--- loncom/homework/functionplotresponse.pm 2010/11/19 20:03:13 1.41
+++ loncom/homework/functionplotresponse.pm 2010/11/20 00:14:44 1.42
@@ -1,7 +1,7 @@
# LearningOnline Network with CAPA
# option list style responses
#
-# $Id: functionplotresponse.pm,v 1.41 2010/11/19 20:03:13 www Exp $
+# $Id: functionplotresponse.pm,v 1.42 2010/11/20 00:14:44 www Exp $
#
# Copyright Michigan State University Board of Trustees
#
@@ -61,7 +61,7 @@ sub geogebra_endcode {
#
sub geogebra_spline_program {
return (<
+
ENDSPLINEPROGRAM
}
@@ -441,7 +441,7 @@ sub start_functionplotrule {
$relationship='eq';
}
my $derivative=&Apache::lonxml::get_param('derivativeorder',$parstack,$safeeval);
- unless (($derivative==0) || ($derivative==1) || ($derivative==2)) {
+ unless (($derivative==-1) || ($derivative==0) || ($derivative==1) || ($derivative==2)) {
&Apache::lonxml::warning(&mt('Rule derivative not defined.'));
$derivative=0;
}
@@ -465,7 +465,8 @@ sub start_functionplotrule {
&Apache::edit::select_arg(&mt('Function:'),'derivativeorder',
[['0','Function itself'],
['1','First derivative'],
- ['2','Second derivative']],$token).'
'.
+ ['2','Second derivative'],
+ ['-1','Integral']],$token).'
'.
&Apache::edit::text_arg('(Initial) x-value:','xinitial',
$token,'8').
&Apache::edit::select_or_text_arg('(Initial) x-value label:','xinitiallabel',
@@ -628,8 +629,8 @@ sub get_answer_from_form_fields {
sub cubic_hermite {
my ($t,$p1,$s1,$p2,$s2)=@_;
- return (2.*$t*$t*$t-3.*$t*$t+1.)*$p1 + 5.*($t*$t*$t-2.*$t*$t+$t)*($s1-$p1)+
- (-2.*$t*$t*$t+3.*$t*$t) *$p2 + 5.*($t*$t*$t-$t*$t) *($s2-$p2);
+ return (2.*$t*$t*$t-3.*$t*$t+1.)*$p1 + 3.*($t*$t*$t-2.*$t*$t+$t)*($s1-$p1)+
+ (-2.*$t*$t*$t+3.*$t*$t) *$p2 + 3.*($t*$t*$t-$t*$t) *($s2-$p2);
}
#
@@ -638,8 +639,8 @@ sub cubic_hermite {
sub ddt_cubic_hermite {
my ($t,$p1,$s1,$p2,$s2)=@_;
- return (6.*$t*$t-6.*$t) *$p1 + 5.*(3.*$t*$t-4.*$t+1.)*($s1-$p1)+
- (-6.*$t*$t+6.*$t)*$p2 + 5.*(3.*$t*$t-2.*$t) *($s2-$p2);
+ return (6.*$t*$t-6.*$t) *$p1 + 3.*(3.*$t*$t-4.*$t+1.)*($s1-$p1)+
+ (-6.*$t*$t+6.*$t)*$p2 + 3.*(3.*$t*$t-2.*$t) *($s2-$p2);
}
#
@@ -648,8 +649,8 @@ sub ddt_cubic_hermite {
sub d2dt2_cubic_hermite {
my ($t,$p1,$s1,$p2,$s2)=@_;
- return (12.*$t-6.) *$p1 + 5.*(6.*$t-4.)*($s1-$p1)+
- (-12.*$t+6.)*$p2 + 5.*(6.*$t-2.)*($s2-$p2);
+ return (12.*$t-6.) *$p1 + 3.*(6.*$t-4.)*($s1-$p1)+
+ (-12.*$t+6.)*$p2 + 3.*(6.*$t-2.)*($s2-$p2);
}
#
@@ -895,7 +896,7 @@ sub functionplotrulecheck {
=split(/\:/,$rule);
$percent=($percent>0?$percent:5);
&addlog("=================");
- &addlog("Rule $label for ".('function itself','first derivative','second derivative')[$derivative]." $relationship $value");
+ &addlog("Rule $label for ".($derivative<0?'integral':('function itself','first derivative','second derivative')[$derivative])." $relationship $value");
my $li=0;
my $lh=400;
@@ -952,14 +953,37 @@ sub functionplotrulecheck {
$tol=4.*$tol/($xmax-$xmin);
} elsif ($derivative==1) {
$tol=2.*$tol/($xmax-$xmin);
+ } elsif ($derivative==-1) {
+ $tol=$tol*($xmax-$xmin)/2.;
}
}
- for (my $i=$li; $i<=$lh; $i++) {
+ my $integral=0;
+ my $binwidth=($xmax-$xmin)/400.;
+ if (($derivative<0) && (!$findupper)) {
+# definite integral, calculate over whole length
+ &addlog("Calculating definite integral");
+ for (my $i=$li; $i<=$lh; $i++) {
+ $integral+=$Apache::functionplotresponse::func[$i]*$binwidth;
+ }
+ unless (&compare_rel($relationship,$value,$integral,$tol)) {
+ &addlog("Actual integral ".(defined($integral)?$integral:'undef').", expected $value, tolerance $tol");
+ &addlog("Rule $label failed.");
+ my $hintlabel=$label;
+ $hintlabel=~s/^R//;
+ push(@Apache::functionplotresponse::failedrules,$hintlabel);
+ &addlog("Set hint condition $hintlabel");
+ return 0;
+ }
+ } else {
+ for (my $i=$li; $i<=$lh; $i++) {
my $val;
if ($derivative==2) {
$val=$Apache::functionplotresponse::d2funcdx2[$i];
} elsif ($derivative==1) {
$val=$Apache::functionplotresponse::dfuncdx[$i];
+ } elsif ($derivative==-1) {
+ $integral+=$Apache::functionplotresponse::func[$i]*$binwidth;
+ $val=$integral;
} else {
$val=$Apache::functionplotresponse::func[$i];
}
@@ -993,6 +1017,7 @@ sub functionplotrulecheck {
return 0;
}
}
+ }
}
&addlog("Rule $label passed.");
return 1;