matsubara_dft()

template<typename T , class GG , int SIZE1>

void cntr::matsubara_dft	(	std::complex< T > *	mdft,
		GG &	G,
		int	sig
	)

Computes the Fourier series coefficients of a Matsubara function by plain DFT.

Purpose

Computes \( I = \sum_{r=0}^m f(\tau_r) e^{i \omega_n \tau_r}\) for \(n=0,\dot,m\), assuming \(\tau_r = r \beta/m\). The Matsubara frequencies are given by \(\omega_n= (2n+1)\pi/\beta\) for fermions, while \(\omega_n= 2n*\pi/\beta\) for bosons.

Parameters

mdft	[complex] on return, pointer storing the Fourier coeffients in element representation
G	[GG] Matsubara function to be Fourier transformed
sig	[int] sig=-1 for fermions, sig=+1 for bosons

Definition at line 134 of file cntr_matsubara_impl.hpp.

                                                        {
    typedef std::complex<T> cplx;
    int ntau, r, m, sg, size1 = G.size1();
    double arg, one;
    cplx *z, *z1, expfac;
    sg = G.element_size();
    ntau = G.ntau();
    z = new cplx[sg];
    z1 = new cplx[sg];
    one = (sig == -1 ? 1.0 : 0.0);
    for (m = 0; m <= ntau; m++) {
        element_set_zero<T, SIZE1>(size1, z);
        for (r = 0; r <= ntau; r++) {
            arg = ((2 * m + one) * r * PI) / ntau;
            expfac = cplx(cos(arg), sin(arg));
            element_set<T, SIZE1>(size1, z1, G.matptr(r));
            element_smul<T, SIZE1>(size1, z1, expfac);
            element_incr<T, SIZE1>(size1, z, z1);
        }
        element_set<T, SIZE1>(size1, mdft + m * sg, z);
    }
    delete[] z;
    delete[] z1;
}