user2687863 - 3 months ago 35

Python Question

I'm having some trouble defining a multivariate gaussian pdf for quadrature using scipy. I write a function that takes a mean vector and covariance matrix as input and returns a gaussian function.

`def make_mvn_pdf(mu, sigma):`

def f(x):

return sp.stats.multivariate_normal.pdf(x, mu, sigma)

return f

When I use make_mvn_pdf to define a Gaussian and try to index into the Gaussian I get an error that does not make sense. I begin by defining a mean vector and covariance matrix and passing them into make_mvn_pdf:

`# define covariance matrix`

Sigma = np.asarray([[1, .15], [.15, 1]])

# define propagator

B = np.diag([2, 2])

# define data

Obs = np.array([[-0.06895746],[ 0.18778 ]])

# define a Gaussian PDF:

g_int_func = make_mvn_pdf(mean = np.dot(B,Obs[t,:]), cov = Sigma)

I try to pass in observations to the density in order to get back probabilities:

`testarray=np.random.random((2,2))`

g_int_func(testarray)

This returns the following error which I do not understand.

`---------------------------------------------------------------------------`

ValueError Traceback (most recent call last)

<ipython-input-50-083a1915f674> in <module>()

1 g_int_func = make_mvn_pdf(np.dot(B,Obs[t,:]),Gamma)

----> 2 g_int_func(testarray)

/Users/...in f(x)

17 def make_mvn_pdf(mu, sigma):

18 def f(x):

---> 19 return sp.stats.multivariate_normal.pdf(x, mu, sigma)

20 return f

21

/Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/site-packages/scipy/stats/_multivariate.pyc in pdf(self, x, mean, cov, allow_singular)

427

428 """

--> 429 dim, mean, cov = _process_parameters(None, mean, cov)

430 x = _process_quantiles(x, dim)

431 psd = _PSD(cov, allow_singular=allow_singular)

/Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/site-packages/scipy/stats/_multivariate.pyc in _process_parameters(dim, mean, cov)

54

55 if mean.ndim != 1 or mean.shape[0] != dim:

---> 56 raise ValueError("Array 'mean' must be a vector of length %d." % dim)

57 if cov.ndim == 0:

58 cov = cov * np.eye(dim)

ValueError: Array 'mean' must be a vector of length 2.

The ValueError states that the array 'mean' must be a vector of length 2 but this is the case. In fact, the dimension of the mean and covariance matrix and data passed in are all of length 2.

Answer

The value that you give as the mean is `np.dot(B, Obs)`

(taking into account the change you suggested in a comment), where `B`

has shape (2, 2) and `Obs`

has shape (2, 1). The result of that `dot`

call has shape (2, 1). The problem is that is a *two*-dimensional array, and `multivariate_normal.pdf`

expects `mu`

to be a *one*-dimensional array, i.e. an array with shape (2,). (The error message uses the word "vector", which is a poor choice, because for many people, an array with shape (n, 1) *is* a (column) vector. It would be less ambiguous if the error message said "Array 'mean' must be a one-dimensional array of length 2.")

There are at least two easy ways to fix the problem:

- You could ensure that
`Obs`

has shape (2,) instead of (2, 1), e.g.`Obs = np.array([-0.06895746, 0.18778])`

. The`np.dot(B, Obs)`

has shape (2,). - "Flatten" the
`mean`

argument by using the`ravel`

method:`mean=np.dot(B,Obs).ravel()`

.