def plot_3D_dirichlet(alpha_values):
def dirichlet_pdf(thetas,alphas):
norm = gamma(np.sum(alphas))/np.prod([gamma(a) for a in alphas])
if(np.isclose(np.sum(alphas),len(alphas))):
return np.ones(thetas.shape[0])*norm
else:
log_prob = np.log(norm)+np.sum((alphas-1)*np.log(thetas),axis=1)
return np.exp(log_prob)
s = 30
t1 = []
t2 = []
for i in range(s):
t1=list(np.arange(i).astype(float))+t1
t2=list(np.arange(i).astype(float)[::-1])+t2
t1 = np.array(t1)
t2 = np.array(t2)
t3 = s-t1-t2-2
t1 = t1/(s-2)
t2 = t2/(s-2)
t3 = t3/(s-2)
t1[t1==0]+=0.0001
t2[t2==0]+=0.0001
t3[t3==0]+=0.0001
pdf = dirichlet_pdf(np.concatenate([t1.reshape(-1,1),t2.reshape(-1,1),t3.reshape(-1,1)],axis=1),alpha_values)
fig = ff.create_ternary_contour(np.array([t1,t2,t3]), np.array(pdf),
pole_labels=['theta1', 'theta2', 'theta3'],
interp_mode='cartesian',
ncontours=20,
colorscale='Viridis')
fig = set_basic_layout(fig)
fig.update_layout(margin=dict(t=75,l=75,b=75,r=75))
return fig
def make_ternary_plot(flammability_data, dropdown_value):
""" Make ternary graph from flammability data. """
data = []
if flammability_data and dropdown_value:
flammability_data = json.loads(flammability_data)
xf = flammability_data['Xf']
xa = flammability_data['Xa']
xi = flammability_data['Xi']
z = np.array(flammability_data[dropdown_value])
colorscale = 'Hot'
ncontours = None
showscale = True
if dropdown_value == 'phi':
# Cap phi values at 2
for i, value in enumerate(z):
if value > 2:
z[i] = 2
ncontours = 8
colorscale = 'Rainbow'
if dropdown_value == 'Flammable':
ncontours = 2
showscale = False
figure = create_ternary_contour(np.array([xf, xa, xi]),
z,
pole_labels=['Fuel', 'Air', 'Inert'],
interp_mode='cartesian',
colorscale=colorscale,
showscale=showscale,
ncontours=ncontours)
data = figure.to_plotly_json()['data']
# Clean up
for item in data:
item.pop('showlegend', None)
layout = copy.deepcopy(plot_layout)
layout['title'] = 'Ternary Contour Plot'
layout['showlegend'] = False
layout['ternary'] = dict(
sum=1,
aaxis=dict(title='Fuel'),
baxis=dict(title='Air'),
caxis=dict(title='Inert'),
showlegend=False,
width=700,
)
figure = dict(data=data, layout=layout)
return figure
def plot(arg=None,X=None,Y=None,Z=None,E=None,I=None):
npzfile = np.load(arg)
x = np.array(X)
y = np.array(Y)
z = np.array(Z)
e = np.array(E)
alloy_name = str(npzfile['e'][0] + npzfile['e'][1] + npzfile['e'][2])
fig = ff.create_ternary_contour(np.array([x,y,z]), e, pole_labels=[npzfile['e'][0], npzfile['e'][1], npzfile['e'][2]], interp_mode='cartesian', ncontours=5, colorscale='Viridis', showscale=True, showmarkers=True, title=str(alloy_name))
htmlfile = str(alloy_name) +'.html'
filename = htmlfile
plotly.offline.plot(fig, filename , auto_open=False)
return htmlfile
def MakePlots(dff, name):
Xf = np.array(dff.Xf.tolist())
Xa = np.array(dff.Xa.tolist())
Xi = np.array(dff.Xi.tolist())
Tad = np.array(dff.Tad.tolist())
phi = np.array(dff.phi.tolist())
phi[phi > 2] = 2
flm = np.array(dff.Flammable.tolist())
pio.orca.ensure_server()
time.sleep(10)
fgg = ff.create_ternary_contour(np.array([Xf, Xa, Xi]),
Tad,
pole_labels=['Fuel', 'Air', 'Inert'],
interp_mode='cartesian',
colorscale='Hot',
showscale=True,
title=name + 'Tad',
showmarkers=True)
fgg.write_image(name + "_Tad.png")
time.sleep(1)
fgg2 = ff.create_ternary_contour(np.array([Xf, Xa, Xi]),
flm,
pole_labels=['Fuel', 'Air', 'Inert'],
interp_mode='cartesian',
colorscale='Hot',
title=name + 'Flammability',
ncontours=2)
fgg2.write_image(name + "_flm.png")
time.sleep(1)
fgg3 = ff.create_ternary_contour(np.array([Xf, Xa, Xi]),
phi,
pole_labels=['Fuel', 'Air', 'Inert'],
interp_mode='cartesian',
colorscale='Rainbow',
ncontours=8,
showscale=True,
title=name + 'Equivalence Ratio')
fgg3.write_image(name + "_phi.png")
return fgg, fgg2, fgg3
def plot(self,title):
self.predict_data_mean()
fig = ff.create_ternary_contour(
np.array([self.tri_grid[:,i] for i in range(3)])/self.resolution,
self.y_score_sum,
pole_labels=self.axis,
interp_mode='cartesian',
ncontours=20,
colorscale='Rainbow',
showmarkers=True,
showscale=True,
title=title
)
fig.show()
def plot_goal_ternary(df: pd.DataFrame, kpis: Dict[str, callable],
goals: Dict[str, callable], control_params: set) -> None:
"""
Arguments
---
df: Observation dataframe
kpis: Dictionary of funtions that scores a given combination of control params
goals: Dictionary of how the goals are metrified. One of the keys must be 'combined'
control_params: Set of the columns to be used as features.
"""
if len(goals.keys()) != 4:
raise ValueError('The `goals` dictionary must have four elements')
# Group by the control params and apply kpi to each combination
output = []
for kpi, kpi_function in kpis.items():
s = df.groupby(list(control_params)).apply(kpi_function)
s.name = kpi
output.append(s)
# Generate a aggregated dataframe for training a regressor
agg_df = pd.DataFrame(output).T.reset_index()
# Get data
y = agg_df.loc[:, kpis.keys()]
X = agg_df.loc[:, control_params]
# Perform a random forest regression on X->y
rf = RandomForestRegressor()
rf.fit(X, y)
# Use the regression to predict values for each simulation
coords = rf.predict(X)
# MinMax normalizer
def norm(x):
return (x - x.min()) / (x.max() - x.min())
# Encapsulate RF regression results in a dict
metrics = dict(zip(kpis.keys(), coords.T))
metrics = {k: norm(v) for (k, v) in metrics.items()}
labels = [k for k in goals.keys() if k != 'combined']
x = goals[labels[0]](metrics)
y = goals[labels[1]](metrics)
z = goals[labels[2]](metrics)
# Combined Goals definition
kpi = norm(goals['combined']([x, y, z]))
# Create a matrix for the sides of the triangle (shape: 3xN)
xyz = np.stack([x, y, z]).T
scaler = MinMaxScaler()
# Normalize each side by MinMax
xyz = scaler.fit_transform(xyz).T
# Normalize each data point so that it sums to 1.0
v = np.round(normalize(xyz, axis=0, norm='l2')**2, decimals=10)
# Generate ternary plot
fig = ff.create_ternary_contour(
v,
kpi,
pole_labels=[labels[0], labels[1], labels[2]],
interp_mode='cartesian',
ncontours=15,
colorscale='Viridis',
showmarkers=True,
showscale=True)
fig.show()