Can I Create A Multivariate_normal Matrix Using Dask?

Somewhat related to this post, I am trying to replicate multivariate_normal in dask: Using numpy I can create a multivariate normal matrix with a specified covariance using: import

Solution 1:

An work arround for now, is to use a cholesky decomposition. Note that any covariance matrix C can be expressed as C=G*G'. It then follows that x = G'*y is correlated as specified in C if y is standard normal (see this excellent post on StackExchange Mathematic). In code:

Numpy

n_dim =4
size = 100000
A = np.random.randn(n_dim, n_dim)
covm = A.dot(A.T)

x=  np.random.multivariate_normal(size=size, mean=np.zeros(len(covm)),cov=covm)
## verify numpys covariance is correct
np.cov(x, rowvar=False)
covm

Dask

## create covariance matrix
A = da.random.standard_normal(size=(n_dim, n_dim),chunks=(2,2))
covm = A.dot(A.T)

## get cholesky decomp
L = da.linalg.cholesky(covm, lower=True)

## drawn standard normal 
sn= da.random.standard_normal(size=(size, n_dim),chunks=(100,100))

## correct for correlation
x =L.dot(sn.T)
x.shape

## verify
covm.compute()
da.cov(x, rowvar=True).compute()