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 1.127 2008/03/05 16:06:39 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 surec 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(" answer is ".
264: # &LONCAPA_INTERNAL_Dumper($LONCAPA::CAPAresponse_answer).":\n");
265: # &LONCAPA_INTERNAL_DEBUG(" respons is ".
266: # &LONCAPA_INTERNAL_Dumper($responses).":\n");
267: &LONCAPA_INTERNAL_DEBUG("args ".join(':',%LONCAPA::CAPAresponse_args));
268: my $type = $LONCAPA::CAPAresponse_args{'type'};
269: &LONCAPA_INTERNAL_DEBUG("Got type :$type:\n");
270:
271: my $num_input_lines =
272: scalar(@{$LONCAPA::CAPAresponse_answer->{'answers'}});
273:
274: if ($type ne '' ) {
275: if (scalar(@$responses) < $num_input_lines) {
276: return 'MISSING_ANSWER';
277: }
278: if (scalar(@$responses) > $num_input_lines) {
279: return 'EXTRA_ANSWER';
280: }
281:
282: }
283:
284: foreach my $which (0..($num_input_lines-1)) {
285: my $answer_size =
286: scalar(@{$LONCAPA::CAPAresponse_answer->{'answers'}[$which]});
287: if ($type ne ''
288: && $answer_size > 1) {
289: $responses->[$which]=[split(/,/,$responses->[$which])];
290: } else {
291: $responses->[$which]=[$responses->[$which]];
292: }
293: }
294: # &LONCAPA_INTERNAL_DEBUG(" parsed response is ".
295: # &LONCAPA_INTERNAL_Dumper($responses).":\n");
296: foreach my $which (0..($num_input_lines-1)) {
297: my $answer_size =
298: scalar(@{$LONCAPA::CAPAresponse_answer->{'answers'}[$which]});
299: my $response_size =
300: scalar(@{$responses->[$which]});
301: if ($answer_size > $response_size) {
302: return 'MISSING_ANSWER';
303: }
304: if ($answer_size < $response_size) {
305: return 'EXTRA_ANSWER';
306: }
307: }
308:
309: &LONCAPA_INTERNAL_DEBUG("Initial final response :$responses->[0][-1]:");
310: my $unit;
311: if ($type eq '' || $type eq 'float') {
312: #for numerical problems split off the unit
313: if ( $responses->[0][-1]=~ /(.*[^\s])\s+([^\s]+)/ ) {
314: $responses->[0][-1]=$1;
315: $unit=$2;
316: }
317: }
318: &LONCAPA_INTERNAL_DEBUG("Final final response :$responses->[0][-1]:$unit:");
319: $unit=~s/\s//;
320: if ($unit ne '') {
321: foreach my $response (@$responses) {
322: foreach my $element (@$response) {
323: $element =~ s/\s//g;
324: $element .= " $unit";
325: }
326: }
327: }
328:
329: foreach my $thisanswer (@{ $LONCAPA::CAPAresponse_answer->{'answers'} }) {
330: if (!defined($thisanswer)) {
331: return ('ERROR','answer was undefined');
332: }
333: }
334:
335:
336: # &LONCAPA_INTERNAL_DEBUG(&LONCAPA_INTERNAL_Dumper($responses));
337: my %memoized;
338: if ($LONCAPA::CAPAresponse_answer->{'type'} eq 'ordered') {
339: for (my $i=0; $i<scalar(@$responses);$i++) {
340: my $answer = $LONCAPA::CAPAresponse_answer->{'answers'}[$i];
341: my $response = $responses->[$i];
342: my $key = "$answer\0$response";
343: my (@awards,@msgs);
344: for (my $j=0; $j<scalar(@$response); $j++) {
345: my ($award,$msg) = &caparesponse_check($answer->[$j],
346: $response->[$j]);
347: push(@awards,$award);
348: push(@msgs, $msg);
349: }
350: my ($award,$msg) =
351: &LONCAPA_INTERNAL_FINALIZEAWARDS(\@awards,\@msgs);
352: $memoized{$key} = [$award,$msg];
353: }
354: } else {
355: #FIXME broken with unorder responses where one is a <value>
356: # and the other is a <vector> (need to delay parse til
357: # inside the loop?)
358: foreach my $response (@$responses) {
359: my $response_size = scalar(@{$response});
360: foreach my $answer (@{ $LONCAPA::CAPAresponse_answer->{'answers'} }) {
361: my $key = "$answer\0$response";
362: my $answer_size = scalar(@{$answer});
363: my ($award,$msg);
364: if ($answer_size > $response_size) {
365: $award = 'MISSING_ANSWER';
366: } elsif ($answer_size < $response_size) {
367: $award = 'EXTRA_ANSWER';
368: } else {
369: my (@awards,@msgs);
370: for (my $j=0; $j<scalar(@$response); $j++) {
371: my ($award,$msg) = &caparesponse_check($answer->[$j],
372: $response->[$j]);
373: push(@awards,$award);
374: push(@msgs, $msg);
375: }
376: ($award,$msg) =
377: &LONCAPA_INTERNAL_FINALIZEAWARDS(\@awards,\@msgs);
378: }
379: $memoized{$key} = [$award,$msg];
380: }
381: }
382: }
383:
384: my ($final_award,$final_msg);
385: &init_permutation(scalar(@$responses),
386: $LONCAPA::CAPAresponse_answer->{'type'});
387:
388: # possible FIXMEs
389: # - significant time is spent calling non-safe space routine
390: # from safe space
391: # - early outs could be possible with classifying awards is to stratas
392: # and stopping as so as hitting the top strata
393: # - some early outs also might be possible with check ing the
394: # memoized hash of results (is correct even possible? etc.)
395:
396: my (@final_awards,@final_msg);
397: while( &get_permutations_left() ) {
398: my $order = &get_next_permutation();
399: my (@awards, @msgs, $i);
400: foreach my $thisanswer (@{ $LONCAPA::CAPAresponse_answer->{'answers'} }) {
401: my $key = "$thisanswer\0".$responses->[$order->[$i]];
402: push(@awards,$memoized{$key}[0]);
403: push(@msgs,$memoized{$key}[1]);
404: $i++;
405:
406: }
407: &LONCAPA_INTERNAL_DEBUG(" all awards ".join(':',@awards));
408:
409: my ($possible_award,$possible_msg) =
410: &LONCAPA_INTERNAL_FINALIZEAWARDS(\@awards,\@msgs);
411: &LONCAPA_INTERNAL_DEBUG(" pos awards ".$possible_award);
412: push(@final_awards,$possible_award);
413: push(@final_msg,$possible_msg);
414: }
415:
416: &LONCAPA_INTERNAL_DEBUG(" all final_awards ".join(':',@final_awards));
417: my ($final_award,$final_msg) =
418: &LONCAPA_INTERNAL_FINALIZEAWARDS(\@final_awards,\@final_msg,undef,1);
419: return ($final_award,$final_msg);
420: }
421:
422: sub cas {
423: my ($system,$input)=@_;
424: my $output;
425: if ($system eq 'maxima') {
426: $output=&maxima_eval($input);
427: }
428: return $output;
429: }
430:
431: sub tex {
432: if ( $external::target eq "tex" ) {
433: return $_[0];
434: } else {
435: return $_[1];
436: }
437: }
438:
439: sub var_in_tex {
440: if ( $external::target eq "tex" ) {
441: return $_[0];
442: } else {
443: return "";
444: }
445: }
446:
447: sub web {
448: if ( $external::target eq "tex" ) {
449: return $_[1];
450: } else {
451: if ( $external::target eq "web" || $external::target eq "answer") {
452: return $_[2];
453: } else {
454: return $_[0];
455: }
456: }
457: }
458:
459: sub html {
460: if ( $external::target eq "web" ) {
461: return shift;
462: }
463: }
464:
465: sub hinton {
466: return 0;
467: }
468:
469: sub random {
470: my ($start,$end,$step)=@_;
471: if ( ! $hidden::RANDOMINIT ) {
472: if ($external::randomseed == 0) { $external::randomseed=1; }
473: if ($external::randomseed =~/,/) {
474: my ($num1,$num2)=split(/,/,$external::randomseed);
475: &random_set_seed(1,abs($num1));
476: } elsif ($external::randomseed =~/:/) {
477: my ($num1,$num2)=split(/:/,$external::randomseed);
478: &random_set_seed(abs($num1),abs($num2));
479: } else {
480: &random_set_seed(1,int(abs($external::randomseed)));
481: }
482: &math_random_uniform();
483: $hidden::RANDOMINIT=1;
484: }
485: if (!defined($step)) { $step=1; }
486: my $num=1+int(($end-$start)/$step);
487: my $result=$start + int(&math_random_uniform() * $num)*$step;
488: return $result;
489: }
490:
491: sub random_normal {
492: my ($item_cnt,$seed,$av,$std_dev) = @_;
493: my @oldseed=&random_get_seed();
494: my @retArray;
495: &random_set_seed_from_phrase($seed);
496: @retArray=&math_random_normal($item_cnt,$av,$std_dev);
497: &random_set_seed(@oldseed);
498: return @retArray;
499: }
500:
501: sub random_beta {
502: my ($item_cnt,$seed,$aa,$bb) = @_;
503: my @oldseed=&random_get_seed();
504: my @retArray;
505: &random_set_seed_from_phrase($seed);
506: @retArray=&math_random_beta($item_cnt,$aa,$bb);
507: &random_set_seed(@oldseed);
508: return @retArray;
509: }
510:
511: sub random_gamma {
512: my ($item_cnt,$seed,$a,$r) = @_;
513: my @oldseed=&random_get_seed();
514: my @retArray;
515: &random_set_seed_from_phrase($seed);
516: @retArray=&math_random_gamma($item_cnt,$a,$r);
517: &random_set_seed(@oldseed);
518: return @retArray;
519: }
520:
521: sub random_exponential {
522: my ($item_cnt,$seed,$av) = @_;
523: my @oldseed=&random_get_seed();
524: my @retArray;
525: &random_set_seed_from_phrase($seed);
526: @retArray=&math_random_exponential($item_cnt,$av);
527: &random_set_seed(@oldseed);
528: return @retArray;
529: }
530:
531: sub random_poisson {
532: my ($item_cnt,$seed,$mu) = @_;
533: my @oldseed=&random_get_seed();
534: my @retArray;
535: &random_set_seed_from_phrase($seed);
536: @retArray=&math_random_poisson($item_cnt,$mu);
537: &random_set_seed(@oldseed);
538: return @retArray;
539: }
540:
541: sub random_chi {
542: my ($item_cnt,$seed,$df) = @_;
543: my @oldseed=&random_get_seed();
544: my @retArray;
545: &random_set_seed_from_phrase($seed);
546: @retArray=&math_random_chi_square($item_cnt,$df);
547: &random_set_seed(@oldseed);
548: return @retArray;
549: }
550:
551: sub random_noncentral_chi {
552: my ($item_cnt,$seed,$df,$nonc) = @_;
553: my @oldseed=&random_get_seed();
554: my @retArray;
555: &random_set_seed_from_phrase($seed);
556: @retArray=&math_random_noncentral_chi_square($item_cnt,$df,$nonc);
557: &random_set_seed(@oldseed);
558: return @retArray;
559: }
560:
561: sub random_f {
562: my ($item_cnt,$seed,$dfn,$dfd) = @_;
563: my @oldseed=&random_get_seed();
564: my @retArray;
565: &random_set_seed_from_phrase($seed);
566: @retArray=&math_random_f($item_cnt,$dfn,$dfd);
567: &random_set_seed(@oldseed);
568: return @retArray;
569: }
570:
571: sub random_noncentral_f {
572: my ($item_cnt,$seed,$dfn,$dfd,$nonc) = @_;
573: my @oldseed=&random_get_seed();
574: my @retArray;
575: &random_set_seed_from_phrase($seed);
576: @retArray=&math_random_noncentral_f($item_cnt,$dfn,$dfd,$nonc);
577: &random_set_seed(@oldseed);
578: return @retArray;
579: }
580:
581: sub random_multivariate_normal {
582: my ($item_cnt,$seed,$mean,$covar) = @_;
583: my @oldseed=&random_get_seed();
584: &random_set_seed_from_phrase($seed);
585: my @retArray=&math_random_multivariate_normal($item_cnt,@$mean,@$covar);
586: &random_set_seed(@oldseed);
587: return @retArray;
588: }
589:
590: sub random_multinomial {
591: my ($item_cnt,$seed,@p) = @_;
592: my @oldseed=&random_get_seed();
593: my @retArray;
594: &random_set_seed_from_phrase($seed);
595: my @retArray=&math_random_multinomial($item_cnt,@p);
596: &random_set_seed(@oldseed);
597: return @retArray;
598: }
599:
600: sub random_permutation {
601: my ($seed,@inArray) = @_;
602: my @oldseed=&random_get_seed();
603: my @retArray;
604: &random_set_seed_from_phrase($seed);
605: @retArray=&math_random_permutation(@inArray);
606: &random_set_seed(@oldseed);
607: return @retArray;
608: }
609:
610: sub random_uniform {
611: my ($item_cnt,$seed,$low,$high) = @_;
612: my @oldseed=&random_get_seed();
613: my @retArray;
614: &random_set_seed_from_phrase($seed);
615: @retArray=&math_random_uniform($item_cnt,$low,$high);
616: &random_set_seed(@oldseed);
617: return @retArray;
618: }
619:
620: sub random_uniform_integer {
621: my ($item_cnt,$seed,$low,$high) = @_;
622: my @oldseed=&random_get_seed();
623: my @retArray;
624: &random_set_seed_from_phrase($seed);
625: @retArray=&math_random_uniform_integer($item_cnt,$low,$high);
626: &random_set_seed(@oldseed);
627: return @retArray;
628: }
629:
630: sub random_binomial {
631: my ($item_cnt,$seed,$nt,$p) = @_;
632: my @oldseed=&random_get_seed();
633: my @retArray;
634: &random_set_seed_from_phrase($seed);
635: @retArray=&math_random_binomial($item_cnt,$nt,$p);
636: &random_set_seed(@oldseed);
637: return @retArray;
638: }
639:
640: sub random_negative_binomial {
641: my ($item_cnt,$seed,$ne,$p) = @_;
642: my @oldseed=&random_get_seed();
643: my @retArray;
644: &random_set_seed_from_phrase($seed);
645: @retArray=&math_random_negative_binomial($item_cnt,$ne,$p);
646: &random_set_seed(@oldseed);
647: return @retArray;
648: }
649:
650: sub abs { CORE::abs(shift) }
651: sub sin { CORE::sin(shift) }
652: sub cos { CORE::cos(shift) }
653: sub exp { CORE::exp(shift) }
654: sub int { CORE::int(shift) }
655: sub log { CORE::log(shift) }
656: sub atan2 { CORE::atan2($_[0],$_[1]) }
657: sub sqrt { CORE::sqrt(shift) }
658:
659: sub tan { CORE::sin($_[0]) / CORE::cos($_[0]) }
660: #sub atan { atan2($_[0], 1); }
661: #sub acos { atan2(sqrt(1 - $_[0] * $_[0]), $_[0] ); }
662: #sub asin { atan2($_[0], sqrt(1- $_[0] * $_[0]) ); }
663:
664: sub log10 { CORE::log($_[0])/CORE::log(10); }
665:
666: sub factorial {
667: my $input = CORE::int(shift);
668: return "Error - unable to take factorial of an negative number ($input)" if $input < 0;
669: return "Error - factorial result is greater than system limit ($input)" if $input > 170;
670: return 1 if $input == 0;
671: my $result = 1;
672: for (my $i=2; $i<=$input; $i++) { $result *= $i }
673: return $result;
674: }
675:
676: sub sgn {
677: return -1 if $_[0] < 0;
678: return 0 if $_[0] == 0;
679: return 1 if $_[0] > 0;
680: }
681:
682: sub min {
683: my @sorted = sort { $a <=> $b || $a cmp $b } @_;
684: return shift @sorted;
685: }
686:
687: sub max {
688: my @sorted = sort { $a <=> $b || $a cmp $b } @_;
689: return pop @sorted;
690: }
691:
692: sub roundto {
693: my ($input,$n) = @_;
694: return sprintf('%.'.$n.'f',$input);
695: }
696:
697: sub to_string {
698: my ($input,$n) = @_;
699: return sprintf($input) if $n eq "";
700: $n = '.'.$n if $n !~ /^\./;
701: return sprintf('%'.$n,$input) if $n ne "";
702: }
703:
704: sub sub_string {
705: my ($str,$start,$len) = @_;
706: return substr($str,$start-1,$len);
707: }
708:
709: sub pow {return $_[0] ** $_[1]; }
710: sub ceil {return (($_[0]-CORE::int($_[0]))== 0.0) ? $_[0] : (($_[0] > 0) ? (CORE::int($_[0])+ 1) : CORE::int($_[0])); }
711: sub floor {return (($_[0]-CORE::int($_[0]))== 0.0) ? $_[0] : (($_[0] > 0) ? CORE::int($_[0]) : (CORE::int($_[0])-1)); }
712: #sub floor {return int($_[0]); }
713:
714: sub format {
715: my ($value,$fmt)=@_;
716: my ($dollarmode,$commamode,$alwaysperiod,$options);
717: if ($fmt =~ /^([^\d]*)(.*)/) { $options=$1; $fmt=$2; }
718: #if ($options =~ /\$/) { $dollamode=1; }
719: #if ($options =~ /,/) { $commamode=1; }
720: if ($options =~ /\./) { $alwaysperiod=1; }
721: my $result;
722: if ($fmt=~/s$/i) {
723: $result=&format_significant_figures($value,$fmt);
724: } else {
725: $fmt=~s/e/E/g;
726: $result=sprintf('%.'.$fmt,$value);
727: if ($alwaysperiod && $fmt eq '0f') { $result .='.'; }
728: $result=~s/(E[+-]*)0/$1/;
729: }
730: #if ($dollarmode) {$result=&dollarformat($result);}
731: #if ($commamode) {$result=&commaformat($result);}
732: return $result;
733: }
734:
735: sub chemparse {
736: my ($reaction) = @_;
737: my @tokens = split(/(\s\+|\->|<=>|<\-|\.)/,$reaction);
738: my $formula = '';
739: foreach my $token (@tokens) {
740: if ($token eq '->' ) {
741: $formula .= '<m>\ensuremath{\rightarrow}</m> ';
742: next;
743: }
744: if ($token eq '<-' ) {
745: $formula .= '<m>\ensuremath{\leftarrow}</m> ';
746: next;
747: }
748: if ($token eq '<=>') {
749: if ($external::target eq 'web' &&
750: &EXT('request.browser.unicode')) {
751: $formula .= '⇌ ';
752: } else {
753: $formula .= &web('<=> ','<m>\ensuremath{\rightleftharpoons}</m> ',
754: '<=> ');
755: }
756: next;
757: }
758: if ($token eq '.') {
759: $formula =~ s/(\ \;| )$//;
760: $formula .= '·';
761: next;
762: }
763: $token =~ /^\s*([\d|\/]*(?:&frac\d\d)?)(.*)/;
764: $formula .= $1 if ($1 ne '1'); # stoichiometric coefficient
765:
766: my $molecule = $2;
767: # subscripts
768: $molecule =~ s|(?<=[a-zA-Z\)\]\s])(\d+)|<sub>$1</sub>|g;
769: # superscripts
770: $molecule =~ s|\^(\d*[+\-]*)|<sup>$1</sup>|g;
771: # strip whitespace
772: $molecule =~ s/\s*//g;
773: # forced space
774: $molecule =~ s/_/ /g;
775: $molecule =~ s/-/−/g;
776: $formula .= $molecule.' ';
777: }
778: # get rid of trailing space
779: $formula =~ s/(\ \;| )$//;
780: return &xmlparse($formula);
781: }
782:
783: sub prettyprint {
784: my ($value,$fmt,$target)=@_;
785: my $result;
786: if (!$target) { $target = $external::target; }
787: if ($fmt =~ /chem/i) { return(&chemparse($value)); }
788: my ($dollarmode,$commamode,$alwaysperiod,$options);
789: if ($fmt =~ /^([^\d]*)(.*)/) { $options=$1; $fmt=$2; }
790: if ($options =~ /\$/) { $dollarmode=1; }
791: if ($options =~ /,/) { $commamode=1; }
792: if ($options =~ /\./) { $alwaysperiod=1; }
793: if ($fmt=~/s$/i) {
794: $value=&format_significant_figures($value,$fmt);
795: } elsif ($fmt) {
796: $value=sprintf('%.'.$fmt,$value);
797: }
798: if ($alwaysperiod && $fmt eq '0f') {
799: if ($target eq 'tex') {
800: $value .='\\ensuremath{.}';
801: } else {
802: $value .='.';
803: }
804: }
805: if ($value =~ /([0-9\.\-\+]+)E([0-9\-\+]+)/i ) {
806: my $frac=$1;
807: if ($dollarmode) { $frac=&dollarformat($frac); }
808: if ($commamode) { $frac=&commaformat($frac); }
809: my $exponent=$2;
810: $exponent=~s/^\+0*//;
811: $exponent=~s/^-0*/-/;
812: $exponent=~s/^-0*/-/;
813: if ($exponent eq '-') { undef($exponent); }
814: if ($exponent) {
815: if ($target eq 'web') {
816: $result=$frac.'×10<sup>'.$exponent.'</sup>';
817: } elsif ($target eq 'tex') {
818: $result='\ensuremath{'.$frac.'\times 10^{'.$exponent.'}}';
819: } else {
820: $result=$value;
821: }
822: } else {
823: $result=$frac;
824: }
825: } else {
826: $result=$value;
827: if ($dollarmode) { $result=&dollarformat($result,$target); }
828: elsif ($commamode) { $result=&commaformat($result,$target); }
829: }
830: return $result;
831: }
832:
833: sub commaformat {
834: my ($number,$target) = @_;
835: if ($number =~ /\./) {
836: while ($number =~ /([^0-9]*)([0-9]+)([^\.,][^\.,][^\.,])([,0-9]*\.[0-9]*)$/) {
837: $number = $1.$2.','.$3.$4;
838: }
839: } else {
840: while ($number =~ /^([^0-9]*)([0-9]+)([^,][^,][^,])([,0-9]*)$/) {
841: $number = $1.$2.','.$3.$4;
842: }
843: }
844: return $number;
845: }
846:
847: sub dollarformat {
848: my ($number,$target) = @_;
849: if (!$target) { $target = $external::target; }
850: $number=&commaformat($number,$target);
851: if ($target eq 'tex') {
852: $number='\$'.$number; #' stupid emacs
853: } else {
854: $number='$'.$number; #' stupid emacs
855: }
856: return $number;
857: }
858:
859: # format of form ns or nS where n is an integer
860: sub format_significant_figures {
861: my ($number,$format) = @_;
862: return '0' if ($number == 0);
863: # extract number of significant figures needed
864: my ($sig) = ($format =~ /(\d+)s/i);
865: # arbitrary choice - suggestions ?? or throw error message?
866: $sig = 3 if ($sig eq '');
867: # save the minus sign
868: my $sign = ($number < 0) ? '-' : '';
869: $number = abs($number);
870: # needed to correct for a number greater than 1 (or
871: my $power = ($number < 1) ? 0 : 1;
872: # could round up. Take the integer part of log10.
873: my $x10 = int(log($number)/log(10));
874: # find number with values left of decimal pt = # of sign figs.
875: my $xsig = $number*10**($sig-$x10-$power);
876: # get just digits left of decimal pt - also rounds off correctly
877: my $xint = sprintf('%.0f',$xsig);
878: # save any trailing zero's
879: my ($zeros) = ($xint =~ /(0+)$/);
880: # return number to original magnitude
881: my $numSig = $xint*10**($x10-$sig+$power);
882: # insert trailing zero's if have decimal point
883: $numSig =~ s/^(\d+)\.(\d+)(\e?(.*)?)$/$1\.$2$zeros$3/;
884: # put a decimal pt for number ending with 0 and length = # of sig fig
885: $numSig.='.' if (length($numSig) == $sig && $numSig =~ /0$/);
886: if (length($numSig) < $sig) {
887: $numSig.='.'.substr($zeros,0,($sig-length($numSig)));
888: }
889: # return number with sign
890: return $sign.$numSig;
891:
892: }
893:
894: sub map {
895: my ($phrase,$dest,$source)=@_;
896: my @oldseed=&random_get_seed();
897: my @seed = &random_seed_from_phrase($phrase);
898: &random_set_seed(@seed);
899: my $destct = scalar(@$dest);
900: if (!$source) {
901: my @output;
902: my @idx = &math_random_permuted_index($destct);
903: my $ctr = 0;
904: while ($ctr < $destct) {
905: $output[$ctr] = $$dest[$idx[$ctr]];
906: $ctr++;
907: }
908: &random_set_seed(@oldseed);
909: return @output;
910: } else {
911: my $num = scalar(@$source);
912: my @idx = &math_random_permuted_index($num);
913: my $ctr = 0;
914: my $tot = $num;
915: $tot = $destct if $destct < $num;
916: if (ref($$dest[0])) {
917: while ($ctr < $tot) {
918: ${$$dest[$ctr]} = $$source[$idx[$ctr]];
919: $ctr++;
920: }
921: } else {
922: while ($ctr < $tot) {
923: $$dest[$ctr] = $$source[$idx[$ctr]];
924: $ctr++;
925: }
926: }
927: }
928: &random_set_seed(@oldseed);
929: return '';
930: }
931:
932: sub rmap {
933: my ($phrase,$dest,$source)=@_;
934: my @oldseed=&random_get_seed();
935: my @seed = &random_seed_from_phrase($phrase);
936: &random_set_seed(@seed);
937: my $destct = scalar(@$dest);
938: if (!$source) {
939: my @idx = &math_random_permuted_index($destct);
940: my $ctr = 0;
941: my @r_idx;
942: while ($ctr < $destct) {
943: $r_idx[$idx[$ctr]] = $ctr;
944: $ctr++;
945: }
946: my @output;
947: $ctr = 0;
948: while ($ctr < $destct) {
949: $output[$ctr] = $$dest[$r_idx[$ctr]];
950: $ctr++;
951: }
952: &random_set_seed(@oldseed);
953: return @output;
954: } else {
955: my $num = scalar(@$source);
956: my @idx = &math_random_permuted_index($num);
957: my $ctr = 0;
958: my $tot = $num;
959: $tot = $destct if $destct < $num;
960: my @r_idx;
961: while ($ctr < $tot) {
962: $r_idx[$idx[$ctr]] = $ctr;
963: $ctr++;
964: }
965: $ctr = 0;
966: if (ref($$dest[0])) {
967: while ($ctr < $tot) {
968: ${$$dest[$ctr]} = $$source[$r_idx[$ctr]];
969: $ctr++;
970: }
971: } else {
972: while ($ctr < $tot) {
973: $$dest[$ctr] = $$source[$r_idx[$ctr]];
974: $ctr++;
975: }
976: }
977: }
978: &random_set_seed(@oldseed);
979: return '';
980: }
981:
982: sub capa_id { return }
983:
984: sub problem { return }
985:
986: sub name{
987: my $fullname = &EXT('environment.lastname').', '.&EXT('environment.firstname').' '.&EXT('environment.middlename');
988: $fullname = "" if $fullname eq ", ";
989: $fullname =~ s/\%2d/-/g;
990: return $fullname;
991: }
992:
993: sub student_number {
994: my $id = &EXT('environment.id');
995: $id = '' if $id eq "";
996: return $id;
997: }
998:
999: sub class {
1000: my $course = &EXT('course.description');
1001: $course = '' if $course eq "";
1002: return $course;
1003: }
1004:
1005: sub firstname {
1006: my $firstname = &EXT('environment.firstname');
1007: $firstname = '' if $firstname eq "";
1008: return $firstname;
1009: }
1010:
1011: sub lastname {
1012: my $lastname = &EXT('environment.lastname');
1013: $lastname = '' if $lastname eq "";
1014: return $lastname;
1015: }
1016:
1017: sub sec {
1018: my $sec = &EXT('request.course.sec');
1019: $sec = '' if $sec eq "";
1020: return $sec;
1021: }
1022:
1023: sub open_date {
1024: my @dc = split(/\s+/,localtime(&EXT('resource.0.opendate')));
1025: return '' if ($dc[0] eq "Wed" and $dc[2] == 31 and $dc[4] == 1969);
1026: my @hm = split(/:/,$dc[3]);
1027: my $ampm = " am";
1028: if ($hm[0] > 12) {
1029: $hm[0]-=12;
1030: $ampm = " pm";
1031: }
1032: return $dc[0].', '.$dc[1].' '.$dc[2].', '.$dc[4].' at '.$hm[0].':'.$hm[1].$ampm;
1033: }
1034:
1035: sub due_date {
1036: my @dc = split(/\s+/,localtime(&EXT('resource.0.duedate')));
1037: return '' if ($dc[0] eq "Wed" and $dc[2] == 31 and $dc[4] == 1969);
1038: my @hm = split(/:/,$dc[3]);
1039: my $ampm = " am";
1040: if ($hm[0] > 12) {
1041: $hm[0]-=12;
1042: $ampm = " pm";
1043: }
1044: return $dc[0].', '.$dc[1].' '.$dc[2].', '.$dc[4].' at '.$hm[0].':'.$hm[1].$ampm;
1045: }
1046:
1047: sub answer_date {
1048: my @dc = split(/\s+/,localtime(&EXT('resource.0.answerdate')));
1049: return '' if ($dc[0] eq "Wed" and $dc[2] == 31 and $dc[4] == 1969);
1050: my @hm = split(/:/,$dc[3]);
1051: my $ampm = " am";
1052: if ($hm[0] > 12) {
1053: $hm[0]-=12;
1054: $ampm = " pm";
1055: }
1056: return $dc[0].', '.$dc[1].' '.$dc[2].', '.$dc[4].' at '.$hm[0].':'.$hm[1].$ampm;
1057: }
1058:
1059: sub array_moments {
1060: my @input=@_;
1061: my (@output,$N);
1062: $N=scalar (@input);
1063: $output[0]=$N;
1064: if ($N <= 1) {
1065: $output[1]=$input[0];
1066: $output[1]="Input array not defined" if ($N == 0);
1067: $output[2]="variance undefined for N<=1";
1068: $output[3]="skewness undefined for N<=1";
1069: $output[4]="kurtosis undefined for N<=1";
1070: return @output;
1071: }
1072: my $sum=0;
1073: foreach my $line (@input) {
1074: $sum+=$line;
1075: }
1076: $output[1] = $sum/$N;
1077: my ($x,$sdev,$var,$skew,$kurt) = 0;
1078: foreach my $line (@input) {
1079: $x=$line-$output[1];
1080: $var+=$x**2;
1081: $skew+=$x**3;
1082: $kurt+=$x**4;
1083: }
1084: $output[2]=$var/($N-1);
1085: $sdev=CORE::sqrt($output[2]);
1086: if ($sdev == 0) {
1087: $output[3]="inf-variance=0";
1088: $output[4]="inf-variance=0";
1089: return @output;
1090: }
1091: $output[3]=$skew/($sdev**3*$N);
1092: $output[4]=$kurt/($sdev**4*$N)-3;
1093: return @output;
1094: }
1095:
1096: sub choose {
1097: my $num = $_[0];
1098: return $_[$num];
1099: }
1100:
1101: #&sum1(1,$x,sub { &sum1($_[0],2*$_[0], sub { fact($_[0])**2 })});
1102: #sub sum1 {
1103: # my ($start,$end,$sub)=@_;
1104: # my $sum=0;
1105: # for (my $i=$start;$i<=$end;$i++) {
1106: # $sum+=&$sub($i);
1107: # }
1108: # return $sum
1109: #}
1110:
1111: #&sum2('a',1,$x,'&sum2(\'b\',$a,2*$a, \'&factorial($b)**2\')');
1112: #sub sum2 {
1113: # my ($varname,$start,$end,$line)=@_;
1114: # my $sum=0;
1115: # for (my $i=$start;$i<=$end;$i++) {
1116: # my $func=sub {
1117: # eval("\$".$varname."=$i");
1118: # eval($line);
1119: # };
1120: # $sum+=&$func($i);
1121: # }
1122: # return $sum
1123: #}
1124:
1125: # expiremental idea
1126: sub proper_path {
1127: my ($path)=@_;
1128: if ( $external::target eq "tex" ) {
1129: return '/home/httpd/html'.$path;
1130: } else {
1131: return $path;
1132: }
1133: }
1134:
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