Draw scatter_3d using plotly 4.10 (+ellipses?)

import plotly.graph_objects as go
import pandas as pd
from sklearn.decomposition import PCA
import numpy as np
from scipy.linalg import eigh, sqrtm




# Read in data as a pandas dataframe
#df = pd.DataFrame({
#    'PC1': [-13.999925, -12.504291, -12.443057, -13.065235, -17.316215],
#    'PC2': [-1.498823, -3.342411, -6.067055, -8.205809, 3.293993],
#    'PC3': [-3.335085, 15.207755, -14.725450, 15.078469, -6.917358],
#    'condition': ['GFP d3', 'GFP d3', 'GFP d8', 'GFP d8', 'GFP+mCh d9/12'],
#    'donor': ['DI', 'DII', 'DI', 'DII', 'DI']
#})
df = pd.read_csv('merged_df_28PCs.csv', index_col=0, header=0)
df['condition'] = df['condition'].replace("GFP+mCh d9/12", "ctrl LTtr+sT d9/12")
df['condition'] = df['condition'].replace("sT+LTtr d9/12", "LTtr+sT d9/12")
df['condition'] = df['condition'].replace("GFP d3", "ctrl LT/LTtr d3")
df['condition'] = df['condition'].replace("GFP d8", "ctrl LT/LTtr d8")
df['condition'] = df['condition'].replace("mCh d3", "ctrl sT d3")
df['condition'] = df['condition'].replace("mCh d8", "ctrl sT d8")

# Fit PCA model to reduce data dimensions to 3
pca = PCA(n_components=3)
pca.fit(df.iloc[:, :-3])
X_reduced = pca.transform(df.iloc[:, :-3])

# Add reduced data back to dataframe
df['PC1'] = X_reduced[:, 0]
df['PC2'] = X_reduced[:, 1]
df['PC3'] = X_reduced[:, 2]

# Create PCA plot with 3D scatter
fig = go.Figure()

#['circle', 'circle-open', 'square', 'square-open', 'diamond', 'diamond-open', 'cross', 'x']
# if donor == 'DI' else marker=dict(size=2, opacity=0.8, color=condition_color, symbol=donor_symbol)

#decrease diamond size to 6 while keep the circle as size 10 in the following code:
#'rgb(128, 150, 128)'
#I need three families of colors, always from light to deep, the first one should close to grey.
#the first serie for 'ctrl LTtr+sT d9/12', 'LTtr+sT d9/12' 
#the second serie for 'ctrl LT/LTtr d3', 'ctrl LT/LTtr d8', 'LT d3', 'LT d8', 'LTtr d3', 'LTtr d8'
#the third serie for 'ctrl sT d3', 'ctrl sT d8', 'sT d3', 'sT d8', 'sT+LT d3'


condition_color_map_untreated = {'untreated':'black'}
donor_symbol_map_untreated = {'DI': 'circle-open', 'DII': 'diamond-open'}
#condition_color_map = {'ctrl LTtr+sT d9/12': 'green', 'GFP d3': 'blue', 'GFP d8': 'red', 'GFP+mCh d9/12': 'green', 'LT d3': 'orange'}
condition_color_map = {
    'ctrl LTtr+sT d9/12': 'black',
    'LTtr+sT d9/12': '#a14a1a',

    'ctrl LT/LTtr d3': '#D3D3D3',
    'ctrl LT/LTtr d8': '#A9A9A9',
    'LT d3': '#b2df8a',
    'LT d8': '#33a02c',
    'LTtr d3': '#a6cee3',
    'LTtr d8': '#1f78b4',

    'ctrl sT d3': '#696969',
    'ctrl sT d8': '#2F4F4F',
    'sT d3': '#fb9a99',
    'sT d8': '#e31a1c',
    'sT+LT d3': 'magenta'
}
donor_symbol_map = {'DI': 'circle', 'DII': 'diamond'}

for donor, donor_symbol in donor_symbol_map_untreated.items():
    for condition, condition_color in condition_color_map_untreated.items():
        mask = (df['condition'] == condition) & (df['donor'] == donor)
        fig.add_trace(go.Scatter3d(x=df.loc[mask, 'PC1'], y=df.loc[mask, 'PC2'], z=df.loc[mask, 'PC3'],
                                   mode='markers',
                                   name=f'{condition}' if donor == 'DI' else None,
                                   legendgroup=f'{condition}',
                                   showlegend=True if donor == 'DI' else False,
                                   marker=dict(size=4 if donor_symbol in ['diamond-open'] else 6, opacity=0.8, color=condition_color, symbol=donor_symbol)))

for donor, donor_symbol in donor_symbol_map.items():
    for condition, condition_color in condition_color_map.items():
        mask = (df['condition'] == condition) & (df['donor'] == donor)
        fig.add_trace(go.Scatter3d(x=df.loc[mask, 'PC1'], y=df.loc[mask, 'PC2'], z=df.loc[mask, 'PC3'],
                                   mode='markers',
                                   name=f'{condition}' if donor == 'DI' else None,
                                   legendgroup=f'{condition}',
                                   showlegend=True if donor == 'DI' else False,
                                   marker=dict(size=4 if donor_symbol in ['diamond'] else 6, opacity=0.8, color=condition_color, symbol=donor_symbol)))

for donor, donor_symbol in donor_symbol_map.items():
    fig.add_trace(go.Scatter3d(x=[None], y=[None], z=[None],
                               mode='markers',
                               name=donor,
                               legendgroup=f'{donor}',
                               showlegend=True,
                               marker=dict(size=6, opacity=1, color='black', symbol=donor_symbol),
                               hoverinfo='none'))


'''
# Calculate mean and covariance for each subset of data for eclipse drawing
DI_mask = (df['donor'] == 'DI') & (~df['condition'].isin(['untreated']))
DII_mask = (df['donor'] == 'DII') & (~df['condition'].isin(['untreated']))
untreated_mask = (df['condition'] == 'untreated')

mean_DI = df.loc[DI_mask, ['PC1', 'PC2', 'PC3']].mean().values
cov_DI = df.loc[DI_mask, ['PC1', 'PC2', 'PC3']].cov().values

mean_DII = df.loc[DII_mask, ['PC1', 'PC2', 'PC3']].mean().values
cov_DII = df.loc[DII_mask, ['PC1', 'PC2', 'PC3']].cov().values

mean_untreated = df.loc[untreated_mask, ['PC1', 'PC2', 'PC3']].mean().values
cov_untreated = df.loc[untreated_mask, ['PC1', 'PC2', 'PC3']].cov().values

# Function to create ellipses
def create_ellipse(center, radii, rotation_matrix, resolution=100):
    u = np.linspace(0, 2 * np.pi, resolution)
    v = np.linspace(0, np.pi, resolution)
    x = radii[0] * np.outer(np.cos(u), np.sin(v))
    y = radii[1] * np.outer(np.sin(u), np.sin(v))
    z = radii[2] * np.outer(np.ones_like(u), np.cos(v))
    for i in range(len(x)):
        for j in range(len(x)):
            [x[i, j], y[i, j], z[i, j]] = np.dot([x[i, j], y[i, j], z[i, j]], rotation_matrix) + center
    return x, y, z
def ellipsoid_params(mean, cov, conf_interval=0.9):
    vals, vecs = eigh(cov)
    vals = vals[::-1]
    vecs = vecs[:, ::-1]
    radii = np.sqrt(vals * chi2.ppf(conf_interval, df=3))
    rotation_matrix = vecs
    return mean, radii, rotation_matrix


from scipy.stats import chi2
center_DI, radii_DI, rotation_matrix_DI = ellipsoid_params(mean_DI, cov_DI)
center_DII, radii_DII, rotation_matrix_DII = ellipsoid_params(mean_DII, cov_DII)
#center_untreated, radii_untreated, rotation_matrix_untreated = ellipsoid_params(mean_untreated, cov_untreated)

# Generate ellipses using create_ellipse function
x_DI, y_DI, z_DI = create_ellipse(center_DI, radii_DI, rotation_matrix_DI)
x_DII, y_DII, z_DII = create_ellipse(center_DII, radii_DII, rotation_matrix_DII)
#x_untreated, y_untreated, z_untreated = create_ellipse(center_untreated, radii_untreated, rotation_matrix_untreated)

fig.add_trace(go.Mesh3d(x=x_DI.flatten(), y=y_DI.flatten(), z=z_DI.flatten(),
                        alphahull=5,
                        opacity=0.1,
                        color='blue',
                        name='DI ellipse',
                        showlegend=False))
fig.add_trace(go.Mesh3d(x=x_DII.flatten(), y=y_DII.flatten(), z=z_DII.flatten(),
                        alphahull=5,
                        opacity=0.1,
                        color='red',
                        name='DII ellipse',
                        showlegend=False))
'''


# Annotations for the legend blocks
fig.update_layout(
    annotations=[
        dict(x=1.1, y=1.0, xref='paper', yref='paper', showarrow=False,
             text='Condition', font=dict(size=15)),
        dict(x=1.1, y=0.6, xref='paper', yref='paper', showarrow=False,
             text='Donor', font=dict(size=15))
    ],
    scene=dict(
        aspectmode='cube',
        xaxis=dict(gridcolor='lightgrey', linewidth=2, linecolor='black', backgroundcolor='white', zerolinecolor='black', zerolinewidth=2, title='PC1: 36% v.'),
        yaxis=dict(gridcolor='lightgrey', linewidth=2, linecolor='black', backgroundcolor='white', zerolinecolor='black', zerolinewidth=2, title='PC2: 17% v.'),
        zaxis=dict(gridcolor='lightgrey', linewidth=2, linecolor='black',backgroundcolor='white', zerolinecolor='black', zerolinewidth=2, title='PC3: 15% variance'),
        bgcolor='white'
    ),
    margin=dict(l=5, r=5, b=5, t=0)  # Adjust the margins to prevent clipping of axis titles
)

#fig.show()
fig.write_image("fig4.svg")

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