[Numpy-discussion] Trick for fast
Sebastian Berg
sebastian@sipsolutions....
Fri Feb 3 09:14:04 CST 2012
I guess Einsum is much cleaner, but I already had started with this and
maybe someone likes it, this is fully vectorized and uses a bit of funny
stuff too:
# The dot product(s), written using broadcasting rules:
a = -(x.reshape(-1,1,3) * x[...,None])
# Magic, to avoid the eye thing, takes all diagonal elements as view,
maybe there is a cooler way for it:
diagonals = np.lib.stride_tricks.as_strided(a, (a.shape[0], 3), (a.dtype.itemsize*9, a.dtype.itemsize*4))
# Add the x**2 (s is a view on the diagonals), the sum is broadcasted.
diagonals += (sum(x**2, 1))[:,None]
# And multiply by mass using broadcasting:
a *= mass[...,None]
# And sum up all the intermediat results:
inert = a.sum(0)
print inert
Regards,
Sebastian
On Fri, 2012-02-03 at 15:43 +0100, Søren Gammelmark wrote:
> What about this?
>
>
> A = einsum("i,ij->", mass, x ** 2)
> B = einsum("i,ij,ik->jk", mass, x, x)
> I = A * eye(3) - B
>
>
> /Søren
>
> On 3 February 2012 15:10, <josef.pktd@gmail.com> wrote:
> On Fri, Feb 3, 2012 at 8:44 AM, Alan G Isaac
> <alan.isaac@gmail.com> wrote:
> > On 2/3/2012 5:16 AM, santhu kumar wrote:
> >> x = nX3 vector.
> >> mass = nX1 vector
> >> inert = zeros((3,3))
> >> for i in range(n):
> >> ri = x[i,:].reshape(1,3)
> >> inert = inert + mass[i,]*(sum(ri*ri)*eye(3) -
> dot(ri.T,ri))
> >>
> >
> >
> > This should buy you a bit.
> >
> > xdot = (x*x).sum(axis=1)
> > for (massi,xi,xdoti) in zip(mass.flat,x,xdot):
> > temp = -np.outer(xi,xi)
> > temp.flat[slice(0,None,4)] += xdoti
> > inert += massi*temp
> >
> > Alan Isaac
>
>
> maybe something like this, (self contained example and name
> spaces to
> make running it easier)
>
> import numpy as np
> n = 15
> x = np.arange(n*3.).reshape(-1,3) #nX3 vector.
> mass = np.linspace(1,2,n)[:,None] #nX1 vector
> inert = np.zeros((3,3))
> for i in range(n):
> ri = x[i,:].reshape(1,3)
>
> inert = inert + mass[i,]*(sum(ri*ri)*np.eye(3) -
> np.dot(ri.T,ri))
> print inert
>
> print np.diag((mass * x**2).sum(0)) - np.dot(x.T, mass*x)
>
> [[ 0. -16755. -17287.5]
> [-16755. 0. -17865. ]
> [-17287.5 -17865. 0. ]]
> [[ 0. -16755. -17287.5]
> [-16755. 0. -17865. ]
> [-17287.5 -17865. 0. ]]
>
> Josef
>
>
> >
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