--- loncom/homework/default_homework.lcpm	2000/10/25 22:02:53	1.7
+++ loncom/homework/default_homework.lcpm	2001/07/13 14:49:28	1.30
@@ -1,58 +1,157 @@
-# file name (temp): default_homework 
+# file name (temp): default_homework
 # used by lonxml::xmlparse() as input variable $safeinit to Apache::run::run()
-# 
 #
+# Guy Albertelli
+#
+# 05/25/2001 H. K. Ng
+# 05/31/2001 H. K. Ng
+#
+#init some globals
 $RANDOMINIT=0;
+$pi=atan2(1,1)*4;
+$rad2deg=180.0/$pi;
+$deg2rad=$pi/180.0;
 
 sub caparesponse_check {
-  my $answer='';
-  my $type='';
-  my $tol_type='';
-  my $tolerance='';
-  my $sig_lbound='';
-  my $sig_ubound='';
+  my $answer='';  #done
+  my $type='';    #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_ubound=''; #done
   my $ans_fmt='';
-  my $unit_str='';
+  my $unit='';     #done
   my $calc='';
   my ($response,$expr)=@_;
   
-  ($answer,$type,$tol_type,$tolerance,$sig_lbound,$sig_ubound,$ans_fmt,
-   $unit_str,$calc) = eval $expr.'return $answer,$type,$tol_type,$tolerance,$sig_lbound,$sig_ubound,$ans_fmt,$unit_str,$calc';
+  ($answer,$type,$tol,$sig,$ans_fmt,
+   $unit,$calc) = eval $expr.';return $answer,$type,$tol,$sig,$ans_fmt,$unit,$calc';
+  #type's definitons come from capaParser.h
+  if ($type eq '' ) {
+    if ( $answer eq ($answer *1.0)) { $type = 2;
+    } else { $type = 3; }
+  } else {
+         if ($type eq 'cs')    { $type = 4;
+    } elsif ($type eq 'ci')    { $type = 3;
+    } elsif ($type eq 'mc')    { $type = 5;
+    } elsif ($type eq 'fml')   { $type = 8;
+    } elsif ($type eq 'subj')  { $type = 7;
+    } else { return "ERROR: Unknown type of answer: $type" }
+  }
+
+  if ($tol eq '') {
+    $tol=0.0;
+    $tol_type=1; #TOL_ABSOLUTE
+  } else {
+    if ($tol =~ /%$/) {
+      chop $tol;
+      $tol_type=2; #TOL_PERCENTAGE
+    } else {
+      $tol_type=1; #TOL_ABSOLUTE
+    }
+  }
+
+  if ($sig eq '') {
+    $sig_lbound = 0; #SIG_LB_DEFAULT
+    $sig_ubound =15; #SIG_UB_DEFAULT
+  } else {
+    ($sig_lbound,$sig_ubound) = split /,/,$sig;
+  }
   my $result = &caparesponse_capa_check_answer($response,$answer,$type,
-					       $tol_type,$tolerance,
+					       $tol_type,$tol,
 					       $sig_lbound,$sig_ubound,
-					       $ans_fmt, $unit_str,$calc);
-  return ":$result:$response:$answer:";
+					       $ans_fmt,$unit,$calc);
+
+  if    ($result == '1') { $result='EXACT_ANS'; } 
+  elsif ($result == '2') { $result='APPROX_ANS'; }
+  elsif ($result == '3') { $result='SIG_FAIL'; }
+  elsif ($result == '4') { $result='UNIT_FAIL'; }
+  elsif ($result == '5') { $result='NO_UNIT'; }
+  elsif ($result == '6') { $result='UNIT_OK'; }
+  elsif ($result == '7') { $result='INCORRECT'; }
+  elsif ($result == '8') { $result='UNIT_NOTNEEDED'; }
+  elsif ($result == '9') { $result='ANS_CNT_NOT_MATCH'; }
+  elsif ($result =='10') { $result='SUB_RECORDED'; }
+  elsif ($result =='11') { $result='BAD_FORMULA'; }
+  elsif ($result =='12') { $result='WANTED_NUMERIC'; }
+  else  {$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 />";
+}
+
+sub caparesponse_check_list {
+  my ($response,$expr)=@_;
+  # 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 $answer';
+  my (@list) = eval $CAPARESPONSE_CHECK_LIST_answer;
+  my $result='';
+  my $aresult='';
+  my $current_answer;
+  my (@responselist)=split /,/,$response;
+  my $unit='';
+  $result.="Final response :$responselist['-1']:<br />";
+  if ( $responselist['-1']=~ /(.*[^\s])\s+([^\s]+)/ ) {
+    $responselist['-1']=$1;
+    $unit=$2;
+  }
+  $result.="Final response :$responselist['-1']:<br />";
+  $unit=~s/\s//;
+  my $i=0;
+  my $awards='';
+  for ($i=0; $i<@list;$i++) {
+    if ($unit eq '') {
+      $aresult=&caparesponse_check($responselist[$i],
+			     $expr.';my $answer='.$list[$i].';');
+    } else {
+      $aresult=&caparesponse_check($responselist[$i]." $unit",
+				   $expr.';my $answer='.$list[$i].';');
+    }
+    my ($temp)=split /:/, $aresult;
+    $awards.="$temp,";
+    $result.=$aresult;
+  }
+  chop $awards;
+  return "$awards:<br />$result";
 }
 
 sub tex {
   if ( $external::target eq "tex" ) {
-    #$SCRIPT_RESULT.=@_[0];
     return @_[0];
   } else {
-    #$SCRIPT_RESULT.=@_[1];
     return @_[1];
   }
 }
 
+sub var_in_tex {
+  if ( $external::target eq "tex" ) {
+    return @_[0];
+  } else {
+    return "";
+  }
+}
+
 sub web {
   if ( $external::target eq "tex" ) {
-    #$SCRIPT_RESULT.=@_[1];
     return @_[1];
   } else {
     if ( $external::target eq "web") {
-      #$SCRIPT_RESULT.=@_[0];
-      return @_[0];
-    } else {
-      #$SCRIPT_RESULT.=@_[2];
       return @_[2];
+    } else {
+      return @_[0];
     }
   }
 }
 
+sub html {
+  if ( $external::target eq "web" ) {
+    return shift;
+  }
+}
+
 sub problem {
-  $SCRIPT_RESULT.='1';
-  return '';
+  return '1';
 }
 
 sub hinton {
@@ -67,52 +166,396 @@ sub random {
   return $result;
 }
 
-sub tan  { sin($_[0]) / cos($_[0]) }
-sub acos { atan2(sqrt(1 - $_[0] * $_[0]), $_[0] ); }
-sub asin { atan2($_[0], sqrt(1- $_[0] * $_[0]) );  }
+sub random_normal {
+  my ($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 html {
-  if ( $external::target eq "web" ) {
-    #$SCRIPT_RESULT.=@_[0];
-    return @_[0];
+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) = @_;
+  return "Number of deviates must be greater than 0" if $item_cnt <= 0;
+  my (@covar,@retArray);
+  my $ind = 0;
+  while ($ind<$item_cnt) {
+     push @covar, pop (@mean);
+     $ind++;
   }
+  &random_set_seed_from_phrase($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 sin { sin(shift) }
+sub cos { cos(shift) }
+sub exp { exp(shift) }
+sub int { int(shift) }
+sub log { log(shift) }
+sub atan2 { atan2($_[0],$_[1]) }
+sub sqrt { sqrt(shift) }
+
+sub tan  { sin($_[0]) / cos($_[0]) }
+#sub atan { atan2($_[0], 1); }
+#sub acos { atan2(sqrt(1 - $_[0] * $_[0]), $_[0] ); }
+#sub asin { atan2($_[0], sqrt(1- $_[0] * $_[0]) );  }
+
+sub log10 { log($_[0])/log(10); }
+
+sub factorial {
+    my $input = int(shift);
+    return "Error - unable to take factorial of an negative number ($input)" if $input < 0;
+    return "Error - factorial result is greater than system limit ($input)" if $input > 170;
+    return 1 if $input == 0;
+    my $result = 1; 
+    for (my $i=2; $i<=$input; $i++) { $result *= $i }
+    return $result;
+}
+
+sub sgn {
+    return -1 if $_[0] < 0;
+    return 0 if $_[0] == 0;
+    return 1 if $_[0] > 0;
+}
+
+sub min {
+    my @sorted = sort { $a <=> $b || $a cmp $b } @_;
+    return shift @sorted;
+}
+
+sub max {
+    my @sorted = sort { $a <=> $b || $a cmp $b } @_;
+    return pop @sorted;
+}
+
+sub roundto {
+    my ($input,$n) = @_;
+    return sprintf('%.'.$n.'f',$input);
+}
+
+sub to_string {
+    my ($input,$n) = @_;
+    return sprintf($input) if $n eq "";
+    $n = '.'.$n if $n !~ /^\./;
+    return sprintf('%'.$n,$input) if $n ne "";
+}
+
+sub sub_string {
+    my ($str,$start,$len) = @_;
+    return substr($str,$start-1,$len);
+}
 
 sub pow   {return $_[0] ** $_[1]; }
-sub ceil  {return (($_[0]-int($_[0]))== 0.0) ? $_[0] : (int($_[0])+ 1); }
-sub floor {return int($_[0]);  }
+sub ceil  {return (($_[0]-int($_[0]))== 0.0) ? $_[0] : (($_[0] > 0) ? (int($_[0])+ 1) : int($_[0])); }
+sub floor  {return (($_[0]-int($_[0]))== 0.0) ? $_[0] : (($_[0] > 0) ? int($_[0]) : (int($_[0])-1)); }
+#sub floor {return int($_[0]); }
 
 sub format {
   my ($value,$fmt)=@_;
-  $SCRIPT_RESULT.=sprintf('%.'.$fmt,$value);
+  return sprintf('%.'.$fmt,$value);
 }
 
 sub map {
-  my $num = $#_/2;
-  my $i;
-  my @used;
-  my @permutation;
-  for ($i=0; $i < $num;) {
-    $rand = &random(1,$num,1);
-    if ( $used[$rand] == '0' ) {
-      $i++;
-      $used[$rand]='1';
-      $permutation[$i]=$rand;
+    my ($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 problem { return }
+
+sub name{
+  my $fullname = &EXT('environment.lastname').', '.&EXT('environment.firstname').' '.&EXT('environment.middlename');
+  $fullname = "" if $fullname eq ",  ";
+  $fullname =~ s/\%2d/-/g;
+  return $fullname;
+}
+
+sub student_number { 
+  my $id = &EXT('environment.id');
+  $id = '' if $id eq "";
+  return $id;
+}
+
+sub class {
+  my $course = &EXT('course.description');
+  $course = '' if $course eq "";
+  return $course;
+}
+
+sub sec { 
+  my $sec = &EXT('request.course.sec');
+  $sec = '' if $sec eq "";
+  return $sec;
+}
+
+sub open_date { 
+  my @dc = split(/\s+/,localtime(&EXT('resource.0.opendate')));
+  return '' if ($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].$ampm;
+}
+
+sub due_date { 
+  my @dc = split(/\s+/,localtime(&EXT('resource.0.duedate')));
+  return '' if ($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 '.$dc[3];
+}
+
+sub answer_date { 
+  my @dc = split(/\s+/,localtime(&EXT('resource.0.answerdate')));
+  return '' if ($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";
   }
-  for ( $i=1 ; $i<$num+1 ; $i++ ) {
-    ${$_[$permutation[$i]]}=$_[$i+$num]
+  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 {
   my $num = $_[0];
   return $_[$num];
 }
-#$external::randomseed=time;
-#$a=2;
-#$b=2;
-#$c=2;
-#&map(1,\$a,\$b,\$c,3,4,5);
-#print $a."\n".$b."\n";
+
+