This document describes the plot_surrogate() method added to the SpotOptim class, which provides visualization capabilities similar to the plotkd() function in the spotpython package.
The plot_surrogate() method creates a comprehensive 4-panel visualization of the fitted surrogate model, showing both predictions and uncertainty estimates across two selected dimensions.
import numpy as np
from spotoptim import SpotOptim
# Define objective function
def sphere(X):
return np.sum(X**2, axis=1)
# Run optimization
optimizer = SpotOptim(fun=sphere, bounds=[(-5, 5), (-5, 5)], max_iter=20)
result = optimizer.optimize()
# Visualize the surrogate model
optimizer.plot_surrogate(i=0, j=1, show=True)
optimizer.plot_surrogate(
i=0, # First dimension to plot
j=1, # Second dimension to plot
var_name=['x1', 'x2'], # Variable names for axes
add_points=True, # Show evaluated points
cmap='viridis', # Colormap
alpha=0.7, # Surface transparency
num=100, # Grid resolution
contour_levels=25, # Number of contour levels
grid_visible=True, # Show grid on contours
figsize=(12, 10), # Figure size
show=True # Display immediately
)
For problems with more than 2 dimensions, plot_surrogate() creates a 2D slice by fixing all other dimensions at their mean values:
# 4D optimization problem
def sphere_4d(X):
return np.sum(X**2, axis=1)
bounds = [(-3, 3)] * 4
optimizer = SpotOptim(fun=sphere_4d, bounds=bounds, max_iter=20)
result = optimizer.optimize()
# Visualize dimensions 0 and 2 (dimensions 1 and 3 fixed at mean)
optimizer.plot_surrogate(
i=0, j=2,
var_name=['x0', 'x1', 'x2', 'x3']
)
# Visualize different dimension pair
optimizer.plot_surrogate(i=1, j=3, var_name=['x0', 'x1', 'x2', 'x3'])
The visualization consists of 4 panels:
i (int, default=0): Index of first dimension to plotj (int, default=1): Index of second dimension to plotvar_name (list of str, optional): Names for each dimensioncmap (str, default=‘jet’): Matplotlib colormap namealpha (float, default=0.8): Surface transparency (0=transparent, 1=opaque)figsize (tuple, default=(12, 10)): Figure size in inches (width, height)num (int, default=100): Number of grid points per dimensioncontour_levels (int, default=30): Number of contour levelsgrid_visible (bool, default=True): Show grid lines on contour plotsvmin (float, optional): Minimum value for color scalevmax (float, optional): Maximum value for color scaleshow (bool, default=True): Display plot immediatelyadd_points (bool, default=True): Overlay evaluated points on contoursimport numpy as np
from spotoptim import SpotOptim
def rosenbrock(X):
X = np.atleast_2d(X)
x, y = X[:, 0], X[:, 1]
return (1 - x)**2 + 100 * (y - x**2)**2
optimizer = SpotOptim(
fun=rosenbrock,
bounds=[(-2, 2), (-2, 2)],
max_iter=30,
seed=42
)
result = optimizer.optimize()
# Visualize with custom colormap
optimizer.plot_surrogate(
var_name=['x', 'y'],
cmap='coolwarm',
add_points=True
)
import numpy as np
from spotoptim import SpotOptim, Kriging
def sphere(X):
return np.sum(X**2, axis=1)
optimizer = SpotOptim(
fun=sphere,
bounds=[(-5, 5), (-5, 5)],
surrogate=Kriging(seed=42), # Use Kriging instead of GP
max_iter=20
)
result = optimizer.optimize()
# The plotting works the same with any surrogate
optimizer.plot_surrogate(var_name=['x1', 'x2'])
# 3D problem - visualize all dimension pairs
def sphere_3d(X):
return np.sum(X**2, axis=1)
optimizer = SpotOptim(
fun=sphere_3d,
bounds=[(-5, 5)] * 3,
max_iter=25
)
result = optimizer.optimize()
# Dimensions 0 vs 1
optimizer.plot_surrogate(i=0, j=1, var_name=['x0', 'x1', 'x2'])
# Dimensions 0 vs 2
optimizer.plot_surrogate(i=0, j=2, var_name=['x0', 'x1', 'x2'])
# Dimensions 1 vs 2
optimizer.plot_surrogate(i=1, j=2, var_name=['x0', 'x1', 'x2'])
Run Optimization First: Always call optimize() before plot_surrogate()
Choose Dimensions Wisely: For high-dimensional problems, plot dimensions that you suspect are most important or interactive
Adjust Resolution: Use lower num values (e.g., 50) for faster plotting, higher values (e.g., 200) for smoother surfaces
Color Scales: Set vmin and vmax explicitly when comparing multiple plots to ensure consistent color scales
Uncertainty Analysis: High uncertainty areas (bright colors in uncertainty plots) are good candidates for additional sampling
Exploration vs Exploitation: Red dots clustered in low-prediction areas show exploitation; spread-out dots show exploration
The plot_surrogate() method is inspired by spotpython’s plotkd() function but adapted for SpotOptim’s simplified interface:
The method validates inputs and provides clear error messages:
# Before optimization runs
optimizer.plot_surrogate() # ValueError: No optimization data available
# Invalid dimension indices
optimizer.plot_surrogate(i=5, j=1) # ValueError: i must be less than n_dim
# Same dimension twice
optimizer.plot_surrogate(i=0, j=0) # ValueError: i and j must be different