kawin.solver

kawin.kawin.solver.Solver

DESolver

class DESolver(self, iterator = rk4Iterator, defaultDT = 0.1, minDtFrac = 1e-8, maxDtFrac = 1):

Generic class for ODE/PDE solvers

Generalization - coupled ODEs or PDEs (bunch of coupled ODEs) can be stated as dX/dt = f(X, t)

Parameters
----------
iterator : Iterator function
    Defines what iteration scheme to use
defaultDt : float (defaults to 0.1)
    Default time increment if no function is implement to estimate a good time increment
minDtFrac : float (defaults to 1e-8)
    Minimum time step as a fraction of simulation time
maxDtFrac : float (defaults to 1)
    Maximum time step as a fraction of simulation time

def DESolver.setFunctions(self, preProcess = None, postProcess = None, printHeader = None, printStatus = None):

Sets functions before solving

If any of these are not defined, then the corresponding function will be the default defined here

def DESolver.setdXdtFunctions(self, f, correctdXdt, getDt, flattenX, unflattenX):

def DESolver.defaultDtFunc(self, dXdt):

Returns the default time increment

def DESolver.defaultPreProcess(self):

Default pre-processing function before an iteration

def DESolver.defaultPostProcess(self, currTime, X_new):

Default post-processing function after an iteration

def DESolver.defaultPrintHeader(self):

Default print function before solving

def DESolver.defaultPrintStatus(self, iteration, modeltime, simTimeElapsed):

Default print function for when n iterations passed and verbose is true

def DESolver.correctdXdtNotImplemented(self, dt, x, dXdt):

Default function to correct dXdt

def DESolver.flattenXNotImplemented(self, X):

Default flattenX function, which assumes X is in the correct format

def DESolver.unflattenXNotImplemented(self, X_flat, X_ref):

Default unflattenX function which assumes X is in the correct format

def DESolver._getdXdt(self, t, x, getDt = False):

Wrapper around getdXdt which will handle the following:
    Handle flattening/unfalttening the x and dx/dt arrays
    Calculate dt if not supplied

The API for the iterator will be that all arrays are 1D np.arrays where operators will be trivial

Parameters
----------
t : float
    Time
x : 1D np.array
    Model values
getDt : bool
    Will calculate dt if True

def DESolver._updateX(self, x, dxdt, dt):

Helper function that hides the correctdXdt function

The API for the iterator will be that all arrays are 1D np.arrays where operators will be trivial

Parameters
----------
x : 1D np.array
    Model values
dxdt : 1D np.array
    Derivatives at x
dt : float
    Time step

def DESolver.solve(self, t0, X0, tf, verbose = False, vIt = 10):

Solves dX/dt over a time increment
This will be the main function that a model will use

Steps during each iteration
    1. Print status if vIt iterations passed
    2. preProcess
    3. Iterate
    4. Update current time
    5. postProcess

Parameters
----------
f : function
    dX/dt - function taking in time and returning dX/dt
t0 : float
    Starting time
X0 : list of arrays
    X at time t
tf : float
    Final time
verbose: bool (defaults to False)
    Whether to print status
vIt : integer (defaults to 10)
    Number of iterations to print status

kawin.kawin.solver.Iterators

def explicitEulerIterator(f, t, X_old, updateX):

Explicit euler iteration scheme

Defined by:
    dXdt = f(t, X_n)
    X_n+1 = X_n + f(t, X_n) * dt

Parameters
----------
f : function
    dX/dt - function taking in time and X and returning dX/dt
t : float
    Current time
X_old : list of arrays
    X at time t
updateX : function
    Helper function to handle any correction to dxdt
    Takes in X_old, dxdt, dt and returns X_new

Returns
-------
X_new : unformatted list of floats
    New values of X in format of X_old
dt : float
    Time step

def rk4Iterator(f, t, X_old, updateX):

4th order Runga Kutta iteration scheme

Defined by:
    k1 = f(t, X_n)
    k2 = f(t + dt/2, X_n + k1 * dt/2)
    k3 = f(t + dt/2, X_n + k2 * dt/2)
    k4 = f(t + dt, X_n, k3 * dt)
    X_n+1 = X_n + 1/6 * (k1 + 2*k2 + 2*k3 + k4) * dt

Parameters
----------
f : function
    dX/dt - function taking in time and X and returning dX/dt
t : float
    Current time
X_old : list of arrays
    X at time t
updateX : function
    Helper function to handle any correction to dxdt
    Takes in X_old, dxdt, dt and returns X_new

Returns
-------
X_new : unformatted list of floats
    New values of X in format of X_old
dt : float
    Time step, important if modified from dtfunc
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