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# include <cppad/romberg_one.hpp>
r = RombergOne(F, a, b, n, e)
r
for a one dimensional integral
\[
r = \int_a^b F(x) {\bf d} x + O \left[ (b - a) / 2^{n-1} \right]^{2(p+1)}
\]
cppad/romberg_one.hpp is included by cppad/cppad.hpp
but it can also be included separately with out the rest of
the CppAD routines.
Float r
It is the estimate computed by RombergOne for the integral above.
F(x)
The argument x to F has prototype
const Float &x
The return value of F is a Float object
(see description of Float
below).
const Float &a
It specifies the lower limit for the integration.
const Float &b
It specifies the upper limit for the integration.
size_t n
A total number of
2^{n-1} + 1
evaluations of F(x)
are used to estimate the integral.
size_t p
It must be less than or equal
n
and determines the accuracy order in the approximation for the integral
that is returned by RombergOne.
To be specific
\[
r = \int_a^b F(x) {\bf d} x + O \left[ (b - a) / 2^{n-1} \right]^{2(p+1)}
\]
Float &e
The input value of e does not matter
and its output value is an approximation for the error in
the integral estimates; i.e.,
\[
e \approx \left| r - \int_a^b F(x) {\bf d} x \right|
\]
x < y
returns the bool value true if x is less than
y and false otherwise.
cppad/romberg_one.hpp.