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 1.118 2006/10/02 18:23:38 albertel 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') {
221: $result = &maxima_check(&maxima_cas_formula_fix($response),&maxima_cas_formula_fix($answer),\$reterror);
222: } else {
223: if ($type eq '8') { # fml type
224: $response = &capa_formula_fix($response);
225: $answer = &capa_formula_fix($answer);
226: }
227: $result = &caparesponse_capa_check_answer($response,$answer,$type,
228: $tol_type,$tol,
229: $sig_lbound,$sig_ubound,
230: $ans_fmt,$unit,$calc,$id_list,
231: $points,$external::randomseed,
232: \$reterror);
233: }
234: if ($result == '1') { $result='EXACT_ANS'; }
235: elsif ($result == '2') { $result='APPROX_ANS'; }
236: elsif ($result == '3') { $result='SIG_FAIL'; }
237: elsif ($result == '4') { $result='UNIT_FAIL'; }
238: elsif ($result == '5') { $result='NO_UNIT'; }
239: elsif ($result == '6') { $result='UNIT_OK'; }
240: elsif ($result == '7') { $result='INCORRECT'; }
241: elsif ($result == '8') { $result='UNIT_NOTNEEDED'; }
242: elsif ($result == '9') { $result='ANS_CNT_NOT_MATCH'; }
243: elsif ($result =='10') { $result='SUB_RECORDED'; }
244: elsif ($result =='11') { $result='BAD_FORMULA'; }
245: elsif ($result =='12' && !$response) { $result='MISSING_ANSWER'; }
246: elsif ($result =='12') { $result='WANTED_NUMERIC'; }
247: elsif ($result =='13') { $result='UNIT_INVALID_INSTRUCTOR'; }
248: elsif ($result =='141') { $result='UNIT_INVALID_STUDENT'; }
249: elsif ($result =='142') { $result='UNIT_INVALID_STUDENT'; }
250: elsif ($result =='143') { $result='UNIT_INVALID_STUDENT'; }
251: elsif ($result =='15') { $result='UNIT_IRRECONCIBLE'; }
252: else {$result = "ERROR: Unknown Result:$result:$@:";}
253:
254: #&LONCAPA_INTERNAL_DEBUG("RetError $reterror: Answer $answer: Response $response: type-$type|$tol|$tol_type|$sig:$sig_lbound:$sig_ubound|$unit|");
255: #&LONCAPA_INTERNAL_DEBUG(" $answer $response $result ");
256: return ($result,$reterror)
257: }
258:
259: sub maxima_cas_formula_fix {
260: my ($expression)=@_;
261: return &implicit_multiplication($expression);
262: }
263:
264: sub capa_formula_fix {
265: my ($expression)=@_;
266: return &implicit_multiplication($expression);
267: }
268:
269: sub implicit_multiplication {
270: my ($expression)=@_;
271: # Escape scientific notation, so 3e8 does not become 3*e*8
272: # 3e8 -> 3&8; 3e-8 -> 3&-8; 3E+8 -> e&+8
273: $expression=~s/(\d+)e([\+\-]*\d+)/$1\&\($2\)/gsi;
274: # 3x10^8 -> 3&8; 3*10^-8 -> 3&-8
275: $expression=~s/(\d+)(?:x|\*)10(?:\^|\*\*)([\+\-]*\d+)/$1\&\($2\)/gsi;
276: # Fill in multiplication signs
277: # a b -> a*b;3 b -> 3*b;3 4 -> 3*4
278: $expression=~s/(\w)\s+(\w)/$1\*$2/gs;
279: # )( -> )*(; ) ( -> )*(
280: $expression=~s/\)\s*\(/\)\*\(/gs;
281: # 3a -> 3*a; 3( -> 3*(; 3 ( -> 3*(; 3A -> 3*A
282: $expression=~s/(\d)\s*([a-zA-Z\(])/$1\*$2/gs;
283: # a ( -> a*(
284: $expression=~s/(\w)\s+\(/$1\*\(/gs;
285: # a3 -> a*3;
286: $expression=~s/([a-zA-Z])(\d)/$1\*$2/gs;
287: # )a -> )*a; )3 -> )*3; ) 3 -> )*3
288: $expression=~s/\)\s*(\w)/\)\*$1/gs;
289: # 3&8 -> 3e8; 3&-4 -> 3e-4
290: $expression=~s/(\d+)\&\(([\+\-]*\d+)\)/$1e$2/gs;
291: return $expression;
292: }
293:
294: sub caparesponse_check_list {
295: my $response=$LONCAPA::CAPAresponse_args{'response'};
296: my $result="Got response :".join(':',@LONCAPA::CAPAresponse_answer).":\n";
297: &LONCAPA_INTERNAL_DEBUG("args ".join(':',%LONCAPA::CAPAresponse_args));
298: my @responselist;
299: my $type = $LONCAPA::CAPAresponse_args{'type'};
300: &LONCAPA_INTERNAL_DEBUG("Got type :$type:\n");
301: my $num_answers = scalar(@{$LONCAPA::CAPAresponse_answer->{'answers'}});
302: if ($type ne ''
303: && $num_answers > 1) {
304: (@responselist)=split(/,/,$response);
305: if (@responselist < $num_answers) {
306: return 'MISSING_ANSWER';
307: }
308: if (@responselist > $num_answers) {
309: return 'EXTRA_ANSWER';
310: }
311: } else {
312: (@responselist)=($response);
313: }
314: &LONCAPA_INTERNAL_DEBUG("Initial final response :$responselist['-1']:");
315: my $unit;
316: if ($type eq '' || $type eq 'float') {
317: #for numerical problems split off the unit
318: if ( $responselist['-1']=~ /(.*[^\s])\s+([^\s]+)/ ) {
319: $responselist['-1']=$1;
320: $unit=$2;
321: }
322: }
323: &LONCAPA_INTERNAL_DEBUG("Final final response :$responselist['-1']:$unit:");
324: $unit=~s/\s//;
325:
326: foreach my $thisanswer (@{ $LONCAPA::CAPAresponse_answer->{'answers'} }) {
327: if (!defined($thisanswer)) {
328: return ('ERROR','answer was undefined');
329: }
330: }
331:
332: if ($unit ne '') {
333: foreach my $response (@responselist) {
334: $response .= " $unit";
335: }
336: }
337:
338: my %memoized;
339: if ($LONCAPA::CAPAresponse_answer->{'type'} eq 'ordered') {
340: for (my $i=0; $i<scalar(@responselist);$i++) {
341: my $answer = $LONCAPA::CAPAresponse_answer->{'answers'}[$i];
342: my $response = $responselist[$i];
343: my $key = "$answer\0$response";
344: $memoized{$key} = [&caparesponse_check($answer, $response)];
345: }
346: } else {
347: foreach my $response (@responselist) {
348: foreach my $answer (@{ $LONCAPA::CAPAresponse_answer->{'answers'} }) {
349: my $key = "$answer\0$response";
350: $memoized{$key} = [&caparesponse_check($answer, $response)];
351: }
352: }
353: }
354:
355: my ($final_award,$final_msg);
356: &init_permutation(scalar(@responselist),
357: $LONCAPA::CAPAresponse_answer->{'type'});
358:
359: # possible FIXMEs
360: # - significant time is spent calling non-safe space routine
361: # from safe space
362: # - early outs could be possible with classifying awards is to stratas
363: # and stopping as so as hitting the top strata
364: # - some early outs also might be possible with check ing the
365: # memoized hash of results (is correct even possible? etc.)
366:
367: my (@final_awards,@final_msg);
368: while( &get_permutations_left() ) {
369: my $order = &get_next_permutation();
370: my (@awards, @msgs, $i);
371: foreach my $thisanswer (@{ $LONCAPA::CAPAresponse_answer->{'answers'} }) {
372: my $key = "$thisanswer\0".$responselist[$order->[$i]];
373: push(@awards,$memoized{$key}[0]);
374: push(@msgs,$memoized{$key}[1]);
375: $i++;
376: }
377: my ($possible_award,$possible_msg) =
378: &LONCAPA_INTERNAL_FINALIZEAWARDS(\@awards,\@msgs);
379: push(@final_awards,$possible_award);
380: push(@final_msg,$possible_msg);
381: }
382:
383: my ($final_award,$final_msg) =
384: &LONCAPA_INTERNAL_FINALIZEAWARDS(\@final_awards,\@final_msg,undef,1);
385: return ($final_award,$final_msg);
386: }
387:
388: sub tex {
389: if ( $external::target eq "tex" ) {
390: return $_[0];
391: } else {
392: return $_[1];
393: }
394: }
395:
396: sub var_in_tex {
397: if ( $external::target eq "tex" ) {
398: return $_[0];
399: } else {
400: return "";
401: }
402: }
403:
404: sub web {
405: if ( $external::target eq "tex" ) {
406: return $_[1];
407: } else {
408: if ( $external::target eq "web" || $external::target eq "answer") {
409: return $_[2];
410: } else {
411: return $_[0];
412: }
413: }
414: }
415:
416: sub html {
417: if ( $external::target eq "web" ) {
418: return shift;
419: }
420: }
421:
422: sub hinton {
423: return 0;
424: }
425:
426: sub random {
427: my ($start,$end,$step)=@_;
428: if ( ! $hidden::RANDOMINIT ) {
429: if ($external::randomseed == 0) { $external::randomseed=1; }
430: if ($external::randomseed =~/,/) {
431: my ($num1,$num2)=split(/,/,$external::randomseed);
432: &random_set_seed(1,abs($num1));
433: } elsif ($external::randomseed =~/:/) {
434: my ($num1,$num2)=split(/:/,$external::randomseed);
435: &random_set_seed(abs($num1),abs($num2));
436: } else {
437: &random_set_seed(1,int(abs($external::randomseed)));
438: }
439: &math_random_uniform();
440: $hidden::RANDOMINIT=1;
441: }
442: if (!defined($step)) { $step=1; }
443: my $num=1+int(($end-$start)/$step);
444: my $result=$start + int(&math_random_uniform() * $num)*$step;
445: return $result;
446: }
447:
448: sub random_normal {
449: my ($item_cnt,$seed,$av,$std_dev) = @_;
450: my @oldseed=&random_get_seed();
451: my @retArray;
452: &random_set_seed_from_phrase($seed);
453: @retArray=&math_random_normal($item_cnt,$av,$std_dev);
454: &random_set_seed(@oldseed);
455: return @retArray;
456: }
457:
458: sub random_beta {
459: my ($item_cnt,$seed,$aa,$bb) = @_;
460: my @oldseed=&random_get_seed();
461: my @retArray;
462: &random_set_seed_from_phrase($seed);
463: @retArray=&math_random_beta($item_cnt,$aa,$bb);
464: &random_set_seed(@oldseed);
465: return @retArray;
466: }
467:
468: sub random_gamma {
469: my ($item_cnt,$seed,$a,$r) = @_;
470: my @oldseed=&random_get_seed();
471: my @retArray;
472: &random_set_seed_from_phrase($seed);
473: @retArray=&math_random_gamma($item_cnt,$a,$r);
474: &random_set_seed(@oldseed);
475: return @retArray;
476: }
477:
478: sub random_exponential {
479: my ($item_cnt,$seed,$av) = @_;
480: my @oldseed=&random_get_seed();
481: my @retArray;
482: &random_set_seed_from_phrase($seed);
483: @retArray=&math_random_exponential($item_cnt,$av);
484: &random_set_seed(@oldseed);
485: return @retArray;
486: }
487:
488: sub random_poisson {
489: my ($item_cnt,$seed,$mu) = @_;
490: my @oldseed=&random_get_seed();
491: my @retArray;
492: &random_set_seed_from_phrase($seed);
493: @retArray=&math_random_poisson($item_cnt,$mu);
494: &random_set_seed(@oldseed);
495: return @retArray;
496: }
497:
498: sub random_chi {
499: my ($item_cnt,$seed,$df) = @_;
500: my @oldseed=&random_get_seed();
501: my @retArray;
502: &random_set_seed_from_phrase($seed);
503: @retArray=&math_random_chi_square($item_cnt,$df);
504: &random_set_seed(@oldseed);
505: return @retArray;
506: }
507:
508: sub random_noncentral_chi {
509: my ($item_cnt,$seed,$df,$nonc) = @_;
510: my @oldseed=&random_get_seed();
511: my @retArray;
512: &random_set_seed_from_phrase($seed);
513: @retArray=&math_random_noncentral_chi_square($item_cnt,$df,$nonc);
514: &random_set_seed(@oldseed);
515: return @retArray;
516: }
517:
518: sub random_f {
519: my ($item_cnt,$seed,$dfn,$dfd) = @_;
520: my @oldseed=&random_get_seed();
521: my @retArray;
522: &random_set_seed_from_phrase($seed);
523: @retArray=&math_random_f($item_cnt,$dfn,$dfd);
524: &random_set_seed(@oldseed);
525: return @retArray;
526: }
527:
528: sub random_noncentral_f {
529: my ($item_cnt,$seed,$dfn,$dfd,$nonc) = @_;
530: my @oldseed=&random_get_seed();
531: my @retArray;
532: &random_set_seed_from_phrase($seed);
533: @retArray=&math_random_noncentral_f($item_cnt,$dfn,$dfd,$nonc);
534: &random_set_seed(@oldseed);
535: return @retArray;
536: }
537:
538: sub random_multivariate_normal {
539: my ($item_cnt,$seed,$mean,$covar) = @_;
540: my @oldseed=&random_get_seed();
541: &random_set_seed_from_phrase($seed);
542: my @retArray=&math_random_multivariate_normal($item_cnt,@$mean,@$covar);
543: &random_set_seed(@oldseed);
544: return @retArray;
545: }
546:
547: sub random_multinomial {
548: my ($item_cnt,$seed,@p) = @_;
549: my @oldseed=&random_get_seed();
550: my @retArray;
551: &random_set_seed_from_phrase($seed);
552: my @retArray=&math_random_multinomial($item_cnt,@p);
553: &random_set_seed(@oldseed);
554: return @retArray;
555: }
556:
557: sub random_permutation {
558: my ($seed,@inArray) = @_;
559: my @oldseed=&random_get_seed();
560: my @retArray;
561: &random_set_seed_from_phrase($seed);
562: @retArray=&math_random_permutation(@inArray);
563: &random_set_seed(@oldseed);
564: return @retArray;
565: }
566:
567: sub random_uniform {
568: my ($item_cnt,$seed,$low,$high) = @_;
569: my @oldseed=&random_get_seed();
570: my @retArray;
571: &random_set_seed_from_phrase($seed);
572: @retArray=&math_random_uniform($item_cnt,$low,$high);
573: &random_set_seed(@oldseed);
574: return @retArray;
575: }
576:
577: sub random_uniform_integer {
578: my ($item_cnt,$seed,$low,$high) = @_;
579: my @oldseed=&random_get_seed();
580: my @retArray;
581: &random_set_seed_from_phrase($seed);
582: @retArray=&math_random_uniform_integer($item_cnt,$low,$high);
583: &random_set_seed(@oldseed);
584: return @retArray;
585: }
586:
587: sub random_binomial {
588: my ($item_cnt,$seed,$nt,$p) = @_;
589: my @oldseed=&random_get_seed();
590: my @retArray;
591: &random_set_seed_from_phrase($seed);
592: @retArray=&math_random_binomial($item_cnt,$nt,$p);
593: &random_set_seed(@oldseed);
594: return @retArray;
595: }
596:
597: sub random_negative_binomial {
598: my ($item_cnt,$seed,$ne,$p) = @_;
599: my @oldseed=&random_get_seed();
600: my @retArray;
601: &random_set_seed_from_phrase($seed);
602: @retArray=&math_random_negative_binomial($item_cnt,$ne,$p);
603: &random_set_seed(@oldseed);
604: return @retArray;
605: }
606:
607: sub abs { CORE::abs(shift) }
608: sub sin { CORE::sin(shift) }
609: sub cos { CORE::cos(shift) }
610: sub exp { CORE::exp(shift) }
611: sub int { CORE::int(shift) }
612: sub log { CORE::log(shift) }
613: sub atan2 { CORE::atan2($_[0],$_[1]) }
614: sub sqrt { CORE::sqrt(shift) }
615:
616: sub tan { CORE::sin($_[0]) / CORE::cos($_[0]) }
617: #sub atan { atan2($_[0], 1); }
618: #sub acos { atan2(sqrt(1 - $_[0] * $_[0]), $_[0] ); }
619: #sub asin { atan2($_[0], sqrt(1- $_[0] * $_[0]) ); }
620:
621: sub log10 { CORE::log($_[0])/CORE::log(10); }
622:
623: sub factorial {
624: my $input = CORE::int(shift);
625: return "Error - unable to take factorial of an negative number ($input)" if $input < 0;
626: return "Error - factorial result is greater than system limit ($input)" if $input > 170;
627: return 1 if $input == 0;
628: my $result = 1;
629: for (my $i=2; $i<=$input; $i++) { $result *= $i }
630: return $result;
631: }
632:
633: sub sgn {
634: return -1 if $_[0] < 0;
635: return 0 if $_[0] == 0;
636: return 1 if $_[0] > 0;
637: }
638:
639: sub min {
640: my @sorted = sort { $a <=> $b || $a cmp $b } @_;
641: return shift @sorted;
642: }
643:
644: sub max {
645: my @sorted = sort { $a <=> $b || $a cmp $b } @_;
646: return pop @sorted;
647: }
648:
649: sub roundto {
650: my ($input,$n) = @_;
651: return sprintf('%.'.$n.'f',$input);
652: }
653:
654: sub to_string {
655: my ($input,$n) = @_;
656: return sprintf($input) if $n eq "";
657: $n = '.'.$n if $n !~ /^\./;
658: return sprintf('%'.$n,$input) if $n ne "";
659: }
660:
661: sub sub_string {
662: my ($str,$start,$len) = @_;
663: return substr($str,$start-1,$len);
664: }
665:
666: sub pow {return $_[0] ** $_[1]; }
667: sub ceil {return (($_[0]-CORE::int($_[0]))== 0.0) ? $_[0] : (($_[0] > 0) ? (CORE::int($_[0])+ 1) : CORE::int($_[0])); }
668: sub floor {return (($_[0]-CORE::int($_[0]))== 0.0) ? $_[0] : (($_[0] > 0) ? CORE::int($_[0]) : (CORE::int($_[0])-1)); }
669: #sub floor {return int($_[0]); }
670:
671: sub format {
672: my ($value,$fmt)=@_;
673: my ($dollarmode,$commamode,$alwaysperiod,$options);
674: if ($fmt =~ /^([^\d]*)(.*)/) { $options=$1; $fmt=$2; }
675: #if ($options =~ /\$/) { $dollamode=1; }
676: #if ($options =~ /,/) { $commamode=1; }
677: if ($options =~ /\./) { $alwaysperiod=1; }
678: my $result;
679: if ($fmt=~/s$/i) {
680: $result=&format_significant_figures($value,$fmt);
681: } else {
682: $fmt=~s/e/E/g;
683: $result=sprintf('%.'.$fmt,$value);
684: if ($alwaysperiod && $fmt eq '0f') { $result .='.'; }
685: $result=~s/(E[+-]*)0/$1/;
686: }
687: #if ($dollarmode) {$result=&dollarformat($result);}
688: #if ($commamode) {$result=&commaformat($result);}
689: return $result;
690: }
691:
692: sub chemparse {
693: my ($reaction) = @_;
694: my @tokens = split(/(\s\+|\->|<=>|<\-|\.)/,$reaction);
695: my $formula = '';
696: foreach my $token (@tokens) {
697: if ($token eq '->' ) {
698: $formula .= '<m>\ensuremath{\rightarrow}</m> ';
699: next;
700: }
701: if ($token eq '<-' ) {
702: $formula .= '<m>\ensuremath{\leftarrow}</m> ';
703: next;
704: }
705: if ($token eq '<=>') {
706: if ($external::target eq 'web' &&
707: &EXT('request.browser.unicode')) {
708: $formula .= '⇌ ';
709: } else {
710: $formula .= &web('<=> ','<m>\ensuremath{\rightleftharpoons}</m> ',
711: '<=> ');
712: }
713: next;
714: }
715: if ($token eq '.') {
716: $formula =~ s/(\ \;| )$//;
717: $formula .= '·';
718: next;
719: }
720: $token =~ /^\s*([\d|\/]*(?:&frac\d\d)?)(.*)/;
721: $formula .= $1 if ($1 ne '1'); # stoichiometric coefficient
722:
723: my $molecule = $2;
724: # subscripts
725: $molecule =~ s|(?<=[a-zA-Z\)\]\s])(\d+)|<sub>$1</sub>|g;
726: # superscripts
727: $molecule =~ s|\^(\d*[+\-]*)|<sup>$1</sup>|g;
728: # strip whitespace
729: $molecule =~ s/\s*//g;
730: # forced space
731: $molecule =~ s/_/ /g;
732: $molecule =~ s/-/−/g;
733: $formula .= $molecule.' ';
734: }
735: # get rid of trailing space
736: $formula =~ s/(\ \;| )$//;
737: return &xmlparse($formula);
738: }
739:
740: sub prettyprint {
741: my ($value,$fmt,$target)=@_;
742: my $result;
743: if (!$target) { $target = $external::target; }
744: if ($fmt =~ /chem/i) { return(&chemparse($value)); }
745: my ($dollarmode,$commamode,$alwaysperiod,$options);
746: if ($fmt =~ /^([^\d]*)(.*)/) { $options=$1; $fmt=$2; }
747: if ($options =~ /\$/) { $dollarmode=1; }
748: if ($options =~ /,/) { $commamode=1; }
749: if ($options =~ /\./) { $alwaysperiod=1; }
750: if ($fmt=~/s$/i) {
751: $value=&format_significant_figures($value,$fmt);
752: } elsif ($fmt) {
753: $value=sprintf('%.'.$fmt,$value);
754: }
755: if ($alwaysperiod && $fmt eq '0f') {
756: if ($target eq 'tex') {
757: $value .='\\ensuremath{.}';
758: } else {
759: $value .='.';
760: }
761: }
762: if ($value =~ /([0-9\.\-\+]+)E([0-9\-\+]+)/i ) {
763: my $frac=$1;
764: if ($dollarmode) { $frac=&dollarformat($frac); }
765: if ($commamode) { $frac=&commaformat($frac); }
766: my $exponent=$2;
767: $exponent=~s/^\+0*//;
768: $exponent=~s/^-0*/-/;
769: $exponent=~s/^-0*/-/;
770: if ($exponent eq '-') { undef($exponent); }
771: if ($exponent) {
772: if ($target eq 'web') {
773: $result=$frac.'×10<sup>'.$exponent.'</sup>';
774: } elsif ($target eq 'tex') {
775: $result='\ensuremath{'.$frac.'\times 10^{'.$exponent.'}}';
776: } else {
777: $result=$value;
778: }
779: } else {
780: $result=$frac;
781: }
782: } else {
783: $result=$value;
784: if ($dollarmode) { $result=&dollarformat($result,$target); }
785: elsif ($commamode) { $result=&commaformat($result,$target); }
786: }
787: return $result;
788: }
789:
790: sub commaformat {
791: my ($number,$target) = @_;
792: if ($number =~ /\./) {
793: while ($number =~ /([^0-9]*)([0-9]+)([^\.,][^\.,][^\.,])([,0-9]*\.[0-9]*)$/) {
794: $number = $1.$2.','.$3.$4;
795: }
796: } else {
797: while ($number =~ /^([^0-9]*)([0-9]+)([^,][^,][^,])([,0-9]*)$/) {
798: $number = $1.$2.','.$3.$4;
799: }
800: }
801: return $number;
802: }
803:
804: sub dollarformat {
805: my ($number,$target) = @_;
806: if (!$target) { $target = $external::target; }
807: $number=&commaformat($number,$target);
808: if ($target eq 'tex') {
809: $number='\$'.$number; #' stupid emacs
810: } else {
811: $number='$'.$number; #' stupid emacs
812: }
813: return $number;
814: }
815:
816: # format of form ns or nS where n is an integer
817: sub format_significant_figures {
818: my ($number,$format) = @_;
819: return '0' if ($number == 0);
820: # extract number of significant figures needed
821: my ($sig) = ($format =~ /(\d+)s/i);
822: # arbitrary choice - suggestions ?? or throw error message?
823: $sig = 3 if ($sig eq '');
824: # save the minus sign
825: my $sign = ($number < 0) ? '-' : '';
826: $number = abs($number);
827: # needed to correct for a number greater than 1 (or
828: my $power = ($number < 1) ? 0 : 1;
829: # could round up. Take the integer part of log10.
830: my $x10 = int(log($number)/log(10));
831: # find number with values left of decimal pt = # of sign figs.
832: my $xsig = $number*10**($sig-$x10-$power);
833: # get just digits left of decimal pt - also rounds off correctly
834: my $xint = sprintf('%.0f',$xsig);
835: # save any trailing zero's
836: my ($zeros) = ($xint =~ /(0+)$/);
837: # return number to original magnitude
838: my $numSig = $xint*10**($x10-$sig+$power);
839: # insert trailing zero's if have decimal point
840: $numSig =~ s/^(\d+)\.(\d+)(\e?(.*)?)$/$1\.$2$zeros$3/;
841: # put a decimal pt for number ending with 0 and length = # of sig fig
842: $numSig.='.' if (length($numSig) == $sig && $numSig =~ /0$/);
843: if (length($numSig) < $sig) {
844: $numSig.='.'.substr($zeros,0,($sig-length($numSig)));
845: }
846: # return number with sign
847: return $sign.$numSig;
848:
849: }
850:
851: sub map {
852: my ($phrase,$dest,$source)=@_;
853: my @oldseed=&random_get_seed();
854: my @seed = &random_seed_from_phrase($phrase);
855: &random_set_seed(@seed);
856: my $destct = scalar(@$dest);
857: if (!$source) {
858: my @output;
859: my @idx = &math_random_permuted_index($destct);
860: my $ctr = 0;
861: while ($ctr < $destct) {
862: $output[$ctr] = $$dest[$idx[$ctr]];
863: $ctr++;
864: }
865: &random_set_seed(@oldseed);
866: return @output;
867: } else {
868: my $num = scalar(@$source);
869: my @idx = &math_random_permuted_index($num);
870: my $ctr = 0;
871: my $tot = $num;
872: $tot = $destct if $destct < $num;
873: if (ref($$dest[0])) {
874: while ($ctr < $tot) {
875: ${$$dest[$ctr]} = $$source[$idx[$ctr]];
876: $ctr++;
877: }
878: } else {
879: while ($ctr < $tot) {
880: $$dest[$ctr] = $$source[$idx[$ctr]];
881: $ctr++;
882: }
883: }
884: }
885: &random_set_seed(@oldseed);
886: return '';
887: }
888:
889: sub rmap {
890: my ($phrase,$dest,$source)=@_;
891: my @oldseed=&random_get_seed();
892: my @seed = &random_seed_from_phrase($phrase);
893: &random_set_seed(@seed);
894: my $destct = scalar(@$dest);
895: if (!$source) {
896: my @idx = &math_random_permuted_index($destct);
897: my $ctr = 0;
898: my @r_idx;
899: while ($ctr < $destct) {
900: $r_idx[$idx[$ctr]] = $ctr;
901: $ctr++;
902: }
903: my @output;
904: $ctr = 0;
905: while ($ctr < $destct) {
906: $output[$ctr] = $$dest[$r_idx[$ctr]];
907: $ctr++;
908: }
909: &random_set_seed(@oldseed);
910: return @output;
911: } else {
912: my $num = scalar(@$source);
913: my @idx = &math_random_permuted_index($num);
914: my $ctr = 0;
915: my $tot = $num;
916: $tot = $destct if $destct < $num;
917: my @r_idx;
918: while ($ctr < $tot) {
919: $r_idx[$idx[$ctr]] = $ctr;
920: $ctr++;
921: }
922: $ctr = 0;
923: if (ref($$dest[0])) {
924: while ($ctr < $tot) {
925: ${$$dest[$ctr]} = $$source[$r_idx[$ctr]];
926: $ctr++;
927: }
928: } else {
929: while ($ctr < $tot) {
930: $$dest[$ctr] = $$source[$r_idx[$ctr]];
931: $ctr++;
932: }
933: }
934: }
935: &random_set_seed(@oldseed);
936: return '';
937: }
938:
939: sub capa_id { return }
940:
941: sub problem { return }
942:
943: sub name{
944: my $fullname = &EXT('environment.lastname').', '.&EXT('environment.firstname').' '.&EXT('environment.middlename');
945: $fullname = "" if $fullname eq ", ";
946: $fullname =~ s/\%2d/-/g;
947: return $fullname;
948: }
949:
950: sub student_number {
951: my $id = &EXT('environment.id');
952: $id = '' if $id eq "";
953: return $id;
954: }
955:
956: sub class {
957: my $course = &EXT('course.description');
958: $course = '' if $course eq "";
959: return $course;
960: }
961:
962: sub firstname {
963: my $firstname = &EXT('environment.firstname');
964: $firstname = '' if $firstname eq "";
965: return $firstname;
966: }
967:
968: sub lastname {
969: my $lastname = &EXT('environment.lastname');
970: $lastname = '' if $lastname eq "";
971: return $lastname;
972: }
973:
974: sub sec {
975: my $sec = &EXT('request.course.sec');
976: $sec = '' if $sec eq "";
977: return $sec;
978: }
979:
980: sub open_date {
981: my @dc = split(/\s+/,localtime(&EXT('resource.0.opendate')));
982: return '' if ($dc[0] eq "Wed" and $dc[2] == 31 and $dc[4] == 1969);
983: my @hm = split(/:/,$dc[3]);
984: my $ampm = " am";
985: if ($hm[0] > 12) {
986: $hm[0]-=12;
987: $ampm = " pm";
988: }
989: return $dc[0].', '.$dc[1].' '.$dc[2].', '.$dc[4].' at '.$hm[0].':'.$hm[1].$ampm;
990: }
991:
992: sub due_date {
993: my @dc = split(/\s+/,localtime(&EXT('resource.0.duedate')));
994: return '' if ($dc[0] eq "Wed" and $dc[2] == 31 and $dc[4] == 1969);
995: my @hm = split(/:/,$dc[3]);
996: my $ampm = " am";
997: if ($hm[0] > 12) {
998: $hm[0]-=12;
999: $ampm = " pm";
1000: }
1001: return $dc[0].', '.$dc[1].' '.$dc[2].', '.$dc[4].' at '.$hm[0].':'.$hm[1].$ampm;
1002: }
1003:
1004: sub answer_date {
1005: my @dc = split(/\s+/,localtime(&EXT('resource.0.answerdate')));
1006: return '' if ($dc[0] eq "Wed" and $dc[2] == 31 and $dc[4] == 1969);
1007: my @hm = split(/:/,$dc[3]);
1008: my $ampm = " am";
1009: if ($hm[0] > 12) {
1010: $hm[0]-=12;
1011: $ampm = " pm";
1012: }
1013: return $dc[0].', '.$dc[1].' '.$dc[2].', '.$dc[4].' at '.$hm[0].':'.$hm[1].$ampm;
1014: }
1015:
1016: sub array_moments {
1017: my @input=@_;
1018: my (@output,$N);
1019: $N=scalar (@input);
1020: $output[0]=$N;
1021: if ($N <= 1) {
1022: $output[1]=$input[0];
1023: $output[1]="Input array not defined" if ($N == 0);
1024: $output[2]="variance undefined for N<=1";
1025: $output[3]="skewness undefined for N<=1";
1026: $output[4]="kurtosis undefined for N<=1";
1027: return @output;
1028: }
1029: my $sum=0;
1030: foreach my $line (@input) {
1031: $sum+=$line;
1032: }
1033: $output[1] = $sum/$N;
1034: my ($x,$sdev,$var,$skew,$kurt) = 0;
1035: foreach my $line (@input) {
1036: $x=$line-$output[1];
1037: $var+=$x**2;
1038: $skew+=$x**3;
1039: $kurt+=$x**4;
1040: }
1041: $output[2]=$var/($N-1);
1042: $sdev=CORE::sqrt($output[2]);
1043: if ($sdev == 0) {
1044: $output[3]="inf-variance=0";
1045: $output[4]="inf-variance=0";
1046: return @output;
1047: }
1048: $output[3]=$skew/($sdev**3*$N);
1049: $output[4]=$kurt/($sdev**4*$N)-3;
1050: return @output;
1051: }
1052:
1053: sub choose {
1054: my $num = $_[0];
1055: return $_[$num];
1056: }
1057:
1058: #&sum1(1,$x,sub { &sum1($_[0],2*$_[0], sub { fact($_[0])**2 })});
1059: #sub sum1 {
1060: # my ($start,$end,$sub)=@_;
1061: # my $sum=0;
1062: # for (my $i=$start;$i<=$end;$i++) {
1063: # $sum+=&$sub($i);
1064: # }
1065: # return $sum
1066: #}
1067:
1068: #&sum2('a',1,$x,'&sum2(\'b\',$a,2*$a, \'&factorial($b)**2\')');
1069: #sub sum2 {
1070: # my ($varname,$start,$end,$line)=@_;
1071: # my $sum=0;
1072: # for (my $i=$start;$i<=$end;$i++) {
1073: # my $func=sub {
1074: # eval("\$".$varname."=$i");
1075: # eval($line);
1076: # };
1077: # $sum+=&$func($i);
1078: # }
1079: # return $sum
1080: #}
1081:
1082: # expiremental idea
1083: sub proper_path {
1084: my ($path)=@_;
1085: if ( $external::target eq "tex" ) {
1086: return '/home/httpd/html'.$path;
1087: } else {
1088: return $path;
1089: }
1090: }
1091:
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