前回作成した架空の行動履歴データでChordDiagram(弦グラフ)を作成します．

• 弦グラフのスクリプト
  • 弦グラフの作成実行
• まとめ
• 参考サイト

弦グラフのスクリプト

下記に弦グラフのスクリプトを示します．

# chord diagram
import matplotlib.pyplot as plt
from matplotlib.path import Path
import matplotlib.patches as patches

import numpy as np

LW = 0.3

# 割合から座標を算出
def polar2xy(r, theta):
    return np.array([r*np.cos(theta), r*np.sin(theta)])

# 16進数からrgb
def hex2rgb(c):
    return tuple(int(c[i:i+2], 16)/256.0 for i in (1, 3 ,5))


# 円周グラフの作成
def IdeogramArc(start=0, end=60, radius=1.0, width=0.2, ax=None, color=(1,0,0)):
    # start, end should be in [0, 360)
    if start > end:
        start, end = end, start
    start *= np.pi/180.
    end *= np.pi/180.
    # optimal distance to the control points
    # https://stackoverflow.com/questions/1734745/how-to-create-circle-with-b%C3%A9zier-curves
    opt = 4./3. * np.tan((end-start)/ 4.) * radius
    inner = radius*(1-width)
    verts = [
        polar2xy(radius, start),
        polar2xy(radius, start) + polar2xy(opt, start+0.5*np.pi),
        polar2xy(radius, end) + polar2xy(opt, end-0.5*np.pi),
        polar2xy(radius, end),
        polar2xy(inner, end),
        polar2xy(inner, end) + polar2xy(opt*(1-width), end-0.5*np.pi),
        polar2xy(inner, start) + polar2xy(opt*(1-width), start+0.5*np.pi),
        polar2xy(inner, start),
        polar2xy(radius, start),
        ]

    codes = [Path.MOVETO,
             Path.CURVE4,
             Path.CURVE4,
             Path.CURVE4,
             Path.LINETO,
             Path.CURVE4,
             Path.CURVE4,
             Path.CURVE4,
             Path.CLOSEPOLY,
             ]

    if ax == None:
        return verts, codes
    else:
        path = Path(verts, codes)
        patch = patches.PathPatch(path, facecolor=color+(0.5,), edgecolor=color+(0.4,), lw=LW)
        ax.add_patch(patch)

# 滞在曲線の作成
def selfChordArc(start=0, end=60, radius=1.0, chordwidth=0.7, ax=None, color=(1,0,0)):
    # start, end should be in [0, 360)
    if start > end:
        start, end = end, start
    start *= np.pi/180.
    end *= np.pi/180.
    opt = 4./3. * np.tan((end-start)/ 4.) * radius
    rchord = radius * (1-chordwidth)
    verts = [
        polar2xy(radius, start),
        polar2xy(radius, start) + polar2xy(opt, start+0.5*np.pi),
        polar2xy(radius, end) + polar2xy(opt, end-0.5*np.pi),
        polar2xy(radius, end),
        polar2xy(rchord, end),
        polar2xy(rchord, start),
        polar2xy(radius, start),
        ]

    codes = [Path.MOVETO,
             Path.CURVE4,
             Path.CURVE4,
             Path.CURVE4,
             Path.CURVE4,
             Path.CURVE4,
             Path.CURVE4,
             ]

    if ax == None:
        return verts, codes
    else:
        path = Path(verts, codes)
        patch = patches.PathPatch(path, facecolor=color+(0.5,), edgecolor=color+(0.4,), lw=LW)
        ax.add_patch(patch)

# 移動曲線の作成
def ChordArc(start1=0, end1=60, start2=180, end2=240, radius=1.0, chordwidth=0.7, ax=None, color=(1,0,0)):
    # start, end should be in [0, 360)
    if start1 > end1:
        start1, end1 = end1, start1
    if start2 > end2:
        start2, end2 = end2, start2
    start1 *= np.pi/180.
    end1 *= np.pi/180.
    start2 *= np.pi/180.
    end2 *= np.pi/180.
    opt1 = 4./3. * np.tan((end1-start1)/ 4.) * radius
    opt2 = 4./3. * np.tan((end2-start2)/ 4.) * radius
    rchord = radius * (1-chordwidth)
    verts = [
        polar2xy(radius, start1),
        polar2xy(radius, start1) + polar2xy(opt1, start1+0.5*np.pi),
        polar2xy(radius, end1) + polar2xy(opt1, end1-0.5*np.pi),
        polar2xy(radius, end1),
        polar2xy(rchord, end1),
        polar2xy(rchord, start2),
        polar2xy(radius, start2),
        polar2xy(radius, start2) + polar2xy(opt2, start2+0.5*np.pi),
        polar2xy(radius, end2) + polar2xy(opt2, end2-0.5*np.pi),
        polar2xy(radius, end2),
        polar2xy(rchord, end2),
        polar2xy(rchord, start1),
        polar2xy(radius, start1),
        ]

    codes = [Path.MOVETO,
             Path.CURVE4,
             Path.CURVE4,
             Path.CURVE4,
             Path.CURVE4,
             Path.CURVE4,
             Path.CURVE4,
             Path.CURVE4,
             Path.CURVE4,
             Path.CURVE4,
             Path.CURVE4,
             Path.CURVE4,
             Path.CURVE4,
             ]

    if ax == None:
        return verts, codes
    else:
        path = Path(verts, codes)
        patch = patches.PathPatch(path, facecolor=color+(0.5,), edgecolor=color+(0.4,), lw=LW)
        ax.add_patch(patch)

def chordDiagram(X, ax, colors=None, width=0.1, pad=2, chordwidth=0.7):
    """Plot a chord diagram
    Parameters
    ----------
    X :
        flux data, X[i, j] is the flux from i to j
    ax :
        matplotlib `axes` to show the plot
    colors : optional
        user defined colors in rgb format. Use function hex2rgb() to convert hex color to rgb color. Default: d3.js category10
    width : optional
        width/thickness of the ideogram arc
    pad : optional
        gap pad between two neighboring ideogram arcs, unit: degree, default: 2 degree
    chordwidth : optional
        position of the control points for the chords, controlling the shape of the chords
    """
    # X[i, j]:  i -> j
    x = X.sum(axis = 1) # sum over rows
    ax.set_xlim(-1.1, 1.1)
    ax.set_ylim(-1.1, 1.1)

    if colors is None:
    # use d3.js category10 https://github.com/d3/d3-3.x-api-reference/blob/master/Ordinal-Scales.md#category10
        colors = ['#1f77b4', '#ff7f0e', '#2ca02c', '#d62728', '#9467bd',
                  '#8c564b', '#e377c2', '#7f7f7f', '#bcbd22', '#17becf']
        if len(x) > 10:
            print('x is too large! Use x smaller than 10')
        colors = [hex2rgb(colors[i]) for i in range(len(x))]

    # find position for each start and end
    y = x/np.sum(x).astype(float) * (360 - pad*len(x))

    pos = {}
    arc = []
    nodePos = []
    start = 0
    for i in range(len(x)):
        end = start + y[i]
        arc.append((start, end))
        angle = 0.5*(start+end)
        #print(start, end, angle)
        if -30 <= angle <= 210:
            angle -= 90
        else:
            angle -= 270
        nodePos.append(tuple(polar2xy(1.1, 0.5*(start+end)*np.pi/180.)) + (angle,))
        z = (X[i, :]/x[i].astype(float)) * (end - start)
        ids = np.argsort(z)
        z0 = start
        for j in ids:
            pos[(i, j)] = (z0, z0+z[j])
            z0 += z[j]
        start = end + pad

    for i in range(len(x)):
        start, end = arc[i]
        # 円周グラフ
        IdeogramArc(start=start, end=end, radius=1.0, ax=ax, color=colors[i], width=width)
        start, end = pos[(i,i)]
        # 滞在曲線
        selfChordArc(start, end, radius=1.-width, color=colors[i], chordwidth=chordwidth*0.7, ax=ax)
        for j in range(i):
            color = colors[i]
            if X[i, j] > X[j, i]:
                color = colors[j]
            start1, end1 = pos[(i,j)]
            start2, end2 = pos[(j,i)]
            # 移動曲線
            ChordArc(start1, end1, start2, end2,
                     radius=1.-width, color=colors[i], chordwidth=chordwidth, ax=ax)
    
    return arc, pos, nodePos

弦グラフの作成実行

下記のコードで弦グラフの作成を実行します．

import matplotlib
import matplotlib.pyplot as plt
from matplotlib import font_manager

# 可視化
fig = plt.figure(figsize=(6,6))
flux = df_crosstab.to_numpy()

# 図の設定1
ax = plt.axes([0,0,1,1])

# 弦グラフの情報
arc, pos, nodePos = chordDiagram(flux, ax)
ax.axis('off')

# 図の設定2
prop = dict(fontsize=16*0.8, ha='center', va='center')

# テキストの設定
nodes = df_crosstab.index.tolist()
for i in range(len(nodes)):
    # x, y, テキスト, rotation=回転
    ax.text(nodePos[i][0], nodePos[i][1], nodes[i], rotation=nodePos[i][2], **prop)

# plt.savefig("example.png", dpi=600,
#         transparent=True,
#         bbox_inches='tight', pad_inches=0.02)

まとめ

架空の行動履歴データでChordDiagram(弦グラフ)を作成しました．

参考サイト

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