如何在 Python 中创建一个二维数组，其中每列都有不同的随机元素数

Question

I'm writing a Monte Carlo simulation of photons arriving at a detector. The total number of detected photons N_detected follows a Poisson distribution (which I'm generating using scipy.stats.poisson ) and the time of detection of every single photon follows a given probability distribution function (PDF). In order to generate the time of detection of the N_detected photons I generate N_detected random numbers between 0 and 1 with the numpy.random.random() function and use the Inverse Transform Method .

I have to run the simulation several times. So, in order to avoid iterating a lot of times, I'd like to do every simulation at once using numpy arrays. As a final result, I'd like to obtain a 2D array of N_sim columns where every column corresponds to a different simulation and contains the generated times of detection. The problem is that each simulation produces a different number of photons (since it's random) and I don't find the way to create the 2D arrray with columns of different lengths.

One idea I had is creating all the columns with the same length (the largest N_deteceted ) and fill the not needed elements with NaN and the rest with the random numbers I need, but I don't know I could do that.

This is the best I've been able to do so far:

import numpy as np
import numpy.ma as ma
from scipy.stats import poisson

beta = 0.0048    # Parameter of the PDF

""" Inverse of the time CDF (needed for the Inverse transform method) """

def inverse_time_cdf(x):
    return -np.log( (np.exp(-1000*beta)-1)*x + 1 )/beta


""" Simulation of N_sim experiments through the inverse transfrom method """

T = 1000    # Duration of the experiment [s]
rate = 3.945    # [events/s]
lam = rate*T    # Poisson distribution parameter

def photon_arrival_simulation(N_sim):
    N_detection = poisson.rvs(lam, size = N_sim)    # Number of detections in each experiment
    t = np.array([inverse_time_cdf(np.random.random(N)) for N in N_detection])

    return N_detection, t

If possible, I wanted to avoid the loop used in the list comprehension of the photon_arrival_simulation() function and also obtain a 2D array instead of an array of arrays (since I can't do array operation such as taking a log on an array of arrays).

I don't know if I should be posting this question here or in Physics Stack Exchange , but thanks in advance to anyone.

Answer 1

I don't think it is possible to make a random array with variable lengths along the rows to fill with NaN values without looping somewhere. But here is how you can resolve the 2d array issue you had, you had the right idea to use NaN. I would definitely use NaN over masked arrays since masked arrays are more for convenience than for performance. Also you should place the docstrings in their appropriate place beneath the function declarations.

def photon_arrival_simulation(N_sim):
    """Simulation of N_sim experiments through the inverse transform method"""

    N_detection = poisson.rvs(lam, size=N_sim)

    rand = np.random.random((len(N_detection), N_detection.max()))

    for i, N in enumerate(N_detection):
        rand[i, N:] = np.nan

    t = inverse_time_cdf(rand)

    return N_detection, t