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inline void RevAtanOp(size_t
d,
const
Base *
z, const
Base *
b, const
Base *
x,
Base *
pz,
Base *
pb,
Base *
px)
G(z, b, x)
and we wish to compute the partial derivatives for
the function
\[
H(x) = G [ Z(x) , B(x) , x ]
\]
where
Z(x)
and
B(x)
are defined as the
d-th order Taylor coefficient row vector for
\arctan(x)
and
1 + x * x
as a function of the corresponding row vector for X; i.e.,
\[
\begin{array}{rcl}
Z & = & \arctan(X) \\
B & = & 1 + X * X
\end{array}
\]
Note that Z and
B
have
been used both the original
functions and for the corresponding mapping of Taylor coefficients.
d+1
and contains the
d-th order Taylor coefficient row vector for X.
d+1
and contains
d-th order Taylor coefficient row vector for z.
d+1
and contains
d-th order Taylor coefficient row vector for B.
d+1
and
px[
j]
contains the partial for G
with respect to the j-th order Taylor coefficient for X.
d+1
and
pz[
j]
contains the partial for G
with respect to the j-th order Taylor coefficient for Z.
d+1
and
pb[
j]
contains the partial for G
with respect to the j-th order Taylor coefficient for B.
d+1
and
px[
j]
contains the partial for H
with respect to the j-th order Taylor coefficient for X.
d+1
and
its contents are no longer specified; i.e., it has
been used for work space.
d+1
and
its contents are no longer specified; i.e., it has
been used for work space.