def blur_compositions(df, noise=0.05, scale=100):
"""
Function to add 'compositional noise' to a set of compositions. In reality, it's
its best to use measured uncertainties to generate these simulated compositions.
"""
# transform into compositional space, add noise, return to simplex
xvals = ilr(df.values)
xvals += np.random.randn(*xvals.shape) * noise
return inverse_ilr(xvals) * scale
def random_compositional_trend(m1, m2, c1, c2, resolution=20, size=1000):
"""
Generate a compositional trend between two compositions with independent
variances.
"""
# generate means intermediate between m1 and m2
mv = np.vstack([ilr(close(m1)).reshape(1, -1), ilr(close(m2)).reshape(1, -1)])
ms = np.apply_along_axis(lambda x: np.linspace(*x, resolution), 0, mv)
# generate covariance matricies intermediate between c1 and c2
cv = np.vstack([c1.reshape(1, -1), c2.reshape(1, -1)])
cs = np.apply_along_axis(lambda x: np.linspace(*x, resolution), 0, cv)
cs = cs.reshape(cs.shape[0], *c1.shape)
# generate samples from each
samples = np.vstack(
[
np.random.multivariate_normal(m.flatten(), cs[ix], size=size // resolution)
for ix, m in enumerate(ms)
]
)
# combine together.
return inverse_ilr(samples)
m1, m2 = np.array([[0.3, 0.1, 2.1]]), np.array([[0.5, 2.5, 0.05]])
c1, c2 = (
random_cov_matrix(2, sigmas=[0.15, 0.05]),
random_cov_matrix(2, sigmas=[0.05, 0.2]),
)
trend = pd.DataFrame(
random_compositional_trend(m1, m2, c1, c2, resolution=100, size=5000),
columns=["A", "B", "C"],
)
########################################################################################
# We can visualise this compositional trend with a density plot.
#
ax = trend.pyroplot.density(mode="density", bins=100)
plt.show()
########################################################################################
# First we can see where the geometric mean would fall:
#
geomean = trend.mean(axis=0).to_frame().T
ax = geomean.pyroplot.scatter(ax=ax, marker="o", color="r", zorder=2, label="GeoMean")
plt.show()
########################################################################################
# Finally, we can also see where the logratio mean would fall:
#
ilrmean = pd.DataFrame(
inverse_ilr(np.nanmean(ilr(trend.values), axis=0)[np.newaxis, :])
)
ax = ilrmean.pyroplot.scatter(ax=ax, marker="D", color="k", label="LogMean")
plt.show()