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 1.138 2008/09/06 21:39:15 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') || ($type eq '8')) && ($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: if (($type eq 'float') || (($type eq '') && ($unit ne ''))) {
320: $element =~ s/\s//g;
321: }
322: my $appendunit=$unit;
323: if ($unit=~/\%/) {
324: $element=$element/100;
325: $appendunit=~s/\%//;
326: }
327: if (($element==0) && ($unit!~/\w/) && ($answerunit=~/\w/)) {
328: $appendunit=$answerunit;
329: }
330: $element .= " $appendunit";
331: &LONCAPA_INTERNAL_DEBUG("Made response element :$element:");
332: }
333: }
334:
335: foreach my $thisanswer (@{ $LONCAPA::CAPAresponse_answer->{'answers'} }) {
336: if (!defined($thisanswer)) {
337: return ('ERROR','answer was undefined');
338: }
339: }
340:
341:
342: # &LONCAPA_INTERNAL_DEBUG(&LONCAPA_INTERNAL_Dumper($responses));
343: my %memoized;
344: if ($LONCAPA::CAPAresponse_answer->{'type'} eq 'ordered') {
345: for (my $i=0; $i<scalar(@$responses);$i++) {
346: my $answer = $LONCAPA::CAPAresponse_answer->{'answers'}[$i];
347: my $response = $responses->[$i];
348: my $key = "$answer\0$response";
349: my (@awards,@msgs);
350: for (my $j=0; $j<scalar(@$response); $j++) {
351: my ($award,$msg) = &caparesponse_check($answer->[$j],
352: $response->[$j]);
353: push(@awards,$award);
354: push(@msgs, $msg);
355: }
356: my ($award,$msg) =
357: &LONCAPA_INTERNAL_FINALIZEAWARDS(\@awards,\@msgs);
358: $memoized{$key} = [$award,$msg];
359: }
360: } else {
361: #FIXME broken with unorder responses where one is a <value>
362: # and the other is a <vector> (need to delay parse til
363: # inside the loop?)
364: foreach my $response (@$responses) {
365: my $response_size = scalar(@{$response});
366: foreach my $answer (@{ $LONCAPA::CAPAresponse_answer->{'answers'} }) {
367: my $key = "$answer\0$response";
368: my $answer_size = scalar(@{$answer});
369: my ($award,$msg);
370: if ($answer_size > $response_size) {
371: $award = 'MISSING_ANSWER';
372: } elsif ($answer_size < $response_size) {
373: $award = 'EXTRA_ANSWER';
374: } else {
375: my (@awards,@msgs);
376: for (my $j=0; $j<scalar(@$response); $j++) {
377: my ($award,$msg) = &caparesponse_check($answer->[$j],
378: $response->[$j]);
379: push(@awards,$award);
380: push(@msgs, $msg);
381: }
382: ($award,$msg) =
383: &LONCAPA_INTERNAL_FINALIZEAWARDS(\@awards,\@msgs);
384: }
385: $memoized{$key} = [$award,$msg];
386: }
387: }
388: }
389:
390: my ($final_award,$final_msg);
391: &init_permutation(scalar(@$responses),
392: $LONCAPA::CAPAresponse_answer->{'type'});
393:
394: # possible FIXMEs
395: # - significant time is spent calling non-safe space routine
396: # from safe space
397: # - early outs could be possible with classifying awards is to stratas
398: # and stopping as so as hitting the top strata
399: # - some early outs also might be possible with check ing the
400: # memoized hash of results (is correct even possible? etc.)
401:
402: my (@final_awards,@final_msg);
403: while( &get_permutations_left() ) {
404: my $order = &get_next_permutation();
405: my (@awards, @msgs, $i);
406: foreach my $thisanswer (@{ $LONCAPA::CAPAresponse_answer->{'answers'} }) {
407: my $key = "$thisanswer\0".$responses->[$order->[$i]];
408: push(@awards,$memoized{$key}[0]);
409: push(@msgs,$memoized{$key}[1]);
410: $i++;
411:
412: }
413: &LONCAPA_INTERNAL_DEBUG(" all awards ".join(':',@awards));
414:
415: my ($possible_award,$possible_msg) =
416: &LONCAPA_INTERNAL_FINALIZEAWARDS(\@awards,\@msgs);
417: &LONCAPA_INTERNAL_DEBUG(" pos awards ".$possible_award);
418: push(@final_awards,$possible_award);
419: push(@final_msg,$possible_msg);
420: }
421:
422: &LONCAPA_INTERNAL_DEBUG(" all final_awards ".join(':',@final_awards));
423: my ($final_award,$final_msg) =
424: &LONCAPA_INTERNAL_FINALIZEAWARDS(\@final_awards,\@final_msg,undef,1);
425: return ($final_award,$final_msg);
426: }
427:
428: sub cas {
429: my ($system,$input,$library)=@_;
430: my $output;
431: if ($system eq 'maxima') {
432: $output=&maxima_eval($input,$library);
433: } else {
434: $output='Error: unrecognized CAS';
435: }
436: return $output;
437: }
438:
439: sub tex {
440: if ( $external::target eq "tex" ) {
441: return $_[0];
442: } else {
443: return $_[1];
444: }
445: }
446:
447: sub var_in_tex {
448: if ( $external::target eq "tex" ) {
449: return $_[0];
450: } else {
451: return "";
452: }
453: }
454:
455: sub web {
456: if ( $external::target eq "tex" ) {
457: return $_[1];
458: } else {
459: if ( $external::target eq "web" || $external::target eq "answer") {
460: return $_[2];
461: } else {
462: return $_[0];
463: }
464: }
465: }
466:
467: sub html {
468: if ( $external::target eq "web" ) {
469: return shift;
470: }
471: }
472:
473: sub hinton {
474: return 0;
475: }
476:
477: sub random {
478: my ($start,$end,$step)=@_;
479: if ( ! $hidden::RANDOMINIT ) {
480: if ($external::randomseed == 0) { $external::randomseed=1; }
481: if ($external::randomseed =~/,/) {
482: my ($num1,$num2)=split(/,/,$external::randomseed);
483: &random_set_seed(1,abs($num1));
484: } elsif ($external::randomseed =~/:/) {
485: my ($num1,$num2)=split(/:/,$external::randomseed);
486: &random_set_seed(abs($num1),abs($num2));
487: } else {
488: &random_set_seed(1,int(abs($external::randomseed)));
489: }
490: &math_random_uniform();
491: $hidden::RANDOMINIT=1;
492: }
493: if (!defined($step)) { $step=1; }
494: my $num=1+int(($end-$start)/$step);
495: my $result=$start + int(&math_random_uniform() * $num)*$step;
496: return $result;
497: }
498:
499: sub random_normal {
500: my ($item_cnt,$seed,$av,$std_dev) = @_;
501: my @oldseed=&random_get_seed();
502: my @retArray;
503: &random_set_seed_from_phrase($seed);
504: @retArray=&math_random_normal($item_cnt,$av,$std_dev);
505: &random_set_seed(@oldseed);
506: return @retArray;
507: }
508:
509: sub random_beta {
510: my ($item_cnt,$seed,$aa,$bb) = @_;
511: my @oldseed=&random_get_seed();
512: my @retArray;
513: &random_set_seed_from_phrase($seed);
514: @retArray=&math_random_beta($item_cnt,$aa,$bb);
515: &random_set_seed(@oldseed);
516: return @retArray;
517: }
518:
519: sub random_gamma {
520: my ($item_cnt,$seed,$a,$r) = @_;
521: my @oldseed=&random_get_seed();
522: my @retArray;
523: &random_set_seed_from_phrase($seed);
524: @retArray=&math_random_gamma($item_cnt,$a,$r);
525: &random_set_seed(@oldseed);
526: return @retArray;
527: }
528:
529: sub random_exponential {
530: my ($item_cnt,$seed,$av) = @_;
531: my @oldseed=&random_get_seed();
532: my @retArray;
533: &random_set_seed_from_phrase($seed);
534: @retArray=&math_random_exponential($item_cnt,$av);
535: &random_set_seed(@oldseed);
536: return @retArray;
537: }
538:
539: sub random_poisson {
540: my ($item_cnt,$seed,$mu) = @_;
541: my @oldseed=&random_get_seed();
542: my @retArray;
543: &random_set_seed_from_phrase($seed);
544: @retArray=&math_random_poisson($item_cnt,$mu);
545: &random_set_seed(@oldseed);
546: return @retArray;
547: }
548:
549: sub random_chi {
550: my ($item_cnt,$seed,$df) = @_;
551: my @oldseed=&random_get_seed();
552: my @retArray;
553: &random_set_seed_from_phrase($seed);
554: @retArray=&math_random_chi_square($item_cnt,$df);
555: &random_set_seed(@oldseed);
556: return @retArray;
557: }
558:
559: sub random_noncentral_chi {
560: my ($item_cnt,$seed,$df,$nonc) = @_;
561: my @oldseed=&random_get_seed();
562: my @retArray;
563: &random_set_seed_from_phrase($seed);
564: @retArray=&math_random_noncentral_chi_square($item_cnt,$df,$nonc);
565: &random_set_seed(@oldseed);
566: return @retArray;
567: }
568:
569: sub random_f {
570: my ($item_cnt,$seed,$dfn,$dfd) = @_;
571: my @oldseed=&random_get_seed();
572: my @retArray;
573: &random_set_seed_from_phrase($seed);
574: @retArray=&math_random_f($item_cnt,$dfn,$dfd);
575: &random_set_seed(@oldseed);
576: return @retArray;
577: }
578:
579: sub random_noncentral_f {
580: my ($item_cnt,$seed,$dfn,$dfd,$nonc) = @_;
581: my @oldseed=&random_get_seed();
582: my @retArray;
583: &random_set_seed_from_phrase($seed);
584: @retArray=&math_random_noncentral_f($item_cnt,$dfn,$dfd,$nonc);
585: &random_set_seed(@oldseed);
586: return @retArray;
587: }
588:
589: sub random_multivariate_normal {
590: my ($item_cnt,$seed,$mean,$covar) = @_;
591: my @oldseed=&random_get_seed();
592: &random_set_seed_from_phrase($seed);
593: my @retArray=&math_random_multivariate_normal($item_cnt,@$mean,@$covar);
594: &random_set_seed(@oldseed);
595: return @retArray;
596: }
597:
598: sub random_multinomial {
599: my ($item_cnt,$seed,@p) = @_;
600: my @oldseed=&random_get_seed();
601: my @retArray;
602: &random_set_seed_from_phrase($seed);
603: my @retArray=&math_random_multinomial($item_cnt,@p);
604: &random_set_seed(@oldseed);
605: return @retArray;
606: }
607:
608: sub random_permutation {
609: my ($seed,@inArray) = @_;
610: my @oldseed=&random_get_seed();
611: my @retArray;
612: &random_set_seed_from_phrase($seed);
613: @retArray=&math_random_permutation(@inArray);
614: &random_set_seed(@oldseed);
615: return @retArray;
616: }
617:
618: sub random_uniform {
619: my ($item_cnt,$seed,$low,$high) = @_;
620: my @oldseed=&random_get_seed();
621: my @retArray;
622: &random_set_seed_from_phrase($seed);
623: @retArray=&math_random_uniform($item_cnt,$low,$high);
624: &random_set_seed(@oldseed);
625: return @retArray;
626: }
627:
628: sub random_uniform_integer {
629: my ($item_cnt,$seed,$low,$high) = @_;
630: my @oldseed=&random_get_seed();
631: my @retArray;
632: &random_set_seed_from_phrase($seed);
633: @retArray=&math_random_uniform_integer($item_cnt,$low,$high);
634: &random_set_seed(@oldseed);
635: return @retArray;
636: }
637:
638: sub random_binomial {
639: my ($item_cnt,$seed,$nt,$p) = @_;
640: my @oldseed=&random_get_seed();
641: my @retArray;
642: &random_set_seed_from_phrase($seed);
643: @retArray=&math_random_binomial($item_cnt,$nt,$p);
644: &random_set_seed(@oldseed);
645: return @retArray;
646: }
647:
648: sub random_negative_binomial {
649: my ($item_cnt,$seed,$ne,$p) = @_;
650: my @oldseed=&random_get_seed();
651: my @retArray;
652: &random_set_seed_from_phrase($seed);
653: @retArray=&math_random_negative_binomial($item_cnt,$ne,$p);
654: &random_set_seed(@oldseed);
655: return @retArray;
656: }
657:
658: sub abs { CORE::abs(shift) }
659: sub sin { CORE::sin(shift) }
660: sub cos { CORE::cos(shift) }
661: sub exp { CORE::exp(shift) }
662: sub int { CORE::int(shift) }
663: sub log { CORE::log(shift) }
664: sub atan2 { CORE::atan2($_[0],$_[1]) }
665: sub sqrt { CORE::sqrt(shift) }
666:
667: sub tan { CORE::sin($_[0]) / CORE::cos($_[0]) }
668: #sub atan { atan2($_[0], 1); }
669: #sub acos { atan2(sqrt(1 - $_[0] * $_[0]), $_[0] ); }
670: #sub asin { atan2($_[0], sqrt(1- $_[0] * $_[0]) ); }
671:
672: sub log10 { CORE::log($_[0])/CORE::log(10); }
673:
674: sub factorial {
675: my $input = CORE::int(shift);
676: return "Error - unable to take factorial of an negative number ($input)" if $input < 0;
677: return "Error - factorial result is greater than system limit ($input)" if $input > 170;
678: return 1 if $input == 0;
679: my $result = 1;
680: for (my $i=2; $i<=$input; $i++) { $result *= $i }
681: return $result;
682: }
683:
684: sub sgn {
685: return -1 if $_[0] < 0;
686: return 0 if $_[0] == 0;
687: return 1 if $_[0] > 0;
688: }
689:
690: sub min {
691: my @sorted = sort { $a <=> $b || $a cmp $b } @_;
692: return shift @sorted;
693: }
694:
695: sub max {
696: my @sorted = sort { $a <=> $b || $a cmp $b } @_;
697: return pop @sorted;
698: }
699:
700: sub roundto {
701: my ($input,$n) = @_;
702: return sprintf('%.'.$n.'f',$input);
703: }
704:
705: sub to_string {
706: my ($input,$n) = @_;
707: return sprintf($input) if $n eq "";
708: $n = '.'.$n if $n !~ /^\./;
709: return sprintf('%'.$n,$input) if $n ne "";
710: }
711:
712: sub sub_string {
713: my ($str,$start,$len) = @_;
714: return substr($str,$start-1,$len);
715: }
716:
717: sub pow {return $_[0] ** $_[1]; }
718: sub ceil {return (($_[0]-CORE::int($_[0]))== 0.0) ? $_[0] : (($_[0] > 0) ? (CORE::int($_[0])+ 1) : CORE::int($_[0])); }
719: sub floor {return (($_[0]-CORE::int($_[0]))== 0.0) ? $_[0] : (($_[0] > 0) ? CORE::int($_[0]) : (CORE::int($_[0])-1)); }
720: #sub floor {return int($_[0]); }
721:
722: sub format {
723: my ($value,$fmt)=@_;
724: my ($dollarmode,$commamode,$alwaysperiod,$options);
725: if ($fmt =~ /^([^\d]*)(.*)/) { $options=$1; $fmt=$2; }
726: #if ($options =~ /\$/) { $dollamode=1; }
727: #if ($options =~ /,/) { $commamode=1; }
728: if ($options =~ /\./) { $alwaysperiod=1; }
729: my $result;
730: if ($fmt=~/s$/i) {
731: $result=&format_significant_figures($value,$fmt);
732: } else {
733: $fmt=~s/e/E/g;
734: $result=sprintf('%.'.$fmt,$value);
735: if ($alwaysperiod && $fmt eq '0f') { $result .='.'; }
736: $result=~s/(E[+-]*)0/$1/;
737: }
738: #if ($dollarmode) {$result=&dollarformat($result);}
739: #if ($commamode) {$result=&commaformat($result);}
740: return $result;
741: }
742:
743: sub chemparse {
744: my ($reaction) = @_;
745: my @tokens = split(/(\s\+|\->|<=>|<\-|\.)/,$reaction);
746: my $formula = '';
747: foreach my $token (@tokens) {
748: if ($token eq '->' ) {
749: $formula .= '<m>\ensuremath{\rightarrow}</m> ';
750: next;
751: }
752: if ($token eq '<-' ) {
753: $formula .= '<m>\ensuremath{\leftarrow}</m> ';
754: next;
755: }
756: if ($token eq '<=>') {
757: if ($external::target eq 'web' &&
758: &EXT('request.browser.unicode')) {
759: $formula .= '⇌ ';
760: } else {
761: $formula .= &web('<=> ','<m>\ensuremath{\rightleftharpoons}</m> ',
762: '<=> ');
763: }
764: next;
765: }
766: if ($token eq '.') {
767: $formula =~ s/(\ \;| )$//;
768: $formula .= '·';
769: next;
770: }
771: $token =~ /^\s*([\d|\/]*(?:&frac\d\d)?)(.*)/;
772: $formula .= $1 if ($1 ne '1'); # stoichiometric coefficient
773:
774: my $molecule = $2;
775: # subscripts
776: $molecule =~ s|(?<=[a-zA-Z\)\]\s])(\d+)|<sub>$1</sub>|g;
777: # superscripts
778: $molecule =~ s|\^(\d*[+\-]*)|<sup>$1</sup>|g;
779: # strip whitespace
780: $molecule =~ s/\s*//g;
781: # forced space
782: $molecule =~ s/_/ /g;
783: $molecule =~ s/-/−/g;
784: $formula .= $molecule.' ';
785: }
786: # get rid of trailing space
787: $formula =~ s/(\ \;| )$//;
788: return &xmlparse($formula);
789: }
790:
791: sub prettyprint {
792: my ($value,$fmt,$target)=@_;
793: my $result;
794: if (!$target) { $target = $external::target; }
795: if ($fmt =~ /chem/i) { return(&chemparse($value)); }
796: my ($dollarmode,$commamode,$alwaysperiod,$options);
797: if ($fmt =~ /^([^\d]*)(.*)/) { $options=$1; $fmt=$2; }
798: if ($options =~ /\$/) { $dollarmode=1; }
799: if ($options =~ /,/) { $commamode=1; }
800: if ($options =~ /\./) { $alwaysperiod=1; }
801: if ($fmt=~/s$/i) {
802: $value=&format_significant_figures($value,$fmt);
803: } elsif ($fmt) {
804: $value=sprintf('%.'.$fmt,$value);
805: }
806: if ($alwaysperiod && $fmt eq '0f') {
807: if ($target eq 'tex') {
808: $value .='\\ensuremath{.}';
809: } else {
810: $value .='.';
811: }
812: }
813: if ($value =~ /([0-9\.\-\+]+)E([0-9\-\+]+)/i ) {
814: my $frac=$1;
815: if ($dollarmode) { $frac=&dollarformat($frac); }
816: if ($commamode) { $frac=&commaformat($frac); }
817: my $exponent=$2;
818: $exponent=~s/^\+0*//;
819: $exponent=~s/^-0*/-/;
820: $exponent=~s/^-0*/-/;
821: if ($exponent eq '-') { undef($exponent); }
822: if ($exponent) {
823: if ($target eq 'web') {
824: $result=$frac.'×10<sup>'.$exponent.'</sup>';
825: } elsif ($target eq 'tex') {
826: $result='\ensuremath{'.$frac.'\times 10^{'.$exponent.'}}';
827: } else {
828: $result=$value;
829: }
830: } else {
831: $result=$frac;
832: }
833: } else {
834: $result=$value;
835: if ($dollarmode) { $result=&dollarformat($result,$target); }
836: elsif ($commamode) { $result=&commaformat($result,$target); }
837: }
838: return $result;
839: }
840:
841: sub commaformat {
842: my ($number,$target) = @_;
843: if ($number =~ /\./) {
844: while ($number =~ /([^0-9]*)([0-9]+)([^\.,][^\.,][^\.,])([,0-9]*\.[0-9]*)$/) {
845: $number = $1.$2.','.$3.$4;
846: }
847: } else {
848: while ($number =~ /^([^0-9]*)([0-9]+)([^,][^,][^,])([,0-9]*)$/) {
849: $number = $1.$2.','.$3.$4;
850: }
851: }
852: return $number;
853: }
854:
855: sub dollarformat {
856: my ($number,$target) = @_;
857: if (!$target) { $target = $external::target; }
858: $number=&commaformat($number,$target);
859: if ($target eq 'tex') {
860: $number='\$'.$number; #' stupid emacs
861: } else {
862: $number='$'.$number; #' stupid emacs
863: }
864: return $number;
865: }
866:
867: # format of form ns or nS where n is an integer
868: sub format_significant_figures {
869: my ($number,$format) = @_;
870: return '0' if ($number == 0);
871: # extract number of significant figures needed
872: my ($sig) = ($format =~ /(\d+)s/i);
873: # arbitrary choice - suggestions ?? or throw error message?
874: $sig = 3 if ($sig eq '');
875: # save the minus sign
876: my $sign = ($number < 0) ? '-' : '';
877: $number = abs($number);
878: # needed to correct for a number greater than 1 (or
879: my $power = ($number < 1) ? 0 : 1;
880: # could round up. Take the integer part of log10.
881: my $x10 = int(log($number)/log(10));
882: # find number with values left of decimal pt = # of sign figs.
883: my $xsig = $number*10**($sig-$x10-$power);
884: # get just digits left of decimal pt - also rounds off correctly
885: my $xint = sprintf('%.0f',$xsig);
886: # save any trailing zero's
887: my ($zeros) = ($xint =~ /(0+)$/);
888: # return number to original magnitude
889: my $numSig = $xint*10**($x10-$sig+$power);
890: # insert trailing zero's if have decimal point
891: $numSig =~ s/^(\d+)\.(\d+)(\e?(.*)?)$/$1\.$2$zeros$3/;
892: # put a decimal pt for number ending with 0 and length = # of sig fig
893: $numSig.='.' if (length($numSig) == $sig && $numSig =~ /0$/);
894: if (length($numSig) < $sig) {
895: $numSig.='.'.substr($zeros,0,($sig-length($numSig)));
896: }
897: # return number with sign
898: return $sign.$numSig;
899:
900: }
901:
902: sub map {
903: my ($phrase,$dest,$source)=@_;
904: my @oldseed=&random_get_seed();
905: my @seed = &random_seed_from_phrase($phrase);
906: &random_set_seed(@seed);
907: my $destct = scalar(@$dest);
908: if (!$source) {
909: my @output;
910: my @idx = &math_random_permuted_index($destct);
911: my $ctr = 0;
912: while ($ctr < $destct) {
913: $output[$ctr] = $$dest[$idx[$ctr]];
914: $ctr++;
915: }
916: &random_set_seed(@oldseed);
917: return @output;
918: } else {
919: my $num = scalar(@$source);
920: my @idx = &math_random_permuted_index($num);
921: my $ctr = 0;
922: my $tot = $num;
923: $tot = $destct if $destct < $num;
924: if (ref($$dest[0])) {
925: while ($ctr < $tot) {
926: ${$$dest[$ctr]} = $$source[$idx[$ctr]];
927: $ctr++;
928: }
929: } else {
930: while ($ctr < $tot) {
931: $$dest[$ctr] = $$source[$idx[$ctr]];
932: $ctr++;
933: }
934: }
935: }
936: &random_set_seed(@oldseed);
937: return '';
938: }
939:
940: sub rmap {
941: my ($phrase,$dest,$source)=@_;
942: my @oldseed=&random_get_seed();
943: my @seed = &random_seed_from_phrase($phrase);
944: &random_set_seed(@seed);
945: my $destct = scalar(@$dest);
946: if (!$source) {
947: my @idx = &math_random_permuted_index($destct);
948: my $ctr = 0;
949: my @r_idx;
950: while ($ctr < $destct) {
951: $r_idx[$idx[$ctr]] = $ctr;
952: $ctr++;
953: }
954: my @output;
955: $ctr = 0;
956: while ($ctr < $destct) {
957: $output[$ctr] = $$dest[$r_idx[$ctr]];
958: $ctr++;
959: }
960: &random_set_seed(@oldseed);
961: return @output;
962: } else {
963: my $num = scalar(@$source);
964: my @idx = &math_random_permuted_index($num);
965: my $ctr = 0;
966: my $tot = $num;
967: $tot = $destct if $destct < $num;
968: my @r_idx;
969: while ($ctr < $tot) {
970: $r_idx[$idx[$ctr]] = $ctr;
971: $ctr++;
972: }
973: $ctr = 0;
974: if (ref($$dest[0])) {
975: while ($ctr < $tot) {
976: ${$$dest[$ctr]} = $$source[$r_idx[$ctr]];
977: $ctr++;
978: }
979: } else {
980: while ($ctr < $tot) {
981: $$dest[$ctr] = $$source[$r_idx[$ctr]];
982: $ctr++;
983: }
984: }
985: }
986: &random_set_seed(@oldseed);
987: return '';
988: }
989:
990: sub capa_id { return }
991:
992: sub problem { return }
993:
994: sub name{
995: my $fullname = &EXT('environment.lastname').', '.&EXT('environment.firstname').' '.&EXT('environment.middlename');
996: $fullname = "" if $fullname eq ", ";
997: $fullname =~ s/\%2d/-/g;
998: return $fullname;
999: }
1000:
1001: sub student_number {
1002: my $id = &EXT('environment.id');
1003: $id = '' if $id eq "";
1004: return $id;
1005: }
1006:
1007: sub class {
1008: my $course = &EXT('course.description');
1009: $course = '' if $course eq "";
1010: return $course;
1011: }
1012:
1013: sub firstname {
1014: my $firstname = &EXT('environment.firstname');
1015: $firstname = '' if $firstname eq "";
1016: return $firstname;
1017: }
1018:
1019: sub lastname {
1020: my $lastname = &EXT('environment.lastname');
1021: $lastname = '' if $lastname eq "";
1022: return $lastname;
1023: }
1024:
1025: sub sec {
1026: my $sec = &EXT('request.course.sec');
1027: $sec = '' if $sec eq "";
1028: return $sec;
1029: }
1030:
1031: sub submission {
1032: my ($partid,$responseid,$subnumber)=@_;
1033: my $sub='';
1034: if ($subnumber) { $sub=$subnumber.':'; }
1035: return &EXT('user.resource.'.$sub.'resource.'.$partid.'.'.$responseid.'.submission');
1036: }
1037:
1038: sub currentpart {
1039: return $external::part;
1040: }
1041:
1042: sub eval_time {
1043: my ($timestamp)=@_;
1044: unless ($timestamp) { return ''; }
1045: return &locallocaltime($timestamp);
1046: }
1047:
1048: sub open_date {
1049: my ($partid)=@_;
1050: unless ($partid) { $partid=0; }
1051: return &eval_time(&EXT('resource.'.$partid.'.opendate'));
1052: }
1053:
1054: sub due_date {
1055: my ($partid)=@_;
1056: unless ($partid) { $partid=0; }
1057: return &eval_time(&EXT('resource.'.$partid.'.duedate'));
1058: }
1059:
1060: sub answer_date {
1061: my ($partid)=@_;
1062: unless ($partid) { $partid=0; }
1063: return &eval_time(&EXT('resource.'.$partid.'.answerdate'));
1064: }
1065:
1066: sub open_date_epoch {
1067: my ($partid)=@_;
1068: unless ($partid) { $partid=0; }
1069: return &EXT('resource.'.$partid.'.opendate');
1070: }
1071:
1072: sub due_date_epoch {
1073: my ($partid)=@_;
1074: unless ($partid) { $partid=0; }
1075: return &EXT('resource.'.$partid.'.duedate');
1076: }
1077:
1078: sub answer_date_epoch {
1079: my ($partid)=@_;
1080: unless ($partid) { $partid=0; }
1081: return &EXT('resource.'.$partid.'.answerdate');
1082: }
1083:
1084: sub array_moments {
1085: my @input=@_;
1086: my (@output,$N);
1087: $N=scalar (@input);
1088: $output[0]=$N;
1089: if ($N <= 1) {
1090: $output[1]=$input[0];
1091: $output[1]="Input array not defined" if ($N == 0);
1092: $output[2]="variance undefined for N<=1";
1093: $output[3]="skewness undefined for N<=1";
1094: $output[4]="kurtosis undefined for N<=1";
1095: return @output;
1096: }
1097: my $sum=0;
1098: foreach my $line (@input) {
1099: $sum+=$line;
1100: }
1101: $output[1] = $sum/$N;
1102: my ($x,$sdev,$var,$skew,$kurt) = 0;
1103: foreach my $line (@input) {
1104: $x=$line-$output[1];
1105: $var+=$x**2;
1106: $skew+=$x**3;
1107: $kurt+=$x**4;
1108: }
1109: $output[2]=$var/($N-1);
1110: $sdev=CORE::sqrt($output[2]);
1111: if ($sdev == 0) {
1112: $output[3]="inf-variance=0";
1113: $output[4]="inf-variance=0";
1114: return @output;
1115: }
1116: $output[3]=$skew/($sdev**3*$N);
1117: $output[4]=$kurt/($sdev**4*$N)-3;
1118: return @output;
1119: }
1120:
1121: sub choose {
1122: my $num = $_[0];
1123: return $_[$num];
1124: }
1125:
1126: #&sum1(1,$x,sub { &sum1($_[0],2*$_[0], sub { fact($_[0])**2 })});
1127: #sub sum1 {
1128: # my ($start,$end,$sub)=@_;
1129: # my $sum=0;
1130: # for (my $i=$start;$i<=$end;$i++) {
1131: # $sum+=&$sub($i);
1132: # }
1133: # return $sum
1134: #}
1135:
1136: #&sum2('a',1,$x,'&sum2(\'b\',$a,2*$a, \'&factorial($b)**2\')');
1137: #sub sum2 {
1138: # my ($varname,$start,$end,$line)=@_;
1139: # my $sum=0;
1140: # for (my $i=$start;$i<=$end;$i++) {
1141: # my $func=sub {
1142: # eval("\$".$varname."=$i");
1143: # eval($line);
1144: # };
1145: # $sum+=&$func($i);
1146: # }
1147: # return $sum
1148: #}
1149:
1150: # expiremental idea
1151: sub proper_path {
1152: my ($path)=@_;
1153: if ( $external::target eq "tex" ) {
1154: return '/home/httpd/html'.$path;
1155: } else {
1156: return $path;
1157: }
1158: }
1159:
FreeBSD-CVSweb <freebsd-cvsweb@FreeBSD.org>
![[BACK]](/icons/back.gif){kind=icon}
Return to default_homework.lcpm CVS log ![[TXT]](/icons/text.gif){kind=icon}
![[DIR]](/icons/dir.gif){kind=icon}
Up to [LON-CAPA] / loncom / homework