--- loncom/homework/functionplotresponse.pm	2010/10/31 12:33:02	1.21
+++ loncom/homework/functionplotresponse.pm	2010/11/06 16:12:39	1.24
@@ -1,7 +1,7 @@
 # LearningOnline Network with CAPA
 # option list style responses
 #
-# $Id: functionplotresponse.pm,v 1.21 2010/10/31 12:33:02 www Exp $
+# $Id: functionplotresponse.pm,v 1.24 2010/11/06 16:12:39 www Exp $
 #
 # Copyright Michigan State University Board of Trustees
 #
@@ -344,10 +344,56 @@ sub end_backgroundplot {
 sub start_splinerule {
    my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
    my $result='';
-   my $internalid = $Apache::inputtags::part.'_'.$Apache::inputtags::response[-1];
-   if ($target eq 'edit') {
-        $result=&Apache::edit::tag_start($target,$token,'Spline Evaluation Rule').
-                &Apache::edit::end_row();
+   my $label=&Apache::lonxml::get_param('index',$parstack,$safeeval);
+   $Apache::functionplotresponse::counter++;
+   if ($label=~/\W/) {
+      &Apache::lonxml::warning(&mt('Spline Rule indices should only contain alphanumeric characters.'));
+   }
+   $label=~s/\W//gs;
+   unless ($label) {
+      $label='R'.$Apache::functionplotresponse::counter;
+   } else {
+      $label='R'.$label;
+   }
+   if ($Apache::functionplotresponse::splineorder{$label}) {
+       &Apache::lonxml::error(&mt('Spline Rule indices must be unique.'));
+   }
+
+
+   if ($target eq 'grade') {
+# Simply remember - in order - for later
+      my $beginninglabel=&Apache::lonxml::get_param('beginninglabel',$parstack,$safeeval);
+      my $endinglabel=&Apache::lonxml::get_param('endinglabel',$parstack,$safeeval);
+      if (($beginninglabel=~/\W/) || ($endinglabel=~/W/)) {
+          &Apache::lonxml::warning(&mt('Spline Rule labels must be alphanumeric.'));
+      }
+      $beginninglabel=~s/\W//gs;
+      $endinglabel=~s/\W//gs;
+      my $relationship=&Apache::lonxml::get_param('relationship',$parstack,$safeeval);
+      $relationship=~s/\W//gs;
+      $relationship=lc($relationship);
+      unless ($relationship=~/^(eq|ge|gt|le|lt|ne)$/) {
+          &Apache::lonxml::warning(&mt('Spline Rule relationship not defined.'));
+          $relationship='eq';
+      }
+      my $derivative=&Apache::lonxml::get_param('derivative',$parstack,$safeeval);
+      unless (($derivative==0) || ($derivative==1) || ($derivative==2)) {
+         &Apache::lonxml::warning(&mt('Spline Rule derivative not defined.'));
+         $derivative=0;
+      }
+      push(@Apache::functionplotresponse::splinerules,join(':',(
+           $label,
+           $derivative,
+           &Apache::lonxml::get_param('beginningvalue',$parstack,$safeeval),
+           $beginninglabel,
+           &Apache::lonxml::get_param('endingvalue',$parstack,$safeeval),
+           $endinglabel,
+           $relationship,
+           &Apache::lonxml::get_param('value',$parstack,$safeeval)
+          )));
+   } elsif ($target eq 'edit') {
+      $result=&Apache::edit::tag_start($target,$token,'Spline Evaluation Rule').
+              &Apache::edit::end_row();
    }
    return $result;
 }
@@ -363,7 +409,7 @@ sub end_splinerule {
 
 
 #
-# <spline label="..." order="1,2,3,4" initx="..." inity="..." scalex="..." scaley="..." />
+# <spline index="..." order="1,2,3,4" initx="..." inity="..." scalex="..." scaley="..." />
 #
 # Unfortunately, GeoGebra seems to want all splines after everything else, so we need to store them
 #
@@ -371,15 +417,19 @@ sub start_spline {
    my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
    my $result='';
    if ($target eq 'web') {
-      my $label=&Apache::lonxml::get_param('label',$parstack,$safeeval);
+      my $label=&Apache::lonxml::get_param('index',$parstack,$safeeval);
       $Apache::functionplotresponse::counter++;
       if ($label=~/\W/) {
-         &Apache::lonxml::warning(&mt('Spline labels should only contain alphanumeric characters.'));
+         &Apache::lonxml::warning(&mt('Spline indices should only contain alphanumeric characters.'));
       }
       $label=~s/\W//gs;
-      unless ($label) { $label='S'.$Apache::functionplotresponse::counter; }
+      unless ($label) { 
+         $label='S'.$Apache::functionplotresponse::counter; 
+      } else {
+         $label='S'.$label;
+      }
       if ($Apache::functionplotresponse::splineorder{$label}) {
-         &Apache::lonxml::error(&mt('Spline labels must be unique.'));
+         &Apache::lonxml::error(&mt('Spline indices must be unique.'));
       }
 
       my $order=&Apache::lonxml::get_param('order',$parstack,$safeeval);
@@ -404,7 +454,7 @@ sub start_spline {
       $Apache::functionplotresponse::splinescaley{$label}=$sy;
    } elsif ($target eq 'edit') {
         $result=&Apache::edit::tag_start($target,$token,'Spline').
-             &Apache::edit::text_arg('Label:','label',
+             &Apache::edit::text_arg('Index:','index',
                                      $token,'4').'&nbsp;'.
              &Apache::edit::select_arg('Order:','order',
                                   ['2','3','4','5','6','7','8','9'],$token).'&nbsp;'.
@@ -419,7 +469,7 @@ sub start_spline {
              &Apache::edit::end_row();
   } elsif ($target eq 'modified') {
     my $constructtag=&Apache::edit::get_new_args($token,$parstack,
-                                                 $safeeval,'label','order','initx','inity',
+                                                 $safeeval,'index','order','initx','inity',
                                                            'scalex','scaley');
     if ($constructtag) { $result=&Apache::edit::rebuild_tag($token); }
   }
@@ -524,7 +574,6 @@ sub indices_scale {
    my ($xmin,$xmax,$x)=@_;
    my $i=&array_index($xmin,$xmax,$x);
    my $xr=&index_x($xmin,$xmax,$i);
-   &Apache::lonnet::logthis("x:$x i:$i xr:$xr");
    if ($xr<$x) {
 # Desired x is right of array index
       if ($i>=200) { return (200,200,0); }
@@ -553,9 +602,37 @@ sub func_val {
    unless (defined($fl) || defined($fh)) { return undef; }
    unless (defined($fl)) { return $fh; }
    unless (defined($fh)) { return $fl; }
-   my $func=$fl+$factor*($fh-$fl);
-   &Apache::lonnet::logthis("x:$x func:$func factor:$factor il:$il ih:$ih fil:$fl fih:$fh");
-   return $func;
+   return $fl+$factor*($fh-$fl);
+}
+
+#
+# First derivative
+#
+
+sub dfuncdx_val {
+   my ($xmin,$xmax,$x)=@_;
+   my ($il,$ih,$factor)=&indices_scale($xmin,$xmax,$x);
+   my $fl=$Apache::functionplotresponse::dfuncdx[$il];
+   my $fh=$Apache::functionplotresponse::dfuncdx[$ih];
+   unless (defined($fl) || defined($fh)) { return undef; }
+   unless (defined($fl)) { return $fh; }
+   unless (defined($fh)) { return $fl; }
+   return $fl+$factor*($fh-$fl);
+}
+
+#
+# Second derivative
+#
+
+sub d2funcdx2_val {
+   my ($xmin,$xmax,$x)=@_;
+   my ($il,$ih,$factor)=&indices_scale($xmin,$xmax,$x);
+   my $fl=$Apache::functionplotresponse::d2funcdx2[$il];
+   my $fh=$Apache::functionplotresponse::d2funcdx2[$ih];
+   unless (defined($fl) || defined($fh)) { return undef; }
+   unless (defined($fl)) { return $fh; }
+   unless (defined($fh)) { return $fl; }
+   return $fl+$factor*($fh-$fl);
 }
 
 #
@@ -566,7 +643,7 @@ sub populate_arrays {
     my ($id,$xmin,$xmax)=@_;
     for (my $i=0; $i<=200; $i++) {
        $Apache::functionplotresponse::func[$i]=undef;
-       $Apache::functionplotresponse::dfunddx[$i]=undef;
+       $Apache::functionplotresponse::dfuncdx[$i]=undef;
        $Apache::functionplotresponse::d2funcd2x[$i]=undef;
     }
     unless ($xmax>$xmin) { return 'no_func'; }
@@ -591,7 +668,18 @@ sub populate_arrays {
                 if (($xi>$xiold) && ($xi>=0) && ($xi<=200)) {
                    if (defined($Apache::functionplotresponse::func[$xi])) { return 'no_func'; }
                    $xiold=$xi;
+# Function value
                    $Apache::functionplotresponse::func[$xi]=&cubic_hermite($t,@yparms);
+# dy/dx=dy/dt/(dx/dt)
+                   my $dxdt=&ddt_cubic_hermite($t,@xparms);
+                   if ($dxdt) {
+                      $Apache::functionplotresponse::dfuncdx[$xi]=&ddt_cubic_hermite($t,@yparms)/$dxdt;
+                   }
+# d^2y/dx^2
+                   my $d2xdt2=&d2dt2_cubic_hermite($t,@xparms);
+                   if ($d2xdt2) {
+                      $Apache::functionplotresponse::d2funcd2x[$xi]=&d2dt2_cubic_hermite($t,@yparms)/$d2xdt2;
+                   }
                 }
             }
         }
@@ -615,6 +703,8 @@ sub start_functionplotresponse {
   undef %Apache::functionplotresponse::previous;
   $Apache::functionplotresponse::inputfields='';
   $Apache::functionplotresponse::counter=0;
+# Remember rules
+  undef @Apache::functionplotresponse::splinerules;
 # Part and ID
   my $partid=$Apache::inputtags::part;
   my $id=&Apache::response::start_response($parstack,$safeeval);
@@ -687,6 +777,12 @@ sub start_functionplotresponse {
   return $result;
 }
 
+sub splinerulecheck {
+   my ($rule)=@_;
+   return 0;
+}
+
+
 sub end_functionplotresponse {
   my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
   &Apache::response::end_response;
@@ -716,31 +812,21 @@ sub end_functionplotresponse {
         $xmin=(defined($xmin)?$xmin:-10);
         my $xmax=&Apache::lonxml::get_param('xmax',$parstack,$safeeval);
         $xmax=(defined($xmax)?$xmax:10);
-        my $ad;
+        my $ad='';
         if (&populate_arrays($internalid,$xmin,$xmax) eq 'no_func') {
            $ad='NOT_FUNCTION';
         } else {
-           $ad='INCORRECT';
+# We have a function that we can actually grade, go through the spline rules.
+           undef  %Apache::functionplotresponse::splinerulelabels;
+           foreach my $rule (@Apache::functionplotresponse::splinerules) {
+              unless (&splinerulecheck($rule)) {
+                 $ad='INCORRECT';
+                 last;
+              }
+           }
+# If it's not wrong, it's correct 
+           unless ($ad) { $ad='EXACT_ANS' };
         }
-        &func_val($xmin,$xmax,3.96);
-
-        &func_val($xmin,$xmax,3.965);
-
-        &func_val($xmin,$xmax,3.97);
-        &func_val($xmin,$xmax,3.975);
-        &func_val($xmin,$xmax,3.98);
-
-        &func_val($xmin,$xmax,3.985);
-        &func_val($xmin,$xmax,3.99);
-        &func_val($xmin,$xmax,3.995);
-
-        &func_val($xmin,$xmax,4);
-        &func_val($xmin,$xmax,4.05);
-        &func_val($xmin,$xmax,4.1);
-
-        &func_val($xmin,$xmax,4.15);
-        &func_val($xmin,$xmax,4.2);
-        &func_val($xmin,$xmax,4.25);
 
 #
 # Store grading info