # get rid of trailing space
783: $formula =~ s/(\ \;| )$//;
784: return &xmlparse($formula);
785: }
786:
787: sub prettyprint {
788: my ($value,$fmt,$target)=@_;
789: my $result;
790: if (!$target) { $target = $external::target; }
791: if ($fmt =~ /chem/i) { return(&chemparse($value)); }
792: my ($dollarmode,$commamode,$alwaysperiod,$options);
793: if ($fmt =~ /^([^\d]*)(.*)/) { $options=$1; $fmt=$2; }
794: if ($options =~ /\$/) { $dollarmode=1; }
795: if ($options =~ /,/) { $commamode=1; }
796: if ($options =~ /\./) { $alwaysperiod=1; }
797: if ($fmt=~/s$/i) {
798: $value=&format_significant_figures($value,$fmt);
799: } elsif ($fmt) {
800: $value=sprintf('%.'.$fmt,$value);
801: }
802: if ($alwaysperiod && $fmt eq '0f') {
803: if ($target eq 'tex') {
804: $value .='\\ensuremath{.}';
805: } else {
806: $value .='.';
807: }
808: }
809: if ($value =~ /([0-9\.\-\+]+)E([0-9\-\+]+)/i ) {
810: my $frac=$1;
811: if ($dollarmode) { $frac=&dollarformat($frac); }
812: if ($commamode) { $frac=&commaformat($frac); }
813: my $exponent=$2;
814: $exponent=~s/^\+0*//;
815: $exponent=~s/^-0*/-/;
816: $exponent=~s/^-0*/-/;
817: if ($exponent eq '-') { undef($exponent); }
818: if ($exponent) {
819: if ($target eq 'web') {
820: $result=$frac.'×10<sup>'.$exponent.'</sup>';
821: } elsif ($target eq 'tex') {
822: $result='\ensuremath{'.$frac.'\times 10^{'.$exponent.'}}';
823: } else {
824: $result=$value;
825: }
826: } else {
827: $result=$frac;
828: }
829: } else {
830: $result=$value;
831: if ($dollarmode) { $result=&dollarformat($result,$target); }
832: elsif ($commamode) { $result=&commaformat($result,$target); }
833: }
834: return $result;
835: }
836:
837: sub commaformat {
838: my ($number,$target) = @_;
839: if ($number =~ /\./) {
840: while ($number =~ /([^0-9]*)([0-9]+)([^\.,][^\.,][^\.,])([,0-9]*\.[0-9]*)$/) {
841: $number = $1.$2.','.$3.$4;
842: }
843: } else {
844: while ($number =~ /^([^0-9]*)([0-9]+)([^,][^,][^,])([,0-9]*)$/) {
845: $number = $1.$2.','.$3.$4;
846: }
847: }
848: return $number;
849: }
850:
851: sub dollarformat {
852: my ($number,$target) = @_;
853: if (!$target) { $target = $external::target; }
854: $number=&commaformat($number,$target);
855: if ($target eq 'tex') {
856: $number='\$'.$number; #' stupid emacs
857: } else {
858: $number='$'.$number; #' stupid emacs
859: }
860: return $number;
861: }
862:
863: # format of form ns or nS where n is an integer
864: sub format_significant_figures {
865: my ($number,$format) = @_;
866: return '0' if ($number == 0);
867: # extract number of significant figures needed
868: my ($sig) = ($format =~ /(\d+)s/i);
869: # arbitrary choice - suggestions ?? or throw error message?
870: $sig = 3 if ($sig eq '');
871: # save the minus sign
872: my $sign = ($number < 0) ? '-' : '';
873: $number = abs($number);
874: # needed to correct for a number greater than 1 (or
875: my $power = ($number < 1) ? 0 : 1;
876: # could round up. Take the integer part of log10.
877: my $x10 = int(log($number)/log(10));
878: # find number with values left of decimal pt = # of sign figs.
879: my $xsig = $number*10**($sig-$x10-$power);
880: # get just digits left of decimal pt - also rounds off correctly
881: my $xint = sprintf('%.0f',$xsig);
882: # save any trailing zero's
883: my ($zeros) = ($xint =~ /(0+)$/);
884: # return number to original magnitude
885: my $numSig = $xint*10**($x10-$sig+$power);
886: # insert trailing zero's if have decimal point
887: $numSig =~ s/^(\d+)\.(\d+)(\e?(.*)?)$/$1\.$2$zeros$3/;
888: # put a decimal pt for number ending with 0 and length = # of sig fig
889: $numSig.='.' if (length($numSig) == $sig && $numSig =~ /0$/);
890: if (length($numSig) < $sig) {
891: $numSig.='.'.substr($zeros,0,($sig-length($numSig)));
892: }
893: # return number with sign
894: return $sign.$numSig;
895:
896: }
897:
898: sub map {
899: my ($phrase,$dest,$source)=@_;
900: my @oldseed=&random_get_seed();
901: my @seed = &random_seed_from_phrase($phrase);
902: &random_set_seed(@seed);
903: my $destct = scalar(@$dest);
904: if (!$source) {
905: my @output;
906: my @idx = &math_random_permuted_index($destct);
907: my $ctr = 0;
908: while ($ctr < $destct) {
909: $output[$ctr] = $$dest[$idx[$ctr]];
910: $ctr++;
911: }
912: &random_set_seed(@oldseed);
913: return @output;
914: } else {
915: my $num = scalar(@$source);
916: my @idx = &math_random_permuted_index($num);
917: my $ctr = 0;
918: my $tot = $num;
919: $tot = $destct if $destct < $num;
920: if (ref($$dest[0])) {
921: while ($ctr < $tot) {
922: ${$$dest[$ctr]} = $$source[$idx[$ctr]];
923: $ctr++;
924: }
925: } else {
926: while ($ctr < $tot) {
927: $$dest[$ctr] = $$source[$idx[$ctr]];
928: $ctr++;
929: }
930: }
931: }
932: &random_set_seed(@oldseed);
933: return '';
934: }
935:
936: sub rmap {
937: my ($phrase,$dest,$source)=@_;
938: my @oldseed=&random_get_seed();
939: my @seed = &random_seed_from_phrase($phrase);
940: &random_set_seed(@seed);
941: my $destct = scalar(@$dest);
942: if (!$source) {
943: my @idx = &math_random_permuted_index($destct);
944: my $ctr = 0;
945: my @r_idx;
946: while ($ctr < $destct) {
947: $r_idx[$idx[$ctr]] = $ctr;
948: $ctr++;
949: }
950: my @output;
951: $ctr = 0;
952: while ($ctr < $destct) {
953: $output[$ctr] = $$dest[$r_idx[$ctr]];
954: $ctr++;
955: }
956: &random_set_seed(@oldseed);
957: return @output;
958: } else {
959: my $num = scalar(@$source);
960: my @idx = &math_random_permuted_index($num);
961: my $ctr = 0;
962: my $tot = $num;
963: $tot = $destct if $destct < $num;
964: my @r_idx;
965: while ($ctr < $tot) {
966: $r_idx[$idx[$ctr]] = $ctr;
967: $ctr++;
968: }
969: $ctr = 0;
970: if (ref($$dest[0])) {
971: while ($ctr < $tot) {
972: ${$$dest[$ctr]} = $$source[$r_idx[$ctr]];
973: $ctr++;
974: }
975: } else {
976: while ($ctr < $tot) {
977: $$dest[$ctr] = $$source[$r_idx[$ctr]];
978: $ctr++;
979: }
980: }
981: }
982: &random_set_seed(@oldseed);
983: return '';
984: }
985:
986: sub capa_id { return }
987:
988: sub problem { return }
989:
990: sub name{
991: my $fullname = &EXT('environment.lastname').', '.&EXT('environment.firstname').' '.&EXT('environment.middlename');
992: $fullname = "" if $fullname eq ", ";
993: $fullname =~ s/\%2d/-/g;
994: return $fullname;
995: }
996:
997: sub student_number {
998: my $id = &EXT('environment.id');
999: $id = '' if $id eq "";
1000: return $id;
1001: }
1002:
1003: sub class {
1004: my $course = &EXT('course.description');
1005: $course = '' if $course eq "";
1006: return $course;
1007: }
1008:
1009: sub firstname {
1010: my $firstname = &EXT('environment.firstname');
1011: $firstname = '' if $firstname eq "";
1012: return $firstname;
1013: }
1014:
1015: sub lastname {
1016: my $lastname = &EXT('environment.lastname');
1017: $lastname = '' if $lastname eq "";
1018: return $lastname;
1019: }
1020:
1021: sub sec {
1022: my $sec = &EXT('request.course.sec');
1023: $sec = '' if $sec eq "";
1024: return $sec;
1025: }
1026:
1027: sub eval_time {
1028: my ($timestamp)=@_;
1029: unless ($timestamp) { return ''; }
1030: return &locallocaltime($timestamp);
1031: }
1032:
1033: sub open_date {
1034: my ($partid)=@_;
1035: unless ($partid) { $partid=0; }
1036: return &eval_time(&EXT('resource.'.$partid.'.opendate'));
1037: }
1038:
1039: sub due_date {
1040: my ($partid)=@_;
1041: unless ($partid) { $partid=0; }
1042: return &eval_time(&EXT('resource.'.$partid.'.duedate'));
1043: }
1044:
1045: sub answer_date {
1046: my ($partid)=@_;
1047: unless ($partid) { $partid=0; }
1048: return &eval_time(&EXT('resource.'.$partid.'.answerdate'));
1049: }
1050:
1051: sub array_moments {
1052: my @input=@_;
1053: my (@output,$N);
1054: $N=scalar (@input);
1055: $output[0]=$N;
1056: if ($N <= 1) {
1057: $output[1]=$input[0];
1058: $output[1]="Input array not defined" if ($N == 0);
1059: $output[2]="variance undefined for N<=1";
1060: $output[3]="skewness undefined for N<=1";
1061: $output[4]="kurtosis undefined for N<=1";
1062: return @output;
1063: }
1064: my $sum=0;
1065: foreach my $line (@input) {
1066: $sum+=$line;
1067: }
1068: $output[1] = $sum/$N;
1069: my ($x,$sdev,$var,$skew,$kurt) = 0;
1070: foreach my $line (@input) {
1071: $x=$line-$output[1];
1072: $var+=$x**2;
1073: $skew+=$x**3;
1074: $kurt+=$x**4;
1075: }
1076: $output[2]=$var/($N-1);
1077: $sdev=CORE::sqrt($output[2]);
1078: if ($sdev == 0) {
1079: $output[3]="inf-variance=0";
1080: $output[4]="inf-variance=0";
1081: return @output;
1082: }
1083: $output[3]=$skew/($sdev**3*$N);
1084: $output[4]=$kurt/($sdev**4*$N)-3;
1085: return @output;
1086: }
1087:
1088: sub choose {
1089: my $num = $_[0];
1090: return $_[$num];
1091: }
1092:
1093: #&sum1(1,$x,sub { &sum1($_[0],2*$_[0], sub { fact($_[0])**2 })});
1094: #sub sum1 {
1095: # my ($start,$end,$sub)=@_;
1096: # my $sum=0;
1097: # for (my $i=$start;$i<=$end;$i++) {
1098: # $sum+=&$sub($i);
1099: # }
1100: # return $sum
1101: #}
1102:
1103: #&sum2('a',1,$x,'&sum2(\'b\',$a,2*$a, \'&factorial($b)**2\')');
1104: #sub sum2 {
1105: # my ($varname,$start,$end,$line)=@_;
1106: # my $sum=0;
1107: # for (my $i=$start;$i<=$end;$i++) {
1108: # my $func=sub {
1109: # eval("\$".$varname."=$i");
1110: # eval($line);
1111: # };
1112: # $sum+=&$func($i);
1113: # }
1114: # return $sum
1115: #}
1116:
1117: # expiremental idea
1118: sub proper_path {
1119: my ($path)=@_;
1120: if ( $external::target eq "tex" ) {
1121: return '/home/httpd/html'.$path;
1122: } else {
1123: return $path;
1124: }
1125: }
1126:
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