--- loncom/homework/functionplotresponse.pm	2010/10/30 02:31:27	1.18
+++ loncom/homework/functionplotresponse.pm	2010/11/01 00:04:09	1.22
@@ -1,7 +1,7 @@
 # LearningOnline Network with CAPA
 # option list style responses
 #
-# $Id: functionplotresponse.pm,v 1.18 2010/10/30 02:31:27 www Exp $
+# $Id: functionplotresponse.pm,v 1.22 2010/11/01 00:04:09 www Exp $
 #
 # Copyright Michigan State University Board of Trustees
 #
@@ -503,8 +503,86 @@ sub d2dt2_cubic_hermite {
 #
 sub array_index {
    my ($xmin,$xmax,$x)=@_;
-   my $index=int(($x-$xmin)/($xmax-$xmin)*200.+0.5);
-   return $index;
+   return int(($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);
 }
 
 #
@@ -514,16 +592,16 @@ sub array_index {
 sub populate_arrays {
     my ($id,$xmin,$xmax)=@_;
     for (my $i=0; $i<=200; $i++) {
-       undef $Apache::functionplotresponse::func[$i];
-       undef $Apache::functionplotresponse::dfunddx[$i];
-       undef $Apache::functionplotresponse::d2funcd2x[$i];
+       $Apache::functionplotresponse::func[$i]=undef;
+       $Apache::functionplotresponse::dfuncdx[$i]=undef;
+       $Apache::functionplotresponse::d2funcd2x[$i]=undef;
     }
-    unless ($xmax>$xmin) { return; }
+    unless ($xmax>$xmin) { return 'no_func'; }
 # Run over all splines in response
     foreach my $label (split(/\,/,$env{"form.HWVAL_AllSplines_$id"})) {
+        my $xiold=-1;
 # Run over all points in spline
-        for (my $i=0; $i<$env{"form.HWVAL_SplineOrder_".$id."_".$label}; $i++) {
-            my $xiold=-1;
+        for (my $i=1; $i<$env{"form.HWVAL_SplineOrder_".$id."_".$label}; $i++) {
             my $ni=$i+1;
             my @xparms=($env{'form.HWVAL_'.$id.'_'.$label.'P'.$i.'_x'},
                         $env{'form.HWVAL_'.$id.'_'.$label.'S'.$i.'_x'},
@@ -533,14 +611,25 @@ sub populate_arrays {
                         $env{'form.HWVAL_'.$id.'_'.$label.'S'.$i.'_y'},
                         $env{'form.HWVAL_'.$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) {
                 my $xi=&array_index($xmin,$xmax,&cubic_hermite($t,@xparms));
-                if ($xi<$xiold-5) { return 'no_func'; }
-                if ($xi>$xiold) {
+                if ($xi<$xiold) { return 'no_func'; }
+                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;
+                   }
                 }
             }
         }
@@ -667,10 +756,11 @@ sub end_functionplotresponse {
         $xmax=(defined($xmax)?$xmax:10);
         my $ad;
         if (&populate_arrays($internalid,$xmin,$xmax) eq 'no_func') {
-           $ad='BAD_FORMULA';
+           $ad='NOT_FUNCTION';
         } else {
            $ad='INCORRECT';
         }
+
 #
 # Store grading info
 #