fntl: Tools for Rcpp with STL FunctionsTBD abstract goes here.
Source code can be found in integrate.h.
Compute the integral \[
\int_a^b f(x) dx,
\] where \(a\) may be finite or \(-\infty\) and \(b\) may be finite or \(\infty\). Calls one of two C functions underlying the R function integrate: Rdqags when both limits are finite and Rdqagi otherwise. These functions are based on routines in QUADPACK (Piessens et al. 1983).
The second form uses defaults for all elements of args.
integrate_result integrate(
1 const uv_function& f,
2 double lower,
3 double upper,
4 const integrate_args& args
)
integrate_result integrate(
const uv_function& f,
double lower,
double upper
)R_NegInf.
R_PosInf.
struct integrate_args {
1 unsigned int subdivisions = 100L;
2 double rel_tol = mach_eps_4r;
3 double abs_tol = mach_eps_4r;
4 bool stop_on_error = true;
};true, errors in integrate raise exceptions.
struct integrate_result : public result {
1 double value;
2 double abs_error;
3 int subdivisions;
4 integrate_status status;
5 int n_eval;
6 std::string message;
7 Rcpp::List to_list() const;
};List representation.
enum class integrate_status : int {
0 OK = 0L,
1 MAX_SUBDIVISIONS = 1L,
2 ROUNDOFF_ERROR = 2L,
3 BAD_INTEGRAND_BEHAVIOR = 3L,
4 ROUNDOFF_ERROR_EXTRAPOLATION_TABLE = 4L,
5 PROBABLY_DIVERGENT_INTEGRAL = 5L,
6 INVALID_INPUT = 6L
};Compute the integral \(\int_{-\infty}^0 e^{-x^2/2} dx\).
const fntl::uv_function& f = [](double x) {
return exp(-pow(x, 2) / 2);
};
auto out = fntl::integrate(f, R_NegInf, 0);
double value = out.value;Source code can be found in fd-deriv.h.
Compute the derivative of \(f : \mathbb{R} \rightarrow \mathbb{R}\) numerically at point \(x\) using Ridders algorithm, adapted from the program dfridr in Section 5.7 of Press et al. (2007).
The second form uses defaults for all elements of args.
fd_deriv_result fd_deriv(
1 const uv_function& f,
2 double x,
3 double h = 1,
4 unsigned int maxiter = 10
)TBD is this true? Taking maxiter = 1 gives the basic (symmetric) finite-difference derivative using the initial value of h as the perturbation.
struct fd_deriv_result : public result {
1 double value;
2 double err;
3 unsigned int iter;
4 Rcpp::List to_list() const;
};List representation.
Compute the derivative of \(f(x) = \sin(x)\) at \(x = 1/2\).
const fntl::uv_function& f = [](double x) {
return sin(x);
};
auto out = fntl::fd_deriv(f, 0.5);
double value = out.value;cgmin...
Corresponding author andrew.raim@gmail.com. Center for Statistical Research & Methodology, U.S. Census Bureau, Washington, DC, 20233, U.S.A. Disclaimer: This document is released to inform interested parties of ongoing research and to encourage discussion of work in progress. Any views expressed are those of the authors and not those of the U.S. Census Bureau.↩︎
Corresponding author andrew.raim@gmail.com. Center for Statistical Research & Methodology, U.S. Census Bureau, Washington, DC, 20233, U.S.A. Disclaimer: This document is released to inform interested parties of ongoing research and to encourage discussion of work in progress. Any views expressed are those of the authors and not those of the U.S. Census Bureau.↩︎
Corresponding author andrew.raim@gmail.com. Center for Statistical Research & Methodology, U.S. Census Bureau, Washington, DC, 20233, U.S.A. Disclaimer: This document is released to inform interested parties of ongoing research and to encourage discussion of work in progress. Any views expressed are those of the authors and not those of the U.S. Census Bureau.↩︎
Comments
I think a nice document will make a huge difference in the usability of this package. The generated documentation from Doxygen is okay, but not the most appealing. It has a lot of cruft that distracts from what I’d want to see as a user.
Here’s what I have in mind right now. Let’s try to manually document the API in a human readable way.
TBD:
fd_hessianuse the Numerical Cookbook version offd_deriv?[[Rcpp::plugins("cpp11")]]somewhere too.