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package maple2c_derivatives;
use List::Util 'all';
use Data::Dumper;
use Exporter;
@ISA = qw(Exporter);
@EXPORT = qw(
maple2c_derivatives
);
1; # return true value
sub maple2c_derivatives
{
my $derivative = $_[0];
my $type = $_[1];
my @out_der = ();
my @words = ("rho", "sigma", "lapl", "tau");
my %partials = (
"rho" => [[[0, 0, 0, 0, 0, 0, 0, 0, 0]], # 0th-order
[[1, 0, 0, 0, 0, 0, 0, 0, 0], # 1st-order
[0, 1, 0, 0, 0, 0, 0, 0, 0]],
[[2, 0, 0, 0, 0, 0, 0, 0, 0], # 2nd-order
[1, 1, 0, 0, 0, 0, 0, 0, 0],
[0, 2, 0, 0, 0, 0, 0, 0, 0]],
[[3, 0, 0, 0, 0, 0, 0, 0, 0], # 3rd-order
[2, 1, 0, 0, 0, 0, 0, 0, 0],
[1, 2, 0, 0, 0, 0, 0, 0, 0],
[0, 3, 0, 0, 0, 0, 0, 0, 0]],
[[4, 0, 0, 0, 0, 0, 0, 0, 0], # 4th-order
[3, 1, 0, 0, 0, 0, 0, 0, 0],
[2, 2, 0, 0, 0, 0, 0, 0, 0],
[1, 3, 0, 0, 0, 0, 0, 0, 0],
[0, 4, 0, 0, 0, 0, 0, 0, 0]],
],
"sigma" => [[[0, 0, 0, 0, 0, 0, 0, 0, 0]], # 0th-order
[[0, 0, 1, 0, 0, 0, 0, 0, 0], # 1st-order
[0, 0, 0, 1, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 1, 0, 0, 0, 0]],
[[0, 0, 2, 0, 0, 0, 0, 0, 0], # 2nd-order
[0, 0, 1, 1, 0, 0, 0, 0, 0],
[0, 0, 1, 0, 1, 0, 0, 0, 0],
[0, 0, 0, 2, 0, 0, 0, 0, 0],
[0, 0, 0, 1, 1, 0, 0, 0, 0],
[0, 0, 0, 0, 2, 0, 0, 0, 0]],
[[0, 0, 3, 0, 0, 0, 0, 0, 0], # 3rd-order
[0, 0, 2, 1, 0, 0, 0, 0, 0],
[0, 0, 2, 0, 1, 0, 0, 0, 0],
[0, 0, 1, 2, 0, 0, 0, 0, 0],
[0, 0, 1, 1, 1, 0, 0, 0, 0],
[0, 0, 1, 0, 2, 0, 0, 0, 0],
[0, 0, 0, 3, 0, 0, 0, 0, 0],
[0, 0, 0, 2, 1, 0, 0, 0, 0],
[0, 0, 0, 1, 2, 0, 0, 0, 0],
[0, 0, 0, 0, 3, 0, 0, 0, 0]],
[[0, 0, 4, 0, 0, 0, 0, 0, 0], # 4th-order
[0, 0, 3, 1, 0, 0, 0, 0, 0],
[0, 0, 3, 0, 1, 0, 0, 0, 0],
[0, 0, 2, 2, 0, 0, 0, 0, 0],
[0, 0, 2, 1, 1, 0, 0, 0, 0],
[0, 0, 2, 0, 2, 0, 0, 0, 0],
[0, 0, 1, 3, 0, 0, 0, 0, 0],
[0, 0, 1, 2, 1, 0, 0, 0, 0],
[0, 0, 1, 1, 2, 0, 0, 0, 0],
[0, 0, 1, 0, 3, 0, 0, 0, 0],
[0, 0, 0, 4, 0, 0, 0, 0, 0],
[0, 0, 0, 3, 1, 0, 0, 0, 0],
[0, 0, 0, 2, 2, 0, 0, 0, 0],
[0, 0, 0, 1, 3, 0, 0, 0, 0],
[0, 0, 0, 0, 4, 0, 0, 0, 0]]
],
"lapl" => [[[0, 0, 0, 0, 0, 0, 0, 0, 0]], # 0th-order
[[0, 0, 0, 0, 0, 1, 0, 0, 0], # 1st-order
[0, 0, 0, 0, 0, 0, 1, 0, 0]],
[[0, 0, 0, 0, 0, 2, 0, 0, 0], # 2nd-order
[0, 0, 0, 0, 0, 1, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 2, 0, 0]],
[[0, 0, 0, 0, 0, 3, 0, 0, 0], # 3rd-order
[0, 0, 0, 0, 0, 2, 1, 0, 0],
[0, 0, 0, 0, 0, 1, 2, 0, 0],
[0, 0, 0, 0, 0, 0, 3, 0, 0]],
[[0, 0, 0, 0, 0, 4, 0, 0, 0], # 4th-order
[0, 0, 0, 0, 0, 3, 1, 0, 0],
[0, 0, 0, 0, 0, 2, 2, 0, 0],
[0, 0, 0, 0, 0, 1, 3, 0, 0],
[0, 0, 0, 0, 0, 0, 4, 0, 0]]
],
"tau" => [[[0, 0, 0, 0, 0, 0, 0, 0, 0]], # 0th-order
[[0, 0, 0, 0, 0, 0, 0, 1, 0], # 1st-order
[0, 0, 0, 0, 0, 0, 0, 0, 1]],
[[0, 0, 0, 0, 0, 0, 0, 2, 0], # 2nd-order
[0, 0, 0, 0, 0, 0, 0, 1, 1],
[0, 0, 0, 0, 0, 0, 0, 0, 2]],
[[0, 0, 0, 0, 0, 0, 0, 3, 0], # 3rd-order
[0, 0, 0, 0, 0, 0, 0, 2, 1],
[0, 0, 0, 0, 0, 0, 0, 1, 2],
[0, 0, 0, 0, 0, 0, 0, 0, 3]],
[[0, 0, 0, 0, 0, 0, 0, 4, 0], # 4th-order
[0, 0, 0, 0, 0, 0, 0, 3, 1],
[0, 0, 0, 0, 0, 0, 0, 2, 2],
[0, 0, 0, 0, 0, 0, 0, 1, 3],
[0, 0, 0, 0, 0, 0, 0, 0, 4]]
]
);
# finds out the order of each partial
my %order = ();
my $total_order = 0;
foreach $word (@words){
$order{$word} = 0;
if($derivative =~ /$word([0-9]*)/){
$order{$word} = $1 == "" ? 1 : int($1);
$total_order += $order{$word};
}
}
my %n_var = ("lda" => 2, "gga" => 5, "mgga" => 9);
my $max_n = $n_var{$type};
my @all_derivatives = ();
my $der_n = 0;
for(my $n_rho=0; $n_rho <= $#{$partials{"rho"}[$order{"rho"}]}; $n_rho++){
for(my $n_sigma=0; $n_sigma <= $#{$partials{"sigma"}[$order{"sigma"}]}; $n_sigma++){
for(my $n_lapl=0; $n_lapl <= $#{$partials{"lapl"}[$order{"lapl"}]}; $n_lapl++){
for(my $n_tau=0; $n_tau <= $#{$partials{"tau"}[$order{"tau"}]}; $n_tau++){
# sum orders in all variables
my @final_der = (0) x $max_n;
for(my $i=0; $i<$max_n; $i++){
$final_der[$i] +=
$partials{"rho"}[$order{"rho"}][$n_rho][$i] +
$partials{"sigma"}[$order{"sigma"}][$n_sigma][$i] +
$partials{"lapl"}[$order{"lapl"}][$n_lapl][$i] +
$partials{"tau"}[$order{"tau"}][$n_tau][$i];
}
push @all_derivatives, [\@final_der, $derivative."_".($der_n++)."_"];
}
}
}
}
return @all_derivatives;
}
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