Annotation of loncom/homework/default_homework.lcpm, revision 1.115

1.42      albertel    1: # The LearningOnline Network with CAPA 
1.1       harris41    2: # used by lonxml::xmlparse() as input variable $safeinit to Apache::run::run()
1.42      albertel    3: #
1.115   ! www         4: # $Id: default_homework.lcpm,v 1.114 2006/07/27 22:56:37 albertel Exp $
1.42      albertel    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: #
1.20      harris41   28: #
1.76      albertel   29: 
1.25      albertel   30: #init some globals
1.38      albertel   31: $hidden::RANDOMINIT=0;
1.22      ng         32: $pi=atan2(1,1)*4;
                     33: $rad2deg=180.0/$pi;
                     34: $deg2rad=$pi/180.0;
1.44      matthew    35: $"=' ';
1.3       albertel   36: 
1.91      albertel   37: sub check_commas {
                     38:     my ($response)=@_;
                     39:     #print("$response ");
                     40:     my @numbers=split(',',$response);
                     41:     #print(" numbers ".join('-',@numbers)." ");
                     42:     if (scalar(@numbers) > 1) {
                     43:         #print(" numbers[0] ".$numbers[0]." "); 
                     44: 	if (length($numbers[0]) > 3 || length($numbers[0]) == 0) { return -1; }
                     45: 	shift(@numbers);
                     46: 	#print(" numbers ".scalar(@numbers)." ");
                     47: 	while (scalar(@numbers) > 1) {
                     48: 	    #print(" numbers ".join('-',@numbers)." ");
                     49: 	    if (length($numbers[0]) != 3) { return -2; }
                     50: 	    shift(@numbers);
                     51: 	}
                     52: 	my ($number)=split('\.',$numbers[0]);
                     53: 	#print(" number ".$number." ");
                     54: 	#print(" numbers[0] ".$numbers[0]." ");
                     55: 	if (length($number) != 3) { return -3; }
                     56:     } else {
                     57: 	my ($number)=split('\.',$numbers[0]);
                     58: 	if (length($number) > 3) { return -4; }
                     59:     }
                     60:     return 1;
                     61: }
                     62: 
1.7       albertel   63: sub caparesponse_check {
1.74      albertel   64:     my ($answer,$response)=@_;
1.73      albertel   65:     #not properly used yet: calc
                     66:     #not to be used: $ans_fmt
1.74      albertel   67:     my $type=$LONCAPA::CAPAresponse_args{'type'};
                     68:     my $tol=$LONCAPA::CAPAresponse_args{'tol'};
                     69:     my $sig=$LONCAPA::CAPAresponse_args{'sig'};
1.88      albertel   70:     my $ans_fmt=$LONCAPA::CAPAresponse_args{'format'};
1.74      albertel   71:     my $unit=$LONCAPA::CAPAresponse_args{'unit'};
                     72:     my $calc=$LONCAPA::CAPAresponse_args{'calc'};
                     73:     my $samples=$LONCAPA::CAPAresponse_args{'samples'};
1.73      albertel   74:     
                     75:     my $tol_type=''; # gets it's value from whether tol has a % or not done
                     76:     my $sig_lbound=''; #done
                     77:     my $sig_ubound=''; #done
                     78: 
                     79: 
                     80:     #type's definitons come from capaParser.h
                     81:     my $message='';
                     82:     #remove leading and trailing whitespace
                     83:     if (!defined($response)) {
                     84: 	$response='';
                     85:     }
                     86:     if ($response=~ /^\s|\s$/) {
                     87: 	$response=~ s:^\s+|\s+$::g;
                     88: 	$message .="Removed ws now :$response:\n";
                     89:     } else {
                     90: 	$message .="no ws in :$response:\n";
                     91:     }
1.100     albertel   92:     &LONCAPA_INTERNAL_DEBUG(" type is $type ");
                     93:     if ($type eq 'cs' || $type eq 'ci') {
1.76      albertel   94: 	#for string answers make surec all places spaces occur, there is 
                     95:         #really only 1 space, in both the answer and the response
                     96: 	$answer=~s/ +/ /g;
                     97: 	$response=~s/ +/ /g;
1.100     albertel   98:     } elsif ($type eq 'mc') {
                     99: 	$answer=~s/[\s,]//g;
                    100: 	$response=~s/[\s,]//g;
1.76      albertel  101:     }
1.91      albertel  102:     if ($type eq 'float' && $unit=~/\$/) {
1.88      albertel  103: 	if ($response!~/^\$/)  { return "NO_UNIT: Missing \$ "; }
                    104: 	$response=~s/\$//g;
                    105:     }
1.91      albertel  106:     if ($type eq 'float' && $unit=~/\,/ && (&check_commas($response)<0)) {
                    107: 	return "COMMA_FAIL:";
                    108:     }
1.88      albertel  109:     $ans_fmt=~s/\W//g;
1.91      albertel  110:     $unit=~s/[\$,]//g;
                    111:     if ($type eq 'float') { $response=~s/,//g; }
1.88      albertel  112: 
1.73      albertel  113:     if (length($response) > 500) { return "TOO_LONG: Answer too long"; }
                    114: 
                    115:     if ($type eq '' ) {
1.74      albertel  116: 	$message .= "Didn't find a type :$type: defaulting\n";
1.73      albertel  117: 	if ( $answer eq ($answer *1.0)) { $type = 2;
                    118: 				      } else { $type = 3; }
                    119:     } else {
1.107     albertel  120: 	if    ($type eq 'cs')    { $type = 4; }
1.73      albertel  121: 	elsif ($type eq 'ci')    { $type = 3 }
                    122: 	elsif ($type eq 'mc')    { $type = 5; }
                    123: 	elsif ($type eq 'fml')   { $type = 8; }
1.107     albertel  124:         elsif ($type eq 'math')  { $type = 9; }
1.73      albertel  125: 	elsif ($type eq 'subj')  { $type = 7; }
                    126: 	elsif ($type eq 'float') { $type = 2; }
                    127: 	elsif ($type eq 'int')   { $type = 1; }
                    128: 	else { return "ERROR: Unknown type of answer: $type" }
                    129:     }
                    130: 
                    131:     my $points;
                    132:     my $id_list;
                    133:     #formula type setup the sample points
                    134:     if ($type eq '8') {
                    135: 	($id_list,$points)=split(/@/,$samples);
                    136: 	$message.="Found :$id_list:$points: points in $samples\n";
                    137:     }
                    138:     if ($tol eq '') {
                    139: 	$tol=0.0;
                    140: 	$tol_type=1; #TOL_ABSOLUTE
                    141:     } else {
                    142: 	if ($tol =~ /%$/) {
                    143: 	    chop $tol;
                    144: 	    $tol_type=2; #TOL_PERCENTAGE
                    145: 	} else {
                    146: 	    $tol_type=1; #TOL_ABSOLUTE
                    147: 	}
                    148:     }
                    149: 
1.85      albertel  150:     ($sig_ubound,$sig_lbound)=&LONCAPA_INTERNAL_get_sigrange($sig);
                    151: 
1.73      albertel  152:     my $reterror="";
1.107     albertel  153:     my $result;
                    154:     if ($type eq '9') {
1.108     www       155:       $result = &maxima_check(&maxima_cas_formula_fix($response),&maxima_cas_formula_fix($answer),\$reterror);
1.107     albertel  156:     } else {
1.109     albertel  157: 	if ($type eq '8') { # fml type
                    158: 	    $response = &capa_formula_fix($response);
                    159: 	    $answer   = &capa_formula_fix($answer);
                    160: 	}
                    161:        $result = &caparesponse_capa_check_answer($response,$answer,$type,
1.73      albertel  162: 						 $tol_type,$tol,
                    163: 						 $sig_lbound,$sig_ubound,
                    164: 						 $ans_fmt,$unit,$calc,$id_list,
                    165: 						 $points,$external::randomseed,
                    166: 						 \$reterror);
1.107     albertel  167:     }
1.73      albertel  168:     if    ($result == '1') { $result='EXACT_ANS'; } 
                    169:     elsif ($result == '2') { $result='APPROX_ANS'; }
                    170:     elsif ($result == '3') { $result='SIG_FAIL'; }
                    171:     elsif ($result == '4') { $result='UNIT_FAIL'; }
                    172:     elsif ($result == '5') { $result='NO_UNIT'; }
                    173:     elsif ($result == '6') { $result='UNIT_OK'; }
                    174:     elsif ($result == '7') { $result='INCORRECT'; }
                    175:     elsif ($result == '8') { $result='UNIT_NOTNEEDED'; }
                    176:     elsif ($result == '9') { $result='ANS_CNT_NOT_MATCH'; }
                    177:     elsif ($result =='10') { $result='SUB_RECORDED'; }
                    178:     elsif ($result =='11') { $result='BAD_FORMULA'; }
1.94      albertel  179:     elsif ($result =='12' && !$response) { $result='MISSING_ANSWER'; }
                    180:     elsif ($result =='12') { $result='WANTED_NUMERIC'; }
1.77      albertel  181:     elsif ($result =='13') { $result='UNIT_INVALID_INSTRUCTOR'; }
                    182:     elsif ($result =='141') { $result='UNIT_INVALID_STUDENT'; }
                    183:     elsif ($result =='142') { $result='UNIT_INVALID_STUDENT'; }
                    184:     elsif ($result =='143') { $result='UNIT_INVALID_STUDENT'; }
                    185:     elsif ($result =='15') { $result='UNIT_IRRECONCIBLE'; }
1.73      albertel  186:     else  {$result = "ERROR: Unknown Result:$result:$@:";}
                    187: 
1.82      albertel  188:     return ("$result:\nRetError $reterror:\nAnswer $answer:\nResponse $response:\n type-$type|$tol|$tol_type|$sig:$sig_lbound:$sig_ubound|$unit|\n$message",$reterror);
1.37      albertel  189: }
                    190: 
1.108     www       191: sub maxima_cas_formula_fix {
                    192:    my ($expression)=@_;
                    193:    return &implicit_multiplication($expression);
                    194: }
                    195: 
                    196: sub capa_formula_fix {
                    197:    my ($expression)=@_;
                    198:    return &implicit_multiplication($expression);
                    199: }
                    200: 
                    201: sub implicit_multiplication {
                    202:     my ($expression)=@_;
1.111     www       203: # Escape scientific notation, so 3e8 does not become 3*e*8
                    204: # 3e8 -> 3&8; 3e-8 -> 3&-8; 3E+8 -> e&+8
1.110     www       205:     $expression=~s/(\d+)e([\+\-]*\d+)/$1\&\($2\)/gsi;
1.111     www       206: # 3x10^8 -> 3&8; 3*10^-8 -> 3&-8
1.110     www       207:     $expression=~s/(\d+)(?:x|\*)10(?:\^|\*\*)([\+\-]*\d+)/$1\&\($2\)/gsi;
1.111     www       208: # Fill in multiplication signs
1.114     albertel  209: # a b -> a*b;3 b -> 3*b;3 4 -> 3*4
                    210:     $expression=~s/(\w)\s+(\w)/$1\*$2/gs;
1.115   ! www       211: # )( -> )*(; ) ( -> )*(
        !           212:     $expression=~s/\)\s*\(/\)\*\(/gs;
        !           213: # 3a -> 3*a; 3( -> 3*(; 3 ( -> 3*(; 3A -> 3*A
        !           214:     $expression=~s/(\d)\s*([a-zA-Z\(])/$1\*$2/gs;
        !           215: # a ( -> a*(
        !           216:     $expression=~s/(\w)\s+\(/$1\*\(/gs;
1.113     www       217: # a3 -> a*3;
1.110     www       218:     $expression=~s/([a-zA-Z])(\d)/$1\*$2/gs;
1.115   ! www       219: # )a -> )*a; )3 -> )*3; ) 3 -> )*3
        !           220:     $expression=~s/\)\s*(\w)/\)\*$1/gs;
1.111     www       221: # 3&8 -> 3e8; 3&-4 -> 3e-4
1.110     www       222:     $expression=~s/(\d+)\&\(([\+\-]*\d+)\)/$1e$2/gs;
1.108     www       223:     return $expression;
                    224: }
1.73      albertel  225: 
1.37      albertel  226: sub caparesponse_check_list {
1.74      albertel  227:     my $response=$LONCAPA::CAPAresponse_args{'response'};
1.105     albertel  228:     my $result="Got response :".join(':',@LONCAPA::CAPAresponse_answer).":\n";
                    229:     &LONCAPA_INTERNAL_DEBUG("args ".join(':',%LONCAPA::CAPAresponse_args));
1.73      albertel  230:     my @responselist;
1.74      albertel  231:     my $type = $LONCAPA::CAPAresponse_args{'type'};
1.73      albertel  232:     $result.="Got type :$type:\n";
1.105     albertel  233:     if ($type ne '' && $#LONCAPA::CAPAresponse_answer > 0) {
1.104     albertel  234: 	(@responselist)=split(/,/,$response);
1.105     albertel  235: 	if (@responselist < @LONCAPA::CAPAresponse_answer) {
                    236: 	    return 'MISSING_ANSWER';
                    237: 	}
                    238: 	if (@responselist > @LONCAPA::CAPAresponse_answer) {
                    239: 	    return 'EXTRA_ANSWER';
                    240: 	}
1.73      albertel  241:     } else {
                    242: 	(@responselist)=($response);
                    243:     }
                    244:     $result.="Initial final response :$responselist['-1']:\n";
1.105     albertel  245:     my $unit;
1.73      albertel  246:     if ($type eq '' || $type eq 'float') {
                    247: 	#for numerical problems split off the unit
                    248: 	if ( $responselist['-1']=~ /(.*[^\s])\s+([^\s]+)/ ) {
                    249: 	    $responselist['-1']=$1;
                    250: 	    $unit=$2;
                    251: 	}
                    252:     }
1.82      albertel  253:     $result.="Final final response :$responselist['-1']:$unit:\n";
1.73      albertel  254:     $unit=~s/\s//;
1.105     albertel  255: 
1.106     albertel  256:     my ($awards, @msgs, $i);
1.105     albertel  257:     foreach my $thisanswer (@LONCAPA::CAPAresponse_answer) {
                    258: 	my ($msg,$aresult);
1.73      albertel  259: 	$result.="trying answer :$thisanswer:\n";
1.105     albertel  260: 	if (defined($thisanswer)) {
1.104     albertel  261: 	    if ($unit eq '') {
                    262: 		($aresult,$msg)=&caparesponse_check($thisanswer,
                    263: 						    $responselist[$i]);
                    264: 	    } else {
                    265: 		($aresult,$msg)=&caparesponse_check($thisanswer,
                    266: 						    $responselist[$i]." $unit");
                    267: 	    }
1.73      albertel  268: 	} else {
1.104     albertel  269: 	    $aresult='ERROR';
1.105     albertel  270: 	    $msg='answer was undefined';
1.73      albertel  271: 	}
1.105     albertel  272: 	&LONCAPA_INTERNAL_DEBUG("after if $aresult -- $msg");
1.104     albertel  273: 	my ($temp)=split(/:/, $aresult);
1.73      albertel  274: 	$awards.="$temp,";
                    275: 	$result.=$aresult;
                    276: 	push(@msgs,$msg);
1.106     albertel  277: 	$i++;
1.73      albertel  278:     }
1.104     albertel  279:     chop($awards);
1.73      albertel  280:     return ("$awards:\n$result",@msgs);
1.7       albertel  281: }
                    282: 
1.4       albertel  283: sub tex {
1.73      albertel  284:     if ( $external::target eq "tex" ) {
                    285: 	return $_[0];
                    286:     } else {
                    287: 	return $_[1];
                    288:     }
1.4       albertel  289: }
                    290: 
1.24      ng        291: sub var_in_tex {
1.73      albertel  292:     if ( $external::target eq "tex" ) {
                    293: 	return $_[0];
                    294:     } else {
                    295: 	return "";
                    296:     }
1.24      ng        297: }
                    298: 
1.4       albertel  299: sub web {
1.73      albertel  300:     if ( $external::target eq "tex" ) {
                    301: 	return $_[1];
1.26      ng        302:     } else {
1.73      albertel  303: 	if ( $external::target eq "web" || $external::target eq "answer") {
                    304: 	    return $_[2];
                    305: 	} else {
                    306: 	    return $_[0];
                    307: 	}
1.4       albertel  308:     }
                    309: }
                    310: 
1.24      ng        311: sub html {
1.73      albertel  312:     if ( $external::target eq "web" ) {
                    313: 	return shift;
                    314:     }
1.24      ng        315: }
                    316: 
1.1       harris41  317: sub hinton {
1.73      albertel  318:     return 0;
1.1       harris41  319: }
                    320: 
                    321: sub random {
1.61      albertel  322:     my ($start,$end,$step)=@_;
                    323:     if ( ! $hidden::RANDOMINIT ) {
                    324: 	if ($external::randomseed == 0) { $external::randomseed=1; }
                    325: 	if ($external::randomseed =~/,/) {
1.84      albertel  326: 	    my ($num1,$num2)=split(/,/,$external::randomseed);
                    327: 	    &random_set_seed(1,abs($num1));
                    328: 	} elsif ($external::randomseed =~/:/) {
                    329: 	    my ($num1,$num2)=split(/:/,$external::randomseed);
1.61      albertel  330: 	    &random_set_seed(abs($num1),abs($num2));
                    331: 	} else {
                    332: 	    &random_set_seed(1,int(abs($external::randomseed)));
                    333: 	}
                    334: 	&math_random_uniform();
                    335: 	$hidden::RANDOMINIT=1;
                    336:     }
                    337:     if (!defined($step)) { $step=1; }
                    338:     my $num=1+int(($end-$start)/$step);
                    339:     my $result=$start + int(&math_random_uniform() * $num)*$step;
                    340:     return $result;
1.1       harris41  341: }
                    342: 
1.26      ng        343: sub random_normal {
1.73      albertel  344:     my ($item_cnt,$seed,$av,$std_dev) = @_;
                    345:     my @oldseed=&random_get_seed();
                    346:     my @retArray;
                    347:     &random_set_seed_from_phrase($seed);
                    348:     @retArray=&math_random_normal($item_cnt,$av,$std_dev);
                    349:     &random_set_seed(@oldseed);
                    350:     return @retArray;
1.26      ng        351: }
                    352: 
                    353: sub random_beta {
1.73      albertel  354:     my ($item_cnt,$seed,$aa,$bb) = @_;
                    355:     my @oldseed=&random_get_seed();
                    356:     my @retArray;
                    357:     &random_set_seed_from_phrase($seed);
                    358:     @retArray=&math_random_beta($item_cnt,$aa,$bb);
                    359:     &random_set_seed(@oldseed);
                    360:     return @retArray;
1.26      ng        361: }
                    362: 
                    363: sub random_gamma {
1.73      albertel  364:     my ($item_cnt,$seed,$a,$r) = @_;
                    365:     my @oldseed=&random_get_seed();
                    366:     my @retArray;
                    367:     &random_set_seed_from_phrase($seed);
                    368:     @retArray=&math_random_gamma($item_cnt,$a,$r);
                    369:     &random_set_seed(@oldseed);
                    370:     return @retArray;
1.26      ng        371: }
                    372: 
                    373: sub random_exponential {
1.73      albertel  374:     my ($item_cnt,$seed,$av) = @_;
                    375:     my @oldseed=&random_get_seed();
                    376:     my @retArray;
                    377:     &random_set_seed_from_phrase($seed);
                    378:     @retArray=&math_random_exponential($item_cnt,$av);
                    379:     &random_set_seed(@oldseed);
                    380:     return @retArray;
1.26      ng        381: }
                    382: 
                    383: sub random_poisson {
1.73      albertel  384:     my ($item_cnt,$seed,$mu) = @_;
                    385:     my @oldseed=&random_get_seed();
                    386:     my @retArray;
                    387:     &random_set_seed_from_phrase($seed);
                    388:     @retArray=&math_random_poisson($item_cnt,$mu);
                    389:     &random_set_seed(@oldseed);
                    390:     return @retArray;
1.26      ng        391: }
                    392: 
                    393: sub random_chi {
1.73      albertel  394:     my ($item_cnt,$seed,$df) = @_;
                    395:     my @oldseed=&random_get_seed();
                    396:     my @retArray;
                    397:     &random_set_seed_from_phrase($seed);
                    398:     @retArray=&math_random_chi_square($item_cnt,$df);
                    399:     &random_set_seed(@oldseed);
                    400:     return @retArray;
1.26      ng        401: }
                    402: 
                    403: sub random_noncentral_chi {
1.73      albertel  404:     my ($item_cnt,$seed,$df,$nonc) = @_;
                    405:     my @oldseed=&random_get_seed();
                    406:     my @retArray;
                    407:     &random_set_seed_from_phrase($seed);
                    408:     @retArray=&math_random_noncentral_chi_square($item_cnt,$df,$nonc);
                    409:     &random_set_seed(@oldseed);
                    410:     return @retArray;
1.26      ng        411: }
                    412: 
                    413: sub random_f {
1.73      albertel  414:     my ($item_cnt,$seed,$dfn,$dfd) = @_;
                    415:     my @oldseed=&random_get_seed();
                    416:     my @retArray;
                    417:     &random_set_seed_from_phrase($seed);
                    418:     @retArray=&math_random_f($item_cnt,$dfn,$dfd);
                    419:     &random_set_seed(@oldseed);
                    420:     return @retArray;
1.26      ng        421: }
                    422: 
                    423: sub random_noncentral_f {
1.73      albertel  424:     my ($item_cnt,$seed,$dfn,$dfd,$nonc) = @_;
                    425:     my @oldseed=&random_get_seed();
                    426:     my @retArray;
                    427:     &random_set_seed_from_phrase($seed);
                    428:     @retArray=&math_random_noncentral_f($item_cnt,$dfn,$dfd,$nonc);
                    429:     &random_set_seed(@oldseed);
                    430:     return @retArray;
1.26      ng        431: }
                    432: 
                    433: sub random_multivariate_normal {
1.73      albertel  434:     my ($item_cnt,$seed,$mean,$covar) = @_;
                    435:     my @oldseed=&random_get_seed();
                    436:     &random_set_seed_from_phrase($seed);
1.87      albertel  437:     my @retArray=&math_random_multivariate_normal($item_cnt,@$mean,@$covar);
1.73      albertel  438:     &random_set_seed(@oldseed);
                    439:     return @retArray;
1.26      ng        440: }
                    441: 
                    442: sub random_multinomial {
1.73      albertel  443:     my ($item_cnt,$seed,@p) = @_;
                    444:     my @oldseed=&random_get_seed();
                    445:     my @retArray;
                    446:     &random_set_seed_from_phrase($seed);
1.87      albertel  447:     my @retArray=&math_random_multinomial($item_cnt,@p);
1.73      albertel  448:     &random_set_seed(@oldseed);
                    449:     return @retArray;
1.26      ng        450: }
                    451: 
                    452: sub random_permutation {
1.73      albertel  453:     my ($seed,@inArray) = @_;
                    454:     my @oldseed=&random_get_seed();
                    455:     my @retArray;
                    456:     &random_set_seed_from_phrase($seed);
                    457:     @retArray=&math_random_permutation(@inArray);
                    458:     &random_set_seed(@oldseed);
                    459:     return @retArray;
1.26      ng        460: }
                    461: 
                    462: sub random_uniform {
1.73      albertel  463:     my ($item_cnt,$seed,$low,$high) = @_;
                    464:     my @oldseed=&random_get_seed();
                    465:     my @retArray;
                    466:     &random_set_seed_from_phrase($seed);
                    467:     @retArray=&math_random_uniform($item_cnt,$low,$high);
                    468:     &random_set_seed(@oldseed);
                    469:     return @retArray;
1.26      ng        470: }
                    471: 
                    472: sub random_uniform_integer {
1.73      albertel  473:     my ($item_cnt,$seed,$low,$high) = @_;
                    474:     my @oldseed=&random_get_seed();
                    475:     my @retArray;
                    476:     &random_set_seed_from_phrase($seed);
                    477:     @retArray=&math_random_uniform_integer($item_cnt,$low,$high);
                    478:     &random_set_seed(@oldseed);
                    479:     return @retArray;
1.26      ng        480: }
                    481: 
                    482: sub random_binomial {
1.73      albertel  483:     my ($item_cnt,$seed,$nt,$p) = @_;
                    484:     my @oldseed=&random_get_seed();
                    485:     my @retArray;
                    486:     &random_set_seed_from_phrase($seed);
                    487:     @retArray=&math_random_binomial($item_cnt,$nt,$p);
                    488:     &random_set_seed(@oldseed);
                    489:     return @retArray;
1.26      ng        490: }
                    491: 
                    492: sub random_negative_binomial {
1.73      albertel  493:     my ($item_cnt,$seed,$ne,$p) = @_;
                    494:     my @oldseed=&random_get_seed();
                    495:     my @retArray;
                    496:     &random_set_seed_from_phrase($seed);
                    497:     @retArray=&math_random_negative_binomial($item_cnt,$ne,$p);
                    498:     &random_set_seed(@oldseed);
                    499:     return @retArray;
1.26      ng        500: }
                    501: 
1.103     albertel  502: sub abs { CORE::abs(shift) }
                    503: sub sin { CORE::sin(shift) }
                    504: sub cos { CORE::cos(shift) }
                    505: sub exp { CORE::exp(shift) }
                    506: sub int { CORE::int(shift) }
                    507: sub log { CORE::log(shift) }
                    508: sub atan2 { CORE::atan2($_[0],$_[1]) }
                    509: sub sqrt { CORE::sqrt(shift) }
1.23      ng        510: 
1.59      albertel  511: sub tan  { CORE::sin($_[0]) / CORE::cos($_[0]) }
1.21      harris41  512: #sub atan { atan2($_[0], 1); }
                    513: #sub acos { atan2(sqrt(1 - $_[0] * $_[0]), $_[0] ); }
                    514: #sub asin { atan2($_[0], sqrt(1- $_[0] * $_[0]) );  }
1.22      ng        515: 
1.59      albertel  516: sub log10 { CORE::log($_[0])/CORE::log(10); }
1.22      ng        517: 
1.20      harris41  518: sub factorial {
1.59      albertel  519:     my $input = CORE::int(shift);
1.20      harris41  520:     return "Error - unable to take factorial of an negative number ($input)" if $input < 0;
                    521:     return "Error - factorial result is greater than system limit ($input)" if $input > 170;
                    522:     return 1 if $input == 0;
                    523:     my $result = 1; 
                    524:     for (my $i=2; $i<=$input; $i++) { $result *= $i }
                    525:     return $result;
                    526: }
                    527: 
                    528: sub sgn {
                    529:     return -1 if $_[0] < 0;
                    530:     return 0 if $_[0] == 0;
                    531:     return 1 if $_[0] > 0;
                    532: }
                    533: 
                    534: sub min {
                    535:     my @sorted = sort { $a <=> $b || $a cmp $b } @_;
                    536:     return shift @sorted;
                    537: }
                    538: 
                    539: sub max {
                    540:     my @sorted = sort { $a <=> $b || $a cmp $b } @_;
                    541:     return pop @sorted;
                    542: }
1.1       harris41  543: 
1.20      harris41  544: sub roundto {
                    545:     my ($input,$n) = @_;
                    546:     return sprintf('%.'.$n.'f',$input);
                    547: }
                    548: 
                    549: sub to_string {
                    550:     my ($input,$n) = @_;
1.26      ng        551:     return sprintf($input) if $n eq "";
                    552:     $n = '.'.$n if $n !~ /^\./;
1.20      harris41  553:     return sprintf('%'.$n,$input) if $n ne "";
                    554: }
                    555: 
                    556: sub sub_string {
                    557:     my ($str,$start,$len) = @_;
                    558:     return substr($str,$start-1,$len);
                    559: }
1.1       harris41  560: 
                    561: sub pow   {return $_[0] ** $_[1]; }
1.59      albertel  562: sub ceil  {return (($_[0]-CORE::int($_[0]))== 0.0) ? $_[0] : (($_[0] > 0) ? (CORE::int($_[0])+ 1) : CORE::int($_[0])); }
                    563: sub floor  {return (($_[0]-CORE::int($_[0]))== 0.0) ? $_[0] : (($_[0] > 0) ? CORE::int($_[0]) : (CORE::int($_[0])-1)); }
1.27      ng        564: #sub floor {return int($_[0]); }
1.1       harris41  565: 
1.2       albertel  566: sub format {
1.73      albertel  567:     my ($value,$fmt)=@_;
1.81      albertel  568:     my ($dollarmode,$commamode,$alwaysperiod,$options);
                    569:     if ($fmt =~ /^([^\d]*)(.*)/) { $options=$1; $fmt=$2; } 
                    570:     #if ($options =~ /\$/) { $dollamode=1; }
                    571:     #if ($options =~ /,/)  { $commamode=1; }
1.82      albertel  572:     if ($options =~ /\./) { $alwaysperiod=1; }
1.99      ng        573:     my $result;
1.97      albertel  574:     if ($fmt=~/s$/i) {
                    575: 	$result=&format_significant_figures($value,$fmt);
                    576:     } else {
                    577: 	$fmt=~s/e/E/g;
1.99      ng        578: 	$result=sprintf('%.'.$fmt,$value);
1.97      albertel  579: 	if ($alwaysperiod && $fmt eq '0f') { $result .='.'; }
                    580: 	$result=~s/(E[+-]*)0/$1/;
                    581:     }
1.81      albertel  582:     #if ($dollarmode) {$result=&dollarformat($result);}
                    583:     #if ($commamode) {$result=&commaformat($result);}
1.73      albertel  584:     return $result;
1.46      albertel  585: }
                    586: 
1.75      albertel  587: sub chemparse {
                    588:     my ($reaction) = @_;
1.96      albertel  589:     my @tokens = split(/(\s\+|\->|<=>|<\-|\.)/,$reaction);
1.75      albertel  590:     my $formula = '';
                    591:     foreach my $token (@tokens) {
                    592: 	if ($token eq '->' ) {
                    593: 	    $formula .= '<m>\ensuremath{\rightarrow}</m> ';
                    594: 	    next;
                    595: 	}
1.96      albertel  596: 	if ($token eq '<-' ) {
                    597: 	    $formula .= '<m>\ensuremath{\leftarrow}</m> ';
                    598: 	    next;
                    599: 	}  
1.75      albertel  600: 	if ($token eq '<=>') {
                    601: 	    if ($external::target eq 'web' &&
                    602: 		&EXT('request.browser.unicode')) {
1.76      albertel  603: 		$formula .= '&#8652; ';
1.75      albertel  604: 	    } else {
                    605: 		$formula .= &web('<=> ','<m>\ensuremath{\rightleftharpoons}</m> ',
1.95      albertel  606: 				 '&lt;=&gt; ');
1.75      albertel  607: 	    }
                    608: 	    next;
                    609: 	}
1.96      albertel  610: 	if ($token eq '.') {
                    611: 	  $formula =~ s/(\&nbsp\;| )$//;
                    612: 	  $formula .= '&middot;';
                    613: 	  next;
                    614: 	}
                    615: 	$token =~ /^\s*([\d|\/]*(?:&frac\d\d)?)(.*)/;
1.90      albertel  616:         $formula .= $1 if ($1 ne '1');  # stoichiometric coefficient
1.75      albertel  617: 	
                    618: 	my $molecule = $2;
                    619: 	# subscripts
1.78      albertel  620: 	$molecule =~ s|(?<=[a-zA-Z\)\]\s])(\d+)|<sub>$1</sub>|g;
1.75      albertel  621: 	# superscripts
                    622: 	$molecule =~ s|\^(\d*[+\-]*)|<sup>$1</sup>|g;
                    623: 	# strip whitespace
                    624: 	$molecule =~ s/\s*//g;
                    625: 	# forced space
                    626: 	$molecule =~ s/_/ /g;
1.96      albertel  627: 	$molecule =~ s/-/&minus;/g;
1.75      albertel  628: 	$formula .= $molecule.'&nbsp;';
                    629:     }
                    630:     # get rid of trailing space
1.87      albertel  631:     $formula =~ s/(\&nbsp\;| )$//;
1.75      albertel  632:     return &xmlparse($formula);
                    633: }
                    634: 
1.46      albertel  635: sub prettyprint {
1.73      albertel  636:     my ($value,$fmt,$target)=@_;
                    637:     my $result;
                    638:     if (!$target) { $target = $external::target; }
1.75      albertel  639:     if ($fmt =~ /chem/i) { return(&chemparse($value)); }
1.81      albertel  640:     my ($dollarmode,$commamode,$alwaysperiod,$options);
                    641:     if ($fmt =~ /^([^\d]*)(.*)/) { $options=$1; $fmt=$2; } 
1.86      albertel  642:     if ($options =~ /\$/) { $dollarmode=1; }
1.81      albertel  643:     if ($options =~ /,/)  { $commamode=1; }
                    644:     if ($options =~ /\./) { $alwaysperiod=1; }
1.97      albertel  645:     if ($fmt=~/s$/i) {
                    646: 	$value=&format_significant_figures($value,$fmt);
                    647:     } elsif ($fmt) {
                    648: 	$value=sprintf('%.'.$fmt,$value);
                    649:     }
1.81      albertel  650:     if ($alwaysperiod && $fmt eq '0f') {
                    651: 	if ($target eq 'tex') {
                    652: 	    $value .='\\ensuremath{.}';
                    653: 	} else {
                    654: 	    $value .='.';
                    655: 	}
                    656:     }
1.73      albertel  657:     if ($value =~ /([0-9\.\-\+]+)E([0-9\-\+]+)/i ) {
                    658: 	my $frac=$1;
                    659: 	if ($dollarmode) { $frac=&dollarformat($frac); }
1.80      albertel  660: 	if ($commamode) { $frac=&commaformat($frac); }
1.73      albertel  661: 	my $exponent=$2;
                    662: 	$exponent=~s/^\+0*//;
                    663: 	$exponent=~s/^-0*/-/;
                    664: 	$exponent=~s/^-0*/-/;
                    665: 	if ($exponent eq '-') { undef($exponent); }
                    666: 	if ($exponent) {
                    667: 	    if ($target eq 'web') {
                    668: 		$result=$frac.'&#215;10<sup>'.$exponent.'</sup>';
                    669: 	    } elsif ($target eq 'tex') {
                    670: 		$result='\ensuremath{'.$frac.'\times 10^{'.$exponent.'}}';
                    671: 	    } else {
                    672: 		$result=$value;
                    673: 	    }
                    674: 	} else {
                    675: 	    $result=$frac;
                    676: 	}
                    677:     } else {
1.48      albertel  678: 	$result=$value;
1.86      albertel  679: 	if    ($dollarmode) { $result=&dollarformat($result,$target); }
                    680: 	elsif ($commamode)  { $result=&commaformat($result,$target); }
1.46      albertel  681:     }
1.73      albertel  682:     return $result;
1.48      albertel  683: }
                    684: 
1.80      albertel  685: sub commaformat {
1.73      albertel  686:     my ($number,$target) = @_;
                    687:     if ($number =~ /\./) {
1.102     albertel  688: 	while ($number =~ /([^0-9]*)([0-9]+)([^\.,][^\.,][^\.,])([,0-9]*\.[0-9]*)$/) {
                    689: 	    $number = $1.$2.','.$3.$4;
1.73      albertel  690: 	}
                    691:     } else {
1.102     albertel  692: 	while ($number =~ /^([^0-9]*)([0-9]+)([^,][^,][^,])([,0-9]*)$/) {
                    693: 	    $number = $1.$2.','.$3.$4;
1.73      albertel  694: 	}
                    695:     }
1.80      albertel  696:     return $number;
                    697: }
                    698: 
                    699: sub dollarformat {
                    700:     my ($number,$target) = @_;
                    701:     if (!$target) { $target = $external::target; }
                    702:     $number=&commaformat($number,$target);
1.73      albertel  703:     if ($target eq 'tex') {
                    704: 	$number='\$'.$number; #' stupid emacs
                    705:     } else {
                    706: 	$number='$'.$number; #' stupid emacs
                    707:     }
                    708:     return $number; 
1.2       albertel  709: }
1.5       albertel  710: 
1.97      albertel  711: # format of form ns or nS where n is an integer
                    712: sub format_significant_figures {
                    713:     my ($number,$format) = @_; 
                    714:     return '0' if ($number == 0);
                    715:     # extract number of significant figures needed
                    716:     my ($sig) = ($format =~ /(\d+)s/i);
                    717:     # arbitrary choice - suggestions ?? or throw error message?
                    718:     $sig = 3 if ($sig eq '');
                    719:     # save the minus sign
                    720:     my $sign = ($number < 0) ? '-' : '';
                    721:     $number = abs($number);
                    722:     # needed to correct for a number greater than 1 (or
                    723:     my $power = ($number < 1) ? 0 : 1;
                    724:     # could round up. Take the integer part of log10.
                    725:     my $x10 = int(log($number)/log(10));
                    726:     # find number with values left of decimal pt = # of sign figs.
                    727:     my $xsig = $number*10**($sig-$x10-$power);
                    728:     # get just digits left of decimal pt - also rounds off correctly
                    729:     my $xint  = sprintf('%.0f',$xsig);
                    730:     # save any trailing zero's
                    731:     my ($zeros) = ($xint =~ /(0+)$/);
                    732:     # return number to original magnitude
                    733:     my $numSig = $xint*10**($x10-$sig+$power);
                    734:     # insert trailing zero's if have decimal point
                    735:     $numSig =~ s/^(\d+)\.(\d+)(\e?(.*)?)$/$1\.$2$zeros$3/;
1.98      albertel  736:     # put a decimal pt for number ending with 0 and length = # of sig fig
                    737:     $numSig.='.' if (length($numSig) == $sig && $numSig =~ /0$/);
                    738:     if (length($numSig) < $sig) {
                    739: 	$numSig.='.'.substr($zeros,0,($sig-length($numSig)));
                    740:     }
1.97      albertel  741:     # return number with sign
                    742:     return $sign.$numSig;
                    743: 
                    744: }
                    745: 
1.5       albertel  746: sub map {
1.27      ng        747:     my ($phrase,$dest,$source)=@_;
1.51      albertel  748:     my @oldseed=&random_get_seed();
1.27      ng        749:     my @seed = &random_seed_from_phrase($phrase);
                    750:     &random_set_seed(@seed);
                    751:     my $destct = scalar(@$dest);
1.28      ng        752:     if (!$source) {
                    753: 	my @output;
                    754: 	my @idx = &math_random_permuted_index($destct);
                    755: 	my $ctr = 0;
                    756: 	while ($ctr < $destct) {
                    757: 	    $output[$ctr] = $$dest[$idx[$ctr]];
1.27      ng        758: 	    $ctr++;
1.28      ng        759: 	}
1.51      albertel  760:         &random_set_seed(@oldseed);
1.28      ng        761: 	return @output;
1.27      ng        762:     } else {
1.28      ng        763: 	my $num = scalar(@$source);
                    764: 	my @idx = &math_random_permuted_index($num);
                    765: 	my $ctr = 0;
                    766: 	my $tot = $num;
                    767: 	$tot = $destct if $destct < $num;
                    768: 	if (ref($$dest[0])) {
                    769: 	    while ($ctr < $tot) {
                    770: 		${$$dest[$ctr]} = $$source[$idx[$ctr]];
                    771: 	        $ctr++;
                    772:             }
                    773:         } else {
                    774: 	    while ($ctr < $tot) {
                    775: 		$$dest[$ctr] = $$source[$idx[$ctr]];
                    776: 		$ctr++;
                    777: 	    }
                    778: 	}
1.27      ng        779:     }
1.56      albertel  780:     &random_set_seed(@oldseed);
1.51      albertel  781:     return '';
1.27      ng        782: }
                    783: 
                    784: sub rmap {
                    785:     my ($phrase,$dest,$source)=@_;
1.51      albertel  786:     my @oldseed=&random_get_seed();
1.27      ng        787:     my @seed = &random_seed_from_phrase($phrase);
                    788:     &random_set_seed(@seed);
                    789:     my $destct = scalar(@$dest);
1.28      ng        790:     if (!$source) {
                    791: 	my @idx = &math_random_permuted_index($destct);
                    792: 	my $ctr = 0;
                    793: 	my @r_idx;
                    794: 	while ($ctr < $destct) {
                    795: 	    $r_idx[$idx[$ctr]] = $ctr;
                    796: 	    $ctr++;
                    797: 	}
                    798: 	my @output;
                    799: 	$ctr = 0;
                    800: 	while ($ctr < $destct) {
                    801: 	    $output[$ctr] = $$dest[$r_idx[$ctr]];
1.27      ng        802: 	    $ctr++;
1.28      ng        803: 	}
1.51      albertel  804:         &random_set_seed(@oldseed);
1.28      ng        805: 	return @output;
1.27      ng        806:     } else {
1.28      ng        807: 	my $num = scalar(@$source);
                    808: 	my @idx = &math_random_permuted_index($num);
                    809: 	my $ctr = 0;
                    810: 	my $tot = $num;
                    811: 	$tot = $destct if $destct < $num;
                    812: 	my @r_idx;
1.27      ng        813: 	while ($ctr < $tot) {
1.28      ng        814: 	    $r_idx[$idx[$ctr]] = $ctr;
1.27      ng        815: 	    $ctr++;
1.28      ng        816: 	}
                    817: 	$ctr = 0;
                    818: 	if (ref($$dest[0])) {
                    819: 	    while ($ctr < $tot) {
                    820: 		${$$dest[$ctr]} = $$source[$r_idx[$ctr]];
                    821: 	        $ctr++;
                    822:             }
                    823:         } else {
                    824: 	    while ($ctr < $tot) {
                    825: 		$$dest[$ctr] = $$source[$r_idx[$ctr]];
                    826: 		$ctr++;
                    827: 	    }
                    828: 	}
1.6       albertel  829:     }
1.51      albertel  830:     &random_set_seed(@oldseed);
                    831:     return '';
1.5       albertel  832: }
1.22      ng        833: 
1.23      ng        834: sub capa_id { return }
                    835: 
                    836: sub problem { return }
                    837: 
1.22      ng        838: sub name{
1.73      albertel  839:     my $fullname = &EXT('environment.lastname').', '.&EXT('environment.firstname').' '.&EXT('environment.middlename');
                    840:     $fullname = "" if $fullname eq ",  ";
                    841:     $fullname =~ s/\%2d/-/g;
                    842:     return $fullname;
1.22      ng        843: }
                    844: 
                    845: sub student_number { 
1.73      albertel  846:     my $id = &EXT('environment.id');
                    847:     $id = '' if $id eq "";
                    848:     return $id;
1.22      ng        849: }
                    850: 
                    851: sub class {
1.73      albertel  852:     my $course = &EXT('course.description');
                    853:     $course = '' if $course eq "";
                    854:     return $course;
1.22      ng        855: }
                    856: 
1.112     www       857: sub firstname {
                    858:     my $firstname = &EXT('environment.firstname');
                    859:     $firstname = '' if $firstname eq "";
                    860:     return $firstname;
                    861: }
                    862:                                                                                 
                    863: sub lastname {
                    864:     my $lastname = &EXT('environment.lastname');
                    865:     $lastname = '' if $lastname eq "";
                    866:     return $lastname;
                    867: }
                    868: 
1.22      ng        869: sub sec { 
1.73      albertel  870:     my $sec = &EXT('request.course.sec');
                    871:     $sec = '' if $sec eq "";
                    872:     return $sec;
1.22      ng        873: }
                    874: 
1.23      ng        875: sub open_date { 
1.73      albertel  876:     my @dc = split(/\s+/,localtime(&EXT('resource.0.opendate')));
                    877:     return '' if ($dc[0] eq "Wed" and $dc[2] == 31 and $dc[4] == 1969);
                    878:     my @hm = split(/:/,$dc[3]);
                    879:     my $ampm = " am";
                    880:     if ($hm[0] > 12) {
                    881: 	$hm[0]-=12;
                    882: 	$ampm = " pm";
                    883:     }
                    884:     return $dc[0].', '.$dc[1].' '.$dc[2].', '.$dc[4].' at '.$hm[0].':'.$hm[1].$ampm;
1.23      ng        885: }
                    886: 
                    887: sub due_date { 
1.73      albertel  888:     my @dc = split(/\s+/,localtime(&EXT('resource.0.duedate')));
                    889:     return '' if ($dc[0] eq "Wed" and $dc[2] == 31 and $dc[4] == 1969);
                    890:     my @hm = split(/:/,$dc[3]);
                    891:     my $ampm = " am";
                    892:     if ($hm[0] > 12) {
                    893: 	$hm[0]-=12;
                    894: 	$ampm = " pm";
                    895:     }
                    896:     return $dc[0].', '.$dc[1].' '.$dc[2].', '.$dc[4].' at '.$hm[0].':'.$hm[1].$ampm;
1.23      ng        897: }
                    898: 
                    899: sub answer_date { 
1.73      albertel  900:     my @dc = split(/\s+/,localtime(&EXT('resource.0.answerdate')));
                    901:     return '' if ($dc[0] eq "Wed" and $dc[2] == 31 and $dc[4] == 1969);
                    902:     my @hm = split(/:/,$dc[3]);
                    903:     my $ampm = " am";
                    904:     if ($hm[0] > 12) {
                    905: 	$hm[0]-=12;
                    906: 	$ampm = " pm";
                    907:     }
                    908:     return $dc[0].', '.$dc[1].' '.$dc[2].', '.$dc[4].' at '.$hm[0].':'.$hm[1].$ampm;
1.24      ng        909: }
                    910: 
                    911: sub array_moments {
1.73      albertel  912:     my @input=@_;
                    913:     my (@output,$N);
                    914:     $N=scalar (@input);
                    915:     $output[0]=$N;
                    916:     if ($N <= 1) {
                    917: 	$output[1]=$input[0];
                    918: 	$output[1]="Input array not defined" if ($N == 0);
                    919: 	$output[2]="variance undefined for N<=1";
                    920: 	$output[3]="skewness undefined for N<=1";
                    921: 	$output[4]="kurtosis undefined for N<=1";
                    922: 	return @output;
                    923:     }
                    924:     my $sum=0;
                    925:     foreach my $line (@input) {
                    926: 	$sum+=$line;
                    927:     }
                    928:     $output[1] = $sum/$N;
                    929:     my ($x,$sdev,$var,$skew,$kurt) = 0;
                    930:     foreach my $line (@input) {
                    931: 	$x=$line-$output[1];
                    932: 	$var+=$x**2;
                    933: 	$skew+=$x**3;
                    934: 	$kurt+=$x**4;
                    935:     }
                    936:     $output[2]=$var/($N-1);
                    937:     $sdev=CORE::sqrt($output[2]);
                    938:     if ($sdev == 0) {
                    939: 	$output[3]="inf-variance=0";
                    940: 	$output[4]="inf-variance=0";
                    941: 	return @output;
                    942:     }
                    943:     $output[3]=$skew/($sdev**3*$N);
                    944:     $output[4]=$kurt/($sdev**4*$N)-3;
1.24      ng        945:     return @output;
                    946: }
1.5       albertel  947: 
                    948: sub choose {
1.73      albertel  949:     my $num = $_[0];
                    950:     return $_[$num];
1.5       albertel  951: }
1.23      ng        952: 
1.101     albertel  953: #&sum1(1,$x,sub { &sum1($_[0],2*$_[0], sub { fact($_[0])**2 })});
                    954: #sub sum1 {
                    955: #    my ($start,$end,$sub)=@_;
                    956: #    my $sum=0;
                    957: #    for (my $i=$start;$i<=$end;$i++) {
                    958: #        $sum+=&$sub($i);
                    959: #    }
                    960: #    return $sum
                    961: #}
                    962: 
                    963: #&sum2('a',1,$x,'&sum2(\'b\',$a,2*$a, \'&factorial($b)**2\')');
                    964: #sub sum2 {
                    965: #    my ($varname,$start,$end,$line)=@_;
                    966: #    my $sum=0;
                    967: #    for (my $i=$start;$i<=$end;$i++) {
                    968: #	my $func=sub {
                    969: #	    eval("\$".$varname."=$i");
                    970: #	    eval($line);
                    971: #	};
                    972: #        $sum+=&$func($i);
                    973: #    }
                    974: #    return $sum
                    975: #}
                    976: 
1.49      albertel  977: # expiremental idea
                    978: sub proper_path {
1.73      albertel  979:     my ($path)=@_;
                    980:     if ( $external::target eq "tex" ) {
                    981: 	return '/home/httpd/html'.$path;
                    982:     } else {
                    983: 	return $path;
                    984:     }
1.49      albertel  985: }
1.23      ng        986: 

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