util.stepper

class jVMC.util.stepper.AdaptiveHeun(timeStep=0.001, tol=1e-08, maxStep=1)

This class implements an adaptive second order consistent integration scheme.

Initializer arguments:

  • timeStep: Initial time step (will be adapted automatically)

  • tol: Tolerance for integration errors.

  • maxStep: Maximal allowed time step.

step(t, f, y, normFunction=<PjitFunction of <function norm>>, **rhsArgs)

This function performs an integration time step.

For a first order ordinary differential equation (ODE) of the form

\(\frac{dy}{dt} = f(y, t, p)\)

where \(t\) denotes the time and \(p\) denotes further external parameters this function computes a second-order consistent integration step for \(y\). The time step \(\Delta t\) is chosen such that the integration error (quantified by a given norm) is smaller than the given tolerance.

Arguments:

  • t: Initial time.

  • f: Right hand side of the ODE. This callable will be called as f(y, t, **rhsArgs, intStep=k), where k is an integer indicating the step number of the underlying Runge-Kutta integration scheme.

  • y: Initial value of \(y\).

  • normFunction: Norm function to be used to quantify the magnitude of errors.

  • **rhsArgs: Further static arguments \(p\) that will be passed to the right hand side function f(y, t, **rhsArgs, intStep=k).

Returns:

New value of \(y\) and time step used \(\Delta t\).

class jVMC.util.stepper.Euler(timeStep=0.001)

This class implements Euler integration

step(t, f, yInitial, **rhsArgs)

This function performs an integration time step.

For a first order ordinary differential equation (ODE) of the form

\(\frac{dy}{dt} = f(y, t, p)\)

where \(t\) denotes the time and \(p\) denotes further external parameters this function computes the Euler integration step

\(y_{n+1} = y_n+\Delta t f(y_n,t_n,p)\)

Arguments:

  • t: Initial time.

  • f: Right hand side of the ODE. This callable will be called as f(y, t, **rhsArgs, intStep=k), where k is an integer indicating the step number of the underlying Runge-Kutta integration scheme.

  • y: Initial value of \(y\).

  • **rhsArgs: Further static arguments \(p\) that will be passed to the right hand side function f(y, t, **rhsArgs, intStep=k).

Returns:

New value of \(y\) and time step used \(\Delta t\).

class jVMC.util.stepper.Heun(timeStep=0.001)

This class implements an adaptive second order consistent integration scheme.

Initializer arguments:

  • timeStep: Initial time step (will be adapted automatically)

step(t, f, yInitial, **rhsArgs)

This function performs an integration time step.

For a first order ordinary differential equation (ODE) of the form

\(\frac{dy}{dt} = f(y, t, p)\)

where \(t\) denotes the time and \(p\) denotes further external parameters this function computes a second-order consistent integration step for \(y\).

Arguments:

  • t: Initial time.

  • f: Right hand side of the ODE. This callable will be called as f(y, t, **rhsArgs, intStep=k), where k is an integer indicating the step number of the underlying Runge-Kutta integration scheme.

  • yInitial: Initial value of \(y\).

  • **rhsArgs: Further static arguments \(p\) that will be passed to the right hand side function f(y, t, **rhsArgs, intStep=k).

Returns:

New value of \(y\) and time step used \(\Delta t\).