regularisation.h File Reference

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Functions

double sqr (double x)

double g (double z)

neuron transfer function

double g_s (double z)

first dervative

double g_s_inv (double z)

inverse of the first derivative

double g_s (double z, double xsi)

$g'(z+xsi) = 1-(tanh(z+xsi))^2$
with additional clipping

double g_ss_div_s (double z, double xsi)

an exact formula for g''/g', with clipped Z = z+xsi

double derive_g_s_inv_exact_clip (double z, double xsi)

with
$g'(z) = 1-(g(z+\xsi))^2$
we get
$\frac{\partial}{\partial z} \frac{1}{g'(Z)} = \frac{g''}{g'^2}$
again with clipped Z

double g_s_expand2 (double z, double xsi)

$g'(z) = 1-(z+\xsi)^2$
which is the series expansion to the second order

double g_s_inv_expand2 (double z, double xsi)

$\frac{1}{g'(z)} \approx 1+(z+\xsi)^2$
with geometric series approximation

double derive_g_s_inv_expand2 (double z, double xsi)

with
$g'(z) = 1-(z+\xsi)^2$
which is the series expansion to the second order we get
$\frac{1}{g'(z)} \approx 1+(z+\xsi)^2$
and therewith
$\frac{\partial}{\partial z} \frac{1}{g'(Z)} 2(z+\xsi)$

Function Documentation

double derive_g_s_inv_exact_clip ( double z,

double xsi

) [inline]

with
$g'(z) = 1-(g(z+\xsi))^2$
we get
$\frac{\partial}{\partial z} \frac{1}{g'(Z)} = \frac{g''}{g'^2}$
again with clipped Z

double derive_g_s_inv_expand2 ( double z,

double xsi

) [inline]

with
$g'(z) = 1-(z+\xsi)^2$
which is the series expansion to the second order we get
$\frac{1}{g'(z)} \approx 1+(z+\xsi)^2$
and therewith
$\frac{\partial}{\partial z} \frac{1}{g'(Z)} 2(z+\xsi)$

double g ( double z ) [inline]

neuron transfer function

double g_s ( double z,

double xsi

) [inline]

$g'(z+xsi) = 1-(tanh(z+xsi))^2$
with additional clipping

double g_s ( double z ) [inline]

first dervative

double g_s_expand2 ( double z,

double xsi

) [inline]

$g'(z) = 1-(z+\xsi)^2$
which is the series expansion to the second order

double g_s_inv ( double z ) [inline]

inverse of the first derivative

double g_s_inv_expand2 ( double z,

double xsi

) [inline]

$\frac{1}{g'(z)} \approx 1+(z+\xsi)^2$
with geometric series approximation

double g_ss_div_s ( double z,

double xsi

) [inline]

an exact formula for g''/g', with clipped Z = z+xsi

double sqr ( double x ) [inline]

Generated on Tue Jan 16 02:14:43 2007 for Robotsystem of the Robot Group Leipzig by

1.3.8


Functions
double	sqr (double x)
double	g (double z)
	neuron transfer function
double	g_s (double z)
	first dervative
double	g_s_inv (double z)
	inverse of the first derivative
double	g_s (double z, double xsi)
	$g'(z+xsi) = 1-(tanh(z+xsi))^2$ with additional clipping
double	g_ss_div_s (double z, double xsi)
	an exact formula for g''/g', with clipped Z = z+xsi
double	derive_g_s_inv_exact_clip (double z, double xsi)
	with $g'(z) = 1-(g(z+\xsi))^2$ we get $\frac{\partial}{\partial z} \frac{1}{g'(Z)} = \frac{g''}{g'^2}$ again with clipped Z
double	g_s_expand2 (double z, double xsi)
	$g'(z) = 1-(z+\xsi)^2$ which is the series expansion to the second order
double	g_s_inv_expand2 (double z, double xsi)
	$\frac{1}{g'(z)} \approx 1+(z+\xsi)^2$ with geometric series approximation
double	derive_g_s_inv_expand2 (double z, double xsi)
	with $g'(z) = 1-(z+\xsi)^2$ which is the series expansion to the second order we get $\frac{1}{g'(z)} \approx 1+(z+\xsi)^2$ and therewith $\frac{\partial}{\partial z} \frac{1}{g'(Z)} 2(z+\xsi)$