# Getting StartedΒΆ

The following code snippet shows a simple example of how to use the C++ interface to celerite. In this example, the kernel has the form:

$k(\tau) = a_1\,e^{-c_1\,\tau} + a_2\,e^{-c_2\,\tau} + \frac{1}{2}\left[ (a_3 + i\,b_3)\,e^{-(c_3+i\,d_3)\,\tau} + (a_3 - i\,b_3)\,e^{-(c_3-i\,d_3)\,\tau} \right]$

For more details of the kernel structure supported by celerite, check out Kernel Building.

#include <cmath>
#include <iostream>
#include <Eigen/Core>
#include "celerite/celerite.h"

using Eigen::VectorXd;

int main () {
// Choose some demo parameters for the solver
int j_real = 2, j_complex = 1;
VectorXd alpha_real(j_real),
beta_real(j_real),
alpha_complex_real(j_complex),
alpha_complex_imag(j_complex),
beta_complex_real(j_complex),
beta_complex_imag(j_complex);
alpha_real << 1.0, 0.3;
beta_real << 0.5, 3.5;
alpha_complex_real << 1.0;
alpha_complex_imag << 0.1;
beta_complex_real << 3.0;
beta_complex_imag << 1.0;

// Generate some fake data
int N = 500;
srand(42);
VectorXd x = VectorXd::Random(N),
yvar = VectorXd::Random(N),
y;
yvar.array() *= 0.1;
yvar.array() += 1.0;
std::sort(x.data(), x.data() + x.size()); // The independent coordinates must be sorted
y = sin(x.array());

// Set up the solver
celerite::solver::BandSolver<double> solver;
solver.compute(
alpha_real, beta_real,
alpha_complex_real, alpha_complex_imag,
beta_complex_real, beta_complex_imag,
x, yvar  // Note: this is the measurement _variance_
);

std::cout << solver.log_determinant() << std::endl;
std::cout << solver.dot_solve(y) << std::endl;

return 0;
}


Compiling and executing this example should output:

86.405
0.82574