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	return $value;
}

sub sigmoid2_slope
{
	my $network = shift;
	my $value = shift;
	my @debug = @{$network->{'debug'}};


	my $return = exp(-$value) * ((1 + exp(-$value)) ** -2);
	if (scalar @debug > 0)
	{$network->dbug("sigmoid_slope returning $value",5);}

	return $return;
}

############################################################
# standard sigmoid activation 
############################################################

sub sigmoid
{
	my $network = shift;
	my $value = shift;	
	$value = 1/(1+exp(1)**-$value);
	$network->dbug("Sigmoid activation returning $value",5);	
	return $value;
}

sub sigmoid_slope
{
	my $network = shift;
	my $value = shift;
	my @debug = @{$network->{'debug'}};


	my $return = $value * (1-$value);
	if (scalar @debug > 0)
	{$network->dbug("sigmoid_slope returning $value",5);}

	return $return;
}

############################################################
# hopfield_threshold
# standard hopfield threshold activation - doesn't need a 
# slope (because hopfield networks don't use them!)
############################################################
sub hopfield_threshold
{
	my $network = shift;
	my $value = shift;

	if ($value <0){return -1}
	if ($value >0){return 1}
	return $value;
}

############################################################
# atanh error function
############################################################
sub atanh
{
	my $network = shift;
	my $value = shift;
	if ($value >-0.5 && $value <0.5)
	{
		$value = log((1+$value)/(1-$value))/2;
	}
	return $value;
}

1;

=pod

=head1 NAME

AI::NNFlex::Mathlib - miscellaneous mathematical functions for the AI::NNFlex NN package

=head1 DESCRIPTION

The AI::NNFlex::Mathlib package contains activation and error functions. At present there are the following:

Activation functions

=over

=item *
tanh

=item *
linear

=item *
hopfield_threshold

=back

Error functions

=over

=item *
atanh

=back

If you want to implement your own activation/error functions, you can add them to this module. All activation functions to be used by certain types of net (like Backprop) require an additional function <function name>_slope, which returns the 1st ord...

This rule doesn't apply to all network types. Hopfield for example requires no slope calculation.

=head1 CHANGES

v1.2 includes hopfield_threshold

=head1 COPYRIGHT

Copyright (c) 2004-2005 Charles Colbourn. All rights reserved. This program is free software; you can redistribute it and/or modify it under the same terms as Perl itself.

=head1 CONTACT

 charlesc@nnflex.g0n.net



=cut