如何在Python中将列表数值分箱为状态类别并生成转移状态数组

Got it, let's break down how to convert your numerical array into the required state array, then use it to build a transition matrix.

First, let's clarify the mapping rules you specified:

• Values in [0, 10) → State 1
• Values in [10, 20) → State 2
• Values in [20, 30) → State 3

Step 1: Convert Numerical Array to State Array #

Your original array is [1.2, 4.6, 3.7, 11.2, 13, 5, 18.9, 0.3, 20.0, 26.7, 1]. Note that the example state array you provided has 10 elements, but your original array has 11—so the correct state array should be [1, 1, 1, 2, 2, 1, 2, 1, 3, 3, 1]. Here are two ways to generate this:

Option 1: Pure Python (No External Libraries)

If you don't want to use numpy, a simple loop or list comprehension works perfectly:

original_array = [1.2, 4.6, 3.7, 11.2, 13, 5, 18.9, 0.3, 20.0, 26.7, 1]

# Concise list comprehension for mapping
state_array = [
    1 if 0 <= num < 10 
    else 2 if 10 <= num < 20 
    else 3 if 20 <= num < 30 
    else None  # Add this to handle out-of-range values if needed
    for num in original_array
]

print(state_array)  # Output: [1, 1, 1, 2, 2, 1, 2, 1, 3, 3, 1]

Option 2: Using NumPy (Better for Large Datasets)

For larger arrays, numpy is faster and more efficient. We can use np.digitize—it's built for exactly this kind of interval mapping:

import numpy as np

original_array = np.array([1.2, 4.6, 3.7, 11.2, 13, 5, 18.9, 0.3, 20.0, 26.7, 1])
bins = [0, 10, 20, 30]  # Define our interval boundaries

# right=False ensures intervals are left-closed, right-open (matches your rules)
state_array = np.digitize(original_array, bins, right=False)

print(state_array.tolist())  # Convert back to a list if needed: [1, 1, 1, 2, 2, 1, 2, 1, 3, 3, 1]

Step 2: Build the Transition Matrix #

Once you have the state array, you can count state transitions and normalize to get a transition matrix. Here's a straightforward implementation:

# Initialize a 3x3 count matrix (for states 1-3)
transition_counts = np.zeros((3, 3), dtype=int)

# Iterate through consecutive state pairs
for i in range(len(state_array) - 1):
    # Convert to 0-indexed for array access
    current_state = state_array[i] - 1
    next_state = state_array[i+1] - 1
    transition_counts[current_state][next_state] += 1

# Normalize rows to get transition probabilities (each row sums to 1)
transition_matrix = transition_counts / transition_counts.sum(axis=1, keepdims=True)

print("Transition Matrix:")
print(transition_matrix)

Running this will give you a matrix where transition_matrix[i][j] represents the probability of moving from state i+1 to state j+1.

内容的提问来源于stack exchange，提问作者Latif Fetahaj