# SI values in l.u.

m: float

s: float

kg: float

# m s kg

param_dimensions = {'distance': [ 1, 0, 0],

'time': [ 0, 1, 0],

'weight': [ 0, 0, 1],

'viscosity': [-1, -1, 1],

'pressure': [-1, -2, 1],

'energy': [ 2, -2, 1],

'density': [-3, 0, 1],

'concentration': [-3, 0, 0],

'surface_tension': [ 0, -2, 1],

'diffusivity': [ 2, -1, 0]}

def __init__(self, verbose=True, dx=None, dt=None, kg=None, **kwargs):

# This can be extended to use other units too

# Set up the unit matrix and the vector of ratios of the lattice and physical values

dimensions = [] # Powers of dimensions for each unit: meters, seconds, kilograms

value_ratios = []

if (dx is not None):

dimensions.append([1, 0, 0])

value_ratios.append(dx)

if (dt is not None):

dimensions.append([0, 1, 0])

value_ratios.append(dt)

if (kg is not None):

dimensions.append([0, 0, 1])

value_ratios.append(1/kg)

for arg in kwargs:

values = kwargs[arg]

if (not hasattr(values, "__len__") or len(values) != 2):

raise Exception(arg + " requires a 2-tuple containing the physical value and the lattice value.")

dimensions.append(self.param_dimensions[arg])

value_ratios.append(values[0]/values[1])

if (len(dimensions)!=3) or (len(value_ratios)!=3):

raise Exception("Three values are needed to initialise the unit converter.")

# Invert the unit matrix to find the values for m, s, kg

inv_dimensions = np.linalg.inv(dimensions)

units = np.ones(3)

for i in range(3):

for j in range(3):

units[i] = units[i] * value_ratios[j]**inv_dimensions[i,j] # Matrix multiplication with linear operators of multiplication and raising to a power

self.m, self.s, self.kg = units

if (verbose): print(self)

def __str__(self):

return "Unit Converter:\n" + \

f"1 l.u. = {self.m} metre\n" + \

f"1 l.u. = {self.s} second\n" + \

f"1 l.u. = {self.kg} kilogram"

def toLattice(self, value, param=None, m=0, s=0, kg=0):

if (param is not None):

m = self.param_dimensions[param][0]

s = self.param_dimensions[param][1]

kg = self.param_dimensions[param][2]

return value / self.m**m / self.s**s / self.kg**kg

def toSI(self, value, param=None, m=0, s=0, kg=0):

if (param is not None):

m = self.param_dimensions[param][0]

s = self.param_dimensions[param][1]

kg = self.param_dimensions[param][2]