A question about broadcasting a general expression graph. The specific use
is in the gradient of the distance to a sphere:
c = T.vector('c') # center
r2 = T.scalar(); # radius
p = T.matrix('g') # points N x 3
e = (r2-(c-p).norm(2,axis=1)) # distances N
G1 = T.grad(e,p) # error - because e is vectorial
GJ = T.jacobian(e,p) # generates a N x N x 3 jacobian,and I don't want the
intermediates
The workaround for the above is to express the equation over a vector:
pv = T.vector('g') # single point
ev = (r2-(c-pv).norm(2)) # 1
Gv = T.grad(ev,pv) # 1 x 3
But then if I want to evaluate a function obtained from Gv over a matrix of
points x sized N x 3 I need to iterate, and that's inefficient:
f = function([r2,c,pv],Gv)
for i in range(0,x.shape[0]):
rg[i,:] = f(3.0,...,x[i,:])
Instead of this loop I would like to create a single symbolic expression
that takes N point and produces all the gradients giving as output N x 3.
Is there anyway to perform this operation? It seems like a broadcasting
operation of a subexpression (ev) by replacing one of the terms (pv) with a
row from the input (x). The replace method of the expression graph does not
work because it is not possible to transform a vector term to a matrix term.
Any suggestion will be appreciated
Best Regards,
Emanuele
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