HiSD Package: SaddleScape V-1.0

A Python package for constructing solution landscapes using High-index Saddle Dynamics (HiSD). This toolkit enables numerical computation of saddle points and their hierarchical organization in dynamical systems.It simplifies the process of saddle point searching, offers flexible parameter settings and many visualization tools.

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Output Objects

.SaddleList

Description
Collection of discovered saddle points with topological metadata.

Type
list[list]

Node Structure

[
  [
    ID: int,               # Index 0 - Unique identifier
    Position: np.ndarray,  # Index 1 - Coordinate vector (d-dim)
    Morse Index: int,      # Index 2 - Number of negative eigenvalues
    Unstable Directions: np.ndarray,  # Index 3 - Eigenvectors (d x k)
    Parent IDs: list[int]   # Index 4 - Ancestor saddle IDs (where -1 indicates initial point)
  ]
  ... # Other saddle points
]

Access

# Get all index-1 saddles
index1_saddles = [node for node in landscape.SaddleList if node[2] == 1]

# Get position of saddle ID 5
saddle5_pos = landscape.SaddleList[5][1]

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.DetailRecord

Description
Complete search trajectory data.

Type
list[list]

Record Structure

[
  [
    End ID: int,            # Index 0 - Terminating saddle ID
    Start ID: int,          # Index 1 - Originating saddle ID
    Path Positions: np.ndarray,  # Index 2 - Trajectory points (N x d)
    Path Times: np.ndarray       # Index 3 - Temporal coordinates (N x 1)
  ]
  ... # Other search trajectory
]

Access

# Plot first search path
first_search = landscape.DetailRecord[0]
plt.plot(first_search[2][:,0], first_search[2][:,1])