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Given a covariance matrix, how can I construct a vector of expressions of randomly distributed variables whose covariance matrix is equal to the given one?

EDIT: All variables are normally distributed.

I have an algorithm that gets the covariances correct, but not the variances on the diagonal:

a = [0]*len(r)
for x, row in enumerate(cov_matrix(r)):
for y, item in enumerate(row):
if x > y: continue
v = noise(math.sqrt(abs(item)))
a[x] += v
if item > 0:
a[y] += v
else:
a[y] -= v


I feel like this should be simple ...

1

# Computing equivalent vector of random variables from covarience matrix

Given a covariance matrix, how can I construct a vector of expressions of randomly distributed variables whose covariance matrix is equal to the given one?

I have an algorithm that gets the covariances correct, but not the variances on the diagonal:

a = [0]*len(r)
for x, row in enumerate(cov_matrix(r)):
for y, item in enumerate(row):
if x > y: continue
v = noise(math.sqrt(abs(item)))
a[x] += v
if item > 0:
a[y] += v
else:
a[y] -= v


I feel like this should be simple ...