Annotation of loncom/homework/default_homework.lcpm, revision 1.111

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: #
1.111   ! www         4: # $Id: default_homework.lcpm,v 1.110 2006/07/17 21:11:21 www 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
        !           209: # a b -> a*b
1.110     www       210:     $expression=~s/\s+/\*/gs;
1.111   ! www       211: # 3a -> 3*a; 3( -> 3*(; 3A -> 3*a
1.110     www       212:     $expression=~s/(\d)([a-zA-Z\(])/$1\*$2/gs;
1.111   ! www       213: # a3 -> a*3; )3 -> )*3
1.110     www       214:     $expression=~s/([a-zA-Z])(\d)/$1\*$2/gs;
1.111   ! www       215: # )a -> )*a
1.110     www       216:     $expression=~s/\)(\w)/\)\*$1/gs;
1.111   ! www       217: # 3&8 -> 3e8; 3&-4 -> 3e-4
1.110     www       218:     $expression=~s/(\d+)\&\(([\+\-]*\d+)\)/$1e$2/gs;
1.108     www       219:     return $expression;
                    220: }
1.73      albertel  221: 
1.37      albertel  222: sub caparesponse_check_list {
1.74      albertel  223:     my $response=$LONCAPA::CAPAresponse_args{'response'};
1.105     albertel  224:     my $result="Got response :".join(':',@LONCAPA::CAPAresponse_answer).":\n";
                    225:     &LONCAPA_INTERNAL_DEBUG("args ".join(':',%LONCAPA::CAPAresponse_args));
1.73      albertel  226:     my @responselist;
1.74      albertel  227:     my $type = $LONCAPA::CAPAresponse_args{'type'};
1.73      albertel  228:     $result.="Got type :$type:\n";
1.105     albertel  229:     if ($type ne '' && $#LONCAPA::CAPAresponse_answer > 0) {
1.104     albertel  230: 	(@responselist)=split(/,/,$response);
1.105     albertel  231: 	if (@responselist < @LONCAPA::CAPAresponse_answer) {
                    232: 	    return 'MISSING_ANSWER';
                    233: 	}
                    234: 	if (@responselist > @LONCAPA::CAPAresponse_answer) {
                    235: 	    return 'EXTRA_ANSWER';
                    236: 	}
1.73      albertel  237:     } else {
                    238: 	(@responselist)=($response);
                    239:     }
                    240:     $result.="Initial final response :$responselist['-1']:\n";
1.105     albertel  241:     my $unit;
1.73      albertel  242:     if ($type eq '' || $type eq 'float') {
                    243: 	#for numerical problems split off the unit
                    244: 	if ( $responselist['-1']=~ /(.*[^\s])\s+([^\s]+)/ ) {
                    245: 	    $responselist['-1']=$1;
                    246: 	    $unit=$2;
                    247: 	}
                    248:     }
1.82      albertel  249:     $result.="Final final response :$responselist['-1']:$unit:\n";
1.73      albertel  250:     $unit=~s/\s//;
1.105     albertel  251: 
1.106     albertel  252:     my ($awards, @msgs, $i);
1.105     albertel  253:     foreach my $thisanswer (@LONCAPA::CAPAresponse_answer) {
                    254: 	my ($msg,$aresult);
1.73      albertel  255: 	$result.="trying answer :$thisanswer:\n";
1.105     albertel  256: 	if (defined($thisanswer)) {
1.104     albertel  257: 	    if ($unit eq '') {
                    258: 		($aresult,$msg)=&caparesponse_check($thisanswer,
                    259: 						    $responselist[$i]);
                    260: 	    } else {
                    261: 		($aresult,$msg)=&caparesponse_check($thisanswer,
                    262: 						    $responselist[$i]." $unit");
                    263: 	    }
1.73      albertel  264: 	} else {
1.104     albertel  265: 	    $aresult='ERROR';
1.105     albertel  266: 	    $msg='answer was undefined';
1.73      albertel  267: 	}
1.105     albertel  268: 	&LONCAPA_INTERNAL_DEBUG("after if $aresult -- $msg");
1.104     albertel  269: 	my ($temp)=split(/:/, $aresult);
1.73      albertel  270: 	$awards.="$temp,";
                    271: 	$result.=$aresult;
                    272: 	push(@msgs,$msg);
1.106     albertel  273: 	$i++;
1.73      albertel  274:     }
1.104     albertel  275:     chop($awards);
1.73      albertel  276:     return ("$awards:\n$result",@msgs);
1.7       albertel  277: }
                    278: 
1.4       albertel  279: sub tex {
1.73      albertel  280:     if ( $external::target eq "tex" ) {
                    281: 	return $_[0];
                    282:     } else {
                    283: 	return $_[1];
                    284:     }
1.4       albertel  285: }
                    286: 
1.24      ng        287: sub var_in_tex {
1.73      albertel  288:     if ( $external::target eq "tex" ) {
                    289: 	return $_[0];
                    290:     } else {
                    291: 	return "";
                    292:     }
1.24      ng        293: }
                    294: 
1.4       albertel  295: sub web {
1.73      albertel  296:     if ( $external::target eq "tex" ) {
                    297: 	return $_[1];
1.26      ng        298:     } else {
1.73      albertel  299: 	if ( $external::target eq "web" || $external::target eq "answer") {
                    300: 	    return $_[2];
                    301: 	} else {
                    302: 	    return $_[0];
                    303: 	}
1.4       albertel  304:     }
                    305: }
                    306: 
1.24      ng        307: sub html {
1.73      albertel  308:     if ( $external::target eq "web" ) {
                    309: 	return shift;
                    310:     }
1.24      ng        311: }
                    312: 
1.1       harris41  313: sub hinton {
1.73      albertel  314:     return 0;
1.1       harris41  315: }
                    316: 
                    317: sub random {
1.61      albertel  318:     my ($start,$end,$step)=@_;
                    319:     if ( ! $hidden::RANDOMINIT ) {
                    320: 	if ($external::randomseed == 0) { $external::randomseed=1; }
                    321: 	if ($external::randomseed =~/,/) {
1.84      albertel  322: 	    my ($num1,$num2)=split(/,/,$external::randomseed);
                    323: 	    &random_set_seed(1,abs($num1));
                    324: 	} elsif ($external::randomseed =~/:/) {
                    325: 	    my ($num1,$num2)=split(/:/,$external::randomseed);
1.61      albertel  326: 	    &random_set_seed(abs($num1),abs($num2));
                    327: 	} else {
                    328: 	    &random_set_seed(1,int(abs($external::randomseed)));
                    329: 	}
                    330: 	&math_random_uniform();
                    331: 	$hidden::RANDOMINIT=1;
                    332:     }
                    333:     if (!defined($step)) { $step=1; }
                    334:     my $num=1+int(($end-$start)/$step);
                    335:     my $result=$start + int(&math_random_uniform() * $num)*$step;
                    336:     return $result;
1.1       harris41  337: }
                    338: 
1.26      ng        339: sub random_normal {
1.73      albertel  340:     my ($item_cnt,$seed,$av,$std_dev) = @_;
                    341:     my @oldseed=&random_get_seed();
                    342:     my @retArray;
                    343:     &random_set_seed_from_phrase($seed);
                    344:     @retArray=&math_random_normal($item_cnt,$av,$std_dev);
                    345:     &random_set_seed(@oldseed);
                    346:     return @retArray;
1.26      ng        347: }
                    348: 
                    349: sub random_beta {
1.73      albertel  350:     my ($item_cnt,$seed,$aa,$bb) = @_;
                    351:     my @oldseed=&random_get_seed();
                    352:     my @retArray;
                    353:     &random_set_seed_from_phrase($seed);
                    354:     @retArray=&math_random_beta($item_cnt,$aa,$bb);
                    355:     &random_set_seed(@oldseed);
                    356:     return @retArray;
1.26      ng        357: }
                    358: 
                    359: sub random_gamma {
1.73      albertel  360:     my ($item_cnt,$seed,$a,$r) = @_;
                    361:     my @oldseed=&random_get_seed();
                    362:     my @retArray;
                    363:     &random_set_seed_from_phrase($seed);
                    364:     @retArray=&math_random_gamma($item_cnt,$a,$r);
                    365:     &random_set_seed(@oldseed);
                    366:     return @retArray;
1.26      ng        367: }
                    368: 
                    369: sub random_exponential {
1.73      albertel  370:     my ($item_cnt,$seed,$av) = @_;
                    371:     my @oldseed=&random_get_seed();
                    372:     my @retArray;
                    373:     &random_set_seed_from_phrase($seed);
                    374:     @retArray=&math_random_exponential($item_cnt,$av);
                    375:     &random_set_seed(@oldseed);
                    376:     return @retArray;
1.26      ng        377: }
                    378: 
                    379: sub random_poisson {
1.73      albertel  380:     my ($item_cnt,$seed,$mu) = @_;
                    381:     my @oldseed=&random_get_seed();
                    382:     my @retArray;
                    383:     &random_set_seed_from_phrase($seed);
                    384:     @retArray=&math_random_poisson($item_cnt,$mu);
                    385:     &random_set_seed(@oldseed);
                    386:     return @retArray;
1.26      ng        387: }
                    388: 
                    389: sub random_chi {
1.73      albertel  390:     my ($item_cnt,$seed,$df) = @_;
                    391:     my @oldseed=&random_get_seed();
                    392:     my @retArray;
                    393:     &random_set_seed_from_phrase($seed);
                    394:     @retArray=&math_random_chi_square($item_cnt,$df);
                    395:     &random_set_seed(@oldseed);
                    396:     return @retArray;
1.26      ng        397: }
                    398: 
                    399: sub random_noncentral_chi {
1.73      albertel  400:     my ($item_cnt,$seed,$df,$nonc) = @_;
                    401:     my @oldseed=&random_get_seed();
                    402:     my @retArray;
                    403:     &random_set_seed_from_phrase($seed);
                    404:     @retArray=&math_random_noncentral_chi_square($item_cnt,$df,$nonc);
                    405:     &random_set_seed(@oldseed);
                    406:     return @retArray;
1.26      ng        407: }
                    408: 
                    409: sub random_f {
1.73      albertel  410:     my ($item_cnt,$seed,$dfn,$dfd) = @_;
                    411:     my @oldseed=&random_get_seed();
                    412:     my @retArray;
                    413:     &random_set_seed_from_phrase($seed);
                    414:     @retArray=&math_random_f($item_cnt,$dfn,$dfd);
                    415:     &random_set_seed(@oldseed);
                    416:     return @retArray;
1.26      ng        417: }
                    418: 
                    419: sub random_noncentral_f {
1.73      albertel  420:     my ($item_cnt,$seed,$dfn,$dfd,$nonc) = @_;
                    421:     my @oldseed=&random_get_seed();
                    422:     my @retArray;
                    423:     &random_set_seed_from_phrase($seed);
                    424:     @retArray=&math_random_noncentral_f($item_cnt,$dfn,$dfd,$nonc);
                    425:     &random_set_seed(@oldseed);
                    426:     return @retArray;
1.26      ng        427: }
                    428: 
                    429: sub random_multivariate_normal {
1.73      albertel  430:     my ($item_cnt,$seed,$mean,$covar) = @_;
                    431:     my @oldseed=&random_get_seed();
                    432:     &random_set_seed_from_phrase($seed);
1.87      albertel  433:     my @retArray=&math_random_multivariate_normal($item_cnt,@$mean,@$covar);
1.73      albertel  434:     &random_set_seed(@oldseed);
                    435:     return @retArray;
1.26      ng        436: }
                    437: 
                    438: sub random_multinomial {
1.73      albertel  439:     my ($item_cnt,$seed,@p) = @_;
                    440:     my @oldseed=&random_get_seed();
                    441:     my @retArray;
                    442:     &random_set_seed_from_phrase($seed);
1.87      albertel  443:     my @retArray=&math_random_multinomial($item_cnt,@p);
1.73      albertel  444:     &random_set_seed(@oldseed);
                    445:     return @retArray;
1.26      ng        446: }
                    447: 
                    448: sub random_permutation {
1.73      albertel  449:     my ($seed,@inArray) = @_;
                    450:     my @oldseed=&random_get_seed();
                    451:     my @retArray;
                    452:     &random_set_seed_from_phrase($seed);
                    453:     @retArray=&math_random_permutation(@inArray);
                    454:     &random_set_seed(@oldseed);
                    455:     return @retArray;
1.26      ng        456: }
                    457: 
                    458: sub random_uniform {
1.73      albertel  459:     my ($item_cnt,$seed,$low,$high) = @_;
                    460:     my @oldseed=&random_get_seed();
                    461:     my @retArray;
                    462:     &random_set_seed_from_phrase($seed);
                    463:     @retArray=&math_random_uniform($item_cnt,$low,$high);
                    464:     &random_set_seed(@oldseed);
                    465:     return @retArray;
1.26      ng        466: }
                    467: 
                    468: sub random_uniform_integer {
1.73      albertel  469:     my ($item_cnt,$seed,$low,$high) = @_;
                    470:     my @oldseed=&random_get_seed();
                    471:     my @retArray;
                    472:     &random_set_seed_from_phrase($seed);
                    473:     @retArray=&math_random_uniform_integer($item_cnt,$low,$high);
                    474:     &random_set_seed(@oldseed);
                    475:     return @retArray;
1.26      ng        476: }
                    477: 
                    478: sub random_binomial {
1.73      albertel  479:     my ($item_cnt,$seed,$nt,$p) = @_;
                    480:     my @oldseed=&random_get_seed();
                    481:     my @retArray;
                    482:     &random_set_seed_from_phrase($seed);
                    483:     @retArray=&math_random_binomial($item_cnt,$nt,$p);
                    484:     &random_set_seed(@oldseed);
                    485:     return @retArray;
1.26      ng        486: }
                    487: 
                    488: sub random_negative_binomial {
1.73      albertel  489:     my ($item_cnt,$seed,$ne,$p) = @_;
                    490:     my @oldseed=&random_get_seed();
                    491:     my @retArray;
                    492:     &random_set_seed_from_phrase($seed);
                    493:     @retArray=&math_random_negative_binomial($item_cnt,$ne,$p);
                    494:     &random_set_seed(@oldseed);
                    495:     return @retArray;
1.26      ng        496: }
                    497: 
1.103     albertel  498: sub abs { CORE::abs(shift) }
                    499: sub sin { CORE::sin(shift) }
                    500: sub cos { CORE::cos(shift) }
                    501: sub exp { CORE::exp(shift) }
                    502: sub int { CORE::int(shift) }
                    503: sub log { CORE::log(shift) }
                    504: sub atan2 { CORE::atan2($_[0],$_[1]) }
                    505: sub sqrt { CORE::sqrt(shift) }
1.23      ng        506: 
1.59      albertel  507: sub tan  { CORE::sin($_[0]) / CORE::cos($_[0]) }
1.21      harris41  508: #sub atan { atan2($_[0], 1); }
                    509: #sub acos { atan2(sqrt(1 - $_[0] * $_[0]), $_[0] ); }
                    510: #sub asin { atan2($_[0], sqrt(1- $_[0] * $_[0]) );  }
1.22      ng        511: 
1.59      albertel  512: sub log10 { CORE::log($_[0])/CORE::log(10); }
1.22      ng        513: 
1.20      harris41  514: sub factorial {
1.59      albertel  515:     my $input = CORE::int(shift);
1.20      harris41  516:     return "Error - unable to take factorial of an negative number ($input)" if $input < 0;
                    517:     return "Error - factorial result is greater than system limit ($input)" if $input > 170;
                    518:     return 1 if $input == 0;
                    519:     my $result = 1; 
                    520:     for (my $i=2; $i<=$input; $i++) { $result *= $i }
                    521:     return $result;
                    522: }
                    523: 
                    524: sub sgn {
                    525:     return -1 if $_[0] < 0;
                    526:     return 0 if $_[0] == 0;
                    527:     return 1 if $_[0] > 0;
                    528: }
                    529: 
                    530: sub min {
                    531:     my @sorted = sort { $a <=> $b || $a cmp $b } @_;
                    532:     return shift @sorted;
                    533: }
                    534: 
                    535: sub max {
                    536:     my @sorted = sort { $a <=> $b || $a cmp $b } @_;
                    537:     return pop @sorted;
                    538: }
1.1       harris41  539: 
1.20      harris41  540: sub roundto {
                    541:     my ($input,$n) = @_;
                    542:     return sprintf('%.'.$n.'f',$input);
                    543: }
                    544: 
                    545: sub to_string {
                    546:     my ($input,$n) = @_;
1.26      ng        547:     return sprintf($input) if $n eq "";
                    548:     $n = '.'.$n if $n !~ /^\./;
1.20      harris41  549:     return sprintf('%'.$n,$input) if $n ne "";
                    550: }
                    551: 
                    552: sub sub_string {
                    553:     my ($str,$start,$len) = @_;
                    554:     return substr($str,$start-1,$len);
                    555: }
1.1       harris41  556: 
                    557: sub pow   {return $_[0] ** $_[1]; }
1.59      albertel  558: sub ceil  {return (($_[0]-CORE::int($_[0]))== 0.0) ? $_[0] : (($_[0] > 0) ? (CORE::int($_[0])+ 1) : CORE::int($_[0])); }
                    559: sub floor  {return (($_[0]-CORE::int($_[0]))== 0.0) ? $_[0] : (($_[0] > 0) ? CORE::int($_[0]) : (CORE::int($_[0])-1)); }
1.27      ng        560: #sub floor {return int($_[0]); }
1.1       harris41  561: 
1.2       albertel  562: sub format {
1.73      albertel  563:     my ($value,$fmt)=@_;
1.81      albertel  564:     my ($dollarmode,$commamode,$alwaysperiod,$options);
                    565:     if ($fmt =~ /^([^\d]*)(.*)/) { $options=$1; $fmt=$2; } 
                    566:     #if ($options =~ /\$/) { $dollamode=1; }
                    567:     #if ($options =~ /,/)  { $commamode=1; }
1.82      albertel  568:     if ($options =~ /\./) { $alwaysperiod=1; }
1.99      ng        569:     my $result;
1.97      albertel  570:     if ($fmt=~/s$/i) {
                    571: 	$result=&format_significant_figures($value,$fmt);
                    572:     } else {
                    573: 	$fmt=~s/e/E/g;
1.99      ng        574: 	$result=sprintf('%.'.$fmt,$value);
1.97      albertel  575: 	if ($alwaysperiod && $fmt eq '0f') { $result .='.'; }
                    576: 	$result=~s/(E[+-]*)0/$1/;
                    577:     }
1.81      albertel  578:     #if ($dollarmode) {$result=&dollarformat($result);}
                    579:     #if ($commamode) {$result=&commaformat($result);}
1.73      albertel  580:     return $result;
1.46      albertel  581: }
                    582: 
1.75      albertel  583: sub chemparse {
                    584:     my ($reaction) = @_;
1.96      albertel  585:     my @tokens = split(/(\s\+|\->|<=>|<\-|\.)/,$reaction);
1.75      albertel  586:     my $formula = '';
                    587:     foreach my $token (@tokens) {
                    588: 	if ($token eq '->' ) {
                    589: 	    $formula .= '<m>\ensuremath{\rightarrow}</m> ';
                    590: 	    next;
                    591: 	}
1.96      albertel  592: 	if ($token eq '<-' ) {
                    593: 	    $formula .= '<m>\ensuremath{\leftarrow}</m> ';
                    594: 	    next;
                    595: 	}  
1.75      albertel  596: 	if ($token eq '<=>') {
                    597: 	    if ($external::target eq 'web' &&
                    598: 		&EXT('request.browser.unicode')) {
1.76      albertel  599: 		$formula .= '&#8652; ';
1.75      albertel  600: 	    } else {
                    601: 		$formula .= &web('<=> ','<m>\ensuremath{\rightleftharpoons}</m> ',
1.95      albertel  602: 				 '&lt;=&gt; ');
1.75      albertel  603: 	    }
                    604: 	    next;
                    605: 	}
1.96      albertel  606: 	if ($token eq '.') {
                    607: 	  $formula =~ s/(\&nbsp\;| )$//;
                    608: 	  $formula .= '&middot;';
                    609: 	  next;
                    610: 	}
                    611: 	$token =~ /^\s*([\d|\/]*(?:&frac\d\d)?)(.*)/;
1.90      albertel  612:         $formula .= $1 if ($1 ne '1');  # stoichiometric coefficient
1.75      albertel  613: 	
                    614: 	my $molecule = $2;
                    615: 	# subscripts
1.78      albertel  616: 	$molecule =~ s|(?<=[a-zA-Z\)\]\s])(\d+)|<sub>$1</sub>|g;
1.75      albertel  617: 	# superscripts
                    618: 	$molecule =~ s|\^(\d*[+\-]*)|<sup>$1</sup>|g;
                    619: 	# strip whitespace
                    620: 	$molecule =~ s/\s*//g;
                    621: 	# forced space
                    622: 	$molecule =~ s/_/ /g;
1.96      albertel  623: 	$molecule =~ s/-/&minus;/g;
1.75      albertel  624: 	$formula .= $molecule.'&nbsp;';
                    625:     }
                    626:     # get rid of trailing space
1.87      albertel  627:     $formula =~ s/(\&nbsp\;| )$//;
1.75      albertel  628:     return &xmlparse($formula);
                    629: }
                    630: 
1.46      albertel  631: sub prettyprint {
1.73      albertel  632:     my ($value,$fmt,$target)=@_;
                    633:     my $result;
                    634:     if (!$target) { $target = $external::target; }
1.75      albertel  635:     if ($fmt =~ /chem/i) { return(&chemparse($value)); }
1.81      albertel  636:     my ($dollarmode,$commamode,$alwaysperiod,$options);
                    637:     if ($fmt =~ /^([^\d]*)(.*)/) { $options=$1; $fmt=$2; } 
1.86      albertel  638:     if ($options =~ /\$/) { $dollarmode=1; }
1.81      albertel  639:     if ($options =~ /,/)  { $commamode=1; }
                    640:     if ($options =~ /\./) { $alwaysperiod=1; }
1.97      albertel  641:     if ($fmt=~/s$/i) {
                    642: 	$value=&format_significant_figures($value,$fmt);
                    643:     } elsif ($fmt) {
                    644: 	$value=sprintf('%.'.$fmt,$value);
                    645:     }
1.81      albertel  646:     if ($alwaysperiod && $fmt eq '0f') {
                    647: 	if ($target eq 'tex') {
                    648: 	    $value .='\\ensuremath{.}';
                    649: 	} else {
                    650: 	    $value .='.';
                    651: 	}
                    652:     }
1.73      albertel  653:     if ($value =~ /([0-9\.\-\+]+)E([0-9\-\+]+)/i ) {
                    654: 	my $frac=$1;
                    655: 	if ($dollarmode) { $frac=&dollarformat($frac); }
1.80      albertel  656: 	if ($commamode) { $frac=&commaformat($frac); }
1.73      albertel  657: 	my $exponent=$2;
                    658: 	$exponent=~s/^\+0*//;
                    659: 	$exponent=~s/^-0*/-/;
                    660: 	$exponent=~s/^-0*/-/;
                    661: 	if ($exponent eq '-') { undef($exponent); }
                    662: 	if ($exponent) {
                    663: 	    if ($target eq 'web') {
                    664: 		$result=$frac.'&#215;10<sup>'.$exponent.'</sup>';
                    665: 	    } elsif ($target eq 'tex') {
                    666: 		$result='\ensuremath{'.$frac.'\times 10^{'.$exponent.'}}';
                    667: 	    } else {
                    668: 		$result=$value;
                    669: 	    }
                    670: 	} else {
                    671: 	    $result=$frac;
                    672: 	}
                    673:     } else {
1.48      albertel  674: 	$result=$value;
1.86      albertel  675: 	if    ($dollarmode) { $result=&dollarformat($result,$target); }
                    676: 	elsif ($commamode)  { $result=&commaformat($result,$target); }
1.46      albertel  677:     }
1.73      albertel  678:     return $result;
1.48      albertel  679: }
                    680: 
1.80      albertel  681: sub commaformat {
1.73      albertel  682:     my ($number,$target) = @_;
                    683:     if ($number =~ /\./) {
1.102     albertel  684: 	while ($number =~ /([^0-9]*)([0-9]+)([^\.,][^\.,][^\.,])([,0-9]*\.[0-9]*)$/) {
                    685: 	    $number = $1.$2.','.$3.$4;
1.73      albertel  686: 	}
                    687:     } else {
1.102     albertel  688: 	while ($number =~ /^([^0-9]*)([0-9]+)([^,][^,][^,])([,0-9]*)$/) {
                    689: 	    $number = $1.$2.','.$3.$4;
1.73      albertel  690: 	}
                    691:     }
1.80      albertel  692:     return $number;
                    693: }
                    694: 
                    695: sub dollarformat {
                    696:     my ($number,$target) = @_;
                    697:     if (!$target) { $target = $external::target; }
                    698:     $number=&commaformat($number,$target);
1.73      albertel  699:     if ($target eq 'tex') {
                    700: 	$number='\$'.$number; #' stupid emacs
                    701:     } else {
                    702: 	$number='$'.$number; #' stupid emacs
                    703:     }
                    704:     return $number; 
1.2       albertel  705: }
1.5       albertel  706: 
1.97      albertel  707: # format of form ns or nS where n is an integer
                    708: sub format_significant_figures {
                    709:     my ($number,$format) = @_; 
                    710:     return '0' if ($number == 0);
                    711:     # extract number of significant figures needed
                    712:     my ($sig) = ($format =~ /(\d+)s/i);
                    713:     # arbitrary choice - suggestions ?? or throw error message?
                    714:     $sig = 3 if ($sig eq '');
                    715:     # save the minus sign
                    716:     my $sign = ($number < 0) ? '-' : '';
                    717:     $number = abs($number);
                    718:     # needed to correct for a number greater than 1 (or
                    719:     my $power = ($number < 1) ? 0 : 1;
                    720:     # could round up. Take the integer part of log10.
                    721:     my $x10 = int(log($number)/log(10));
                    722:     # find number with values left of decimal pt = # of sign figs.
                    723:     my $xsig = $number*10**($sig-$x10-$power);
                    724:     # get just digits left of decimal pt - also rounds off correctly
                    725:     my $xint  = sprintf('%.0f',$xsig);
                    726:     # save any trailing zero's
                    727:     my ($zeros) = ($xint =~ /(0+)$/);
                    728:     # return number to original magnitude
                    729:     my $numSig = $xint*10**($x10-$sig+$power);
                    730:     # insert trailing zero's if have decimal point
                    731:     $numSig =~ s/^(\d+)\.(\d+)(\e?(.*)?)$/$1\.$2$zeros$3/;
1.98      albertel  732:     # put a decimal pt for number ending with 0 and length = # of sig fig
                    733:     $numSig.='.' if (length($numSig) == $sig && $numSig =~ /0$/);
                    734:     if (length($numSig) < $sig) {
                    735: 	$numSig.='.'.substr($zeros,0,($sig-length($numSig)));
                    736:     }
1.97      albertel  737:     # return number with sign
                    738:     return $sign.$numSig;
                    739: 
                    740: }
                    741: 
1.5       albertel  742: sub map {
1.27      ng        743:     my ($phrase,$dest,$source)=@_;
1.51      albertel  744:     my @oldseed=&random_get_seed();
1.27      ng        745:     my @seed = &random_seed_from_phrase($phrase);
                    746:     &random_set_seed(@seed);
                    747:     my $destct = scalar(@$dest);
1.28      ng        748:     if (!$source) {
                    749: 	my @output;
                    750: 	my @idx = &math_random_permuted_index($destct);
                    751: 	my $ctr = 0;
                    752: 	while ($ctr < $destct) {
                    753: 	    $output[$ctr] = $$dest[$idx[$ctr]];
1.27      ng        754: 	    $ctr++;
1.28      ng        755: 	}
1.51      albertel  756:         &random_set_seed(@oldseed);
1.28      ng        757: 	return @output;
1.27      ng        758:     } else {
1.28      ng        759: 	my $num = scalar(@$source);
                    760: 	my @idx = &math_random_permuted_index($num);
                    761: 	my $ctr = 0;
                    762: 	my $tot = $num;
                    763: 	$tot = $destct if $destct < $num;
                    764: 	if (ref($$dest[0])) {
                    765: 	    while ($ctr < $tot) {
                    766: 		${$$dest[$ctr]} = $$source[$idx[$ctr]];
                    767: 	        $ctr++;
                    768:             }
                    769:         } else {
                    770: 	    while ($ctr < $tot) {
                    771: 		$$dest[$ctr] = $$source[$idx[$ctr]];
                    772: 		$ctr++;
                    773: 	    }
                    774: 	}
1.27      ng        775:     }
1.56      albertel  776:     &random_set_seed(@oldseed);
1.51      albertel  777:     return '';
1.27      ng        778: }
                    779: 
                    780: sub rmap {
                    781:     my ($phrase,$dest,$source)=@_;
1.51      albertel  782:     my @oldseed=&random_get_seed();
1.27      ng        783:     my @seed = &random_seed_from_phrase($phrase);
                    784:     &random_set_seed(@seed);
                    785:     my $destct = scalar(@$dest);
1.28      ng        786:     if (!$source) {
                    787: 	my @idx = &math_random_permuted_index($destct);
                    788: 	my $ctr = 0;
                    789: 	my @r_idx;
                    790: 	while ($ctr < $destct) {
                    791: 	    $r_idx[$idx[$ctr]] = $ctr;
                    792: 	    $ctr++;
                    793: 	}
                    794: 	my @output;
                    795: 	$ctr = 0;
                    796: 	while ($ctr < $destct) {
                    797: 	    $output[$ctr] = $$dest[$r_idx[$ctr]];
1.27      ng        798: 	    $ctr++;
1.28      ng        799: 	}
1.51      albertel  800:         &random_set_seed(@oldseed);
1.28      ng        801: 	return @output;
1.27      ng        802:     } else {
1.28      ng        803: 	my $num = scalar(@$source);
                    804: 	my @idx = &math_random_permuted_index($num);
                    805: 	my $ctr = 0;
                    806: 	my $tot = $num;
                    807: 	$tot = $destct if $destct < $num;
                    808: 	my @r_idx;
1.27      ng        809: 	while ($ctr < $tot) {
1.28      ng        810: 	    $r_idx[$idx[$ctr]] = $ctr;
1.27      ng        811: 	    $ctr++;
1.28      ng        812: 	}
                    813: 	$ctr = 0;
                    814: 	if (ref($$dest[0])) {
                    815: 	    while ($ctr < $tot) {
                    816: 		${$$dest[$ctr]} = $$source[$r_idx[$ctr]];
                    817: 	        $ctr++;
                    818:             }
                    819:         } else {
                    820: 	    while ($ctr < $tot) {
                    821: 		$$dest[$ctr] = $$source[$r_idx[$ctr]];
                    822: 		$ctr++;
                    823: 	    }
                    824: 	}
1.6       albertel  825:     }
1.51      albertel  826:     &random_set_seed(@oldseed);
                    827:     return '';
1.5       albertel  828: }
1.22      ng        829: 
1.23      ng        830: sub capa_id { return }
                    831: 
                    832: sub problem { return }
                    833: 
1.22      ng        834: sub name{
1.73      albertel  835:     my $fullname = &EXT('environment.lastname').', '.&EXT('environment.firstname').' '.&EXT('environment.middlename');
                    836:     $fullname = "" if $fullname eq ",  ";
                    837:     $fullname =~ s/\%2d/-/g;
                    838:     return $fullname;
1.22      ng        839: }
                    840: 
                    841: sub student_number { 
1.73      albertel  842:     my $id = &EXT('environment.id');
                    843:     $id = '' if $id eq "";
                    844:     return $id;
1.22      ng        845: }
                    846: 
                    847: sub class {
1.73      albertel  848:     my $course = &EXT('course.description');
                    849:     $course = '' if $course eq "";
                    850:     return $course;
1.22      ng        851: }
                    852: 
                    853: sub sec { 
1.73      albertel  854:     my $sec = &EXT('request.course.sec');
                    855:     $sec = '' if $sec eq "";
                    856:     return $sec;
1.22      ng        857: }
                    858: 
1.23      ng        859: sub open_date { 
1.73      albertel  860:     my @dc = split(/\s+/,localtime(&EXT('resource.0.opendate')));
                    861:     return '' if ($dc[0] eq "Wed" and $dc[2] == 31 and $dc[4] == 1969);
                    862:     my @hm = split(/:/,$dc[3]);
                    863:     my $ampm = " am";
                    864:     if ($hm[0] > 12) {
                    865: 	$hm[0]-=12;
                    866: 	$ampm = " pm";
                    867:     }
                    868:     return $dc[0].', '.$dc[1].' '.$dc[2].', '.$dc[4].' at '.$hm[0].':'.$hm[1].$ampm;
1.23      ng        869: }
                    870: 
                    871: sub due_date { 
1.73      albertel  872:     my @dc = split(/\s+/,localtime(&EXT('resource.0.duedate')));
                    873:     return '' if ($dc[0] eq "Wed" and $dc[2] == 31 and $dc[4] == 1969);
                    874:     my @hm = split(/:/,$dc[3]);
                    875:     my $ampm = " am";
                    876:     if ($hm[0] > 12) {
                    877: 	$hm[0]-=12;
                    878: 	$ampm = " pm";
                    879:     }
                    880:     return $dc[0].', '.$dc[1].' '.$dc[2].', '.$dc[4].' at '.$hm[0].':'.$hm[1].$ampm;
1.23      ng        881: }
                    882: 
                    883: sub answer_date { 
1.73      albertel  884:     my @dc = split(/\s+/,localtime(&EXT('resource.0.answerdate')));
                    885:     return '' if ($dc[0] eq "Wed" and $dc[2] == 31 and $dc[4] == 1969);
                    886:     my @hm = split(/:/,$dc[3]);
                    887:     my $ampm = " am";
                    888:     if ($hm[0] > 12) {
                    889: 	$hm[0]-=12;
                    890: 	$ampm = " pm";
                    891:     }
                    892:     return $dc[0].', '.$dc[1].' '.$dc[2].', '.$dc[4].' at '.$hm[0].':'.$hm[1].$ampm;
1.24      ng        893: }
                    894: 
                    895: sub array_moments {
1.73      albertel  896:     my @input=@_;
                    897:     my (@output,$N);
                    898:     $N=scalar (@input);
                    899:     $output[0]=$N;
                    900:     if ($N <= 1) {
                    901: 	$output[1]=$input[0];
                    902: 	$output[1]="Input array not defined" if ($N == 0);
                    903: 	$output[2]="variance undefined for N<=1";
                    904: 	$output[3]="skewness undefined for N<=1";
                    905: 	$output[4]="kurtosis undefined for N<=1";
                    906: 	return @output;
                    907:     }
                    908:     my $sum=0;
                    909:     foreach my $line (@input) {
                    910: 	$sum+=$line;
                    911:     }
                    912:     $output[1] = $sum/$N;
                    913:     my ($x,$sdev,$var,$skew,$kurt) = 0;
                    914:     foreach my $line (@input) {
                    915: 	$x=$line-$output[1];
                    916: 	$var+=$x**2;
                    917: 	$skew+=$x**3;
                    918: 	$kurt+=$x**4;
                    919:     }
                    920:     $output[2]=$var/($N-1);
                    921:     $sdev=CORE::sqrt($output[2]);
                    922:     if ($sdev == 0) {
                    923: 	$output[3]="inf-variance=0";
                    924: 	$output[4]="inf-variance=0";
                    925: 	return @output;
                    926:     }
                    927:     $output[3]=$skew/($sdev**3*$N);
                    928:     $output[4]=$kurt/($sdev**4*$N)-3;
1.24      ng        929:     return @output;
                    930: }
1.5       albertel  931: 
                    932: sub choose {
1.73      albertel  933:     my $num = $_[0];
                    934:     return $_[$num];
1.5       albertel  935: }
1.23      ng        936: 
1.101     albertel  937: #&sum1(1,$x,sub { &sum1($_[0],2*$_[0], sub { fact($_[0])**2 })});
                    938: #sub sum1 {
                    939: #    my ($start,$end,$sub)=@_;
                    940: #    my $sum=0;
                    941: #    for (my $i=$start;$i<=$end;$i++) {
                    942: #        $sum+=&$sub($i);
                    943: #    }
                    944: #    return $sum
                    945: #}
                    946: 
                    947: #&sum2('a',1,$x,'&sum2(\'b\',$a,2*$a, \'&factorial($b)**2\')');
                    948: #sub sum2 {
                    949: #    my ($varname,$start,$end,$line)=@_;
                    950: #    my $sum=0;
                    951: #    for (my $i=$start;$i<=$end;$i++) {
                    952: #	my $func=sub {
                    953: #	    eval("\$".$varname."=$i");
                    954: #	    eval($line);
                    955: #	};
                    956: #        $sum+=&$func($i);
                    957: #    }
                    958: #    return $sum
                    959: #}
                    960: 
1.49      albertel  961: # expiremental idea
                    962: sub proper_path {
1.73      albertel  963:     my ($path)=@_;
                    964:     if ( $external::target eq "tex" ) {
                    965: 	return '/home/httpd/html'.$path;
                    966:     } else {
                    967: 	return $path;
                    968:     }
1.49      albertel  969: }
1.23      ng        970: 

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