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 1.145 2009/06/23 03:01:15 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') || ($type eq '8')) {
221: if ($response=~/\=/) {
222: return ('BAD_FORMULA','Please submit just an expression, not an equation.');
223: } elsif ($response =~ /\,/ and $response !~ /^\s*\{.*\}\s*$/) {
224: return ('BAD_FORMULA');
225: }
226: }
227: if ($type eq '9') {
228: $result = &maxima_check(&maxima_cas_formula_fix($response),&maxima_cas_formula_fix($answer),\$reterror);
229: } else {
230: if ($type eq '8') { # fml type
231: $response = &capa_formula_fix($response);
232: $answer = &capa_formula_fix($answer);
233: }
234: $result = &caparesponse_capa_check_answer($response,$answer,$type,
235: $tol_type,$tol,
236: $sig_lbound,$sig_ubound,
237: $ans_fmt,$unit,$calc,$id_list,
238: $points,$external::randomseed,
239: \$reterror);
240: }
241: if ($result == '1') { $result='EXACT_ANS'; }
242: elsif ($result == '2') { $result='APPROX_ANS'; }
243: elsif ($result == '3') { $result='SIG_FAIL'; }
244: elsif ($result == '4') { $result='UNIT_FAIL'; }
245: elsif ($result == '5') { $result='NO_UNIT'; }
246: elsif ($result == '6') { $result='UNIT_OK'; }
247: elsif ($result == '7') { $result='INCORRECT'; }
248: elsif ($result == '8') { $result='UNIT_NOTNEEDED'; }
249: elsif ($result == '9') { $result='ANS_CNT_NOT_MATCH'; }
250: elsif ($result =='10') { $result='SUB_RECORDED'; }
251: elsif ($result =='11') { $result='BAD_FORMULA'; }
252: elsif ($result =='12' && !$response) { $result='MISSING_ANSWER'; }
253: elsif ($result =='12') { $result='WANTED_NUMERIC'; }
254: elsif ($result =='13') { $result='UNIT_INVALID_INSTRUCTOR'; }
255: elsif ($result =='141') { $result='UNIT_INVALID_STUDENT'; }
256: elsif ($result =='142') { $result='UNIT_INVALID_STUDENT'; }
257: elsif ($result =='143') { $result='UNIT_INVALID_STUDENT'; }
258: elsif ($result =='15') { $result='UNIT_IRRECONCIBLE'; }
259: else {$result = "ERROR: Unknown Result:$result:$@:";}
260:
261: &LONCAPA_INTERNAL_DEBUG("RetError $reterror: Answer $answer: Response $response: type-$type|$tol|$tol_type|$sig:$sig_lbound:$sig_ubound|$unit|");
262: &LONCAPA_INTERNAL_DEBUG(" $answer $response $result ");
263: return ($result,$reterror);
264: }
265:
266:
267: sub caparesponse_check_list {
268: my $responses=$LONCAPA::CAPAresponse_args{'response'};
269: &LONCAPA_INTERNAL_DEBUG("args ".join(':',%LONCAPA::CAPAresponse_args));
270: my $type = $LONCAPA::CAPAresponse_args{'type'};
271: my $answerunit=$LONCAPA::CAPAresponse_args{'unit'};
272: &LONCAPA_INTERNAL_DEBUG("Got type :$type: answer unit :$answerunit:\n");
273:
274: my $num_input_lines =
275: scalar(@{$LONCAPA::CAPAresponse_answer->{'answers'}});
276:
277: if ($type ne '' ) {
278: if (scalar(@$responses) < $num_input_lines) {
279: return 'MISSING_ANSWER';
280: }
281: if (scalar(@$responses) > $num_input_lines) {
282: return 'EXTRA_ANSWER';
283: }
284:
285: }
286:
287: foreach my $which (0..($num_input_lines-1)) {
288: my $answer_size =
289: scalar(@{$LONCAPA::CAPAresponse_answer->{'answers'}[$which]});
290: if ($type ne ''
291: && $answer_size > 1) {
292: $responses->[$which]=[split(/,/,$responses->[$which])];
293: } else {
294: $responses->[$which]=[$responses->[$which]];
295: }
296: }
297: foreach my $which (0..($num_input_lines-1)) {
298: my $answer_size =
299: scalar(@{$LONCAPA::CAPAresponse_answer->{'answers'}[$which]});
300: my $response_size =
301: scalar(@{$responses->[$which]});
302: if ($answer_size > $response_size) {
303: return 'MISSING_ANSWER';
304: }
305: if ($answer_size < $response_size) {
306: return 'EXTRA_ANSWER';
307: }
308: }
309:
310: &LONCAPA_INTERNAL_DEBUG("Initial final response :$responses->[0][-1]:");
311: my $unit;
312: if ($type eq 'float' || $type eq '') {
313: #for numerical problems split off the unit
314: # if ( $responses->[0][-1]=~ /(.*[^\s])\s+([^\s]+)/ ) {
315: if ( $responses->[0][-1]=~ /^([\d\.\,\s\$]*(?:(?:[xX\*]10[\^\*]*|[eE]*)[\+\-]*\d*)*(?:^|\S)\d+)([\$\s\w\^\*\/\(\)\+\-]*[^\d\.\s\,][\$\s\w\^\*\/\(\)\+\-]*)$/ ) {
316: $responses->[0][-1]=$1;
317: $unit=&capa_formula_fix($2);
318: &LONCAPA_INTERNAL_DEBUG("Found unit :$unit:");
319: }
320: }
321: &LONCAPA_INTERNAL_DEBUG("Final final response :$responses->[0][-1]:$unit:");
322: $unit=~s/\s//;
323: foreach my $response (@$responses) {
324: foreach my $element (@$response) {
325: if (($type eq 'float') || (($type eq '') && ($unit ne ''))) {
326: $element =~ s/\s//g;
327: }
328: my $appendunit=$unit;
329: if (($unit=~/\%/) && ($answerunit ne '%')) {
330: $element=$element/100;
331: $appendunit=~s/\%//;
332: }
333: if (($element==0) && ($unit!~/\w/) && ($answerunit=~/\w/)) {
334: $appendunit=$answerunit;
335: }
336: $element .= " $appendunit";
337: &LONCAPA_INTERNAL_DEBUG("Made response element :$element:");
338: }
339: }
340:
341: foreach my $thisanswer (@{ $LONCAPA::CAPAresponse_answer->{'answers'} }) {
342: if (!defined($thisanswer)) {
343: return ('ERROR','answer was undefined');
344: }
345: }
346:
347:
348: # &LONCAPA_INTERNAL_DEBUG(&LONCAPA_INTERNAL_Dumper($responses));
349: my %memoized;
350: if ($LONCAPA::CAPAresponse_answer->{'type'} eq 'ordered') {
351: for (my $i=0; $i<scalar(@$responses);$i++) {
352: my $answer = $LONCAPA::CAPAresponse_answer->{'answers'}[$i];
353: my $response = $responses->[$i];
354: my $key = "$answer\0$response";
355: my (@awards,@msgs);
356: for (my $j=0; $j<scalar(@$response); $j++) {
357: my ($award,$msg) = &caparesponse_check($answer->[$j],
358: $response->[$j]);
359: push(@awards,$award);
360: push(@msgs, $msg);
361: }
362: my ($award,$msg) =
363: &LONCAPA_INTERNAL_FINALIZEAWARDS(\@awards,\@msgs);
364: $memoized{$key} = [$award,$msg];
365: }
366: } else {
367: #FIXME broken with unorder responses where one is a <value>
368: # and the other is a <vector> (need to delay parse til
369: # inside the loop?)
370: foreach my $response (@$responses) {
371: my $response_size = scalar(@{$response});
372: foreach my $answer (@{ $LONCAPA::CAPAresponse_answer->{'answers'} }) {
373: my $key = "$answer\0$response";
374: my $answer_size = scalar(@{$answer});
375: my ($award,$msg);
376: if ($answer_size > $response_size) {
377: $award = 'MISSING_ANSWER';
378: } elsif ($answer_size < $response_size) {
379: $award = 'EXTRA_ANSWER';
380: } else {
381: my (@awards,@msgs);
382: for (my $j=0; $j<scalar(@$response); $j++) {
383: my ($award,$msg) = &caparesponse_check($answer->[$j],
384: $response->[$j]);
385: push(@awards,$award);
386: push(@msgs, $msg);
387: }
388: ($award,$msg) =
389: &LONCAPA_INTERNAL_FINALIZEAWARDS(\@awards,\@msgs);
390: }
391: $memoized{$key} = [$award,$msg];
392: }
393: }
394: }
395:
396: my ($final_award,$final_msg);
397: &init_permutation(scalar(@$responses),
398: $LONCAPA::CAPAresponse_answer->{'type'});
399:
400: # possible FIXMEs
401: # - significant time is spent calling non-safe space routine
402: # from safe space
403: # - early outs could be possible with classifying awards is to stratas
404: # and stopping as so as hitting the top strata
405: # - some early outs also might be possible with check ing the
406: # memoized hash of results (is correct even possible? etc.)
407:
408: my (@final_awards,@final_msg);
409: while( &get_permutations_left() ) {
410: my $order = &get_next_permutation();
411: my (@awards, @msgs, $i);
412: foreach my $thisanswer (@{ $LONCAPA::CAPAresponse_answer->{'answers'} }) {
413: my $key = "$thisanswer\0".$responses->[$order->[$i]];
414: push(@awards,$memoized{$key}[0]);
415: push(@msgs,$memoized{$key}[1]);
416: $i++;
417:
418: }
419: &LONCAPA_INTERNAL_DEBUG(" all awards ".join(':',@awards));
420:
421: my ($possible_award,$possible_msg) =
422: &LONCAPA_INTERNAL_FINALIZEAWARDS(\@awards,\@msgs);
423: &LONCAPA_INTERNAL_DEBUG(" pos awards ".$possible_award);
424: push(@final_awards,$possible_award);
425: push(@final_msg,$possible_msg);
426: }
427:
428: &LONCAPA_INTERNAL_DEBUG(" all final_awards ".join(':',@final_awards));
429: my ($final_award,$final_msg) =
430: &LONCAPA_INTERNAL_FINALIZEAWARDS(\@final_awards,\@final_msg,undef,1);
431: return ($final_award,$final_msg);
432: }
433:
434: sub cas {
435: my ($system,$input,$library)=@_;
436: my $output;
437: my $dump;
438: if ($system eq 'maxima') {
439: $output=&maxima_eval($input,$library);
440: } elsif ($system eq 'R') {
441: ($output,$dump)=&r_eval($input,$library,0);
442: } else {
443: $output='Error: unrecognized CAS';
444: }
445: return $output;
446: }
447:
448: sub cas_hashref {
449: my ($system,$input,$library)=@_;
450: if ($system eq 'maxima') {
451: return 'Error: unsupported CAS';
452: } elsif ($system eq 'R') {
453: return &r_eval($input,$library,1);
454: } else {
455: return 'Error: unrecognized CAS';
456: }
457: }
458:
459: #
460: # cas_hashref_entry takes a list of indices and gets the entry in a hash generated by Rreturn.
461: # Call: cas_hashref_entry(Rvalue, index1, index2, ...) where Rvalue is a hash returned by Rreturn.
462: # Rentry will return the first scalar value it encounters (ignoring excess indices).
463: # If an invalid key is given, it returns undef.
464: #
465: sub cas_hashref_entry {
466: return &Rentry(@_);
467: }
468:
469: #
470: # cas_hashref_array takes a list of indices and gets a column array from a hash generated by Rreturn.
471: # Call: cas_hashref_array(Rvalue, index1, index2, ...) where Rvalue is a hash returned by Rreturn.
472: # If an invalid key is given, it returns undef.
473: #
474: sub cas_hashref_array {
475: return &Rarray(@_);
476: }
477:
478: sub tex {
479: if ( $external::target eq "tex" ) {
480: return $_[0];
481: } else {
482: return $_[1];
483: }
484: }
485:
486: sub var_in_tex {
487: if ( $external::target eq "tex" ) {
488: return $_[0];
489: } else {
490: return "";
491: }
492: }
493:
494: sub web {
495: if ( $external::target eq "tex" ) {
496: return $_[1];
497: } else {
498: if ( $external::target eq "web" || $external::target eq "answer") {
499: return $_[2];
500: } else {
501: return $_[0];
502: }
503: }
504: }
505:
506: sub html {
507: if ( $external::target eq "web" ) {
508: return shift;
509: }
510: }
511:
512: sub hinton {
513: return 0;
514: }
515:
516: sub random {
517: my ($start,$end,$step)=@_;
518: if ( ! $hidden::RANDOMINIT ) {
519: if ($external::randomseed == 0) { $external::randomseed=1; }
520: if ($external::randomseed =~/,/) {
521: my ($num1,$num2)=split(/,/,$external::randomseed);
522: &random_set_seed(1,abs($num1));
523: } elsif ($external::randomseed =~/:/) {
524: my ($num1,$num2)=split(/:/,$external::randomseed);
525: &random_set_seed(abs($num1),abs($num2));
526: } else {
527: &random_set_seed(1,int(abs($external::randomseed)));
528: }
529: &math_random_uniform();
530: $hidden::RANDOMINIT=1;
531: }
532: if (!defined($step)) { $step=1; }
533: my $num=1+int(($end-$start)/$step);
534: my $result=$start + int(&math_random_uniform() * $num)*$step;
535: return $result;
536: }
537:
538: sub random_normal {
539: my ($item_cnt,$seed,$av,$std_dev) = @_;
540: my @oldseed=&random_get_seed();
541: my @retArray;
542: &random_set_seed_from_phrase($seed);
543: @retArray=&math_random_normal($item_cnt,$av,$std_dev);
544: &random_set_seed(@oldseed);
545: return @retArray;
546: }
547:
548: sub random_beta {
549: my ($item_cnt,$seed,$aa,$bb) = @_;
550: my @oldseed=&random_get_seed();
551: my @retArray;
552: &random_set_seed_from_phrase($seed);
553: @retArray=&math_random_beta($item_cnt,$aa,$bb);
554: &random_set_seed(@oldseed);
555: return @retArray;
556: }
557:
558: sub random_gamma {
559: my ($item_cnt,$seed,$a,$r) = @_;
560: my @oldseed=&random_get_seed();
561: my @retArray;
562: &random_set_seed_from_phrase($seed);
563: @retArray=&math_random_gamma($item_cnt,$a,$r);
564: &random_set_seed(@oldseed);
565: return @retArray;
566: }
567:
568: sub random_exponential {
569: my ($item_cnt,$seed,$av) = @_;
570: my @oldseed=&random_get_seed();
571: my @retArray;
572: &random_set_seed_from_phrase($seed);
573: @retArray=&math_random_exponential($item_cnt,$av);
574: &random_set_seed(@oldseed);
575: return @retArray;
576: }
577:
578: sub random_poisson {
579: my ($item_cnt,$seed,$mu) = @_;
580: my @oldseed=&random_get_seed();
581: my @retArray;
582: &random_set_seed_from_phrase($seed);
583: @retArray=&math_random_poisson($item_cnt,$mu);
584: &random_set_seed(@oldseed);
585: return @retArray;
586: }
587:
588: sub random_chi {
589: my ($item_cnt,$seed,$df) = @_;
590: my @oldseed=&random_get_seed();
591: my @retArray;
592: &random_set_seed_from_phrase($seed);
593: @retArray=&math_random_chi_square($item_cnt,$df);
594: &random_set_seed(@oldseed);
595: return @retArray;
596: }
597:
598: sub random_noncentral_chi {
599: my ($item_cnt,$seed,$df,$nonc) = @_;
600: my @oldseed=&random_get_seed();
601: my @retArray;
602: &random_set_seed_from_phrase($seed);
603: @retArray=&math_random_noncentral_chi_square($item_cnt,$df,$nonc);
604: &random_set_seed(@oldseed);
605: return @retArray;
606: }
607:
608: sub random_f {
609: my ($item_cnt,$seed,$dfn,$dfd) = @_;
610: my @oldseed=&random_get_seed();
611: my @retArray;
612: &random_set_seed_from_phrase($seed);
613: @retArray=&math_random_f($item_cnt,$dfn,$dfd);
614: &random_set_seed(@oldseed);
615: return @retArray;
616: }
617:
618: sub random_noncentral_f {
619: my ($item_cnt,$seed,$dfn,$dfd,$nonc) = @_;
620: my @oldseed=&random_get_seed();
621: my @retArray;
622: &random_set_seed_from_phrase($seed);
623: @retArray=&math_random_noncentral_f($item_cnt,$dfn,$dfd,$nonc);
624: &random_set_seed(@oldseed);
625: return @retArray;
626: }
627:
628: sub random_multivariate_normal {
629: my ($item_cnt,$seed,$mean,$covar) = @_;
630: my @oldseed=&random_get_seed();
631: &random_set_seed_from_phrase($seed);
632: my @retArray=&math_random_multivariate_normal($item_cnt,@$mean,@$covar);
633: &random_set_seed(@oldseed);
634: return @retArray;
635: }
636:
637: sub random_multinomial {
638: my ($item_cnt,$seed,@p) = @_;
639: my @oldseed=&random_get_seed();
640: my @retArray;
641: &random_set_seed_from_phrase($seed);
642: my @retArray=&math_random_multinomial($item_cnt,@p);
643: &random_set_seed(@oldseed);
644: return @retArray;
645: }
646:
647: sub random_permutation {
648: my ($seed,@inArray) = @_;
649: my @oldseed=&random_get_seed();
650: my @retArray;
651: &random_set_seed_from_phrase($seed);
652: @retArray=&math_random_permutation(@inArray);
653: &random_set_seed(@oldseed);
654: return @retArray;
655: }
656:
657: sub random_uniform {
658: my ($item_cnt,$seed,$low,$high) = @_;
659: my @oldseed=&random_get_seed();
660: my @retArray;
661: &random_set_seed_from_phrase($seed);
662: @retArray=&math_random_uniform($item_cnt,$low,$high);
663: &random_set_seed(@oldseed);
664: return @retArray;
665: }
666:
667: sub random_uniform_integer {
668: my ($item_cnt,$seed,$low,$high) = @_;
669: my @oldseed=&random_get_seed();
670: my @retArray;
671: &random_set_seed_from_phrase($seed);
672: @retArray=&math_random_uniform_integer($item_cnt,$low,$high);
673: &random_set_seed(@oldseed);
674: return @retArray;
675: }
676:
677: sub random_binomial {
678: my ($item_cnt,$seed,$nt,$p) = @_;
679: my @oldseed=&random_get_seed();
680: my @retArray;
681: &random_set_seed_from_phrase($seed);
682: @retArray=&math_random_binomial($item_cnt,$nt,$p);
683: &random_set_seed(@oldseed);
684: return @retArray;
685: }
686:
687: sub random_negative_binomial {
688: my ($item_cnt,$seed,$ne,$p) = @_;
689: my @oldseed=&random_get_seed();
690: my @retArray;
691: &random_set_seed_from_phrase($seed);
692: @retArray=&math_random_negative_binomial($item_cnt,$ne,$p);
693: &random_set_seed(@oldseed);
694: return @retArray;
695: }
696:
697: sub abs { CORE::abs(shift) }
698: sub sin { CORE::sin(shift) }
699: sub cos { CORE::cos(shift) }
700: sub exp { CORE::exp(shift) }
701: sub int { CORE::int(shift) }
702: sub log { CORE::log(shift) }
703: sub atan2 { CORE::atan2($_[0],$_[1]) }
704: sub sqrt { CORE::sqrt(shift) }
705:
706: sub tan { CORE::sin($_[0]) / CORE::cos($_[0]) }
707: #sub atan { atan2($_[0], 1); }
708: #sub acos { atan2(sqrt(1 - $_[0] * $_[0]), $_[0] ); }
709: #sub asin { atan2($_[0], sqrt(1- $_[0] * $_[0]) ); }
710:
711: sub log10 { CORE::log($_[0])/CORE::log(10); }
712:
713: sub factorial {
714: my $input = CORE::int(shift);
715: return "Error - unable to take factorial of an negative number ($input)" if $input < 0;
716: return "Error - factorial result is greater than system limit ($input)" if $input > 170;
717: return 1 if $input == 0;
718: my $result = 1;
719: for (my $i=2; $i<=$input; $i++) { $result *= $i }
720: return $result;
721: }
722:
723: sub sgn {
724: return -1 if $_[0] < 0;
725: return 0 if $_[0] == 0;
726: return 1 if $_[0] > 0;
727: }
728:
729: sub min {
730: my @sorted = sort { $a <=> $b || $a cmp $b } @_;
731: return shift @sorted;
732: }
733:
734: sub max {
735: my @sorted = sort { $a <=> $b || $a cmp $b } @_;
736: return pop @sorted;
737: }
738:
739: sub roundto {
740: my ($input,$n) = @_;
741: return sprintf('%.'.$n.'f',$input);
742: }
743:
744: sub to_string {
745: my ($input,$n) = @_;
746: return sprintf($input) if $n eq "";
747: $n = '.'.$n if $n !~ /^\./;
748: return sprintf('%'.$n,$input) if $n ne "";
749: }
750:
751: sub sub_string {
752: my ($str,$start,$len) = @_;
753: return substr($str,$start-1,$len);
754: }
755:
756: sub pow {return $_[0] ** $_[1]; }
757: sub ceil {return (($_[0]-CORE::int($_[0]))== 0.0) ? $_[0] : (($_[0] > 0) ? (CORE::int($_[0])+ 1) : CORE::int($_[0])); }
758: sub floor {return (($_[0]-CORE::int($_[0]))== 0.0) ? $_[0] : (($_[0] > 0) ? CORE::int($_[0]) : (CORE::int($_[0])-1)); }
759: #sub floor {return int($_[0]); }
760:
761: sub format {
762: my ($value,$fmt)=@_;
763: my ($dollarmode,$commamode,$alwaysperiod,$options);
764: if ($fmt =~ /^([^\d]*)(.*)/) { $options=$1; $fmt=$2; }
765: #if ($options =~ /\$/) { $dollamode=1; }
766: #if ($options =~ /,/) { $commamode=1; }
767: if ($options =~ /\./) { $alwaysperiod=1; }
768: my $result;
769: if ($fmt=~/s$/i) {
770: $result=&format_significant_figures($value,$fmt);
771: } else {
772: $fmt=~s/e/E/g;
773: $result=sprintf('%.'.$fmt,$value);
774: if ($alwaysperiod && $fmt eq '0f') { $result .='.'; }
775: $result=~s/(E[+-]*)0/$1/;
776: }
777: #if ($dollarmode) {$result=&dollarformat($result);}
778: #if ($commamode) {$result=&commaformat($result);}
779: return $result;
780: }
781:
782: sub chemparse {
783: my ($reaction) = @_;
784: my @tokens = split(/(\s\+|\->|<=>|<\-|\.)/,$reaction);
785: my $formula = '';
786: foreach my $token (@tokens) {
787: if ($token eq '->' ) {
788: $formula .= '<m>\ensuremath{\rightarrow}</m> ';
789: next;
790: }
791: if ($token eq '<-' ) {
792: $formula .= '<m>\ensuremath{\leftarrow}</m> ';
793: next;
794: }
795: if ($token eq '<=>') {
796: if ($external::target eq 'web' &&
797: &EXT('request.browser.unicode')) {
798: $formula .= '⇌ ';
799: } else {
800: $formula .= &web('<=> ','<m>\ensuremath{\rightleftharpoons}</m> ',
801: '<=> ');
802: }
803: next;
804: }
805: if ($token eq '.') {
806: $formula =~ s/(\ \;| )$//;
807: $formula .= '·';
808: next;
809: }
810: $token =~ /^\s*([\d|\/]*(?:&frac\d\d)?)(.*)/;
811: $formula .= $1 if ($1 ne '1'); # stoichiometric coefficient
812:
813: my $molecule = $2;
814: # subscripts
815: $molecule =~ s|(?<=[a-zA-Z\)\]\s])(\d+)|<sub>$1</sub>|g;
816: # superscripts
817: $molecule =~ s|\^(\d*[+\-]*)|<sup>$1</sup>|g;
818: # strip whitespace
819: $molecule =~ s/\s*//g;
820: # forced space
821: $molecule =~ s/_/ /g;
822: $molecule =~ s/-/−/g;
823: $formula .= $molecule.' ';
824: }
825: # get rid of trailing space
826: $formula =~ s/(\ \;| )$//;
827: return &xmlparse($formula);
828: }
829:
830: sub prettyprint {
831: my ($value,$fmt,$target)=@_;
832: my $result;
833: if (!$target) { $target = $external::target; }
834: if ($fmt =~ /chem/i) { return(&chemparse($value)); }
835: my ($dollarmode,$commamode,$alwaysperiod,$options);
836: if ($fmt =~ /^([^\d]*)(.*)/) { $options=$1; $fmt=$2; }
837: if ($options =~ /\$/) { $dollarmode=1; }
838: if ($options =~ /,/) { $commamode=1; }
839: if ($options =~ /\./) { $alwaysperiod=1; }
840: if ($fmt=~/s$/i) {
841: $value=&format_significant_figures($value,$fmt);
842: } elsif ($fmt) {
843: $value=sprintf('%.'.$fmt,$value);
844: }
845: if ($alwaysperiod && $fmt eq '0f') {
846: if ($target eq 'tex') {
847: $value .='\\ensuremath{.}';
848: } else {
849: $value .='.';
850: }
851: }
852: if ($value =~ /([0-9\.\-\+]+)E([0-9\-\+]+)/i ) {
853: my $frac=$1;
854: if ($dollarmode) { $frac=&dollarformat($frac); }
855: if ($commamode) { $frac=&commaformat($frac); }
856: my $exponent=$2;
857: $exponent=~s/^\+0*//;
858: $exponent=~s/^-0*/-/;
859: $exponent=~s/^-0*/-/;
860: if ($exponent eq '-') { undef($exponent); }
861: if ($exponent) {
862: if ($target eq 'web') {
863: $result=$frac.'×10<sup>'.$exponent.'</sup>';
864: } elsif ($target eq 'tex') {
865: $result='\ensuremath{'.$frac.'\times 10^{'.$exponent.'}}';
866: } else {
867: $result=$value;
868: }
869: } else {
870: $result=$frac;
871: }
872: } else {
873: $result=$value;
874: if ($dollarmode) { $result=&dollarformat($result,$target); }
875: elsif ($commamode) { $result=&commaformat($result,$target); }
876: }
877: return $result;
878: }
879:
880: sub commaformat {
881: my ($number,$target) = @_;
882: if ($number =~ /\./) {
883: while ($number =~ /([^0-9]*)([0-9]+)([^\.,][^\.,][^\.,])([,0-9]*\.[0-9]*)$/) {
884: $number = $1.$2.','.$3.$4;
885: }
886: } else {
887: while ($number =~ /^([^0-9]*)([0-9]+)([^,][^,][^,])([,0-9]*)$/) {
888: $number = $1.$2.','.$3.$4;
889: }
890: }
891: return $number;
892: }
893:
894: sub dollarformat {
895: my ($number,$target) = @_;
896: if (!$target) { $target = $external::target; }
897: $number=&commaformat($number,$target);
898: if ($target eq 'tex') {
899: $number='\$'.$number; #' stupid emacs
900: } else {
901: $number='$'.$number; #' stupid emacs
902: }
903: return $number;
904: }
905:
906: # format of form ns or nS where n is an integer
907: sub format_significant_figures {
908: my ($number,$format) = @_;
909: return '0' if ($number == 0);
910: # extract number of significant figures needed
911: my ($sig) = ($format =~ /(\d+)s/i);
912: # arbitrary choice - suggestions ?? or throw error message?
913: $sig = 3 if ($sig eq '');
914: # save the minus sign
915: my $sign = ($number < 0) ? '-' : '';
916: $number = abs($number);
917: # needed to correct for a number greater than 1 (or
918: my $power = ($number < 1) ? 0 : 1;
919: # could round up. Take the integer part of log10.
920: my $x10 = int(log($number)/log(10));
921: # find number with values left of decimal pt = # of sign figs.
922: my $xsig = $number*10**($sig-$x10-$power);
923: # get just digits left of decimal pt - also rounds off correctly
924: my $xint = sprintf('%.0f',$xsig);
925: # save any trailing zero's
926: my ($zeros) = ($xint =~ /(0+)$/);
927: # return number to original magnitude
928: my $numSig = $xint*10**($x10-$sig+$power);
929: # insert trailing zero's if have decimal point
930: $numSig =~ s/^(\d+)\.(\d+)(\e?(.*)?)$/$1\.$2$zeros$3/;
931: # put a decimal pt for number ending with 0 and length = # of sig fig
932: $numSig.='.' if (length($numSig) == $sig && $numSig =~ /0$/);
933: if (length($numSig) < $sig) {
934: $numSig.='.'.substr($zeros,0,($sig-length($numSig)));
935: }
936: # return number with sign
937: return $sign.$numSig;
938:
939: }
940:
941: sub map {
942: my ($phrase,$dest,$source)=@_;
943: my @oldseed=&random_get_seed();
944: my @seed = &random_seed_from_phrase($phrase);
945: &random_set_seed(@seed);
946: my $destct = scalar(@$dest);
947: if (!$source) {
948: my @output;
949: my @idx = &math_random_permuted_index($destct);
950: my $ctr = 0;
951: while ($ctr < $destct) {
952: $output[$ctr] = $$dest[$idx[$ctr]];
953: $ctr++;
954: }
955: &random_set_seed(@oldseed);
956: return @output;
957: } else {
958: my $num = scalar(@$source);
959: my @idx = &math_random_permuted_index($num);
960: my $ctr = 0;
961: my $tot = $num;
962: $tot = $destct if $destct < $num;
963: if (ref($$dest[0])) {
964: while ($ctr < $tot) {
965: ${$$dest[$ctr]} = $$source[$idx[$ctr]];
966: $ctr++;
967: }
968: } else {
969: while ($ctr < $tot) {
970: $$dest[$ctr] = $$source[$idx[$ctr]];
971: $ctr++;
972: }
973: }
974: }
975: &random_set_seed(@oldseed);
976: return '';
977: }
978:
979: sub rmap {
980: my ($phrase,$dest,$source)=@_;
981: my @oldseed=&random_get_seed();
982: my @seed = &random_seed_from_phrase($phrase);
983: &random_set_seed(@seed);
984: my $destct = scalar(@$dest);
985: if (!$source) {
986: my @idx = &math_random_permuted_index($destct);
987: my $ctr = 0;
988: my @r_idx;
989: while ($ctr < $destct) {
990: $r_idx[$idx[$ctr]] = $ctr;
991: $ctr++;
992: }
993: my @output;
994: $ctr = 0;
995: while ($ctr < $destct) {
996: $output[$ctr] = $$dest[$r_idx[$ctr]];
997: $ctr++;
998: }
999: &random_set_seed(@oldseed);
1000: return @output;
1001: } else {
1002: my $num = scalar(@$source);
1003: my @idx = &math_random_permuted_index($num);
1004: my $ctr = 0;
1005: my $tot = $num;
1006: $tot = $destct if $destct < $num;
1007: my @r_idx;
1008: while ($ctr < $tot) {
1009: $r_idx[$idx[$ctr]] = $ctr;
1010: $ctr++;
1011: }
1012: $ctr = 0;
1013: if (ref($$dest[0])) {
1014: while ($ctr < $tot) {
1015: ${$$dest[$ctr]} = $$source[$r_idx[$ctr]];
1016: $ctr++;
1017: }
1018: } else {
1019: while ($ctr < $tot) {
1020: $$dest[$ctr] = $$source[$r_idx[$ctr]];
1021: $ctr++;
1022: }
1023: }
1024: }
1025: &random_set_seed(@oldseed);
1026: return '';
1027: }
1028:
1029: sub capa_id { return }
1030:
1031: sub problem { return }
1032:
1033: sub name{
1034: my $fullname = &EXT('environment.lastname').', '.&EXT('environment.firstname').' '.&EXT('environment.middlename');
1035: $fullname = "" if $fullname eq ", ";
1036: $fullname =~ s/\%2d/-/g;
1037: return $fullname;
1038: }
1039:
1040: sub student_number {
1041: my $id = &EXT('environment.id');
1042: $id = '' if $id eq "";
1043: return $id;
1044: }
1045:
1046: sub class {
1047: my $course = &EXT('course.description');
1048: $course = '' if $course eq "";
1049: return $course;
1050: }
1051:
1052: sub firstname {
1053: my $firstname = &EXT('environment.firstname');
1054: $firstname = '' if $firstname eq "";
1055: return $firstname;
1056: }
1057:
1058: sub lastname {
1059: my $lastname = &EXT('environment.lastname');
1060: $lastname = '' if $lastname eq "";
1061: return $lastname;
1062: }
1063:
1064: sub sec {
1065: my $sec = &EXT('request.course.sec');
1066: $sec = '' if $sec eq "";
1067: return $sec;
1068: }
1069:
1070: sub submission {
1071: my ($partid,$responseid,$subnumber)=@_;
1072: my $sub='';
1073: if ($subnumber) { $sub=$subnumber.':'; }
1074: return &EXT('user.resource.'.$sub.'resource.'.$partid.'.'.$responseid.'.submission');
1075: }
1076:
1077: sub currentpart {
1078: return $external::part;
1079: }
1080:
1081: sub eval_time {
1082: my ($timestamp)=@_;
1083: unless ($timestamp) { return ''; }
1084: return &locallocaltime($timestamp);
1085: }
1086:
1087: sub open_date {
1088: my ($partid)=@_;
1089: unless ($partid) { $partid=0; }
1090: return &eval_time(&EXT('resource.'.$partid.'.opendate'));
1091: }
1092:
1093: sub due_date {
1094: my ($partid)=@_;
1095: unless ($partid) { $partid=0; }
1096: return &eval_time(&EXT('resource.'.$partid.'.duedate'));
1097: }
1098:
1099: sub answer_date {
1100: my ($partid)=@_;
1101: unless ($partid) { $partid=0; }
1102: return &eval_time(&EXT('resource.'.$partid.'.answerdate'));
1103: }
1104:
1105: sub open_date_epoch {
1106: my ($partid)=@_;
1107: unless ($partid) { $partid=0; }
1108: return &EXT('resource.'.$partid.'.opendate');
1109: }
1110:
1111: sub due_date_epoch {
1112: my ($partid)=@_;
1113: unless ($partid) { $partid=0; }
1114: return &EXT('resource.'.$partid.'.duedate');
1115: }
1116:
1117: sub answer_date_epoch {
1118: my ($partid)=@_;
1119: unless ($partid) { $partid=0; }
1120: return &EXT('resource.'.$partid.'.answerdate');
1121: }
1122:
1123: sub array_moments {
1124: my @input=@_;
1125: my (@output,$N);
1126: $N=scalar (@input);
1127: $output[0]=$N;
1128: if ($N <= 1) {
1129: $output[1]=$input[0];
1130: $output[1]="Input array not defined" if ($N == 0);
1131: $output[2]="variance undefined for N<=1";
1132: $output[3]="skewness undefined for N<=1";
1133: $output[4]="kurtosis undefined for N<=1";
1134: return @output;
1135: }
1136: my $sum=0;
1137: foreach my $line (@input) {
1138: $sum+=$line;
1139: }
1140: $output[1] = $sum/$N;
1141: my ($x,$sdev,$var,$skew,$kurt) = 0;
1142: foreach my $line (@input) {
1143: $x=$line-$output[1];
1144: $var+=$x**2;
1145: $skew+=$x**3;
1146: $kurt+=$x**4;
1147: }
1148: $output[2]=$var/($N-1);
1149: $sdev=CORE::sqrt($output[2]);
1150: if ($sdev == 0) {
1151: $output[3]="inf-variance=0";
1152: $output[4]="inf-variance=0";
1153: return @output;
1154: }
1155: $output[3]=$skew/($sdev**3*$N);
1156: $output[4]=$kurt/($sdev**4*$N)-3;
1157: return @output;
1158: }
1159:
1160: sub choose {
1161: my $num = $_[0];
1162: return $_[$num];
1163: }
1164:
1165: #&sum1(1,$x,sub { &sum1($_[0],2*$_[0], sub { fact($_[0])**2 })});
1166: #sub sum1 {
1167: # my ($start,$end,$sub)=@_;
1168: # my $sum=0;
1169: # for (my $i=$start;$i<=$end;$i++) {
1170: # $sum+=&$sub($i);
1171: # }
1172: # return $sum
1173: #}
1174:
1175: #&sum2('a',1,$x,'&sum2(\'b\',$a,2*$a, \'&factorial($b)**2\')');
1176: #sub sum2 {
1177: # my ($varname,$start,$end,$line)=@_;
1178: # my $sum=0;
1179: # for (my $i=$start;$i<=$end;$i++) {
1180: # my $func=sub {
1181: # eval("\$".$varname."=$i");
1182: # eval($line);
1183: # };
1184: # $sum+=&$func($i);
1185: # }
1186: # return $sum
1187: #}
1188:
1189: # expiremental idea
1190: sub proper_path {
1191: my ($path)=@_;
1192: if ( $external::target eq "tex" ) {
1193: return '/home/httpd/html'.$path;
1194: } else {
1195: return $path;
1196: }
1197: }
1198:
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