StatsLib is a templated C++ library of statistical distribution functions.
Features:
- A header-only library of probability density functions, cumulative distribution functions, quantile functions, and random sampling methods.
- Functions are written in C++11
constexpr
format.- Built on the GCE-Math library, StatsLib can operate as a compile-time or run-time computation engine.
- A simple, R-like syntax.
- Optional vector-matrix functionality with wrappers to support several popular linear algebra libraries, including:
- Matrix-based operations are parallelizable with OpenMP.
- Released under a permissive, non-GPL license.
Contents:
- Distributions
- Installation
- Compile-time Options
- Syntax and Examples
- Compile-time Computation
- Author and License
Distributions
Functions to compute the cdf, pdf, and quantile, as well as random sampling, are available for the following distributions:
- Bernoulli
- Beta
- Binomial
- Cauchy
- Chi-squared
- Exponential
- F
- Gamma
- Inverse-Gamma
- Laplace
- Logistic
- Log-Normal
- Normal (Gaussian)
- Poisson
- Student's t
- Uniform
- Weibull
In addition, pdf and random sampling functions are available for several multivariate distributions:
- inverse-Wishart
- Multivariate Normal
- Wishart
Installation
StatsLib is a header-only library. Simply copy the contents of the include folder and add the header files to your project using
#include "stats.hpp"
Compile-time Options
- For inline-only functionality (i.e., no
constexpr
specifiers):
#define STATS_GO_INLINE
- OpenMP functionality is enabled by default if the
_OPENMP
macro is detected (e.g., by invoking-fopenmp
with a GCC or Clang compiler). To explicitly enable OpenMP features use:
#define STATS_USE_OPENMP
- To disable OpenMP functionality:
#define STATS_DONT_USE_OPENMP
- To use StatsLib with the Armadillo, Blaze or Eigen libraries:
#define STATS_USE_ARMA
#define STATS_USE_BLAZE
#define STATS_USE_EIGEN
Syntax and Examples
Functions are called using an R-like syntax. Some general rules:
- density functions:
stats::d*
. For example, the Normal (Gaussian) density is called using
stats::dnorm(<value>,<mean parameter>,<standard deviation>);
- cumulative distribution functions:
stats::p*
. For example, the Gamma CDF is called using
stats::pgamma(<value>,<shape parameter>,<scale parameter>);
- quantile functions:
stats::q*
. For example, the Beta quantile is called using
stats::qbeta(<value>,<a parameter>,<b parameter>);
- random sampling:
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.
- The pdf, cdf, and quantile functions can take matrix-valued arguments. For example,
// Using Armadillo:
arma::mat norm_pdf_vals = stats::dnorm(arma::ones(10,20),1.0,2.0);
- The randomization functions (
r*
) can output random matrices of arbitrary size. For example,
// 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);
will generate a 100-by-50 matrix of iid draws from a Gamma(3,2) distribution.
- All matrix-based operations are parallelizable with OpenMP. For GCC and Clang compilers, simply include the
-fopenmp
option during compilation.
Random number seeding is available in two forms: seed values or random number engines (preferred).
- Seed values are passed as unsigned integers. For example, to generate a draw from a normal distribution N(1,2) with seed value 1776:
stats::rnorm(1,2,1776);
- Random engines in StatsLib use the 64-bit Mersenne-Twister generator (
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);
Compile-time Computation
In addition to being a standard run-time library, StatsLib can operate as a compile-time computation engine. Compile-time features are enabled using the constexpr
specifier:
#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:
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
Author
Keith O'Hara
License
Apache Version 2