Preliminaries

Namespaces

cntr	All relevant classes and functions of libcntr are defined here
fourier	Fourier transformation routines. Used almost exclusively internally.

Needed for developers only:

integration	Weights for quadrature and differentiation routines.
linalg	Linear algebra routines (out-dated).

Scalar and matrix types

Complex numbers:

The numerical routines in NESSi are built on standard complex-valued algebra.

For the most commonly-used double precision numbers, the following shortcuts are defined:

#include <complex>
#define cdouble std::complex<double>
#define II cdouble(0.0,1.0)

Matrices and linear algebra:

Green’s functions \(C(t,t')\) can be matrix-valued. We use the eigen3 library for handling matrices.

The following shortcuts are defined:

#include <eigen3/Eigen/Dense>
// integer precision variable-size vector
#define ivector VectorXi
// double precision variable-size vector
#define dvector VectorXd
// complex-valued double precision variable-size vector
#define cdvector VectorXcd
// integer precision variable-size matrix
#define imatrix MatrixXi
// double precision variable-size matrix
#define dmatrix MatrixXd
// complex-valued double precision variable-size matrix
#define cdmatrix MatrixXcd

Example:

cdmatrix mm(2,2);  // a complex-valued 2x2 matrix
cdmatrix mm2;
// set mm to sigma_x
mm.setZero();
mm(0,1)=1;
mm(1,0)=1;
mm2=mm*mm;  // mm^2
// etc ...

(For a complete documentation, see eigen3)

Some global #defines

Listed for reference only. Explanation in the sections below.

#define CNTR_PI 3.14159265358979323846
#define CNTR_MAT_FOURIER 0
#define CNTR_MAT_CG 1
#define CNTR_MAT_FIXPOINT 2
#define FERMION -1
#define BOSON 1
#define GREEN cntr::herm_matrix<double>
#define GREEN_TSTP cntr::herm_matrix_timestep<double>
#define CFUNC cntr::herm_function<double>