File:
[LON-CAPA] /
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homework /
default_homework.lcpm
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1.147:
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Wed Jan 6 16:59:30 2010 UTC (14 years, 3 months ago) by
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CVS tags:
version_2_9_X,
version_2_9_99_0,
version_2_9_1,
version_2_9_0,
version_2_8_99_1,
version_2_10_0_RC1,
bz6209-base,
bz6209,
PRINT_INCOMPLETE_base,
PRINT_INCOMPLETE,
HEAD
Dealing with percentages if the author entered %, but the student did not.
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 1.147 2010/01/06 16:59:30 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: # Deal with percentages
330: # unit is unit entered by student, answerunit is unit by author
331: # Deprecated: divide answer by 100 if student entered percent,
332: # but author did not. Too much confusion
333: # if (($unit=~/\%/) && ($answerunit ne '%')) {
334: # $element=$element/100;
335: # $appendunit=~s/\%//;
336: # }
337: # Author entered percent, student did not
338: if (($unit!~/\%/) && ($answerunit=~/\%/)) {
339: $element=$element*100;
340: $appendunit='%'.$appendunit;
341: }
342: # Zero does not need a dimension
343: if (($element==0) && ($unit!~/\w/) && ($answerunit=~/\w/)) {
344: $appendunit=$answerunit;
345: }
346: $element .= " $appendunit";
347: &LONCAPA_INTERNAL_DEBUG("Made response element :$element:");
348: }
349: }
350:
351: foreach my $thisanswer (@{ $LONCAPA::CAPAresponse_answer->{'answers'} }) {
352: if (!defined($thisanswer)) {
353: return ('ERROR','answer was undefined');
354: }
355: }
356:
357:
358: # &LONCAPA_INTERNAL_DEBUG(&LONCAPA_INTERNAL_Dumper($responses));
359: my %memoized;
360: if ($LONCAPA::CAPAresponse_answer->{'type'} eq 'ordered') {
361: for (my $i=0; $i<scalar(@$responses);$i++) {
362: my $answer = $LONCAPA::CAPAresponse_answer->{'answers'}[$i];
363: my $response = $responses->[$i];
364: my $key = "$answer\0$response";
365: my (@awards,@msgs);
366: for (my $j=0; $j<scalar(@$response); $j++) {
367: my ($award,$msg) = &caparesponse_check($answer->[$j],
368: $response->[$j]);
369: push(@awards,$award);
370: push(@msgs, $msg);
371: }
372: my ($award,$msg) =
373: &LONCAPA_INTERNAL_FINALIZEAWARDS(\@awards,\@msgs);
374: $memoized{$key} = [$award,$msg];
375: }
376: } else {
377: #FIXME broken with unorder responses where one is a <value>
378: # and the other is a <vector> (need to delay parse til
379: # inside the loop?)
380: foreach my $response (@$responses) {
381: my $response_size = scalar(@{$response});
382: foreach my $answer (@{ $LONCAPA::CAPAresponse_answer->{'answers'} }) {
383: my $key = "$answer\0$response";
384: my $answer_size = scalar(@{$answer});
385: my ($award,$msg);
386: if ($answer_size > $response_size) {
387: $award = 'MISSING_ANSWER';
388: } elsif ($answer_size < $response_size) {
389: $award = 'EXTRA_ANSWER';
390: } else {
391: my (@awards,@msgs);
392: for (my $j=0; $j<scalar(@$response); $j++) {
393: my ($award,$msg) = &caparesponse_check($answer->[$j],
394: $response->[$j]);
395: push(@awards,$award);
396: push(@msgs, $msg);
397: }
398: ($award,$msg) =
399: &LONCAPA_INTERNAL_FINALIZEAWARDS(\@awards,\@msgs);
400: }
401: $memoized{$key} = [$award,$msg];
402: }
403: }
404: }
405:
406: my ($final_award,$final_msg);
407: &init_permutation(scalar(@$responses),
408: $LONCAPA::CAPAresponse_answer->{'type'});
409:
410: # possible FIXMEs
411: # - significant time is spent calling non-safe space routine
412: # from safe space
413: # - early outs could be possible with classifying awards is to stratas
414: # and stopping as so as hitting the top strata
415: # - some early outs also might be possible with check ing the
416: # memoized hash of results (is correct even possible? etc.)
417:
418: my (@final_awards,@final_msg);
419: while( &get_permutations_left() ) {
420: my $order = &get_next_permutation();
421: my (@awards, @msgs, $i);
422: foreach my $thisanswer (@{ $LONCAPA::CAPAresponse_answer->{'answers'} }) {
423: my $key = "$thisanswer\0".$responses->[$order->[$i]];
424: push(@awards,$memoized{$key}[0]);
425: push(@msgs,$memoized{$key}[1]);
426: $i++;
427:
428: }
429: &LONCAPA_INTERNAL_DEBUG(" all awards ".join(':',@awards));
430:
431: my ($possible_award,$possible_msg) =
432: &LONCAPA_INTERNAL_FINALIZEAWARDS(\@awards,\@msgs);
433: &LONCAPA_INTERNAL_DEBUG(" pos awards ".$possible_award);
434: push(@final_awards,$possible_award);
435: push(@final_msg,$possible_msg);
436: }
437:
438: &LONCAPA_INTERNAL_DEBUG(" all final_awards ".join(':',@final_awards));
439: my ($final_award,$final_msg) =
440: &LONCAPA_INTERNAL_FINALIZEAWARDS(\@final_awards,\@final_msg,undef,1);
441: return ($final_award,$final_msg);
442: }
443:
444: sub cas {
445: my ($system,$input,$library)=@_;
446: my $output;
447: my $dump;
448: if ($system eq 'maxima') {
449: $output=&maxima_eval($input,$library);
450: } elsif ($system eq 'R') {
451: ($output,$dump)=&r_eval($input,$library,0);
452: } else {
453: $output='Error: unrecognized CAS';
454: }
455: return $output;
456: }
457:
458: sub cas_hashref {
459: my ($system,$input,$library)=@_;
460: if ($system eq 'maxima') {
461: return 'Error: unsupported CAS';
462: } elsif ($system eq 'R') {
463: return &r_eval($input,$library,1);
464: } else {
465: return 'Error: unrecognized CAS';
466: }
467: }
468:
469: #
470: # cas_hashref_entry takes a list of indices and gets the entry in a hash generated by Rreturn.
471: # Call: cas_hashref_entry(Rvalue, index1, index2, ...) where Rvalue is a hash returned by Rreturn.
472: # Rentry will return the first scalar value it encounters (ignoring excess indices).
473: # If an invalid key is given, it returns undef.
474: #
475: sub cas_hashref_entry {
476: return &Rentry(@_);
477: }
478:
479: #
480: # cas_hashref_array takes a list of indices and gets a column array from a hash generated by Rreturn.
481: # Call: cas_hashref_array(Rvalue, index1, index2, ...) where Rvalue is a hash returned by Rreturn.
482: # If an invalid key is given, it returns undef.
483: #
484: sub cas_hashref_array {
485: return &Rarray(@_);
486: }
487:
488: sub tex {
489: if ( $external::target eq "tex" ) {
490: return $_[0];
491: } else {
492: return $_[1];
493: }
494: }
495:
496: sub var_in_tex {
497: if ( $external::target eq "tex" ) {
498: return $_[0];
499: } else {
500: return "";
501: }
502: }
503:
504: sub web {
505: if ( $external::target eq "tex" ) {
506: return $_[1];
507: } else {
508: if ( $external::target eq "web" || $external::target eq "answer") {
509: return $_[2];
510: } else {
511: return $_[0];
512: }
513: }
514: }
515:
516: sub html {
517: if ( $external::target eq "web" ) {
518: return shift;
519: }
520: }
521:
522: sub hinton {
523: return 0;
524: }
525:
526: sub random {
527: my ($start,$end,$step)=@_;
528: if ( ! $hidden::RANDOMINIT ) {
529: if ($external::randomseed == 0) { $external::randomseed=1; }
530: if ($external::randomseed =~/,/) {
531: my ($num1,$num2)=split(/,/,$external::randomseed);
532: &random_set_seed(1,abs($num1));
533: } elsif ($external::randomseed =~/:/) {
534: my ($num1,$num2)=split(/:/,$external::randomseed);
535: &random_set_seed(abs($num1),abs($num2));
536: } else {
537: &random_set_seed(1,int(abs($external::randomseed)));
538: }
539: &math_random_uniform();
540: $hidden::RANDOMINIT=1;
541: }
542: if (!defined($step)) { $step=1; }
543: my $num=1+int(($end-$start)/$step);
544: my $result=$start + int(&math_random_uniform() * $num)*$step;
545: return $result;
546: }
547:
548: sub random_normal {
549: my ($item_cnt,$seed,$av,$std_dev) = @_;
550: my @oldseed=&random_get_seed();
551: my @retArray;
552: &random_set_seed_from_phrase($seed);
553: @retArray=&math_random_normal($item_cnt,$av,$std_dev);
554: &random_set_seed(@oldseed);
555: return @retArray;
556: }
557:
558: sub random_beta {
559: my ($item_cnt,$seed,$aa,$bb) = @_;
560: my @oldseed=&random_get_seed();
561: my @retArray;
562: &random_set_seed_from_phrase($seed);
563: @retArray=&math_random_beta($item_cnt,$aa,$bb);
564: &random_set_seed(@oldseed);
565: return @retArray;
566: }
567:
568: sub random_gamma {
569: my ($item_cnt,$seed,$a,$r) = @_;
570: my @oldseed=&random_get_seed();
571: my @retArray;
572: &random_set_seed_from_phrase($seed);
573: @retArray=&math_random_gamma($item_cnt,$a,$r);
574: &random_set_seed(@oldseed);
575: return @retArray;
576: }
577:
578: sub random_exponential {
579: my ($item_cnt,$seed,$av) = @_;
580: my @oldseed=&random_get_seed();
581: my @retArray;
582: &random_set_seed_from_phrase($seed);
583: @retArray=&math_random_exponential($item_cnt,$av);
584: &random_set_seed(@oldseed);
585: return @retArray;
586: }
587:
588: sub random_poisson {
589: my ($item_cnt,$seed,$mu) = @_;
590: my @oldseed=&random_get_seed();
591: my @retArray;
592: &random_set_seed_from_phrase($seed);
593: @retArray=&math_random_poisson($item_cnt,$mu);
594: &random_set_seed(@oldseed);
595: return @retArray;
596: }
597:
598: sub random_chi {
599: my ($item_cnt,$seed,$df) = @_;
600: my @oldseed=&random_get_seed();
601: my @retArray;
602: &random_set_seed_from_phrase($seed);
603: @retArray=&math_random_chi_square($item_cnt,$df);
604: &random_set_seed(@oldseed);
605: return @retArray;
606: }
607:
608: sub random_noncentral_chi {
609: my ($item_cnt,$seed,$df,$nonc) = @_;
610: my @oldseed=&random_get_seed();
611: my @retArray;
612: &random_set_seed_from_phrase($seed);
613: @retArray=&math_random_noncentral_chi_square($item_cnt,$df,$nonc);
614: &random_set_seed(@oldseed);
615: return @retArray;
616: }
617:
618: sub random_f {
619: my ($item_cnt,$seed,$dfn,$dfd) = @_;
620: my @oldseed=&random_get_seed();
621: my @retArray;
622: &random_set_seed_from_phrase($seed);
623: @retArray=&math_random_f($item_cnt,$dfn,$dfd);
624: &random_set_seed(@oldseed);
625: return @retArray;
626: }
627:
628: sub random_noncentral_f {
629: my ($item_cnt,$seed,$dfn,$dfd,$nonc) = @_;
630: my @oldseed=&random_get_seed();
631: my @retArray;
632: &random_set_seed_from_phrase($seed);
633: @retArray=&math_random_noncentral_f($item_cnt,$dfn,$dfd,$nonc);
634: &random_set_seed(@oldseed);
635: return @retArray;
636: }
637:
638: sub random_multivariate_normal {
639: my ($item_cnt,$seed,$mean,$covar) = @_;
640: my @oldseed=&random_get_seed();
641: &random_set_seed_from_phrase($seed);
642: my @retArray=&math_random_multivariate_normal($item_cnt,@$mean,@$covar);
643: &random_set_seed(@oldseed);
644: return @retArray;
645: }
646:
647: sub random_multinomial {
648: my ($item_cnt,$seed,@p) = @_;
649: my @oldseed=&random_get_seed();
650: my @retArray;
651: &random_set_seed_from_phrase($seed);
652: my @retArray=&math_random_multinomial($item_cnt,@p);
653: &random_set_seed(@oldseed);
654: return @retArray;
655: }
656:
657: sub random_permutation {
658: my ($seed,@inArray) = @_;
659: my @oldseed=&random_get_seed();
660: my @retArray;
661: &random_set_seed_from_phrase($seed);
662: @retArray=&math_random_permutation(@inArray);
663: &random_set_seed(@oldseed);
664: return @retArray;
665: }
666:
667: sub random_uniform {
668: my ($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($item_cnt,$low,$high);
673: &random_set_seed(@oldseed);
674: return @retArray;
675: }
676:
677: sub random_uniform_integer {
678: my ($item_cnt,$seed,$low,$high) = @_;
679: my @oldseed=&random_get_seed();
680: my @retArray;
681: &random_set_seed_from_phrase($seed);
682: @retArray=&math_random_uniform_integer($item_cnt,$low,$high);
683: &random_set_seed(@oldseed);
684: return @retArray;
685: }
686:
687: sub random_binomial {
688: my ($item_cnt,$seed,$nt,$p) = @_;
689: my @oldseed=&random_get_seed();
690: my @retArray;
691: &random_set_seed_from_phrase($seed);
692: @retArray=&math_random_binomial($item_cnt,$nt,$p);
693: &random_set_seed(@oldseed);
694: return @retArray;
695: }
696:
697: sub random_negative_binomial {
698: my ($item_cnt,$seed,$ne,$p) = @_;
699: my @oldseed=&random_get_seed();
700: my @retArray;
701: &random_set_seed_from_phrase($seed);
702: @retArray=&math_random_negative_binomial($item_cnt,$ne,$p);
703: &random_set_seed(@oldseed);
704: return @retArray;
705: }
706:
707: sub abs { CORE::abs(shift) }
708: sub sin { CORE::sin(shift) }
709: sub cos { CORE::cos(shift) }
710: sub exp { CORE::exp(shift) }
711: sub int { CORE::int(shift) }
712: sub log { CORE::log(shift) }
713: sub atan2 { CORE::atan2($_[0],$_[1]) }
714: sub sqrt { CORE::sqrt(shift) }
715:
716: sub tan { CORE::sin($_[0]) / CORE::cos($_[0]) }
717: #sub atan { atan2($_[0], 1); }
718: #sub acos { atan2(sqrt(1 - $_[0] * $_[0]), $_[0] ); }
719: #sub asin { atan2($_[0], sqrt(1- $_[0] * $_[0]) ); }
720:
721: sub log10 { CORE::log($_[0])/CORE::log(10); }
722:
723: sub factorial {
724: my $input = CORE::int(shift);
725: return "Error - unable to take factorial of an negative number ($input)" if $input < 0;
726: return "Error - factorial result is greater than system limit ($input)" if $input > 170;
727: return 1 if $input == 0;
728: my $result = 1;
729: for (my $i=2; $i<=$input; $i++) { $result *= $i }
730: return $result;
731: }
732:
733: sub sgn {
734: return -1 if $_[0] < 0;
735: return 0 if $_[0] == 0;
736: return 1 if $_[0] > 0;
737: }
738:
739: sub min {
740: my @sorted = sort { $a <=> $b || $a cmp $b } @_;
741: return shift @sorted;
742: }
743:
744: sub max {
745: my @sorted = sort { $a <=> $b || $a cmp $b } @_;
746: return pop @sorted;
747: }
748:
749: sub roundto {
750: my ($input,$n) = @_;
751: return sprintf('%.'.$n.'f',$input);
752: }
753:
754: sub to_string {
755: my ($input,$n) = @_;
756: return sprintf($input) if $n eq "";
757: $n = '.'.$n if $n !~ /^\./;
758: return sprintf('%'.$n,$input) if $n ne "";
759: }
760:
761: sub sub_string {
762: my ($str,$start,$len) = @_;
763: return substr($str,$start-1,$len);
764: }
765:
766: sub pow {return $_[0] ** $_[1]; }
767: sub ceil {return (($_[0]-CORE::int($_[0]))== 0.0) ? $_[0] : (($_[0] > 0) ? (CORE::int($_[0])+ 1) : CORE::int($_[0])); }
768: sub floor {return (($_[0]-CORE::int($_[0]))== 0.0) ? $_[0] : (($_[0] > 0) ? CORE::int($_[0]) : (CORE::int($_[0])-1)); }
769: #sub floor {return int($_[0]); }
770:
771: sub format {
772: my ($value,$fmt)=@_;
773: my ($dollarmode,$commamode,$alwaysperiod,$options);
774: if ($fmt =~ /^([^\d]*)(.*)/) { $options=$1; $fmt=$2; }
775: #if ($options =~ /\$/) { $dollamode=1; }
776: #if ($options =~ /,/) { $commamode=1; }
777: if ($options =~ /\./) { $alwaysperiod=1; }
778: my $result;
779: if ($fmt=~/s$/i) {
780: $result=&format_significant_figures($value,$fmt);
781: } else {
782: $fmt=~s/e/E/g;
783: $result=sprintf('%.'.$fmt,$value);
784: if ($alwaysperiod && $fmt eq '0f') { $result .='.'; }
785: $result=~s/(E[+-]*)0/$1/;
786: }
787: #if ($dollarmode) {$result=&dollarformat($result);}
788: #if ($commamode) {$result=&commaformat($result);}
789: return $result;
790: }
791:
792: sub chemparse {
793: my ($reaction) = @_;
794: my @tokens = split(/(\s\+|\->|<=>|<\-|\.)/,$reaction);
795: my $formula = '';
796: foreach my $token (@tokens) {
797: if ($token eq '->' ) {
798: $formula .= '<m>\ensuremath{\rightarrow}</m> ';
799: next;
800: }
801: if ($token eq '<-' ) {
802: $formula .= '<m>\ensuremath{\leftarrow}</m> ';
803: next;
804: }
805: if ($token eq '<=>') {
806: if ($external::target eq 'web' &&
807: &EXT('request.browser.unicode')) {
808: $formula .= '⇌ ';
809: } else {
810: $formula .= &web('<=> ','<m>\ensuremath{\rightleftharpoons}</m> ',
811: '<=> ');
812: }
813: next;
814: }
815: if ($token eq '.') {
816: $formula =~ s/(\ \;| )$//;
817: $formula .= '·';
818: next;
819: }
820: $token =~ /^\s*([\d|\/]*(?:&frac\d\d)?)(.*)/;
821: $formula .= $1 if ($1 ne '1'); # stoichiometric coefficient
822:
823: my $molecule = $2;
824: # subscripts
825: $molecule =~ s|(?<=[a-zA-Z\)\]\s])(\d+)|<sub>$1</sub>|g;
826: # superscripts
827: $molecule =~ s|\^(\d*[+\-]*)|<sup>$1</sup>|g;
828: # strip whitespace
829: $molecule =~ s/\s*//g;
830: # forced space
831: $molecule =~ s/_/ /g;
832: $molecule =~ s/-/−/g;
833: $formula .= $molecule.' ';
834: }
835: # get rid of trailing space
836: $formula =~ s/(\ \;| )$//;
837: return &xmlparse($formula);
838: }
839:
840: sub prettyprint {
841: my ($value,$fmt,$target)=@_;
842: my $result;
843: if (!$target) { $target = $external::target; }
844: if ($fmt =~ /chem/i) { return(&chemparse($value)); }
845: my ($dollarmode,$commamode,$alwaysperiod,$options);
846: if ($fmt =~ /^([^\d]*)(.*)/) { $options=$1; $fmt=$2; }
847: if ($options =~ /\$/) { $dollarmode=1; }
848: if ($options =~ /,/) { $commamode=1; }
849: if ($options =~ /\./) { $alwaysperiod=1; }
850: if ($fmt=~/s$/i) {
851: $value=&format_significant_figures($value,$fmt);
852: } elsif ($fmt) {
853: $value=sprintf('%.'.$fmt,$value);
854: }
855: if ($alwaysperiod && $fmt eq '0f') {
856: if ($target eq 'tex') {
857: $value .='\\ensuremath{.}';
858: } else {
859: $value .='.';
860: }
861: }
862: if ($value =~ /([0-9\.\-\+]+)E([0-9\-\+]+)/i ) {
863: my $frac=$1;
864: if ($dollarmode) { $frac=&dollarformat($frac); }
865: if ($commamode) { $frac=&commaformat($frac); }
866: my $exponent=$2;
867: $exponent=~s/^\+0*//;
868: $exponent=~s/^-0*/-/;
869: $exponent=~s/^-0*/-/;
870: if ($exponent eq '-') { undef($exponent); }
871: if ($exponent) {
872: if ($target eq 'web') {
873: $result=$frac.'×10<sup>'.$exponent.'</sup>';
874: } elsif ($target eq 'tex') {
875: $result='\ensuremath{'.$frac.'\times 10^{'.$exponent.'}}';
876: } else {
877: $result=$value;
878: }
879: } else {
880: $result=$frac;
881: }
882: } else {
883: $result=$value;
884: if ($dollarmode) { $result=&dollarformat($result,$target); }
885: elsif ($commamode) { $result=&commaformat($result,$target); }
886: }
887: return $result;
888: }
889:
890: sub commaformat {
891: my ($number,$target) = @_;
892: if ($number =~ /\./) {
893: while ($number =~ /([^0-9]*)([0-9]+)([^\.,][^\.,][^\.,])([,0-9]*\.[0-9]*)$/) {
894: $number = $1.$2.','.$3.$4;
895: }
896: } else {
897: while ($number =~ /^([^0-9]*)([0-9]+)([^,][^,][^,])([,0-9]*)$/) {
898: $number = $1.$2.','.$3.$4;
899: }
900: }
901: return $number;
902: }
903:
904: sub dollarformat {
905: my ($number,$target) = @_;
906: if (!$target) { $target = $external::target; }
907: $number=&commaformat($number,$target);
908: if ($target eq 'tex') {
909: $number='\$'.$number; #' stupid emacs
910: } else {
911: $number='$'.$number; #' stupid emacs
912: }
913: return $number;
914: }
915:
916: # format of form ns or nS where n is an integer
917: sub format_significant_figures {
918: my ($number,$format) = @_;
919: return '0' if ($number == 0);
920: # extract number of significant figures needed
921: my ($sig) = ($format =~ /(\d+)s/i);
922: # arbitrary choice - suggestions ?? or throw error message?
923: $sig = 3 if ($sig eq '');
924: # save the minus sign
925: my $sign = ($number < 0) ? '-' : '';
926: $number = abs($number);
927: # needed to correct for a number greater than 1 (or
928: my $power = ($number < 1) ? 0 : 1;
929: # could round up. Take the integer part of log10.
930: my $x10 = int(log($number)/log(10));
931: # find number with values left of decimal pt = # of sign figs.
932: my $xsig = $number*10**($sig-$x10-$power);
933: # get just digits left of decimal pt - also rounds off correctly
934: my $xint = sprintf('%.0f',$xsig);
935: # save any trailing zero's
936: my ($zeros) = ($xint =~ /(0+)$/);
937: # return number to original magnitude
938: my $numSig = $xint*10**($x10-$sig+$power);
939: # insert trailing zero's if have decimal point
940: $numSig =~ s/^(\d+)\.(\d+)(\e?(.*)?)$/$1\.$2$zeros$3/;
941: # put a decimal pt for number ending with 0 and length = # of sig fig
942: $numSig.='.' if (length($numSig) == $sig && $numSig =~ /0$/);
943: if (length($numSig) < $sig) {
944: $numSig.='.'.substr($zeros,0,($sig-length($numSig)));
945: }
946: # return number with sign
947: return $sign.$numSig;
948:
949: }
950:
951: sub map {
952: my ($phrase,$dest,$source)=@_;
953: my @oldseed=&random_get_seed();
954: my @seed = &random_seed_from_phrase($phrase);
955: &random_set_seed(@seed);
956: my $destct = scalar(@$dest);
957: if (!$source) {
958: my @output;
959: my @idx = &math_random_permuted_index($destct);
960: my $ctr = 0;
961: while ($ctr < $destct) {
962: $output[$ctr] = $$dest[$idx[$ctr]];
963: $ctr++;
964: }
965: &random_set_seed(@oldseed);
966: return @output;
967: } else {
968: my $num = scalar(@$source);
969: my @idx = &math_random_permuted_index($num);
970: my $ctr = 0;
971: my $tot = $num;
972: $tot = $destct if $destct < $num;
973: if (ref($$dest[0])) {
974: while ($ctr < $tot) {
975: ${$$dest[$ctr]} = $$source[$idx[$ctr]];
976: $ctr++;
977: }
978: } else {
979: while ($ctr < $tot) {
980: $$dest[$ctr] = $$source[$idx[$ctr]];
981: $ctr++;
982: }
983: }
984: }
985: &random_set_seed(@oldseed);
986: return '';
987: }
988:
989: sub rmap {
990: my ($phrase,$dest,$source)=@_;
991: my @oldseed=&random_get_seed();
992: my @seed = &random_seed_from_phrase($phrase);
993: &random_set_seed(@seed);
994: my $destct = scalar(@$dest);
995: if (!$source) {
996: my @idx = &math_random_permuted_index($destct);
997: my $ctr = 0;
998: my @r_idx;
999: while ($ctr < $destct) {
1000: $r_idx[$idx[$ctr]] = $ctr;
1001: $ctr++;
1002: }
1003: my @output;
1004: $ctr = 0;
1005: while ($ctr < $destct) {
1006: $output[$ctr] = $$dest[$r_idx[$ctr]];
1007: $ctr++;
1008: }
1009: &random_set_seed(@oldseed);
1010: return @output;
1011: } else {
1012: my $num = scalar(@$source);
1013: my @idx = &math_random_permuted_index($num);
1014: my $ctr = 0;
1015: my $tot = $num;
1016: $tot = $destct if $destct < $num;
1017: my @r_idx;
1018: while ($ctr < $tot) {
1019: $r_idx[$idx[$ctr]] = $ctr;
1020: $ctr++;
1021: }
1022: $ctr = 0;
1023: if (ref($$dest[0])) {
1024: while ($ctr < $tot) {
1025: ${$$dest[$ctr]} = $$source[$r_idx[$ctr]];
1026: $ctr++;
1027: }
1028: } else {
1029: while ($ctr < $tot) {
1030: $$dest[$ctr] = $$source[$r_idx[$ctr]];
1031: $ctr++;
1032: }
1033: }
1034: }
1035: &random_set_seed(@oldseed);
1036: return '';
1037: }
1038:
1039: sub capa_id { return }
1040:
1041: sub problem { return }
1042:
1043: sub name{
1044: my $fullname = &EXT('environment.lastname').', '.&EXT('environment.firstname').' '.&EXT('environment.middlename');
1045: $fullname = "" if $fullname eq ", ";
1046: $fullname =~ s/\%2d/-/g;
1047: return $fullname;
1048: }
1049:
1050: sub student_number {
1051: my $id = &EXT('environment.id');
1052: $id = '' if $id eq "";
1053: return $id;
1054: }
1055:
1056: sub class {
1057: my $course = &EXT('course.description');
1058: $course = '' if $course eq "";
1059: return $course;
1060: }
1061:
1062: sub firstname {
1063: my $firstname = &EXT('environment.firstname');
1064: $firstname = '' if $firstname eq "";
1065: return $firstname;
1066: }
1067:
1068: sub lastname {
1069: my $lastname = &EXT('environment.lastname');
1070: $lastname = '' if $lastname eq "";
1071: return $lastname;
1072: }
1073:
1074: sub sec {
1075: my $sec = &EXT('request.course.sec');
1076: $sec = '' if $sec eq "";
1077: return $sec;
1078: }
1079:
1080: sub submission {
1081: my ($partid,$responseid,$subnumber)=@_;
1082: my $sub='';
1083: if ($subnumber) { $sub=$subnumber.':'; }
1084: return &EXT('user.resource.'.$sub.'resource.'.$partid.'.'.$responseid.'.submission');
1085: }
1086:
1087: sub currentpart {
1088: return $external::part;
1089: }
1090:
1091: sub eval_time {
1092: my ($timestamp)=@_;
1093: unless ($timestamp) { return ''; }
1094: return &locallocaltime($timestamp);
1095: }
1096:
1097: sub open_date {
1098: my ($partid)=@_;
1099: unless ($partid) { $partid=0; }
1100: return &eval_time(&EXT('resource.'.$partid.'.opendate'));
1101: }
1102:
1103: sub due_date {
1104: my ($partid)=@_;
1105: unless ($partid) { $partid=0; }
1106: return &eval_time(&EXT('resource.'.$partid.'.duedate'));
1107: }
1108:
1109: sub answer_date {
1110: my ($partid)=@_;
1111: unless ($partid) { $partid=0; }
1112: return &eval_time(&EXT('resource.'.$partid.'.answerdate'));
1113: }
1114:
1115: sub open_date_epoch {
1116: my ($partid)=@_;
1117: unless ($partid) { $partid=0; }
1118: return &EXT('resource.'.$partid.'.opendate');
1119: }
1120:
1121: sub due_date_epoch {
1122: my ($partid)=@_;
1123: unless ($partid) { $partid=0; }
1124: return &EXT('resource.'.$partid.'.duedate');
1125: }
1126:
1127: sub answer_date_epoch {
1128: my ($partid)=@_;
1129: unless ($partid) { $partid=0; }
1130: return &EXT('resource.'.$partid.'.answerdate');
1131: }
1132:
1133: sub array_moments {
1134: my @input=@_;
1135: my (@output,$N);
1136: $N=scalar (@input);
1137: $output[0]=$N;
1138: if ($N <= 1) {
1139: $output[1]=$input[0];
1140: $output[1]="Input array not defined" if ($N == 0);
1141: $output[2]="variance undefined for N<=1";
1142: $output[3]="skewness undefined for N<=1";
1143: $output[4]="kurtosis undefined for N<=1";
1144: return @output;
1145: }
1146: my $sum=0;
1147: foreach my $line (@input) {
1148: $sum+=$line;
1149: }
1150: $output[1] = $sum/$N;
1151: my ($x,$sdev,$var,$skew,$kurt) = 0;
1152: foreach my $line (@input) {
1153: $x=$line-$output[1];
1154: $var+=$x**2;
1155: $skew+=$x**3;
1156: $kurt+=$x**4;
1157: }
1158: $output[2]=$var/($N-1);
1159: $sdev=CORE::sqrt($output[2]);
1160: if ($sdev == 0) {
1161: $output[3]="inf-variance=0";
1162: $output[4]="inf-variance=0";
1163: return @output;
1164: }
1165: $output[3]=$skew/($sdev**3*$N);
1166: $output[4]=$kurt/($sdev**4*$N)-3;
1167: return @output;
1168: }
1169:
1170: sub choose {
1171: my $num = $_[0];
1172: return $_[$num];
1173: }
1174:
1175: #&sum1(1,$x,sub { &sum1($_[0],2*$_[0], sub { fact($_[0])**2 })});
1176: #sub sum1 {
1177: # my ($start,$end,$sub)=@_;
1178: # my $sum=0;
1179: # for (my $i=$start;$i<=$end;$i++) {
1180: # $sum+=&$sub($i);
1181: # }
1182: # return $sum
1183: #}
1184:
1185: #&sum2('a',1,$x,'&sum2(\'b\',$a,2*$a, \'&factorial($b)**2\')');
1186: #sub sum2 {
1187: # my ($varname,$start,$end,$line)=@_;
1188: # my $sum=0;
1189: # for (my $i=$start;$i<=$end;$i++) {
1190: # my $func=sub {
1191: # eval("\$".$varname."=$i");
1192: # eval($line);
1193: # };
1194: # $sum+=&$func($i);
1195: # }
1196: # return $sum
1197: #}
1198:
1199: # expiremental idea
1200: sub proper_path {
1201: my ($path)=@_;
1202: if ( $external::target eq "tex" ) {
1203: return '/home/httpd/html'.$path;
1204: } else {
1205: return $path;
1206: }
1207: }
1208:
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