.ipynb

3D Elliptic Fourier Analysis#

import numpy as np
import pandas as pd

import matplotlib.pyplot as plt
import seaborn as sns
import plotly.express as px

from sklearn.decomposition import PCA

from ktch.datasets import load_outline_leaf_bending
from ktch.harmonic import EllipticFourierAnalysis
from ktch.plot import explained_variance_ratio_plot, morphospace_plot

Load the leaf bending outline dataset#

data = load_outline_leaf_bending(as_frame=True)
data.coords
x y z
specimen_id coord_id
0 0 0.000000 0.000000 0.000000
1 0.000000 -0.046295 0.000000
2 0.000000 -0.092589 0.000000
3 0.000630 -0.095962 0.045238
4 0.002576 -0.098305 0.091431
... ... ... ... ...
59 195 0.000000 0.148530 0.000000
196 0.000000 0.118824 0.000000
197 0.000000 0.089118 0.000000
198 0.000000 0.059412 0.000000
199 0.000000 0.029706 0.000000

12000 rows × 3 columns

df_meta = data.meta.copy()
df_meta["bending_angle"] = (
    np.degrees(df_meta["alphaB"]).round().astype(int).astype(str) + "\u00b0"
)
df_meta["aspect_ratio"] = df_meta["alpha"]
df_meta
lmax c alpha A alphaB kB alpha_random alphaB_random bending_angle aspect_ratio
specimen_id
0 0.4 0.65 0.08 1.0 2.443461 0.2 0.060572 2.528513 140° 0.08
1 0.4 0.65 0.08 1.0 2.443461 0.2 0.090911 2.318855 140° 0.08
2 0.4 0.65 0.08 1.0 2.443461 0.2 0.088957 2.417189 140° 0.08
3 0.4 0.65 0.08 1.0 2.443461 0.2 0.074596 2.506030 140° 0.08
4 0.4 0.65 0.08 1.0 2.443461 0.2 0.098990 2.294188 140° 0.08
5 0.4 0.65 0.08 1.0 2.443461 0.2 0.073196 2.492090 140° 0.08
6 0.4 0.65 0.08 1.0 2.443461 0.2 0.077120 2.287193 140° 0.08
7 0.4 0.65 0.08 1.0 2.443461 0.2 0.083971 2.280600 140° 0.08
8 0.4 0.65 0.08 1.0 2.443461 0.2 0.073029 2.431389 140° 0.08
9 0.4 0.65 0.08 1.0 2.443461 0.2 0.099243 2.553002 140° 0.08
10 0.4 0.65 0.08 1.0 1.396263 0.2 0.089302 1.409695 80° 0.08
11 0.4 0.65 0.08 1.0 1.396263 0.2 0.076330 1.242604 80° 0.08
12 0.4 0.65 0.08 1.0 1.396263 0.2 0.060501 1.299788 80° 0.08
13 0.4 0.65 0.08 1.0 1.396263 0.2 0.087227 1.536335 80° 0.08
14 0.4 0.65 0.08 1.0 1.396263 0.2 0.098797 1.548685 80° 0.08
15 0.4 0.65 0.08 1.0 1.396263 0.2 0.076723 1.280753 80° 0.08
16 0.4 0.65 0.08 1.0 1.396263 0.2 0.093675 1.558039 80° 0.08
17 0.4 0.65 0.08 1.0 1.396263 0.2 0.095911 1.566630 80° 0.08
18 0.4 0.65 0.08 1.0 1.396263 0.2 0.078236 1.387295 80° 0.08
19 0.4 0.65 0.08 1.0 1.396263 0.2 0.095689 1.447270 80° 0.08
20 0.4 0.65 0.08 1.0 0.349066 0.2 0.082873 0.390205 20° 0.08
21 0.4 0.65 0.08 1.0 0.349066 0.2 0.064031 0.266366 20° 0.08
22 0.4 0.65 0.08 1.0 0.349066 0.2 0.089630 0.373168 20° 0.08
23 0.4 0.65 0.08 1.0 0.349066 0.2 0.078860 0.330521 20° 0.08
24 0.4 0.65 0.08 1.0 0.349066 0.2 0.087673 0.318159 20° 0.08
25 0.4 0.65 0.08 1.0 0.349066 0.2 0.088925 0.305914 20° 0.08
26 0.4 0.65 0.08 1.0 0.349066 0.2 0.077160 0.372707 20° 0.08
27 0.4 0.65 0.08 1.0 0.349066 0.2 0.083355 0.268017 20° 0.08
28 0.4 0.65 0.08 1.0 0.349066 0.2 0.083693 0.406805 20° 0.08
29 0.4 0.65 0.08 1.0 0.349066 0.2 0.081946 0.311726 20° 0.08
30 0.4 0.65 0.16 1.0 2.443461 0.2 0.173997 2.326146 140° 0.16
31 0.4 0.65 0.16 1.0 2.443461 0.2 0.178168 2.367912 140° 0.16
32 0.4 0.65 0.16 1.0 2.443461 0.2 0.166143 2.497124 140° 0.16
33 0.4 0.65 0.16 1.0 2.443461 0.2 0.142324 2.521001 140° 0.16
34 0.4 0.65 0.16 1.0 2.443461 0.2 0.159544 2.492420 140° 0.16
35 0.4 0.65 0.16 1.0 2.443461 0.2 0.176739 2.296786 140° 0.16
36 0.4 0.65 0.16 1.0 2.443461 0.2 0.170455 2.304695 140° 0.16
37 0.4 0.65 0.16 1.0 2.443461 0.2 0.148710 2.478740 140° 0.16
38 0.4 0.65 0.16 1.0 2.443461 0.2 0.141903 2.555287 140° 0.16
39 0.4 0.65 0.16 1.0 2.443461 0.2 0.171313 2.610918 140° 0.16
40 0.4 0.65 0.16 1.0 1.396263 0.2 0.176521 1.244129 80° 0.16
41 0.4 0.65 0.16 1.0 1.396263 0.2 0.167533 1.252522 80° 0.16
42 0.4 0.65 0.16 1.0 1.396263 0.2 0.175097 1.438110 80° 0.16
43 0.4 0.65 0.16 1.0 1.396263 0.2 0.146855 1.570428 80° 0.16
44 0.4 0.65 0.16 1.0 1.396263 0.2 0.143005 1.422087 80° 0.16
45 0.4 0.65 0.16 1.0 1.396263 0.2 0.174511 1.497144 80° 0.16
46 0.4 0.65 0.16 1.0 1.396263 0.2 0.170496 1.470243 80° 0.16
47 0.4 0.65 0.16 1.0 1.396263 0.2 0.151212 1.282264 80° 0.16
48 0.4 0.65 0.16 1.0 1.396263 0.2 0.176779 1.257857 80° 0.16
49 0.4 0.65 0.16 1.0 1.396263 0.2 0.157964 1.505475 80° 0.16
50 0.4 0.65 0.16 1.0 0.349066 0.2 0.166466 0.346456 20° 0.16
51 0.4 0.65 0.16 1.0 0.349066 0.2 0.177635 0.386719 20° 0.16
52 0.4 0.65 0.16 1.0 0.349066 0.2 0.155776 0.441191 20° 0.16
53 0.4 0.65 0.16 1.0 0.349066 0.2 0.175787 0.407493 20° 0.16
54 0.4 0.65 0.16 1.0 0.349066 0.2 0.146865 0.504861 20° 0.16
55 0.4 0.65 0.16 1.0 0.349066 0.2 0.163440 0.445301 20° 0.16
56 0.4 0.65 0.16 1.0 0.349066 0.2 0.160243 0.366476 20° 0.16
57 0.4 0.65 0.16 1.0 0.349066 0.2 0.158335 0.354346 20° 0.16
58 0.4 0.65 0.16 1.0 0.349066 0.2 0.148304 0.235357 20° 0.16
59 0.4 0.65 0.16 1.0 0.349066 0.2 0.160054 0.206858 20° 0.16 
coords = data.coords.to_numpy().reshape(-1, 200, 3)
coords.shape

(60, 200, 3)

Visualize 3D outlines#

representative_ids = [0, 10, 20, 30, 40, 50]
bending_order = [ str(deg)+ "\u00b0" for deg in  [20, 80, 140] ]

dfs = []
for sid in representative_ids:
    df = pd.DataFrame(coords[sid], columns=["x", "y", "z"])
    df["idx"] = data.meta.index[sid]
    df["bending_angle"] = df_meta.iloc[sid]["bending_angle"]
    dfs.append(df)
df_vis = pd.concat(dfs, ignore_index=True)

fig = px.line_3d(
    df_vis,
    x="x",
    y="y",
    z="z",
    line_group="idx",
    color="bending_angle",
    category_orders ={"bending_angle":bending_order},
    color_discrete_sequence=px.colors.qualitative.Set2,
)
fig.update_layout(scene=dict(aspectmode="data"))
fig.show()

3D EFA without normalization#

efa = EllipticFourierAnalysis(n_harmonics=20, n_dim=3, norm=False)

coef = efa.fit_transform(coords)
coef.shape

(60, 126)

Reconstruction from coefficients#

coords_recon = efa.inverse_transform(coef, t_num=200)

sid = 0
df_orig = pd.DataFrame(coords[sid], columns=["x", "y", "z"])
df_orig["type"] = "original"
df_rec = pd.DataFrame(coords_recon[sid], columns=["x", "y", "z"])
df_rec["type"] = "reconstructed"
df_cmp = pd.concat([df_orig, df_rec], ignore_index=True)

fig = px.line_3d(df_cmp, x="x", y="y", z="z", color="type")
fig.update_layout(scene=dict(aspectmode="data"))
fig.show()

3D EFA#

efa = EllipticFourierAnalysis(n_harmonics=20, n_dim=3, norm=True)

coef = efa.fit_transform(coords)
coef.shape

(60, 126)

Reconstruction from coefficients#

coords_recon = efa.inverse_transform(coef, t_num=200)

representative_ids = [0, 10, 20, 30, 40, 50]

dfs = []
for sid in representative_ids:
    df = pd.DataFrame(coords_recon[sid], columns=["x", "y", "z"])
    df["idx"] = data.meta.index[sid]
    df["bending_angle"] = df_meta.iloc[sid]["bending_angle"]
    dfs.append(df)
df_vis = pd.concat(dfs, ignore_index=True)

fig = px.line_3d(
    df_vis, x="x", y="y", z="z",
    line_group="idx",
    color="bending_angle",
    category_orders ={"bending_angle":bending_order},
    color_discrete_sequence=px.colors.qualitative.Set2
    )
fig.update_layout(scene=dict(aspectmode="data"))
fig.show()

PCA#

pca = PCA(n_components=12)
pcscores = pca.fit_transform(coef)

df_pca = pd.DataFrame(pcscores, columns=[f"PC{i+1}" for i in range(12)])
df_pca.index = df_meta.index
df_pca = df_pca.join(df_meta)
df_pca
PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9 PC10 ... lmax c alpha A alphaB kB alpha_random alphaB_random bending_angle aspect_ratio
specimen_id
0 -1.212191 1.121579 0.107171 0.011560 0.012842 0.001138 -0.002117 -0.000665 5.195792e-04 0.000332 ... 0.4 0.65 0.08 1.0 2.443461 0.2 0.060572 2.528513 140° 0.08
1 -0.936970 0.436713 0.028150 0.005296 -0.004628 0.001218 -0.000426 -0.000119 -3.270928e-04 -0.000379 ... 0.4 0.65 0.08 1.0 2.443461 0.2 0.090911 2.318855 140° 0.08
2 -1.035797 0.439970 0.047183 0.004650 -0.004887 0.000129 -0.000774 -0.000030 -2.139763e-04 -0.000394 ... 0.4 0.65 0.08 1.0 2.443461 0.2 0.088957 2.417189 140° 0.08
3 -1.145406 0.728617 0.075460 0.008020 0.000725 -0.001096 -0.000554 0.000422 2.015761e-04 -0.000002 ... 0.4 0.65 0.08 1.0 2.443461 0.2 0.074596 2.506030 140° 0.08
4 -0.912451 0.301951 0.016461 0.004460 -0.006107 0.000491 0.000658 0.000267 -4.775718e-04 0.000075 ... 0.4 0.65 0.08 1.0 2.443461 0.2 0.098990 2.294188 140° 0.08
5 -1.133819 0.771139 0.073925 0.008667 0.001817 -0.000782 -0.000424 0.000412 2.093879e-04 0.000050 ... 0.4 0.65 0.08 1.0 2.443461 0.2 0.073196 2.492090 140° 0.08
6 -0.906528 0.758235 0.025590 0.009584 0.001321 0.000946 0.001348 0.000506 -1.056459e-04 0.000153 ... 0.4 0.65 0.08 1.0 2.443461 0.2 0.077120 2.287193 140° 0.08
7 -0.897786 0.598010 0.021691 0.007696 -0.002021 0.001004 0.000776 0.000309 -2.412954e-04 -0.000039 ... 0.4 0.65 0.08 1.0 2.443461 0.2 0.083971 2.280600 140° 0.08
8 -1.069214 0.803718 0.060063 0.009552 0.002635 -0.000024 0.000220 0.000442 1.188405e-04 0.000132 ... 0.4 0.65 0.08 1.0 2.443461 0.2 0.073029 2.431389 140° 0.08
9 -1.153353 0.201580 0.064673 0.000142 -0.008252 -0.002337 -0.001004 0.000056 -2.327827e-04 -0.000266 ... 0.4 0.65 0.08 1.0 2.443461 0.2 0.099243 2.553002 140° 0.08
10 0.098271 0.584667 -0.070353 0.000910 -0.003291 0.000134 -0.000159 -0.000284 1.208559e-04 -0.000146 ... 0.4 0.65 0.08 1.0 1.396263 0.2 0.089302 1.409695 80° 0.08
11 0.409715 0.866223 -0.078336 -0.004074 0.001146 -0.002104 0.000748 0.000136 2.644008e-04 -0.000073 ... 0.4 0.65 0.08 1.0 1.396263 0.2 0.076330 1.242604 80° 0.08
12 0.479149 1.371337 -0.078663 -0.005317 0.015571 -0.000932 0.000856 -0.001264 -3.552821e-04 -0.000120 ... 0.4 0.65 0.08 1.0 1.396263 0.2 0.060501 1.299788 80° 0.08
13 -0.043950 0.641566 -0.067710 0.002521 -0.002334 0.000573 0.000627 -0.000120 2.669955e-05 -0.000117 ... 0.4 0.65 0.08 1.0 1.396263 0.2 0.087227 1.536335 80° 0.08
14 -0.113632 0.414991 -0.066985 0.002730 -0.005277 0.000412 0.000743 0.000109 -3.860665e-05 0.000190 ... 0.4 0.65 0.08 1.0 1.396263 0.2 0.098797 1.548685 80° 0.08
15 0.355298 0.864501 -0.078721 -0.003226 0.001113 -0.001853 0.000901 0.000137 2.508130e-04 -0.000074 ... 0.4 0.65 0.08 1.0 1.396263 0.2 0.076723 1.280753 80° 0.08
16 -0.102059 0.508699 -0.065106 0.002932 -0.004082 0.000865 0.000324 -0.000143 -2.991154e-05 -0.000056 ... 0.4 0.65 0.08 1.0 1.396263 0.2 0.093675 1.558039 80° 0.08
17 -0.121821 0.467478 -0.065432 0.002982 -0.004627 0.000701 0.000571 -0.000006 -4.302129e-05 0.000058 ... 0.4 0.65 0.08 1.0 1.396263 0.2 0.095911 1.566630 80° 0.08
18 0.202180 0.844041 -0.077693 -0.000848 0.000793 -0.001103 0.001261 0.000145 1.984502e-04 -0.000068 ... 0.4 0.65 0.08 1.0 1.396263 0.2 0.078236 1.387295 80° 0.08
19 0.018057 0.463559 -0.069791 0.001618 -0.004887 0.000130 0.000180 -0.000058 8.152559e-05 0.000060 ... 0.4 0.65 0.08 1.0 1.396263 0.2 0.095689 1.447270 80° 0.08
20 1.395888 0.273970 0.029565 -0.007117 -0.002888 -0.000400 -0.000432 0.000188 2.413662e-04 0.000073 ... 0.4 0.65 0.08 1.0 0.349066 0.2 0.082873 0.390205 20° 0.08
21 1.900065 0.629052 0.074601 -0.016125 0.008819 0.000725 -0.000925 0.000235 -1.295535e-03 0.000062 ... 0.4 0.65 0.08 1.0 0.349066 0.2 0.064031 0.266366 20° 0.08
22 1.312209 0.126744 0.033607 -0.002834 -0.004087 0.000589 -0.000661 -0.000273 3.846086e-04 -0.000025 ... 0.4 0.65 0.08 1.0 0.349066 0.2 0.089630 0.373168 20° 0.08
23 1.529104 0.313506 0.044290 -0.008627 -0.001265 -0.000009 -0.000039 0.000378 2.528159e-05 0.000031 ... 0.4 0.65 0.08 1.0 0.349066 0.2 0.078860 0.330521 20° 0.08
24 1.399288 0.122454 0.045810 -0.003021 -0.003469 0.001047 -0.000126 -0.000142 2.996893e-04 -0.000061 ... 0.4 0.65 0.08 1.0 0.349066 0.2 0.087673 0.318159 20° 0.08
25 1.393050 0.089307 0.048629 -0.002012 -0.003558 0.001354 -0.000096 -0.000240 3.159606e-04 -0.000099 ... 0.4 0.65 0.08 1.0 0.349066 0.2 0.088925 0.305914 20° 0.08
26 1.510394 0.385975 0.034734 -0.010259 -0.000794 -0.000713 -0.000342 0.000435 -6.106588e-07 0.000077 ... 0.4 0.65 0.08 1.0 0.349066 0.2 0.077160 0.372707 20° 0.08
27 1.521174 0.167297 0.058388 -0.004676 -0.002244 0.001328 0.000450 0.000133 1.237559e-04 -0.000085 ... 0.4 0.65 0.08 1.0 0.349066 0.2 0.083355 0.268017 20° 0.08
28 1.364556 0.269302 0.025877 -0.006852 -0.003181 -0.000500 -0.000550 0.000141 2.802554e-04 0.000081 ... 0.4 0.65 0.08 1.0 0.349066 0.2 0.083693 0.406805 20° 0.08
29 1.497570 0.231904 0.047980 -0.006423 -0.002178 0.000534 0.000109 0.000229 1.266806e-04 -0.000008 ... 0.4 0.65 0.08 1.0 0.349066 0.2 0.081946 0.311726 20° 0.08
30 -0.964406 -0.547059 0.002380 -0.009928 0.003770 0.001159 0.001010 0.000236 1.190184e-04 0.000090 ... 0.4 0.65 0.16 1.0 2.443461 0.2 0.173997 2.326146 140° 0.16
31 -0.995482 -0.588329 0.007357 -0.011664 0.004883 0.001041 0.000952 0.000277 3.944896e-04 -0.000080 ... 0.4 0.65 0.16 1.0 2.443461 0.2 0.178168 2.367912 140° 0.16
32 -1.084258 -0.534348 0.027336 -0.012744 0.001073 -0.000244 0.000548 -0.000191 1.501517e-04 0.000003 ... 0.4 0.65 0.16 1.0 2.443461 0.2 0.166143 2.497124 140° 0.16
33 -1.103990 -0.332649 0.037067 -0.008456 -0.004835 -0.001270 0.000250 -0.000419 -4.231776e-04 0.000217 ... 0.4 0.65 0.16 1.0 2.443461 0.2 0.142324 2.521001 140° 0.16
34 -1.081148 -0.481900 0.029774 -0.011638 -0.000656 0.000172 -0.000081 -0.000507 1.641188e-04 -0.000331 ... 0.4 0.65 0.16 1.0 2.443461 0.2 0.159544 2.492420 140° 0.16
35 -0.944329 -0.560544 -0.001406 -0.009806 0.004606 0.001423 0.000978 0.000315 2.221716e-04 -0.000010 ... 0.4 0.65 0.16 1.0 2.443461 0.2 0.176739 2.296786 140° 0.16
36 -0.947443 -0.515159 0.000247 -0.008860 0.002833 0.001258 0.000954 0.000162 -2.426856e-05 0.000138 ... 0.4 0.65 0.16 1.0 2.443461 0.2 0.170455 2.304695 140° 0.16
37 -1.071686 -0.381330 0.029611 -0.008917 -0.003227 -0.000261 0.000127 -0.000506 -2.460090e-04 -0.000004 ... 0.4 0.65 0.16 1.0 2.443461 0.2 0.148710 2.478740 140° 0.16
38 -1.129563 -0.340092 0.042721 -0.009278 -0.005135 -0.001730 0.000113 -0.000464 -3.810645e-04 0.000181 ... 0.4 0.65 0.16 1.0 2.443461 0.2 0.141903 2.555287 140° 0.16
39 -1.160450 -0.608589 0.042258 -0.017069 0.002021 -0.001675 0.000585 -0.000203 4.786634e-04 0.000006 ... 0.4 0.65 0.16 1.0 2.443461 0.2 0.171313 2.610918 140° 0.16
40 -0.100311 -0.512332 -0.061102 0.000277 0.003444 -0.000393 -0.001453 0.000471 6.027916e-05 -0.000128 ... 0.4 0.65 0.16 1.0 1.396263 0.2 0.176521 1.244129 80° 0.16
41 -0.079981 -0.441534 -0.061914 0.000620 0.001185 -0.000248 -0.001414 0.000194 -1.683988e-05 0.000093 ... 0.4 0.65 0.16 1.0 1.396263 0.2 0.167533 1.252522 80° 0.16
42 -0.259471 -0.477805 -0.061752 -0.000556 0.003429 0.000534 -0.000928 0.000441 -6.780287e-06 -0.000085 ... 0.4 0.65 0.16 1.0 1.396263 0.2 0.175097 1.438110 80° 0.16
43 -0.302468 -0.225359 -0.060633 0.001001 -0.002737 0.001199 -0.000374 -0.000215 -2.950729e-04 0.000315 ... 0.4 0.65 0.16 1.0 1.396263 0.2 0.146855 1.570428 80° 0.16
44 -0.152787 -0.194943 -0.065320 0.001167 -0.003807 0.000371 -0.000481 -0.000161 -2.123430e-04 0.000508 ... 0.4 0.65 0.16 1.0 1.396263 0.2 0.143005 1.422087 80° 0.16
45 -0.307667 -0.469121 -0.060844 -0.000789 0.003396 0.000805 -0.000743 0.000429 -3.411932e-05 -0.000063 ... 0.4 0.65 0.16 1.0 1.396263 0.2 0.174511 1.497144 80° 0.16
46 -0.275157 -0.439585 -0.061692 -0.000384 0.002311 0.000701 -0.000792 0.000313 -8.908570e-05 0.000045 ... 0.4 0.65 0.16 1.0 1.396263 0.2 0.170496 1.470243 80° 0.16
47 -0.052624 -0.296443 -0.062555 0.001237 -0.002283 0.000227 -0.001640 -0.000360 -4.048301e-07 0.000094 ... 0.4 0.65 0.16 1.0 1.396263 0.2 0.151212 1.282264 80° 0.16
48 -0.112605 -0.512113 -0.061268 0.000202 0.003539 -0.000323 -0.001436 0.000476 6.406333e-05 -0.000145 ... 0.4 0.65 0.16 1.0 1.396263 0.2 0.176779 1.257857 80° 0.16
49 -0.274825 -0.335715 -0.059410 0.000581 -0.000319 0.001512 -0.001492 -0.000330 -3.504779e-05 -0.000270 ... 0.4 0.65 0.16 1.0 1.396263 0.2 0.157964 1.505475 80° 0.16
50 0.666826 -0.751041 0.016709 0.010780 0.002460 -0.000799 0.000803 0.000095 -1.436529e-04 0.000089 ... 0.4 0.65 0.16 1.0 0.349066 0.2 0.166466 0.346456 20° 0.16
51 0.578040 -0.806088 0.008922 0.010286 0.005021 -0.001514 0.000503 0.000469 -2.606051e-04 -0.000155 ... 0.4 0.65 0.16 1.0 0.349066 0.2 0.177635 0.386719 20° 0.16
52 0.653467 -0.624203 0.006614 0.009087 -0.000103 -0.000554 -0.000854 -0.000533 1.463360e-04 -0.000157 ... 0.4 0.65 0.16 1.0 0.349066 0.2 0.155776 0.441191 20° 0.16
53 0.572528 -0.783451 0.005996 0.009685 0.004365 -0.001549 0.000388 0.000436 -2.251687e-04 -0.000036 ... 0.4 0.65 0.16 1.0 0.349066 0.2 0.175787 0.407493 20° 0.16
54 0.659641 -0.513237 -0.004183 0.006170 -0.002880 -0.000997 -0.000403 -0.000293 2.174160e-04 0.000516 ... 0.4 0.65 0.16 1.0 0.349066 0.2 0.146865 0.504861 20° 0.16
55 0.608625 -0.678892 0.002987 0.008683 0.001219 -0.001112 -0.000207 -0.000031 -6.913243e-06 0.000121 ... 0.4 0.65 0.16 1.0 0.349066 0.2 0.163440 0.445301 20° 0.16
56 0.686187 -0.696469 0.015975 0.010500 0.001120 -0.000493 0.000174 -0.000254 3.747075e-06 -0.000045 ... 0.4 0.65 0.16 1.0 0.349066 0.2 0.160243 0.366476 20° 0.16
57 0.706113 -0.689142 0.018765 0.010884 0.000886 -0.000274 0.000101 -0.000391 3.554720e-05 -0.000137 ... 0.4 0.65 0.16 1.0 0.349066 0.2 0.158335 0.354346 20° 0.16
58 0.863564 -0.675819 0.039638 0.012348 -0.000697 0.000855 0.001824 -0.000443 5.866481e-05 0.000142 ... 0.4 0.65 0.16 1.0 0.349066 0.2 0.148304 0.235357 20° 0.16
59 0.804667 -0.784796 0.042667 0.014671 0.002395 0.000714 0.001847 -0.000351 -1.425091e-04 -0.000275 ... 0.4 0.65 0.16 1.0 0.349066 0.2 0.160054 0.206858 20° 0.16

60 rows × 22 columns

fig, ax = plt.subplots()
explained_variance_ratio_plot(pca, ax=ax, verbose=True)

                                         PC1         PC2         PC3         PC4         PC5         PC6         PC7         PC8         PC9        PC10        PC11        PC12
  Explained Variance Ratio (EVR)      0.7105      0.2872      0.0023      0.0001      0.0000      0.0000      0.0000      0.0000      0.0000      0.0000      0.0000      0.0000
                   Cumsum of EVR      0.7105      0.9977      0.9999      1.0000      1.0000      1.0000      1.0000      1.0000      1.0000      1.0000      1.0000      1.0000

<Axes: >
../../_images/8933e51063931b0ef590e224d318fd316b40dab41d21710233f4059fda5e4632.png 
fig, ax = plt.subplots()
sns.scatterplot(
    data=df_pca,
    x="PC1",
    y="PC2",
    hue="bending_angle",
    hue_order=bending_order,
    style="aspect_ratio",
    palette="Set2",
    ax=ax,
)

<Axes: xlabel='PC1', ylabel='PC2'>
../../_images/72a932599f7f2c37c2dd794ea6ccebe12ebf940e747427e3b830957c9e1009a4.png

Morphospace#

def render_curve_3d_fixed_view(coords, ax, *, color="gray", alpha=0.7, **kw):
    kw.pop("links", None)
    ax.plot(coords[:, 0], coords[:, 1], coords[:, 2], color=color, alpha=alpha)
    ptp = [max(np.max(coords[:, i]) - np.min(coords[:, i]), 1e-10) for i in range(3)]
    ax.set_box_aspect(ptp)
    ax.view_init(elev=60, azim=-120)

fig, axes = plt.subplots(2, 2, figsize=(16, 16), dpi=200)

for ax, (i, j) in zip(axes.flat[:3], [(0, 1), (1, 2), (2, 0)]):
    morphospace_plot(
        data=df_pca,
        x=f"PC{i + 1}", y=f"PC{j + 1}",
        hue="bending_angle", hue_order=bending_order,
        palette="Set2",
        reducer=pca,
        descriptor=efa,
        shape_type="curve_3d",
        render_fn=render_curve_3d_fixed_view,
        components=(i, j),
        n_shapes=5,
        shape_scale=0.8,
        shape_color="gray",
        shape_alpha=0.8,
        ax=ax,
        scatter_kw=dict(style="aspect_ratio"),
    )

explained_variance_ratio_plot(pca, ax=axes[1, 1], verbose=True)

                                         PC1         PC2         PC3         PC4         PC5         PC6         PC7         PC8         PC9        PC10        PC11        PC12
  Explained Variance Ratio (EVR)      0.7105      0.2872      0.0023      0.0001      0.0000      0.0000      0.0000      0.0000      0.0000      0.0000      0.0000      0.0000
                   Cumsum of EVR      0.7105      0.9977      0.9999      1.0000      1.0000      1.0000      1.0000      1.0000      1.0000      1.0000      1.0000      1.0000

<Axes: >
../../_images/fcaa3bd6d9c0af9fb014c0d36899294e9c7d0a423153f3c141a0ff323e91c457.png