import numpy as np

def calculate(input_list): if len(input_list) != 9: raise ValueError("List must contain nine numbers.")

# Convert the list to a 3x3 numpy array
matrix = np.array(input_list).reshape(3, 3)

# Calculate required statistics
calculations = {
    'mean': [
        matrix.mean(axis=0).tolist(),  # Mean for each column
        matrix.mean(axis=1).tolist(),  # Mean for each row
        matrix.mean().tolist()          # Mean of flattened matrix
    ],
    'variance': [
        matrix.var(axis=0).tolist(),    # Variance for each column
        matrix.var(axis=1).tolist(),    # Variance for each row
        matrix.var().tolist()            # Variance of flattened matrix
    ],
    'standard deviation': [
        matrix.std(axis=0).tolist(),     # Std dev for each column
        matrix.std(axis=1).tolist(),     # Std dev for each row
        matrix.std().tolist()             # Std dev of flattened matrix
    ],
    'max': [
        matrix.max(axis=0).tolist(),     # Max for each column
        matrix.max(axis=1).tolist(),     # Max for each row
        matrix.max().tolist()             # Max of flattened matrix
    ],
    'min': [
        matrix.min(axis=0).tolist(),     # Min for each column
        matrix.min(axis=1).tolist(),     # Min for each row
        matrix.min().tolist()             # Min of flattened matrix
    ],
    'sum': [
        matrix.sum(axis=0).tolist(),     # Sum for each column
        matrix.sum(axis=1).tolist(),     # Sum for each row
        matrix.sum().tolist()             # Sum of flattened matrix
    ]
}

return calculations