A C++ header-only library of statistical distribution functions.
StatsLib is a templated C++ library of statistical distribution functions, featuring unique compile-time computing capabilities and seamless integration with several popular linear algebra libraries.
Features:
constexpr
format, enabling the library to operate as both a compile-time and run-time computation engine.Functions to compute the cdf, pdf, quantile, as well as random sampling methods, are available for the following distributions:
In addition, pdf and random sampling functions are available for several multivariate distributions:
StatsLib is a header-only library. Simply add the header files to your project using
#include "stats.hpp"
The only dependency is the latest version of GCEM and a C++11 compatible compiler.
Full documentation is available online:
A PDF version of the documentation is available here.
You can test the library online using an interactive Jupyter notebook:
The following options should be declared before including the StatsLib header files.
constexpr
specifiers):#define STATS_GO_INLINE
_OPENMP
macro is detected (e.g., by invoking -fopenmp
with GCC or Clang). To explicitly enable OpenMP features use:#define STATS_USE_OPENMP
#define STATS_DONT_USE_OPENMP
#define STATS_ENABLE_ARMA_WRAPPERS
#define STATS_ENABLE_BLAZE_WRAPPERS
#define STATS_ENABLE_EIGEN_WRAPPERS
std::vector
:#define STATS_ENABLE_STDVEC_WRAPPERS
Functions are called using an R-like syntax. Some general rules:
stats::d*
. For example, the Normal (Gaussian) density is called usingstats::dnorm(<value>,<mean parameter>,<standard deviation>);
stats::p*
. For example, the Gamma CDF is called usingstats::pgamma(<value>,<shape parameter>,<scale parameter>);
stats::q*
. For example, the Beta quantile is called usingstats::qbeta(<value>,<a parameter>,<b parameter>);
stats::r*
. For example, to generate a single draw from the Logistic distribution:stats::rlogis(<location parameter>,<scale parameter>,<seed value or random number engine>);
All of these functions have matrix-based equivalents using Armadillo, Blaze, and Eigen dense matrices.
// Using Armadillo:
arma::mat norm_pdf_vals = stats::dnorm(arma::ones(10,20),1.0,2.0);
r*
) can output random matrices of arbitrary size. For example, For example, the following code will generate a 100-by-50 matrix of iid draws from a Gamma(3,2) distribution:// Armadillo:
arma::mat gamma_rvs = stats::rgamma<arma::mat>(100,50,3.0,2.0);
// Blaze:
blaze::DynamicMatrix<double> gamma_rvs = stats::rgamma<blaze::DynamicMatrix<double>>(100,50,3.0,2.0);
// Eigen:
Eigen::MatrixXd gamma_rvs = stats::rgamma<Eigen::MatrixXd>(100,50,3.0,2.0);
-fopenmp
option during compilation.Random number seeding is available in two forms: seed values and random number engines.
stats::rnorm(1,2,1776);
std::mt19937_64
) and are passed by reference. Example:std::mt19937_64 engine(1776);
stats::rnorm(1,2,engine);
More examples with code:
// evaluate the normal PDF at x = 1, mu = 0, sigma = 1
double dval_1 = stats::dnorm(1.0,0.0,1.0);
// evaluate the normal PDF at x = 1, mu = 0, sigma = 1, and return the log value
double dval_2 = stats::dnorm(1.0,0.0,1.0,true);
// evaluate the normal CDF at x = 1, mu = 0, sigma = 1
double pval = stats::pnorm(1.0,0.0,1.0);
// evaluate the Laplacian quantile at p = 0.1, mu = 0, sigma = 1
double qval = stats::qlaplace(0.1,0.0,1.0);
// draw from a t-distribution dof = 30
double rval = stats::rt(30);
// matrix output
arma::mat beta_rvs = stats::rbeta<arma::mat>(100,100,3.0,2.0);
// matrix input
arma::mat beta_cdf_vals = stats::pbeta(beta_rvs,3.0,2.0);
StatsLib is designed to operate equally well as a compile-time computation engine. Compile-time computation allows the compiler to replace function calls (e.g., dnorm(0,0,1)
) with static values in the source code. That is, functions are evaluated during the compilation process, rather than at run-time. This capability is made possible due to the templated constexpr
design of the library and can be verified by inspecting the assembly code generated by the compiler.
The compile-time features are enabled using the constexpr
specifier. The example below computes the pdf, cdf, and quantile function of the Laplace distribution.
#include "stats.hpp"
int main()
{
constexpr double dens_1 = stats::dlaplace(1.0,1.0,2.0); // answer = 0.25
constexpr double prob_1 = stats::plaplace(1.0,1.0,2.0); // answer = 0.5
constexpr double quant_1 = stats::qlaplace(0.1,1.0,2.0); // answer = -2.218875...
return 0;
}
Assembly code generated by Clang without any optimization:
LCPI0_0:
.quad -4611193153885729483 ## double -2.2188758248682015
LCPI0_1:
.quad 4602678819172646912 ## double 0.5
LCPI0_2:
.quad 4598175219545276417 ## double 0.25000000000000006
.section __TEXT,__text,regular,pure_instructions
.globl _main
.p2align 4, 0x90
_main: ## @main
push rbp
mov rbp, rsp
xor eax, eax
movsd xmm0, qword ptr [rip + LCPI0_0] ## xmm0 = mem[0],zero
movsd xmm1, qword ptr [rip + LCPI0_1] ## xmm1 = mem[0],zero
movsd xmm2, qword ptr [rip + LCPI0_2] ## xmm2 = mem[0],zero
mov dword ptr [rbp - 4], 0
movsd qword ptr [rbp - 16], xmm2
movsd qword ptr [rbp - 24], xmm1
movsd qword ptr [rbp - 32], xmm0
pop rbp
ret
Keith O'Hara
Apache Version 2