Draw multiple samples using numpy.random.multivariate_normal(mean, cov[, size])

Question

Using the numpy function numpy.random.multivariate_normal(), if I give the mean and covariance, I am able to draw random samples from a multivariate Gaussian.

As an example,

import numpy as np
mean = np.zeros(1000)  # a zero array shaped (1000,)
covariance = np.random.rand(1000, 1000) 
# a matrix of random values shaped (1000,1000)
draw = np.random.multivariate_normal(mean, covariance)
# this outputs one "draw" of a multivariate norm, shaped (1000,)

The above function outputs one "draw" from a multivariate Gaussian, shaped (1000,) (as the covariance matrix is shaped 1000,1000)).

I would like 200 draws. How does one do this? I would create a list comprehension, but I don't see how to create the iteration.

EDIT: Is there a difference between

draw_A = np.random.rand(1000, 1000, 200)

and

draw_B = [np.random.multivariate_normal(mean, covariance) for i in range(200)]

?

Yes, draw_B is a list, but are they both 200 independent draws shaped 1000,1000)?

Solution

Did you notice the size argument in the docstring?

For example, this call generates 5 samples from a 3-d distribution:

In [22]: np.random.multivariate_normal(np.zeros(3), np.eye(3), size=5)
Out[22]: 
array([[ 1.08534253,  0.70492174, -0.8625333 ],
       [ 0.16955737, -0.89453284,  0.8347796 ],
       [ 0.49506717, -1.18087912, -0.89118919],
       [-0.97837406, -0.42304268,  0.4326744 ],
       [-1.18836816,  1.33389231,  0.23616035]])

---

Response to edited question:

• np.random.rand(d0, d1, d2) makes d0*d1*d2 random draws from the univariate uniform distribution on [0, 1), and returns them in an array with shape (d0, d1, d2).
• np.random.multivariate_normal(mean, cov, size=n), where mean is an array with shape (m,) and cov is an array with shape (m, m), makes n draws from a multivariate normal distribution, and returns them as the rows of an array with shape (n, m). Your list comprehension draw_B also draws samples from a multivariate normal distribution, with one sample per function call, and it puts the samples into a list instead of an array.