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version 1.23, 2001/05/30 21:49:13 version 1.47, 2002/05/31 22:19:06
Line 1 Line 1
 # file name (temp): default_homework   # The LearningOnline Network with CAPA 
 # used by lonxml::xmlparse() as input variable $safeinit to Apache::run::run()  # used by lonxml::xmlparse() as input variable $safeinit to Apache::run::run()
 #   
 #  #
 #init some globals  # $Id$
   #
   # Copyright Michigan State University Board of Trustees
   #
   # This file is part of the LearningOnline Network with CAPA (LON-CAPA).
   #
   # LON-CAPA is free software; you can redistribute it and/or modify
   # it under the terms of the GNU General Public License as published by
   # the Free Software Foundation; either version 2 of the License, or
   # (at your option) any later version.
   #
   # LON-CAPA is distributed in the hope that it will be useful,
   # but WITHOUT ANY WARRANTY; without even the implied warranty of
   # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
   # GNU General Public License for more details.
   #
   # You should have received a copy of the GNU General Public License
   # along with LON-CAPA; if not, write to the Free Software
   # Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
   #
   # /home/httpd/html/adm/gpl.txt
   #
   # http://www.lon-capa.org/
   #
 #  #
 # Guy Albertelli  # Guy Albertelli
 #  #
 # 05/25/2001 H. K. Ng  # 05/25/2001 H. K. Ng
   # 05/31/2001 H. K. Ng
   # 12/21/2001 Matthew
 #  #
 $RANDOMINIT=0;  #init some globals
   $hidden::RANDOMINIT=0;
 $pi=atan2(1,1)*4;  $pi=atan2(1,1)*4;
 $rad2deg=180.0/$pi;  $rad2deg=180.0/$pi;
 $deg2rad=$pi/180.0;  $deg2rad=$pi/180.0;
   $"=' ';
   
 sub caparesponse_check {  sub caparesponse_check {
   my $answer='';  #done    #not properly used yet: calc
   my $type='';    #done    #not to be used: $ans_fmt
     my ($answer,$type,$tol,$sig,$ans_fmt,$unit,$calc,$samples) =
       eval $_[1].
         ';return ($answer,$type,$tol,$sig,$ans_fmt,$unit,$calc,$samples);';
   
   my $tol_type=''; # gets it's value from whether tol has a % or not done    my $tol_type=''; # gets it's value from whether tol has a % or not done
   my $tol='';     #done  
   my $sig='';     #done lowerbnd,upperbnd  
   my $sig_lbound=''; #done    my $sig_lbound=''; #done
   my $sig_ubound=''; #done    my $sig_ubound=''; #done
   my $ans_fmt='';  
   my $units='';     #done  
   my $calc='';  
   my ($response,$expr)=@_;    my ($response,$expr)=@_;
     
   ($answer,$type,$tol,$sig,$ans_fmt,  
    $units,$calc) = eval $expr.';return $answer,$type,$tol,$sig,$ans_fmt,$units,$calc';  
   #type's definitons come from capaParser.h    #type's definitons come from capaParser.h
     my $message='';
     #remove leading and trailing whitespace
     if ($response=~ /^\s|\s$/) {
       $response=~ s:^\s+|\s+$::g;
       $message .="Removed ws now :$response:<br />";
     } else {
       $message .="no ws in :$response:<br />";
     }
   
   if ($type eq '' ) {    if ($type eq '' ) {
       $message .= "Didn't find a type :$type:$expr: defaulting<br />";
     if ( $answer eq ($answer *1.0)) { $type = 2;      if ( $answer eq ($answer *1.0)) { $type = 2;
     } else { $type = 3; }      } else { $type = 3; }
   } else {    } else {
Line 38  sub caparesponse_check { Line 72  sub caparesponse_check {
     } elsif ($type eq 'mc')    { $type = 5;      } elsif ($type eq 'mc')    { $type = 5;
     } elsif ($type eq 'fml')   { $type = 8;      } elsif ($type eq 'fml')   { $type = 8;
     } elsif ($type eq 'subj')  { $type = 7;      } elsif ($type eq 'subj')  { $type = 7;
       } elsif ($type eq 'float') { $type = 2;
       } elsif ($type eq 'int')   { $type = 1;
     } else { return "ERROR: Unknown type of answer: $type" }      } else { return "ERROR: Unknown type of answer: $type" }
   }    }
   
     my $points;
     my $id_list;
     #formula type setup the sample points
     if ($type eq '8') {
       ($id_list,$points)=split(/@/,$samples);
       $message.="Found :$points: points<br />";
     }
   if ($tol eq '') {    if ($tol eq '') {
     $tol=0.0;      $tol=0.0;
     $tol_type=1; #TOL_ABSOLUTE      $tol_type=1; #TOL_ABSOLUTE
Line 58  sub caparesponse_check { Line 101  sub caparesponse_check {
     $sig_ubound =15; #SIG_UB_DEFAULT      $sig_ubound =15; #SIG_UB_DEFAULT
   } else {    } else {
     ($sig_lbound,$sig_ubound) = split /,/,$sig;      ($sig_lbound,$sig_ubound) = split /,/,$sig;
       if (!$sig_lbound) {
         $sig_lbound = 0; #SIG_LB_DEFAULT
         $sig_ubound =15; #SIG_UB_DEFAULT
       }
       if (!$sig_ubound) { $sig_ubound=$sig_lbound; }
   }    }
   my $result = &caparesponse_capa_check_answer($response,$answer,$type,    my $result = &caparesponse_capa_check_answer($response,$answer,$type,
        $tol_type,$tol,         $tol_type,$tol,
        $sig_lbound,$sig_ubound,         $sig_lbound,$sig_ubound,
        $ans_fmt,$units,$calc);         $ans_fmt,$unit,$calc,$id_list,
          $points,$external::randomseed);
   
   if    ($result == '1') { $result='EXACT_ANS'; }     if    ($result == '1') { $result='EXACT_ANS'; } 
   elsif ($result == '2') { $result='APPROX_ANS'; }    elsif ($result == '2') { $result='APPROX_ANS'; }
Line 78  sub caparesponse_check { Line 127  sub caparesponse_check {
   elsif ($result =='12') { $result='WANTED_NUMERIC'; }    elsif ($result =='12') { $result='WANTED_NUMERIC'; }
   else  {$result = "ERROR: Unknown Result:$result:$@:";}    else  {$result = "ERROR: Unknown Result:$result:$@:";}
   
   return "$result:<br />Error $error:<br />Answer $answer:<br />Response $response:<br />$type|$tol|$tol_type|$sig:$sig_lbound:$sig_ubound|$units<br />";    return "$result:<br />Error $error:<br />Answer $answer:<br />Response $response:<br /> type-$type|$tol|$tol_type|$sig:$sig_lbound:$sig_ubound|$unit|<br />$message$expr";
   }
   
   sub get_array_args {
     my ($expr,$arg)=@_;
     # do these first, because who knows what varname the instructor might have used
     # but it probably isn't $CAPARESPONSE_CHECK_LIST_answer
     my $CAPARESPONSE_CHECK_LIST_answer = eval $expr.';return $'.$arg; #'
     my $GET_ARRAY_ARGS_result;
     my @GET_ARRAY_ARGS_list;
     if ($CAPARESPONSE_CHECK_LIST_answer =~ /^\s*[\$\@]/) {
       (@GET_ARRAY_ARGS_list) = eval $CAPARESPONSE_CHECK_LIST_answer;
     }
     $GET_ARRAY_ARGS_result.="error:$@:<br />";
     # if the eval fails just use what is in the answer exactly
     if (!defined(@GET_ARRAY_ARGS_list) || !defined($GET_ARRAY_ARGS_list[0])) {
       $GET_ARRAY_ARGS_result.="list zero is undefined<br />";
       $GET_ARRAY_ARGS_list[0]=$CAPARESPONSE_CHECK_LIST_answer;
     }
     return $GET_ARRAY_ARGS_result,@GET_ARRAY_ARGS_list;
 }  }
   
 sub caparesponse_check_list {  sub caparesponse_check_list {
   my ($response,$expr)=@_;    my ($response,$expr)=@_;
   my $result='';    my $result;
     my ($result,@list) = &get_array_args($expr,'answer');
   my $aresult='';    my $aresult='';
   my $current_answer;    my $current_answer;
   my $answer = eval $expr.';return $answer';    my $answers=join(':',@list);
   my (@list) = eval $answer;    $result.="Got response :$answers:<br />";
   my (@responselist)=split /,/,$response;    my @responselist;
     my $type =eval $expr.';return $answer;';
     if ($type ne '' && $#list > 0) {
       (@responselist)=split /,/,$response;
     } else {
       (@responselist)=($response);
     }
   my $unit='';    my $unit='';
   $result.="Final response :$responselist['-1']:<br />";    $result.="Initial final response :$responselist['-1']:<br />";
   if ( $responselist['-1']=~ /(.*[^\s])\s+([^\s]+)/ ) {    if ($type eq '') {
     $responselist['-1']=$1;      #for numerical problems split off the unit
     $unit=$2;      if ( $responselist['-1']=~ /(.*[^\s])\s+([^\s]+)/ ) {
         $responselist['-1']=$1;
         $unit=$2;
       }
   }    }
   $result.="Final response :$responselist['-1']:<br />";    $result.="Final final response :$responselist['-1']:<br />";
     $result.=":$#list: answers<br />";
   $unit=~s/\s//;    $unit=~s/\s//;
   my $i=0;    my $i=0;
   my $awards='';    my $awards='';
   for ($i=0; $i<@list;$i++) {    for ($i=0; $i<@list;$i++) {
       $result.="trying answer :$list[$i]:<br />";
     if ($unit eq '') {      if ($unit eq '') {
       $aresult=&caparesponse_check($responselist[$i],        $aresult=&caparesponse_check($responselist[$i],
      $expr.';my $answer='.$list[$i].';');       $expr.';my $answer=\''.$list[$i].'\';');
     } else {      } else {
       $aresult=&caparesponse_check($responselist[$i]." $unit",        $aresult=&caparesponse_check($responselist[$i]." $unit",
    $expr.';my $answer='.$list[$i].';');     $expr.';my $answer=\''.$list[$i].'\';');
     }      }
     my ($temp)=split /:/, $aresult;      my ($temp)=split /:/, $aresult;
     $awards.="$temp,";      $awards.="$temp,";
Line 123  sub tex { Line 203  sub tex {
   }    }
 }  }
   
   sub var_in_tex {
     if ( $external::target eq "tex" ) {
       return @_[0];
     } else {
       return "";
     }
   }
   
 sub web {  sub web {
   if ( $external::target eq "tex" ) {    if ( $external::target eq "tex" ) {
     return @_[1];      return @_[1];
   } else {    } else {
     if ( $external::target eq "web") {      if ( $external::target eq "web" || $external::target eq "answer") {
       return @_[0];  
     } else {  
       return @_[2];        return @_[2];
       } else {
         return @_[0];
     }      }
   }    }
 }  }
   
   sub html {
     if ( $external::target eq "web" ) {
       return shift;
     }
   }
   
 sub problem {  sub problem {
   return '1';    return '1';
 }  }
Line 145  sub hinton { Line 239  sub hinton {
   
 sub random {  sub random {
   my ($start,$end,$step)=@_;    my ($start,$end,$step)=@_;
   if ( ! $RANDOMINIT ) { srand($external::randomseed); $RANDOMINIT=1; }    if ( ! $hidden::RANDOMINIT ) {
       srand($external::randomseed);
       $hidden::RANDOMINIT=1;
     }
     if (!defined($step)) { $step=1; }
   my $num=1+int(($end-$start)/$step);    my $num=1+int(($end-$start)/$step);
   my $result=$start + int(rand() * $num)*$step;    my $result=$start + int(rand() * $num)*$step;
   return $result;    return $result;
 }  }
   
   sub random_normal {
     my ($item_cnt,$seed,$av,$std_dev) = @_;
     my @retArray;
     &random_set_seed_from_phrase($seed);
     @retArray=&math_random_normal($item_cnt,$av,$std_dev);
     return @retArray;
   }
   
   sub random_beta {
     my ($item_cnt,$seed,$aa,$bb) = @_;
     my @retArray;
     &random_set_seed_from_phrase($seed);
     @retArray=&math_random_beta($item_cnt,$aa,$bb);
     return @retArray;
   }
   
   sub random_gamma {
     my ($item_cnt,$seed,$a,$r) = @_;
     my @retArray;
     &random_set_seed_from_phrase($seed);
     @retArray=&math_random_gamma($item_cnt,$a,$r);
     return @retArray;
   }
   
   sub random_exponential {
     my ($item_cnt,$seed,$av) = @_;
     my @retArray;
     &random_set_seed_from_phrase($seed);
     @retArray=&math_random_exponential($item_cnt,$av);
     return @retArray;
   }
   
   sub random_poisson {
     my ($item_cnt,$seed,$mu) = @_;
     my @retArray;
     &random_set_seed_from_phrase($seed);
     @retArray=&math_random_poisson($item_cnt,$mu);
     return @retArray;
   }
   
   sub random_chi {
     my ($item_cnt,$seed,$df) = @_;
     my @retArray;
     &random_set_seed_from_phrase($seed);
     @retArray=&math_random_chi_square($item_cnt,$df);
     return @retArray;
   }
   
   sub random_noncentral_chi {
     my ($item_cnt,$seed,$df,$nonc) = @_;
     my @retArray;
     &random_set_seed_from_phrase($seed);
     @retArray=&math_random_noncentral_chi_square($item_cnt,$df,$nonc);
     return @retArray;
   }
   
   sub random_f {
     my ($item_cnt,$seed,$dfn,$dfd) = @_;
     my @retArray;
     &random_set_seed_from_phrase($seed);
     @retArray=&math_random_f($item_cnt,$dfn,$dfd);
     return @retArray;
   }
   
   sub random_noncentral_f {
     my ($item_cnt,$seed,$dfn,$dfd,$nonc) = @_;
     my @retArray;
     &random_set_seed_from_phrase($seed);
     @retArray=&math_random_noncentral_f($item_cnt,$dfn,$dfd,$nonc);
     return @retArray;
   }
   
   sub random_multivariate_normal {
     my ($item_cnt,$seed,$mean,$covar) = @_;
     &random_set_seed_from_phrase($seed);
     @retArray=&math_random_multivariate_normal($item_cnt,@$mean,@$covar);
     return @retArray;
   }
   
   sub random_multinomial {
     my ($item_cnt,$seed,@p) = @_;
     my @retArray;
     &random_set_seed_from_phrase($seed);
     @retArray=&math_random_multinomial($item_cnt,@p);
     return @retArray;
   }
   
   sub random_permutation {
     my ($seed,@inArray) = @_;
     my @retArray;
     &random_set_seed_from_phrase($seed);
     @retArray=&math_random_permutation(@inArray);
     return @retArray;
   }
   
   sub random_uniform {
     my ($item_cnt,$seed,$low,$high) = @_;
     my @retArray;
     &random_set_seed_from_phrase($seed);
     @retArray=&math_random_uniform($item_cnt,$low,$high);
     return @retArray;
   }
   
   sub random_uniform_integer {
     my ($item_cnt,$seed,$low,$high) = @_;
     my @retArray;
     &random_set_seed_from_phrase($seed);
     @retArray=&math_random_uniform_integer($item_cnt,$low,$high);
     return @retArray;
   }
   
   sub random_binomial {
     my ($item_cnt,$seed,$nt,$p) = @_;
     my @retArray;
     &random_set_seed_from_phrase($seed);
     @retArray=&math_random_binomial($item_cnt,$nt,$p);
     return @retArray;
   }
   
   sub random_negative_binomial {
     my ($item_cnt,$seed,$ne,$p) = @_;
     my @retArray;
     &random_set_seed_from_phrase($seed);
     @retArray=&math_random_negative_binomial($item_cnt,$ne,$p);
     return @retArray;
   }
   
 sub abs { abs(shift) }  sub abs { abs(shift) }
 sub sin { sin(shift) }  sub sin { sin(shift) }
 sub cos { cos(shift) }  sub cos { cos(shift) }
Line 193  sub max { Line 418  sub max {
     return pop @sorted;      return pop @sorted;
 }  }
   
 sub html {  
   if ( $external::target eq "web" ) {  
     return @_[0];  
   }  
 }  
   
 sub roundto {  sub roundto {
     my ($input,$n) = @_;      my ($input,$n) = @_;
     return sprintf('%.'.$n.'f',$input);      return sprintf('%.'.$n.'f',$input);
Line 206  sub roundto { Line 425  sub roundto {
   
 sub to_string {  sub to_string {
     my ($input,$n) = @_;      my ($input,$n) = @_;
     return sprintf('%'.$n,$input) if $n ne "";  
     return sprintf($input) if $n eq "";      return sprintf($input) if $n eq "";
       $n = '.'.$n if $n !~ /^\./;
       return sprintf('%'.$n,$input) if $n ne "";
 }  }
   
 sub sub_string {  sub sub_string {
Line 216  sub sub_string { Line 436  sub sub_string {
 }  }
   
 sub pow   {return $_[0] ** $_[1]; }  sub pow   {return $_[0] ** $_[1]; }
 sub ceil  {return (($_[0]-int($_[0]))== 0.0) ? $_[0] : (int($_[0])+ 1); }  sub ceil  {return (($_[0]-int($_[0]))== 0.0) ? $_[0] : (($_[0] > 0) ? (int($_[0])+ 1) : int($_[0])); }
 sub floor {return int($_[0]);  }  sub floor  {return (($_[0]-int($_[0]))== 0.0) ? $_[0] : (($_[0] > 0) ? int($_[0]) : (int($_[0])-1)); }
   #sub floor {return int($_[0]); }
   
 sub format {  sub format {
   my ($value,$fmt)=@_;    my ($value,$fmt)=@_;
   return sprintf('%.'.$fmt,$value);    return sprintf('%.'.$fmt,$value);
 }  }
   
 sub map {  sub prettyprint {
   my $num = $#_/2;    my ($value,$fmt)=@_;
   my $i;    my $result;
   my @used;    if ($fmt) { $value=sprintf('%.'.$fmt,$value); }
   my @permutation;    if ($value =~ /([0-9\.\-\+]+)E([0-9\-\+]+)/ ) {
   for ($i=0; $i < $num;) {      my $frac=$1;
     $rand = &random(1,$num,1);      my $exponent=$2;
     if ( $used[$rand] == '0' ) {      $exponent=~s/^\+0*//;
       $i++;      if (!$exponent) { return $frac; }
       $used[$rand]='1';      if ($external::target eq 'web') {
       $permutation[$i]=$rand;        $result=$frac.'&#215;10<sup>'.$exponent.'</sup>';
       } elsif ($external::target eq 'tex') {
         $result='\ensuremath{'.$frac.'\times 10^{'.$exponent.'}}';
       } else {
         $result=$value;
     }      }
     } else {
       $result=$value;
   }    }
   for ( $i=1 ; $i<$num+1 ; $i++ ) {    return $result;
     ${$_[$permutation[$i]]}=$_[$i+$num]  }
   }  
   sub map {
       my ($phrase,$dest,$source)=@_;
       my @seed = &random_seed_from_phrase($phrase);
       &random_set_seed(@seed);
       my $destct = scalar(@$dest);
       if (!$source) {
    my @output;
    my @idx = &math_random_permuted_index($destct);
    my $ctr = 0;
    while ($ctr < $destct) {
       $output[$ctr] = $$dest[$idx[$ctr]];
       $ctr++;
    }
    return @output;
       } else {
    my $num = scalar(@$source);
    my @idx = &math_random_permuted_index($num);
    my $ctr = 0;
    my $tot = $num;
    $tot = $destct if $destct < $num;
    if (ref($$dest[0])) {
       while ($ctr < $tot) {
    ${$$dest[$ctr]} = $$source[$idx[$ctr]];
           $ctr++;
               }
           } else {
       while ($ctr < $tot) {
    $$dest[$ctr] = $$source[$idx[$ctr]];
    $ctr++;
       }
    }
       }
   }
   
   sub rmap {
       my ($phrase,$dest,$source)=@_;
       my @seed = &random_seed_from_phrase($phrase);
       &random_set_seed(@seed);
       my $destct = scalar(@$dest);
       if (!$source) {
    my @idx = &math_random_permuted_index($destct);
    my $ctr = 0;
    my @r_idx;
    while ($ctr < $destct) {
       $r_idx[$idx[$ctr]] = $ctr;
       $ctr++;
    }
    my @output;
    $ctr = 0;
    while ($ctr < $destct) {
       $output[$ctr] = $$dest[$r_idx[$ctr]];
       $ctr++;
    }
    return @output;
       } else {
    my $num = scalar(@$source);
    my @idx = &math_random_permuted_index($num);
    my $ctr = 0;
    my $tot = $num;
    $tot = $destct if $destct < $num;
    my @r_idx;
    while ($ctr < $tot) {
       $r_idx[$idx[$ctr]] = $ctr;
       $ctr++;
    }
    $ctr = 0;
    if (ref($$dest[0])) {
       while ($ctr < $tot) {
    ${$$dest[$ctr]} = $$source[$r_idx[$ctr]];
           $ctr++;
               }
           } else {
       while ($ctr < $tot) {
    $$dest[$ctr] = $$source[$r_idx[$ctr]];
    $ctr++;
       }
    }
       }
 }  }
   
 sub capa_id { return }  sub capa_id { return }
Line 249  sub problem { return } Line 554  sub problem { return }
 sub name{  sub name{
   my $fullname = &EXT('environment.lastname').', '.&EXT('environment.firstname').' '.&EXT('environment.middlename');    my $fullname = &EXT('environment.lastname').', '.&EXT('environment.firstname').' '.&EXT('environment.middlename');
   $fullname = "" if $fullname eq ",  ";    $fullname = "" if $fullname eq ",  ";
   $fullname =~ s/\%2d/-/;    $fullname =~ s/\%2d/-/g;
   return $fullname;    return $fullname;
 }  }
   
Line 273  sub sec { Line 578  sub sec {
   
 sub open_date {   sub open_date { 
   my @dc = split(/\s+/,localtime(&EXT('resource.0.opendate')));    my @dc = split(/\s+/,localtime(&EXT('resource.0.opendate')));
   return $dc[0].', '.$dc[1].' '.$dc[2].', '.$dc[4].' at '.$dc[3];    return '' if ($dc[0] eq "Wed" and $dc[2] == 31 and $dc[4] == 1969);
     my @hm = split(/:/,$dc[3]);
     my $ampm = " am";
     if ($hm[0] > 12) {
       $hm[0]-=12;
       $ampm = " pm";
     }
     return $dc[0].', '.$dc[1].' '.$dc[2].', '.$dc[4].' at '.$hm[0].':'.$hm[1].$ampm;
 }  }
   
 sub due_date {   sub due_date { 
   my @dc = split(/\s+/,localtime(&EXT('resource.0.duedate')));    my @dc = split(/\s+/,localtime(&EXT('resource.0.duedate')));
   return $dc[0].', '.$dc[1].' '.$dc[2].', '.$dc[4].' at '.$dc[3];    return '' if ($dc[0] eq "Wed" and $dc[2] == 31 and $dc[4] == 1969);
     my @hm = split(/:/,$dc[3]);
     my $ampm = " am";
     if ($hm[0] > 12) {
       $hm[0]-=12;
       $ampm = " pm";
     }
     return $dc[0].', '.$dc[1].' '.$dc[2].', '.$dc[4].' at '.$hm[0].':'.$hm[1].$ampm;
   #  return $dc[0].', '.$dc[1].' '.$dc[2].', '.$dc[4].' at '.$dc[3];
 }  }
   
 sub answer_date {   sub answer_date { 
   my @dc = split(/\s+/,localtime(&EXT('resource.0.answerdate')));    my @dc = split(/\s+/,localtime(&EXT('resource.0.answerdate')));
   return $dc[0].', '.$dc[1].' '.$dc[2].', '.$dc[4].' at '.$dc[3];    return '' if ($dc[0] eq "Wed" and $dc[2] == 31 and $dc[4] == 1969);
  }    my @hm = split(/:/,$dc[3]);
     my $ampm = " am";
     if ($hm[0] > 12) {
       $hm[0]-=12;
       $ampm = " pm";
     }
     return $dc[0].', '.$dc[1].' '.$dc[2].', '.$dc[4].' at '.$hm[0].':'.$hm[1].$ampm;
   #  return $dc[0].', '.$dc[1].' '.$dc[2].', '.$dc[4].' at '.$dc[3];
   }
   
   sub array_moments {
     my @input=@_;
     my (@output,$N);
     $N=scalar (@input);
     $output[0]=$N;
     if ($N <= 1) {
       $output[1]=$input[0];
       $output[1]="Input array not defined" if ($N == 0);
       $output[2]="variance undefined for N<=1";
       $output[3]="skewness undefined for N<=1";
       $output[4]="kurtosis undefined for N<=1";
       return @output;
     }
     my $sum=0;
     foreach my $line (@input) {
       $sum+=$line;
     }
     $output[1] = $sum/$N;
     my ($x,$sdev,$var,$skew,$kurt) = 0;
     foreach my $line (@input) {
       $x=$line-$output[1];
       $var+=$x**2;
       $skew+=$x**3;
       $kurt+=$x**4;
     }
     $output[2]=$var/($N-1);
     $sdev=sqrt($output[2]);
     if ($sdev == 0) {
        $output[3]="inf-variance=0";
        $output[4]="inf-variance=0";
        return @output;
     }
     $output[3]=$skew/($sdev**3*$N);
     $output[4]=$kurt/($sdev**4*$N)-3;
     return @output;
   }
   
 sub choose {  sub choose {
   my $num = $_[0];    my $num = $_[0];
   return $_[$num];    return $_[$num];
 }  }
   
 #$external::randomseed=time;  
 #$a=2;  
 #$b=2;  
 #$c=2;  
 #&map(1,\$a,\$b,\$c,3,4,5);  
 #print $a."\n".$b."\n";  
   
   
   
   
   
   
Removed from v.1.23  
changed lines
  Added in v.1.47

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