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python - 使用取决于先前值的操作矢量化 numpy 代码

问题描述

以下代码模拟了一个可以随时采样 3 种不同状态的系统，这些状态之间的恒定转移概率由矩阵 给出prob_nor。因此，每个点都trace取决于先前的状态。

n_states, n_frames = 3, 1000
state_val = np.linspace(0, 1, n_states)

prob = np.random.randint(1, 10, size=(n_states,)*2)
prob[np.diag_indices(n_states)] += 50

prob_nor = prob/prob.sum(1)[:,None] # transition probability matrix, 
                                    # row sum normalized to 1.0

state_idx = range(n_states) # states is a list of integers 0, 1, 2...
current_state = np.random.choice(state_idx)

trace = []      
sigma = 0.1     
for _ in range(n_frames):
    trace.append(np.random.normal(loc=state_val[current_state], scale=sigma))
    current_state = np.random.choice(state_idx, p=prob_nor[current_state, :])

上面代码中的循环使它运行得很慢，特别是当我必须对数百万个数据点进行建模时。有没有办法矢量化/加速它？

标签： pythonnumpyvectorization

解决方案

尽快卸载概率计算：

possible_paths = np.vstack(
    np.random.choice(state_idx, p=prob_nor[curr_state, :], size=n_frames)
    for curr_state in range(n_states)
)

然后，您可以简单地进行查找以遵循您的路径：

path_trace = [None]*n_frames
for step in range(n_frames):
    path_trace[step] = possible_paths[current_state, step]
    current_state = possible_paths[current_state, step]

一旦你有了你的路径，你就可以计算你的踪迹：

sigma = 0.1
trace = np.random.normal(loc=state_val[path_trace], scale=sigma, size=n_frames)

比较时间：

纯pythonfor循环

%%timeit
trace_list = []
current_state = np.random.choice(state_idx)
for _ in range(n_frames):
    trace_list.append(np.random.normal(loc=state_val[current_state], scale=sigma))
    current_state = np.random.choice(state_idx, p=prob_nor[current_state, :])

结果：

30.1 ms ± 436 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)

矢量化查找：

%%timeit
current_state = np.random.choice(state_idx)
path_trace = [None]*n_frames
possible_paths = np.vstack(
    np.random.choice(state_idx, p=prob_nor[curr_state, :], size=n_frames)
    for curr_state in range(n_states)
)
for step in range(n_frames):
    path_trace[step] = possible_paths[current_state, step]
    current_state = possible_paths[current_state, step]
trace = np.random.normal(loc=state_val[path_trace], scale=sigma, size=n_frames)

结果：

641 µs ± 6.03 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)

加速约 50 倍。

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