--- loncom/homework/functionplotresponse.pm	2010/11/07 01:57:50	1.25
+++ loncom/homework/functionplotresponse.pm	2010/11/11 03:52:35	1.33
@@ -1,7 +1,7 @@
 # LearningOnline Network with CAPA
 # option list style responses
 #
-# $Id: functionplotresponse.pm,v 1.25 2010/11/07 01:57:50 www Exp $
+# $Id: functionplotresponse.pm,v 1.33 2010/11/11 03:52:35 www Exp $
 #
 # Copyright Michigan State University Board of Trustees
 #
@@ -389,11 +389,45 @@ sub start_functionplotrule {
            &Apache::lonxml::get_param('xfinal',$parstack,$safeeval),
            $endinglabel,
            $relationship,
-           &Apache::lonxml::get_param('value',$parstack,$safeeval)
+           &Apache::lonxml::get_param('value',$parstack,$safeeval),
+           &Apache::lonxml::get_param('percenterror',$parstack,$safeeval)
           )));
    } elsif ($target eq 'edit') {
-      $result=&Apache::edit::tag_start($target,$token,'Function Plot Evaluation Rule').
-              &Apache::edit::end_row();
+        $result=&Apache::edit::tag_start($target,$token,'Function Plot Evaluation Rule').
+             &Apache::edit::text_arg('Index:','index',
+                                     $token,'4').' '.
+             &Apache::edit::select_arg(&mt('Function:'),'derivative',
+                                  [['0','Function itself'],
+                                   ['1','First derivative'],
+                                   ['2','Second derivative']],$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 $result;
 }
@@ -553,86 +587,7 @@ sub d2dt2_cubic_hermite {
 #
 sub array_index {
    my ($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);
 }
 
 #
@@ -641,7 +596,7 @@ 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;
@@ -662,23 +617,36 @@ 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;
                    }
                 }
             }
@@ -752,7 +720,7 @@ 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',
@@ -760,7 +728,7 @@ 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();
@@ -786,63 +754,127 @@ sub start_functionplotresponse {
 }
 
 sub compare_rel {
-   my ($relationship,$value,$val,$tol)=@_;
-   if (abs($value-$val)<$tol) { return 1; }
+   my ($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,$value)
+   my ($rule,$xmin,$xmax,$ymin,$ymax)=@_;
+
+#   &Apache::lonnet::logthis("Rule $rule $xmin $xmax $ymin $ymax");
+
+   my ($label,$derivative,$xinitial,$xinitiallabel,$xfinal,$xfinallabel,$relationship,$value,$percent)
       =split(/\:/,$rule);
-# if a hard value is set for the boundaries, it overrides the label
-   if (($xinitial ne '') && ($xinitiallabel ne '')) {
-      $Apache::functionplotresponse::functionplotrulelabels{$xinitiallabel}=$xinitial;
+   $percent=($percent>0?$percent:5);
+
+   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)) {
+       $findupper=1;
    }
-   if (($xfinal ne '') && ($xfinallabel ne '')) {
-      $Apache::functionplotresponse::functionplotrulelabels{$xfinallabel}=$xfinal;
+
+# if a hard value is set for the boundaries, it overrides the label
+   if (($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})) {
-      $xinitial=$Apache::functionplotresponse::functionplotrulelabels{$xinitiallabel};
+      $li=$Apache::functionplotresponse::functionplotrulelabels{$xinitiallabel};
+   } else {
+      $li=&array_index($xmin,$xmax,$xinitial);
    }
-   if (defined($Apache::functionplotresponse::functionplotrulelabels{$xfinallabel})) {
-      $xfinal=$Apache::functionplotresponse::functionplotrulelabels{$xfinallabel};
+   unless ($findupper) {
+      if (defined($Apache::functionplotresponse::functionplotrulelabels{$xfinallabel})) {
+         $lh=$Apache::functionplotresponse::functionplotrulelabels{$xfinallabel}-1;
+      } else {
+         $lh=&array_index($xmin,$xmax,$xfinal);
+      }
    }
 # Basic sanity checks
-   if ($xinitial eq '') {
-      $xinitial=0;
+   if ($li<0) { $li=0; }
+   if ($lh>400) { $lh=400; }
+   if ($li>$lh) {
+       $lh=$li;
    }
-   if ($xfinal ne '') {
-      if ($xinitial>$xfinal) {
-         $xfinal=$xinitial;
+
+#   &Apache::lonnet::logthis("Init $xinitial=$li Final $xfinal=$lh Findupper: $findupper");
+   my $tol=$percent*($ymax-$ymin)/100;
+   if ($xmax>$xmin) {
+      if ($derivative==2) {
+         $tol=4.*$tol/($xmax-$xmin);
+      } elsif ($derivative==1) {
+         $tol=2.*$tol/($xmax-$xmin);
       }
    }
-   &Apache::lonnet::logthis("Init $xinitial Final $xfinal");
-   if (($xfinal eq '') || ($xinitial==$xfinal)) {
-# This is only one point
-        &Apache::lonnet::logthis("One point $xinitial");
-        my $tol;
+   for (my $i=$li; $i<=$lh; $i++) {
         my $val;
         if ($derivative==2) {
-           $val=&d2funcdx2_val($xmin,$xmax,$xinitial);
-           $tol=$told2fdx2;
+           $val=$Apache::functionplotresponse::d2funcdx2[$i];
         } elsif ($derivative==1) {
-           $val=&dfuncdx_val($xmin,$xmax,$xinitial);
-           $tol=$toldfdx;
+           $val=$Apache::functionplotresponse::dfuncdx[$i];
         } else {
-           $val=&func_val($xmin,$xmax,$xinitial);
-           $tol=$tolfunc;
+           $val=$Apache::functionplotresponse::func[$i];
+        }
+        unless (&compare_rel($relationship,$value,$val,$tol)) { 
+#           &Apache::lonnet::logthis("Condition false $findupper at $i with $val tol:$tol from $value");
+           if (($findupper) && ($i>$li)) {
+              $Apache::functionplotresponse::functionplotrulelabels{$xfinallabel}=$i;
+#              &Apache::lonnet::logthis("Setting $xfinallabel to $i");
+              return 1;
+           } else {
+              return 0; 
+           }
         }
-        &Apache::lonnet::logthis("Value $value ActVal $val Tol $tol");
-        return &compare_rel($relationship,$value,$val,$tol);
-   } else {
-# This is a range
    }
-   return 0;
+   return 1;
 }
 
-
 sub end_functionplotresponse {
   my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
   &Apache::response::end_response;
@@ -857,7 +889,7 @@ 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()
@@ -876,22 +908,17 @@ sub end_functionplotresponse {
         $ymin=(defined($ymin)?$ymin:-10);
         my $ymax=&Apache::lonxml::get_param('ymax',$parstack,$safeeval);
         $ymax=(defined($ymax)?$ymax:10);
-        my $tolfunc=($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 {
 # We have a function that we can actually grade, go through the spline rules.
-           undef  %Apache::functionplotresponse::functionplotrulelabels;
            foreach my $rule (@Apache::functionplotresponse::functionplotrules) {
-              unless (&functionplotrulecheck($rule,$xmin,$xmax,$tolfunc,$toldfdx,$told2fdx2)) {
+              unless (&functionplotrulecheck($rule,$xmin,$xmax,$ymin,$ymax)) {
                  $ad='INCORRECT';
                  last;
               }