Need help vectorizing code

[Kevin K]

I have some code that I need help vectorizing.
I want to convert the following to vector form, how can I? I want to get rid of the inner loop - apparently, it's possible to do so.
X is an NxD matrix. y is a 1xD vector.

def foo(X, y, mylambda, N, D, epsilon):
...
for j in xrange(D):
aj = 0
cj = 0
for i in xrange(N):
aj += 2 * (X[i,j] ** 2)
cj += 2 * (X[i,j] * (y[i] - w.transpose()*X[i].transpose() + w[j]*X[i,j]))

...

If I call numpy.vectorize() on the function, it throws an error at runtime.

Thanks

[Joshua Landau]

On 18 January 2014 20:51, Kevin K <richy...@gmail.com> wrote:
> def foo(X, y, mylambda, N, D, epsilon):
> ...
> for j in xrange(D):
> aj = 0
> cj = 0
> for i in xrange(N):
> aj += 2 * (X[i,j] ** 2)
> cj += 2 * (X[i,j] * (y[i] - w.transpose()*X[i].transpose() + w[j]*X[i,j]))

Currently this just computes and throws away values...

[Kevin K]

I didn't paste the whole function, note the ... before and after. I do use the values.

I want to get rid of one of the loops so that the computation becomes O(D). Assume vectors a and c should get populated during the compute, each being 1xD.

Thanks

[Peter Otten]

Maybe

a = (2*X**2).sum(axis=0)
c = no idea.

Judging from the code y should be 1xN rather than 1xD. Also, should

w.transpose()*X[i].transpose()

be a vector or a scalar? If the latter, did you mean

numpy.dot(w, X[i])

?

[Oscar Benjamin]

On 18 January 2014 20:51, Kevin K <richy...@gmail.com> wrote:

> I have some code that I need help vectorizing.
> I want to convert the following to vector form, how can I? I want to get rid of the inner loop - apparently, it's possible to do so.
> X is an NxD matrix. y is a 1xD vector.
>
> def foo(X, y, mylambda, N, D, epsilon):
> ...
> for j in xrange(D):
> aj = 0
> cj = 0
> for i in xrange(N):
> aj += 2 * (X[i,j] ** 2)
> cj += 2 * (X[i,j] * (y[i] - w.transpose()*X[i].transpose() + w[j]*X[i,j]))

As Peter said the y[i] above suggests that y has the shape (1, N) or
(N, 1) or (N,) but not (1, D). Is that an error? Should it actually be
y[j]?

You don't give the shape of w but I guess that it is (1, D) since you
index it with j. That means that w.transpose() is (D, 1). But then
X[i] has the shape (D,). Broadcasting those two shapes gives a shape
of (D, D) for cj. OTOH if w has the shape (D, 1) then cj has the shape
(1, D).

Basically your description is insufficient for me to know what your
code is doing in terms of all the array shapes. So I can't really
offer a vectorisation of it.

>
> ...
>
> If I call numpy.vectorize() on the function, it throws an error at runtime.

You've misunderstood what the numpy.vectorize function is for. The
vectorize function is a convenient way of generating a function that
can operate on arrays of arbitrary shape out of a function that
operates only on scalar values.


Oscar