def cvRun(gridLength, alloyFraction, dimensions, eList, T, localEam,
nIterationsPerSim):
grid = srf.initializeGrid(gridLength, alloyFraction, dimensions)
grid, eList = srf.runSim(grid, eList, T, localEam, nIterationsPerSim,
gridLength, dimensions)
currentOrderValue, actualList, binList = sref.getOrder(
grid, alloyFraction, dimensions)
return currentOrderValue
def cValidateTest(dimensions=2):
gridLength, alloyFraction = 50, 50
grid = srf.initializeGrid(gridLength, alloyFraction, dimensions)
# xCase (+1)
result = srf.cValidate(gridLength + 1, grid, gridLength, 'x', dimensions)
if result != 0:
print("cValidate does NOT work for x case")
# xCase (-1)
result = srf.cValidate(-1, grid, gridLength, 'x', dimensions)
if result == 0:
print(
"ERROR: xCase - 1 doesn't work") # i.e. would produce index error
def createBarDistribution(gridLength=40,
alloyFraction=50,
nIterations=3000000,
Eam=0.1,
T=300,
dimensions=2):
alloyGrid = srf.initializeGrid(gridLength, alloyFraction, dimensions)
# Sets up list to take current system energy as simulation progresses
energyList = [0] * (nIterations + 1)
energyList[0] = sref.getTotalEnergy(alloyGrid, Eam, dimensions)
alloyGrid, energyList = srf.runSim(alloyGrid, energyList, T, Eam,
nIterations, gridLength, dimensions)
randomMeasure2, actualList, binList = sref.getOrder(
alloyGrid, alloyFraction, dimensions)
trace1 = plotly.graph_objs.Bar(
x=[str(i) for i in range(dimensions * 2 + 1)],
y=actualList,
name='actualDistribution')
trace2 = plotly.graph_objs.Bar(
x=[str(i) for i in range(dimensions * 2 + 1)],
y=binList,
name='binomialDistribution')
data = [trace1, trace2]
layout = plotly.graph_objs.Layout(
barmode='group',
xaxis=dict(title='No. of unlike neighbours',
titlefont=dict(family='Courier New, monospace',
size=18,
color='#7f7f7f')),
yaxis=dict(title='Frequency',
titlefont=dict(family='Courier New, monospace',
size=18,
color='#7f7f7f')))
fig = plotly.graph_objs.Figure(data=data, layout=layout)
plotly.offline.plot(
fig,
filename="""barDistribution [gL={}, n={}, comp={}, Eam={},
T={}, dimensions={}].html""".format(str(gridLength), str(nIterations),
str(alloyFraction / 100.0), str(Eam),
str(T), str(dimensions)).replace(
'\n', '').replace('\t', ''))
def orderVsCompVaryingEam(gridLength=40,
T=300,
nIterations=3000000,
eOptions=[-0.1, 0.0, 0.1],
compList=range(0, 101, 5),
dimensions=2,
numTimesToAvg=3,
multiProcess=True):
"""Plotting order vs composition, with varying Eam. Eam values are taken from
eOptions, while composition values are taken from compList"""
alloyGrid = srf.initializeGrid(gridLength, 50, dimensions)
# Sets up list to take current system energy as simulation progresses
energyList = [0] * (nIterations + 1)
energyList[0] = sref.getTotalEnergy(alloyGrid, 0.1, dimensions)
dataSet = []
for i, j in enumerate(eOptions):
rList = sif.compVary(energyList, compList, j, gridLength, T,
dimensions, numTimesToAvg, nIterations,
multiProcess)
dataSet.append(rList)
colourOptions = ['b', 'g', 'r', 'c', 'm', 'y', 'k'] * ceil(
len(eOptions) / 7)
fig, ax = pyplot.subplots()
for i, j in enumerate(dataSet):
ax.plot(compList,
j,
colourOptions[i],
label='Eam = {} eV'.format(str(eOptions[i])))
# Now add the legend with some customizations
legend = ax.legend(loc='upper right', shadow=False)
# The frame is matplotlib.patches.Rectangle instance surrounding the legend
frame = legend.get_frame()
frame.set_facecolor('white')
# Set the fontsize
for label in legend.get_texts():
label.set_fontsize('large')
for label in legend.get_lines():
label.set_linewidth(1.5) # the legend line width
pyplot.xlabel('Composition (%% foreign atoms)')
pyplot.ylabel('orderValue')
pyplot.show()
def orderVsComp(gridLength=40,
T=300,
nIterations=3000000,
Eam=0.1,
compList=range(0, 101, 5),
dimensions=2,
numTimesToAvg=3,
multiProcess=True):
"""Plotting order vs composition"""
alloyGrid = srf.initializeGrid(gridLength, 50, dimensions)
# Sets up list to take current system energy as simulation progresses
energyList = [0] * (nIterations + 1)
energyList[0] = sref.getTotalEnergy(alloyGrid, Eam, dimensions)
rList = sif.compVary(energyList, compList, Eam, gridLength, T, dimensions,
numTimesToAvg, nIterations, multiProcess)
pyplot.plot(compList, rList)
pyplot.xlabel('Composition (%% foreign atoms)')
pyplot.ylabel('orderValue')
pyplot.show()
def orderVsTemp(gridLength=40,
alloyFraction=50,
nIterations=3000000,
Eam=0.1,
tempList=range(300, 4100, 500),
dimensions=2,
numTimesToAvg=3,
multiProcess=True):
"""Plotting order vs temperature"""
alloyGrid = srf.initializeGrid(gridLength, alloyFraction, dimensions)
# Sets up list to take current system energy as simulation progresses
energyList = [0] * (nIterations + 1)
energyList[0] = sref.getTotalEnergy(alloyGrid, Eam, dimensions)
rList = sif.tempVary(energyList, tempList, Eam, gridLength, alloyFraction,
dimensions, numTimesToAvg, nIterations, multiProcess)
pyplot.plot(tempList, rList)
pyplot.xlabel('Temperature (K)')
pyplot.ylabel('orderValue')
pyplot.show()
def plotEnergyConvergence(gridLength=40,
alloyFraction=50,
nIterations=3000000,
Eam=0.1,
T=300,
dimensions=2):
"""Produces graph of system energy vs no of iterations"""
alloyGrid = srf.initializeGrid(gridLength, alloyFraction, dimensions)
# Sets up list to take current system energy as simulation progresses
energyList = [0] * (nIterations + 1)
energyList[0] = sref.getTotalEnergy(alloyGrid, Eam, dimensions)
alloyGrid, energyList = srf.runSim(alloyGrid, energyList, T, Eam,
nIterations, gridLength, dimensions)
iterationList = range(nIterations + 1)
pyplot.plot(iterationList, energyList)
pyplot.xlabel('No. of iterations')
pyplot.ylabel('System Energy (eV')
pyplot.show()
def initializeGridTest(dimensions):
"""tests if intial grid is random and displays intial grid"""
gridLength, alloyFraction = 20, 50
grid = srf.initializeGrid(gridLength, alloyFraction, dimensions)
# checks order of inital grid
result, actualList, binList = sref.getOrder(grid, alloyFraction,
dimensions)
if result > gridLength * 0.1:
print("CORRECT: initializeGrid produces random grid")
else:
print(
"""ERROR: initializeGrid most likely does NOT produce a random grid. Run 1
more time to make sure.""")
if dimensions == 2:
# displays intial grid, if 2D
pyplot.figure(num="Initial Grid Test")
img = pyplot.imshow(grid, interpolation='nearest')
pyplot.colorbar(img)
pyplot.show()
def orderVsTempVaryingComp(gridLength=40,
compList=range(0, 101, 10),
nIterations=3000000,
Eam=0.1,
tempList=range(300, 4100, 500),
dimensions=2,
numTimesToAvg=3,
multiProcess=True):
alloyGrid = srf.initializeGrid(gridLength, 50, dimensions)
# Sets up list to take current system energy as simulation progresses
energyList = [0] * (nIterations + 1)
energyList[0] = sref.getTotalEnergy(alloyGrid, Eam, dimensions)
dataSet = []
for i, j in enumerate(compList):
rList = sif.tempVary(energyList, tempList, Eam, gridLength, j,
dimensions, numTimesToAvg, nIterations,
multiProcess)
dataSet.append(rList)
colourOptions = ['b', 'g', 'r', 'c', 'm', 'y', 'k'] * ceil(
len(compList) / 7)
fig, ax = pyplot.subplots()
for i, j in enumerate(dataSet):
ax.plot(tempList,
j,
colourOptions[i],
label='f={} %%'.format(str(compList[i])))
# Now add the legend with some customizations
legend = ax.legend(loc='upper right', shadow=False)
# The frame is matplotlib.patches.Rectangle instance surrounding the legend
frame = legend.get_frame()
frame.set_facecolor('white')
# Set the fontsize
for label in legend.get_texts():
label.set_fontsize('large')
for label in legend.get_lines():
label.set_linewidth(1.5) # the legend line width
pyplot.xlabel('Temperature (K)')
pyplot.ylabel('orderValue')
pyplot.show()
def standardRun(nIterations=3000000,
gridLength=40,
alloyFraction=50,
Eam=0.1,
T=300,
dimensions=2,
showMatrixImages=True):
"""Runs through simulation for one set of parameters"""
alloyGrid = srf.initializeGrid(gridLength, alloyFraction, dimensions)
# Sets up list list to take current system energy as simulation progresses
energyList = [0] * (nIterations + 1)
energyList[0] = sref.getTotalEnergy(alloyGrid, Eam, dimensions)
if showMatrixImages and dimensions == 2:
# Display initial matrix
pyplot.figure(num="Initial config")
img1 = pyplot.imshow(alloyGrid, interpolation='nearest')
pyplot.colorbar(img1)
orderMeasure1, actualList, binList = sref.getOrder(alloyGrid,
alloyFraction,
dimensions)
print("Initial order is: {}".format(str(orderMeasure1)))
alloyGrid, energyList = srf.runSim(alloyGrid, energyList, T, Eam,
nIterations, gridLength, dimensions)
if showMatrixImages and dimensions == 2:
# Display matrix in prettier form, as a coloured graph
pyplot.figure(num="Final config")
img2 = pyplot.imshow(alloyGrid, interpolation='nearest')
pyplot.colorbar(img2)
pyplot.show()
orderMeasure2, actualList, binList = sref.getOrder(alloyGrid,
alloyFraction,
dimensions)
print("Final order is: {}".format(str(orderMeasure2)))
def getOrderTest(dimensions):
gridLength = 20
comp = 40
ranGrid = srf.initializeGrid(gridLength, comp, dimensions)
nForeignAtoms = int(comp * 0.01 * gridLength**dimensions)
orderedGrid = np.zeros([gridLength] * dimensions)
numAdded = 0
try: # try, except statement creates ordered grid (2 blocks)
for i in range(gridLength):
for j in range(gridLength):
if dimensions == 2:
orderedGrid[i, j] = 1
numAdded += 1
elif dimensions == 3:
for k in range(gridLength):
orderedGrid[i, j, k] = 1
numAdded += 1
assert (numAdded < nForeignAtoms)
except (AssertionError
): # exception raised simply means we should stop adding
# atoms, not that there is a problem
pass
if dimensions == 2:
# shows ordered grid to show that we are testing an ordered grid
pyplot.figure(num="orderedGrid")
tempImg = pyplot.imshow(orderedGrid, interpolation='nearest')
pyplot.colorbar(tempImg)
pyplot.show()
ranRan, actualList, binList = sref.getOrder(ranGrid, comp, dimensions)
ranOrd, actualList, binList = sref.getOrder(orderedGrid, comp, dimensions)
# ranRan should be much lower than ranOrd
if ranRan < 0.2 * ranOrd:
print(
"CORRECT: random and ordered grids produces correct orderValues.")
print("The order value for the random grid is: {}".format(str(ranRan)))
print("The order value for the random grid is: {}".format(str(ranOrd)))
def tempVary(eList, tList, localEam, gridLength, alloyFraction, dimensions,
numTimesToAvg, nIterationsPerSim, multiProcess):
"""Runs simulation at every temperature in specfied list"""
initialGrid = srf.initializeGrid(gridLength, alloyFraction, dimensions)
if multiProcess:
p = MyPool(processes=10)
mainPartial = partial(tvAvgRun, initialGrid, eList, localEam,
nIterationsPerSim, gridLength, dimensions,
alloyFraction, numTimesToAvg)
orderList = p.map(mainPartial, tList)
p.close()
else:
orderList = [0] * len(tList)
for i, j in enumerate(tList):
avgList = [0] * numTimesToAvg
for k, l in enumerate(avgList):
currentOrderValue = tvRun(initialGrid, eList, j, localEam,
nIterationsPerSim, gridLength,
dimensions, alloyFraction, 1)
avgList[k] = currentOrderValue
orderList[i] = sum(avgList) / float(len(avgList))
print(j)
return orderList
def createTempVaryingBarDistribution(gridLength=40,
alloyFraction=50,
nIterations=3000000,
Eam=0.1,
tempList=[300, 1000, 3000, 5000],
dimensions=2,
multiProcess=True):
initialGrid = srf.initializeGrid(gridLength, alloyFraction, dimensions)
# Sets up list to take current system energy as simulation progresses
energyList = [0] * (nIterations + 1)
energyList[0] = sref.getTotalEnergy(initialGrid, Eam, dimensions)
if multiProcess:
p = Pool(processes=10)
mainPartial = partial(tvbdRun, initialGrid, energyList, Eam,
nIterations, gridLength, dimensions,
alloyFraction)
combined_lists = p.map(mainPartial, tempList)
traceList = [i[0] for i in combined_lists]
binList = combined_lists[-1][1]
else:
traceList = [0] * len(tempList)
for i, j in enumerate(tempList):
alloyGrid, energyList = srf.runSim(initialGrid, energyList, j, Eam,
nIterations, gridLength,
dimensions)
randomMeasure2, actualList, binList = sref.getOrder(
alloyGrid, alloyFraction, dimensions)
traceList[i] = actualList
xTraceList = str([str(i) for i in range(dimensions * 2 + 1)])
traceObjs = []
for i, j in enumerate(traceList):
traceObjs.append(
plotly.graph_objs.Bar(x=eval(xTraceList),
y=j,
name=str(tempList[i]) + " K"))
traceObjs.append(
plotly.graph_objs.Bar(x=xTraceList,
y=binList,
name='Binomial Distribution'))
layout = plotly.graph_objs.Layout(
barmode='group',
xaxis=dict(title='No. of unlike neighbours',
titlefont=dict(family='Courier New, monospace',
size=18,
color='#7f7f7f')),
yaxis=dict(title='Frequency',
titlefont=dict(family='Courier New, monospace',
size=18,
color='#7f7f7f')))
fig = plotly.graph_objs.Figure(data=traceObjs, layout=layout)
plotly.offline.plot(
fig,
filename="""tempVaryingBarDistribution [gL={}, n={}, comp={},Eam={},
dimensions={}].html""".format(str(gridLength), str(nIterations),
str(alloyFraction / 100.0), str(Eam),
str(dimensions)).replace('\n',
'').replace('\t', ''))