version 1.19, 2010/10/30 15:32:36
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version 1.22, 2010/11/01 00:04:09
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Line 503 sub d2dt2_cubic_hermite {
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Line 503 sub d2dt2_cubic_hermite {
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# |
# |
sub array_index { |
sub array_index { |
my ($xmin,$xmax,$x)=@_; |
my ($xmin,$xmax,$x)=@_; |
my $index=int(($x-$xmin)/($xmax-$xmin)*200.+0.5); |
return int(($x-$xmin)/($xmax-$xmin)*200.+0.5); |
return $index; |
} |
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# |
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# Actual x-value of array index |
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# |
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sub index_x { |
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my ($xmin,$xmax,$i)=@_; |
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return $i*($xmax-$xmin)/200.+$xmin; |
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} |
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# |
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# Assume function to be linear between array points |
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# Return the two indices and the scale factor |
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# |
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sub indices_scale { |
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my ($xmin,$xmax,$x)=@_; |
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my $i=&array_index($xmin,$xmax,$x); |
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my $xr=&index_x($xmin,$xmax,$i); |
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if ($xr<$x) { |
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# Desired x is right of array index |
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if ($i>=200) { return (200,200,0); } |
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return($i,$i+1,200.*($x-$xr)/($xmax-$xmin)); |
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} elsif ($xr>$x) { |
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# Desired x is left of array index |
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if ($i<=0) { return (0,0,0); } |
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return($i-1,$i,1.-200.*($xr-$x)/($xmax-$xmin)); |
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} else { |
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# Desired x is at array index (unlikely, but ...) |
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if ($i>=200) { return (200,200,0); } |
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if ($i<=0) { return (0,0,0); } |
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return ($i,$i,0); |
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} |
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} |
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# |
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# Function value |
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# |
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sub func_val { |
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my ($xmin,$xmax,$x)=@_; |
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my ($il,$ih,$factor)=&indices_scale($xmin,$xmax,$x); |
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my $fl=$Apache::functionplotresponse::func[$il]; |
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my $fh=$Apache::functionplotresponse::func[$ih]; |
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unless (defined($fl) || defined($fh)) { return undef; } |
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unless (defined($fl)) { return $fh; } |
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unless (defined($fh)) { return $fl; } |
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return $fl+$factor*($fh-$fl); |
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} |
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# |
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# First derivative |
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# |
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sub dfuncdx_val { |
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my ($xmin,$xmax,$x)=@_; |
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my ($il,$ih,$factor)=&indices_scale($xmin,$xmax,$x); |
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my $fl=$Apache::functionplotresponse::dfuncdx[$il]; |
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my $fh=$Apache::functionplotresponse::dfuncdx[$ih]; |
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unless (defined($fl) || defined($fh)) { return undef; } |
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unless (defined($fl)) { return $fh; } |
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unless (defined($fh)) { return $fl; } |
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return $fl+$factor*($fh-$fl); |
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} |
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# |
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# Second derivative |
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# |
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sub d2funcdx2_val { |
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my ($xmin,$xmax,$x)=@_; |
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my ($il,$ih,$factor)=&indices_scale($xmin,$xmax,$x); |
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my $fl=$Apache::functionplotresponse::d2funcdx2[$il]; |
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my $fh=$Apache::functionplotresponse::d2funcdx2[$ih]; |
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unless (defined($fl) || defined($fh)) { return undef; } |
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unless (defined($fl)) { return $fh; } |
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unless (defined($fh)) { return $fl; } |
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return $fl+$factor*($fh-$fl); |
} |
} |
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# |
# |
Line 515 sub populate_arrays {
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Line 593 sub populate_arrays {
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my ($id,$xmin,$xmax)=@_; |
my ($id,$xmin,$xmax)=@_; |
for (my $i=0; $i<=200; $i++) { |
for (my $i=0; $i<=200; $i++) { |
$Apache::functionplotresponse::func[$i]=undef; |
$Apache::functionplotresponse::func[$i]=undef; |
$Apache::functionplotresponse::dfunddx[$i]=undef; |
$Apache::functionplotresponse::dfuncdx[$i]=undef; |
$Apache::functionplotresponse::d2funcd2x[$i]=undef; |
$Apache::functionplotresponse::d2funcd2x[$i]=undef; |
} |
} |
unless ($xmax>$xmin) { return 'no_func'; } |
unless ($xmax>$xmin) { return 'no_func'; } |
Line 540 sub populate_arrays {
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Line 618 sub populate_arrays {
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if (($xi>$xiold) && ($xi>=0) && ($xi<=200)) { |
if (($xi>$xiold) && ($xi>=0) && ($xi<=200)) { |
if (defined($Apache::functionplotresponse::func[$xi])) { return 'no_func'; } |
if (defined($Apache::functionplotresponse::func[$xi])) { return 'no_func'; } |
$xiold=$xi; |
$xiold=$xi; |
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# Function value |
$Apache::functionplotresponse::func[$xi]=&cubic_hermite($t,@yparms); |
$Apache::functionplotresponse::func[$xi]=&cubic_hermite($t,@yparms); |
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# dy/dx=dy/dt/(dx/dt) |
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my $dxdt=&ddt_cubic_hermite($t,@xparms); |
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if ($dxdt) { |
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$Apache::functionplotresponse::dfuncdx[$xi]=&ddt_cubic_hermite($t,@yparms)/$dxdt; |
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} |
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# d^2y/dx^2 |
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my $d2xdt2=&d2dt2_cubic_hermite($t,@xparms); |
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if ($d2xdt2) { |
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$Apache::functionplotresponse::d2funcd2x[$xi]=&d2dt2_cubic_hermite($t,@yparms)/$d2xdt2; |
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} |
} |
} |
} |
} |
} |
} |
Line 667 sub end_functionplotresponse {
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Line 756 sub end_functionplotresponse {
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$xmax=(defined($xmax)?$xmax:10); |
$xmax=(defined($xmax)?$xmax:10); |
my $ad; |
my $ad; |
if (&populate_arrays($internalid,$xmin,$xmax) eq 'no_func') { |
if (&populate_arrays($internalid,$xmin,$xmax) eq 'no_func') { |
$ad='BAD_FORMULA'; |
$ad='NOT_FUNCTION'; |
} else { |
} else { |
$ad='INCORRECT'; |
$ad='INCORRECT'; |
} |
} |
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# |
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# Store grading info |
# Store grading info |
# |
# |