Deviation ellipses example

altair/vegalite/v2/examples/deviation_ellipses.py

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+"""
+Deviation ellipse
+-----------------------
+This example shows bivariate deviation ellipses of petal length and width of three iris species.
+"""
+
+import numpy as np
+import pandas as pd
+from scipy.stats import f as ssf
+import altair as alt
+from vega_datasets import data
+
+iris = data.iris()
+
+def ellipse(X, level=0.95, method='deviation', npoints=100):
+    """
+    X: data, 2D numpy array with 2 columns
+    level: confidence level
+    method: either 'deviation' (swarning data) or 'error (swarning the mean)'
+    npoints: number of points describing the ellipse
+    """
+    cov_mat = np.cov(X.T)
+    dfd = X.shape[0]-1
+    dfn = 2
+    center = np.apply_along_axis(np.mean, arr=X, axis=0) # np.mean(X, axis=0)
+    if method == 'deviation':
+        radius = np.sqrt(2 * ssf.ppf(q=level, dfn=dfn, dfd=dfd))
+    elif method == 'error':
+        radius = np.sqrt(2 * ssf.ppf(q=level, dfn=dfn, dfd=dfd)) / np.sqrt(X.shape[0])
+    else:
+        raise ValueError("Method should be either 'deviation' or 'error'.")
+    angles = (np.arange(0,npoints+1)) * 2 * np.pi/npoints
+    circle = np.vstack((np.cos(angles), np.sin(angles))).T
+    ellipse = center + (radius * np.dot(circle, np.linalg.cholesky(cov_mat).T).T).T
+    return ellipse
+
+columns = ['petalLength', 'petalWidth']
+petal_ellipse = []
+for species in iris.species.unique():
+    ell_df = pd.DataFrame(ellipse(X=iris.loc[iris.species == species, columns].as_matrix()),
+                                      columns = columns)
+    ell_df['species'] = species
+    petal_ellipse.append(ell_df)
+
+petal_ellipse = pd.concat(petal_ellipse, axis=0).reset_index()
+
+chart_deviation = alt.Chart(petal_ellipse).mark_line().\
+    encode(
+        x=alt.X('petalLength', scale=alt.Scale(zero=False)),
+        y=alt.Y('petalWidth', scale=alt.Scale(zero=False)),
+        color='species',
+        order='index')
+# works only if chart_deviation is printed here
+# chart_deviation
+
+chart_points = alt.Chart(iris).mark_point().\
+    encode(
+        x=alt.X('petalLength', scale=alt.Scale(zero=False)),
+        y=alt.Y('petalWidth', scale=alt.Scale(zero=False)),
+        color='species')
+
+chart = chart_points + chart_deviation
+chart