--- loncom/homework/functionplotresponse.pm	2010/11/01 00:04:09	1.22
+++ loncom/homework/functionplotresponse.pm	2010/11/10 22:53:32	1.32
@@ -1,7 +1,7 @@
 # LearningOnline Network with CAPA
 # option list style responses
 #
-# $Id: functionplotresponse.pm,v 1.22 2010/11/01 00:04:09 www Exp $
+# $Id: functionplotresponse.pm,v 1.32 2010/11/10 22:53:32 www Exp $
 #
 # Copyright Michigan State University Board of Trustees
 #
@@ -33,7 +33,7 @@ use Apache::lonlocal;
 use Apache::lonnet;
 
 BEGIN {
-  &Apache::lonxml::register('Apache::functionplotresponse',('functionplotresponse','backgroundplot','spline','splinerule'));
+  &Apache::lonxml::register('Apache::functionplotresponse',('functionplotresponse','backgroundplot','spline','functionplotrule'));
 }
 
 #
@@ -339,20 +339,99 @@ sub end_backgroundplot {
 }
 
 #
-# <splinerule ... />
+# <functionplotrule ... />
 #
-sub start_splinerule {
+sub start_functionplotrule {
    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('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('Rule indices must be unique.'));
+   }
+
+
+   if ($target eq 'grade') {
+# Simply remember - in order - for later
+      my $beginninglabel=&Apache::lonxml::get_param('xinitiallabel',$parstack,$safeeval);
+      my $endinglabel=&Apache::lonxml::get_param('xfinallabel',$parstack,$safeeval);
+      if (($beginninglabel=~/\W/) || ($endinglabel=~/W/)) {
+          &Apache::lonxml::warning(&mt('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('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('Rule derivative not defined.'));
+         $derivative=0;
+      }
+      push(@Apache::functionplotresponse::functionplotrules,join(':',(
+           $label,
+           $derivative,
+           &Apache::lonxml::get_param('xinitial',$parstack,$safeeval),
+           $beginninglabel,
+           &Apache::lonxml::get_param('xfinal',$parstack,$safeeval),
+           $endinglabel,
+           $relationship,
+           &Apache::lonxml::get_param('value',$parstack,$safeeval)
+          )));
+   } elsif ($target eq 'edit') {
+        $result=&Apache::edit::tag_start($target,$token,'Function Plot Evaluation Rule').
+             &Apache::edit::text_arg('Index:','index',
+                                     $token,'4').'&nbsp;'.
+             &Apache::edit::select_arg(&mt('Function:'),'derivative',
+                                  [['0','Function itself'],
+                                   ['1','First derivative'],
+                                   ['2','Second derivative']],$token).'<br />'.
+
+             &Apache::edit::text_arg('(Initial) x-value:','xinitial',
+                                      $token,'4').
+             &Apache::edit::select_or_text_arg('(Initial) x-value label:','xinitiallabel',
+                                               [['start','Start of Plot']],$token,'8').'<br />'.
+
+             &Apache::edit::text_arg('Optional final x-value for ranges:','xfinal',
+                                      $token,'4').
+             &Apache::edit::select_or_text_arg('Optional final x-value label:','xfinallabel',
+                                               [['end','End of Plot']],$token,'8').'<br />'.
+
+             &Apache::edit::select_arg(&mt('Relationship:'),'relationship',
+                                  [['eq','equal'],
+                                   ['ne','not equal'],
+                                   ['ge','greater than or equal'],
+                                   ['gt','greater than'],
+                                   ['lt','less than'],
+                                   ['le','less than or equal']],$token).
+             $result.= &Apache::edit::select_or_text_arg('Value:','value',
+                                               [['undef','not defined']],$token,'4').
+             &Apache::edit::text_arg('Percent error:','percenterror',
+                                     $token,'4').
+             &Apache::edit::end_row();
+  } elsif ($target eq 'modified') {
+    my $constructtag=&Apache::edit::get_new_args($token,$parstack,
+                                                 $safeeval,'index','derivative','xinitial','xinitiallabel','xfinal','xfinallabel','relationship',
+                                                           'value','percenterror');
+    if ($constructtag) { $result=&Apache::edit::rebuild_tag($token); }
    }
    return $result;
 }
 
-sub end_splinerule {
+sub end_functionplotrule {
    my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
    my $result='';
    if ($target eq 'edit') {
@@ -363,7 +442,7 @@ 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 +450,19 @@ 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 +487,7 @@ 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 +502,7 @@ 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); }
   }
@@ -503,86 +586,7 @@ sub d2dt2_cubic_hermite {
 #
 sub array_index {
    my ($xmin,$xmax,$x)=@_;
-   return int(($x-$xmin)/($xmax-$xmin)*200.+0.5);
-}
-
-#
-# Actual x-value of array index
-#
-
-sub index_x {
-   my ($xmin,$xmax,$i)=@_;
-   return $i*($xmax-$xmin)/200.+$xmin;
-}
-
-#
-# Assume function to be linear between array points
-# Return the two indices and the scale factor
-#
-
-sub indices_scale {
-   my ($xmin,$xmax,$x)=@_;
-   my $i=&array_index($xmin,$xmax,$x);
-   my $xr=&index_x($xmin,$xmax,$i);
-   if ($xr<$x) {
-# Desired x is right of array index
-      if ($i>=200) { return (200,200,0); }
-      return($i,$i+1,200.*($x-$xr)/($xmax-$xmin));
-   } elsif ($xr>$x) {
-# Desired x is left of array index
-      if ($i<=0) { return (0,0,0); }
-      return($i-1,$i,1.-200.*($xr-$x)/($xmax-$xmin));
-   } else {
-# Desired x is at array index (unlikely, but ...)
-      if ($i>=200) { return (200,200,0); }
-      if ($i<=0) { return (0,0,0); }
-      return ($i,$i,0);
-   }
-}
-
-#
-# Function value
-#
-
-sub func_val {
-   my ($xmin,$xmax,$x)=@_;
-   my ($il,$ih,$factor)=&indices_scale($xmin,$xmax,$x);
-   my $fl=$Apache::functionplotresponse::func[$il];
-   my $fh=$Apache::functionplotresponse::func[$ih];
-   unless (defined($fl) || defined($fh)) { return undef; }
-   unless (defined($fl)) { return $fh; }
-   unless (defined($fh)) { return $fl; }
-   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);
+   return int(($x-$xmin)/($xmax-$xmin)*400.+0.5);
 }
 
 #
@@ -591,7 +595,7 @@ sub d2funcdx2_val {
 
 sub populate_arrays {
     my ($id,$xmin,$xmax)=@_;
-    for (my $i=0; $i<=200; $i++) {
+    for (my $i=0; $i<=400; $i++) {
        $Apache::functionplotresponse::func[$i]=undef;
        $Apache::functionplotresponse::dfuncdx[$i]=undef;
        $Apache::functionplotresponse::d2funcd2x[$i]=undef;
@@ -612,23 +616,36 @@ sub populate_arrays {
                         $env{'form.HWVAL_'.$id.'_'.$label.'P'.$ni.'_y'},
                         $env{'form.HWVAL_'.$id.'_'.$label.'S'.$ni.'_y'});
 # Run in small steps over spline parameter
-            for (my $t=0; $t<=1; $t+=0.00025) {
+            for (my $t=0; $t<=1; $t+=0.0001) {
                 my $xi=&array_index($xmin,$xmax,&cubic_hermite($t,@xparms));
                 if ($xi<$xiold) { return 'no_func'; }
-                if (($xi>$xiold) && ($xi>=0) && ($xi<=200)) {
+                if (($xi>$xiold) && ($xi>=0) && ($xi<=400)) {
                    if (defined($Apache::functionplotresponse::func[$xi])) { return 'no_func'; }
                    $xiold=$xi;
 # Function value
-                   $Apache::functionplotresponse::func[$xi]=&cubic_hermite($t,@yparms);
+                   my $funcval=&cubic_hermite($t,@yparms);
+                   $Apache::functionplotresponse::func[$xi]=$funcval;
+                   if (defined($funcval)) {
+                      if ($xi<$Apache::functionplotresponse::functionplotrulelabels{'start'}) {
+                         $Apache::functionplotresponse::functionplotrulelabels{'start'}=$xi;
+                      }
+                      if ($xi>$Apache::functionplotresponse::functionplotrulelabels{'end'}) {
+                         $Apache::functionplotresponse::functionplotrulelabels{'end'}=$xi;
+                      }
+                   }
+# Chain rule
 # 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
+# Faa di Bruno
+# d^2y/dx^2=(d^2y/dt^2)/(dx/dt)^2+(dy/dt)/(d^2x/dt^2)
                    my $d2xdt2=&d2dt2_cubic_hermite($t,@xparms);
-                   if ($d2xdt2) {
-                      $Apache::functionplotresponse::d2funcd2x[$xi]=&d2dt2_cubic_hermite($t,@yparms)/$d2xdt2;
+                   if (($dxdt) && ($d2xdt2)) {
+                      $Apache::functionplotresponse::d2funcdx2[$xi]=
+                         &d2dt2_cubic_hermite($t,@yparms)/($dxdt*$dxdt)
+                        +&ddt_cubic_hermite($t,@yparms)/$d2xdt2;
                    }
                 }
             }
@@ -653,6 +670,8 @@ sub start_functionplotresponse {
   undef %Apache::functionplotresponse::previous;
   $Apache::functionplotresponse::inputfields='';
   $Apache::functionplotresponse::counter=0;
+# Remember rules
+  undef @Apache::functionplotresponse::functionplotrules;
 # Part and ID
   my $partid=$Apache::inputtags::part;
   my $id=&Apache::response::start_response($parstack,$safeeval);
@@ -670,6 +689,14 @@ sub start_functionplotresponse {
   $ymin=(defined($ymin)?$ymin:-10);
   my $ymax=&Apache::lonxml::get_param('ymax',$parstack,$safeeval);
   $ymax=(defined($ymax)?$ymax:10);
+  if ($xmax<=$xmin) {
+     &Apache::lonxml::warning('Maximum x-value needs to be larger than minimum value.');
+     $xmax=$xmin+20;
+  }
+  if ($ymax<=$ymin) {
+     &Apache::lonxml::warning('Maximum y-value needs to be larger than minimum value.');
+     $ymax=$ymin+20;
+  }
   my $xaxisvisible=(&Apache::lonxml::get_param('xaxisvisible',$parstack,$safeeval)=~/on|true|yes|1/i?'true':'false');
   my $yaxisvisible=(&Apache::lonxml::get_param('yaxisvisible',$parstack,$safeeval)=~/on|true|yes|1/i?'true':'false');
   my $gridvisible=(&Apache::lonxml::get_param('gridvisible',$parstack,$safeeval)=~/on|true|yes|1/i?'true':'false');
@@ -692,7 +719,7 @@ sub start_functionplotresponse {
              &Apache::edit::text_arg('Maximum x-value:','xmax',
                                      $token,'4').'&nbsp;'.
              &Apache::edit::select_arg('x-axis visible:','xaxisvisible',
-                                  ['yes','no'],$token).'&nbsp;&nbsp;'.
+                                  ['yes','no'],$token).'<br />'.
              &Apache::edit::text_arg('Label y-axis:','ylabel',
                                      $token,'6').'&nbsp;'.
              &Apache::edit::text_arg('Minimum y-value:','ymin',
@@ -700,7 +727,7 @@ sub start_functionplotresponse {
              &Apache::edit::text_arg('Maximum y-value:','ymax',
                                      $token,'4').'&nbsp;'.
              &Apache::edit::select_arg('y-axis visible:','yaxisvisible',
-                                  ['yes','no'],$token).'&nbsp;&nbsp;'.
+                                  ['yes','no'],$token).'<br />'.
              &Apache::edit::select_arg('Grid visible:','gridvisible',
                                   ['yes','no'],$token).
              &Apache::edit::end_row().&Apache::edit::start_spanning_row();
@@ -725,6 +752,123 @@ sub start_functionplotresponse {
   return $result;
 }
 
+sub compare_rel {
+   my ($relationship,$value,$realval,$tol)=@_;
+# is the real value defined?
+   unless (defined($realval)) {
+      if ($relationship eq 'eq') {
+         if ($value eq 'undef') {
+            return 1;
+         } else {
+            return 0;
+         }
+      } elsif ($relationship eq 'ne') {
+         if ($value eq 'undef') {
+            return 0;
+         } else {
+            return 1;
+         }
+      } else {
+         return 0;
+      }
+   }
+
+# it is defined.
+   if ($relationship eq 'gt') {
+      return ($realval>$value);
+   } elsif ($relationship eq 'ge') {
+      return ($realval>$value-$tol);
+   } elsif ($relationship eq 'lt') {
+      return ($realval<$value);
+   } elsif ($relationship eq 'le') {
+      return ($realval<$value+$tol);
+   } elsif ($relationship eq 'ne') {
+      return (abs($value-$realval)>$tol);
+   } else {
+      return (abs($value-$realval)<$tol);
+   }
+   return 0;
+}
+
+sub functionplotrulecheck {
+   my ($rule,$xmin,$xmax,$tolfunc,$toldfdx,$told2fdx2)=@_;
+#   &Apache::lonnet::logthis("Rule $rule TolFunc $tolfunc TolDfDx $toldfdx TolD2fDx2 $told2fdx2");
+   my ($label,$derivative,$xinitial,$xinitiallabel,$xfinal,$xfinallabel,$relationship,$value)
+      =split(/\:/,$rule);
+
+   my $li=0;
+   my $lh=400;
+
+# Special case: the upper boundary was not defined
+# and needs to be set to the value where
+# the condition is not true anymore => set flag
+
+   my $findupper=0;
+   if (($xfinal eq '')
+    && (!defined($Apache::functionplotresponse::functionplotrulelabels{$xfinallabel}))
+    && ($xfinallabel)) {
+       $findupper=1;
+   }
+
+# if a hard value is set for the boundaries, it overrides the label
+   if (($xinitial ne '') && ($xinitiallabel ne '') && ($xinitiallabel ne 'start')) {
+      $li=&array_index($xmin,$xmax,$xinitial);
+      $Apache::functionplotresponse::functionplotrulelabels{$xinitiallabel}=$li;
+   }
+   if (($xfinal ne '') && ($xfinallabel ne '') && ($xfinallabel ne 'end')) {
+      $lh=&array_index($xmin,$xmax,$xfinal);
+      $Apache::functionplotresponse::functionplotrulelabels{$xfinallabel}=$lh;
+   }
+# if the label is defined, use it
+   if (defined($Apache::functionplotresponse::functionplotrulelabels{$xinitiallabel})) {
+      $li=$Apache::functionplotresponse::functionplotrulelabels{$xinitiallabel};
+   } else {
+      $li=&array_index($xmin,$xmax,$xinitial);
+   }
+   unless ($findupper) {
+      if (defined($Apache::functionplotresponse::functionplotrulelabels{$xfinallabel})) {
+         $lh=$Apache::functionplotresponse::functionplotrulelabels{$xfinallabel};
+      } else {
+         $lh=&array_index($xmin,$xmax,$xfinal);
+      }
+   }
+# Basic sanity checks
+   if ($li<0) { $li=0; }
+   if ($lh>400) { $lh=400; }
+   if ($li>$lh) {
+       $lh=$li;
+   }
+
+#   &Apache::lonnet::logthis("Init $xinitial=$li Final $xfinal=$lh Findupper: $findupper");
+   my $tol=$tolfunc;
+   if ($derivative==2) {
+      $tol=$told2fdx2;
+   } elsif ($derivative==1) {
+      $tol=$toldfdx;
+   }
+   for (my $i=$li; $i<=$lh; $i++) {
+        my $val;
+        if ($derivative==2) {
+           $val=$Apache::functionplotresponse::d2funcdx2[$i];
+        } elsif ($derivative==1) {
+           $val=$Apache::functionplotresponse::dfuncdx[$i];
+        } else {
+           $val=$Apache::functionplotresponse::func[$i];
+        }
+        unless (&compare_rel($relationship,$value,$val,$tol)) { 
+#           &Apache::lonnet::logthis("Condition false $findupper at $i with $val");
+           if (($findupper) && ($i>$li)) {
+              $Apache::functionplotresponse::functionplotrulelabels{$xfinallabel}=$i;
+#              &Apache::lonnet::logthis("Setting $xfinallabel to $i");
+              return 1;
+           } else {
+              return 0; 
+           }
+        }
+   }
+   return 1;
+}
+
 sub end_functionplotresponse {
   my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
   &Apache::response::end_response;
@@ -739,7 +883,7 @@ sub end_functionplotresponse {
          && &Apache::response::submitted()
          && $Apache::lonhomework::type eq 'exam') {
 
-        #&Apache::response::scored_response($partid,$id);
+        &Apache::response::scored_response($partid,$id);
 
     } elsif ($target eq 'grade'
          && &Apache::response::submitted()
@@ -754,11 +898,38 @@ 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 $ymin=&Apache::lonxml::get_param('ymin',$parstack,$safeeval);
+        $ymin=(defined($ymin)?$ymin:-10);
+        my $ymax=&Apache::lonxml::get_param('ymax',$parstack,$safeeval);
+        $ymax=(defined($ymax)?$ymax:10);
+
+        my $percent=&Apache::lonxml::get_param('percenterror',$parstack,$safeeval);
+        $percent=(defined($percent)?$percent:5);
+
+        my $tolfunc=$percent*($ymax-$ymin)/100.;
+        my $toldfdx=1;
+        my $told2fdx2=1;
+        if ($xmax>$xmin) {
+           $toldfdx=$tolfunc/($xmax-$xmin);
+           $told2fdx2=$toldfdx/($xmax-$xmin);
+        }
+
+        my $ad='';
+        undef  %Apache::functionplotresponse::functionplotrulelabels;
+        $Apache::functionplotresponse::functionplotrulelabels{'start'}=400;
+        $Apache::functionplotresponse::functionplotrulelabels{'end'}=0;
         if (&populate_arrays($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.
+           foreach my $rule (@Apache::functionplotresponse::functionplotrules) {
+              unless (&functionplotrulecheck($rule,$xmin,$xmax,$tolfunc,$toldfdx,$told2fdx2)) {
+                 $ad='INCORRECT';
+                 last;
+              }
+           }
+# If it's not wrong, it's correct 
+           unless ($ad) { $ad='EXACT_ANS' };
         }
 
 #