Generate each column of the numpy array with random number from different range

What you can do is produce all random numbers in the interval [0, 1) first and then scale and shift them accordingly:

import numpy as np
num = 5
ranges = np.asarray([[0,1],[4,5]])
starts = ranges[:, 0]
widths = ranges[:, 1]-ranges[:, 0]
a = starts + widths*np.random.random(size=(num, widths.shape[0]))

So basically, you create an array of the right size via np.random.random(size=(num, widths.shape[0])) with random number between 0 and 1. Then you scale each value by a factor corresponding to the width of the interval that you actually want to sample. Finally, you shift them by starts to account for the different starting values of the intervals.

numpy.random.uniform will broadcast its arguments, it can generate the desired samples by passing the following arguments:

• low: the sequence of low values.
• high: the sequence of high values.
• size: a tuple like (num, m), where m is the number of ranges and num the number of groups of m samples to generate.

For example:

In [23]: num = 5

In [24]: ranges = np.array([[0, 1], [4, 5], [10, 15]])

In [25]: np.random.uniform(low=ranges[:, 0], high=ranges[:, 1], size=(num, ranges.shape[0]))
Out[25]: 
array([[  0.98752526,   4.70946614,  10.35525699],
       [  0.86137374,   4.22046152,  12.28458447],
       [  0.92446543,   4.52859103,  11.30326391],
       [  0.0535877 ,   4.8597036 ,  14.50266784],
       [  0.55854656,   4.86820001,  14.84934564]])