LatticeInfo(latt_size: List[int], t_boundary: Literal[1, -1] = 1, anisotropy: float = 1.0)

mpi_comm: MPI.Comm

mpi_size: int

mpi_rank: int

grid_size: List[int]

grid_coord: List[int]

global_size: List[int]

global_volume: int

size: List[int]

volume: int

size_cb2: List[int]

volume_cb2: int

t_boundary: Literat[-1, 1]

anisotropy: float

latt_info: LatticeInfo

data: numpy.ndarray | cupy.ndarray | torch.Tensor

backend: "numpy" | "cupy" | "torch"

location: "numpy" | "cupy" | "torch"

def backup() -> numpy.ndarray | cupy.ndarray | torch.Tensor

def copy() -> numpy.ndarray | cupy.ndarray | torch.Tensor

def toDevice()

def toHost()

def getHost() -> numpy.ndarray

LatticeGauge(latt_info: LatticeInfo, value=None)

def setAntiPeriodicT()

def setAnisotropy()

data_ptr: Pointer

data_ptrs: Pointers

def lexico() -> numpy.ndarray

def ensurePureGauge()

covDev(x: LatticeFerimon, covdev_mu: int) -> LatticeFermion

Applies the covariant derivative on x in the direction covdev_mu. x should be LatticeFermion. 0/1/2/3 represent +x/+y/+z/+t and 4/5/6/7 represent -x/-y/-z/-t. The covariant derivative is defined as $\psi'(x)=U_\mu(x)\psi(x+\hat{\mu})$.

def laplace(x: LatticeStaggeredFermion, laplace3D: int) -> LatticeStaggeredFermion

Applies the Laplacian operator on x, and laplace3D takes 3 or 4 to apply Laplacian on spacial or all directions. x should be LatticeStaggeredFermion. The Laplacian operator is defined as $\psi'(x)=\frac{1}{N_\mathrm{Lap}}\sum_\mu\psi(x)-\dfrac{1}{2}\left[U_\mu(x)\psi(x+\hat{\mu})+U_\mu^\dagger(x-\hat{\mu})\psi(x-\hat{\mu})\right]$

def staggeredPhase()

Applies the staggered phase to the gauge field. The convention is controld by LatticeGauge.pure_gauge.gauge_param.staggered_phase_type, which is QudaStaggeredPhase.QUDA_STAGGERED_PHASE_MILC by default.

def projectSU3(tol: float)

Projects the gauge field onto SU(3) matrix. tol is the tolerance of how matrix deviates from SU(3). 2e-15 (which is 10x the epsilon of fp64) should be a good choice.

def path(paths: List[List[int]])

def loop(loops: List[List[List[int]]], coeff: List[float])

loops is a list of length 4, which is [paths_x, paths_y, paths_z, paths_t]. All paths_* should have the same shape. paths_x is a list of any length.

def loopTrace(loops: List[List[int]]) -> numpy.ndarray

loops is similar to paths_x in LatticeGauge.path, but the function returns the traces of all loops. The traces is a numpy.ndarray of complex number, and every element is defined as $\sum_x\mathrm{Tr}W(x)$.

def apeSmear(n_steps: int, alpha: float, dir_ignore: int)

Applies the APE smearing to the gauge field. alpha is the smearing strength.

def smearAPE(n_steps, factor, dir_ignore)

Similar to LatticeGauge.apeSmear() but factor matchs Chroma.

def stoutSmear(n_steps, rho, dir_ignore)

Applies the stout smearing to the gauge field. rho is the smearing strength.

def smearSTOUT(n_steps, rho, dir_ignore)

Similar to LatticeGauge.stoutSmear().

def hypSmear(n_steps, alpha1, alpha2, alpha3, dir_ignore)

Applies the stout smearing to the gauge field. alpha1/alpha2/alpha3 is the smearing strength on level 3/2/1.

def smearHYP(n_steps, alpha1, alpha2, alpha3, dir_ignore)

Similar to LatticeGauge.hypSmear().

def wilsonFlow(n_steps, epsilon)

Applies the Wilson flow to the gauge field. Returns the energy (all, spacial, temporal) for every step.

def wilsonFlowScale(max_steps, epsilon)

Returns $t_0$ and $w_0$ with up to max_steps Wilson flow step.

def symanzikFlow(n_steps, epsilon)

Applies the Symanzik flow to the gauge field. Returns the energy (all, spacial, temporal) for every step.

def symanzikFlowScale(max_steps, epsilon)

Returns $t_0$ and $w_0$ with up to max_steps Symanzik flow step.

def plaquette()

Returns the plaquette (all, spatial, temporal) of the gauge field.

def polyakovLoop()

Returns the Polyakov loop (real, image) of the gauge field.

def energy() -> List[int]

Returns the energy (all, spacial, temporal) of the gauge field.

def qcharge() -> float

Returns the topological charge of the gauge field.

def qchargeDensity() -> numpy.ndarray

Returns the topological charge density with shape (2, Lt, Lz, Ly, Lx // 2))`.

def gauss(seed, sigma)

Fills the gauge field with random SU(3) matrices. sigma=1 corresponds to the standard normal distribution.

def fixingOVR(gauge_dir, Nsteps, verbose_interval, relax_boost, tolerance, reunit_interval, stopWtheta)

Applies the gauge gixing to the gauge field and over relaxation is used to speed up the operation.

gauge_dir: {3, 4}
    3 for Coulomb gauge fixing, 4 for Landau gauge fixing
Nsteps: int
    maximum number of steps to perform gauge fixing
verbose_interval: int
    print gauge fixing info when iteration count is a multiple of this
relax_boost: float
    gauge fixing parameter of the overrelaxation method, most common value is 1.5 or 1.7.
tolerance: float
    torelance value to stop the method, if this value is zero then the method stops when
    iteration reachs the maximum number of steps defined by Nsteps
reunit_interval: int
    reunitarize gauge field when iteration count is a multiple of this
stopWtheta: int
    0 for MILC criterion and 1 to use the theta value

def fixingFFT(gauge_dir, Nsteps, verbose_interval, alpha, autotune, tolerance, stopWtheta)

Applies the gauge gixing to the gauge field and fast Fourier transform is used to speed up the operation.

gauge_dir: {3, 4}
    3 for Coulomb gauge fixing, 4 for Landau gauge fixing
Nsteps: int
    maximum number of steps to perform gauge fixing
verbose_interval: int
    print gauge fixing info when iteration count is a multiple of this
alpha: float
    gauge fixing parameter of the method, most common value is 0.08
autotune: int
    1 to autotune the method, i.e., if the Fg inverts its tendency we decrease the alpha value
tolerance: float
    torelance value to stop the method, if this value is zero then the method stops when
    iteration reachs the maximum number of steps defined by Nsteps
stopWtheta: int
    0 for MILC criterion and 1 to use the theta value