Cannot enforce zero correlation in samples

Reproducing code example:

import numpy as np
np.random.seed(11)
n=100
mean = [0, 0]
cov = [[1, 0], [0, 1]]      # Should have zero covariance

x, y = np.random.multivariate_normal(mean=mean, cov=cov, size=n).T

np.corrcoef(x,y)

yields:

array([[ 1., -0.02736689],
       [-0.02736689,  1.]])  

While I’d expect to see :

array([[ 1., 0],
       [0,  1.]])  

or some irrelevant numbers like 1e-16. This can be reproduced for any seed.

This doesn’t cause any problem in R for example :

library(MASS)
library(purrr)

# Means
m1 <- 5
m2 <- 10
# variances
s1 <- 5
s2 <- 1
# Correlations
cov <- 0

set.seed(11)

dat <- mvrnorm(20, mu = c(m1, m2),
                     Sigma = matrix(c(s1,cov,
                                      cov, s2),
                                    ncol = 2, byrow = TRUE),
                     empirical = TRUE)

dat %>% cor()

Where the correlation matrix behaves as I’d expect.

Numpy/Python version information:

1.18.3 3.8.2 | packaged by conda-forge | (default, Apr 24 2020, 08:20:52) [GCC 7.3.0]

[rkern]

You want vh.T. Our svd() routine follows the convention where the Hermitian of the V matrix gets returned (which is why we name it vh in the docstring), whereas your R code is using the straight V matrix.

[eric-wieser]

I’d ask it again, and link to this issue.

I recommend you phrase it in terms of transforming the samples to have exactly the requested statistics, and adding an empirical argument to match R.

It seems like this would be a reasonable request for many distributions, not just mvr. Even a standard normal could have this behavior.