Computing Inverse of a stack of matrices

General Usage
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13

Thanks for posting this. Coincidentally, I was trying to compare the previous versions with a numba-accelerated python version (just to see if LLVM made any difference) but now with this, Julia is about 6x faster :slight_smile:

from numpy.linalg import inv as npinv
from numpy import zeros_like, einsum, random
from timeit import timeit
from numba import jit, prange

@jit(nopython=True, cache=True, nogil=True)
def vdet(F):
    J = zeros_like(F[0,0])
    for a in range(J.shape[0]):
        for b in range(J.shape[1]):
            J[a,b] += F[0, 0, a, b] * (F[1, 1, a, b] * F[2, 2, a, b] -
                                        F[1, 2, a, b] * F[2, 1, a, b]) -\
                    F[0, 1, a, b] * (F[1, 0, a, b] * F[2, 2, a, b] -
                                        F[1, 2, a, b] * F[2, 0, a, b]) +\
                    F[0, 2, a, b] * (F[1, 0,a ,b] * F[2, 1, a, b] -
                                        F[1, 1, a, b] * F[2, 0, a, b])
    return J


@jit(nopython=True, cache=True, nogil=True)
def vinv(F):
    J = vdet(F)
    Finv = zeros_like(F)
    for a in range(J.shape[0]):
        for b in range(J.shape[1]):
            Finv[0, 0, a, b] += (-F[1, 2, a, b] * F[2, 1, a, b] +
                                F[1, 1, a, b] * F[2, 2, a, b]) / J[a, b]
            Finv[1, 0, a, b] += (F[1, 2, a, b] * F[2, 0, a, b] -
                                F[1, 0, a, b] * F[2, 2, a, b]) / J[a, b]
            Finv[2, 0, a, b] += (-F[1, 1, a, b] * F[2, 0, a, b] +
                                F[1, 0, a, b] * F[2, 1, a, b]) / J[a, b]
            Finv[0, 1, a, b] += (F[0, 2, a, b] * F[2, 1, a, b] -
                                F[0, 1, a, b] * F[2, 2, a, b]) / J[a, b]
            Finv[1, 1, a, b] += (-F[0, 2, a, b] * F[2, 0, a, b] +
                                F[0, 0, a, b] * F[2, 2, a, b]) / J[a, b]
            Finv[2, 1, a, b] += (F[0, 1, a, b] * F[2, 0, a, b] -
                                F[0, 0, a, b] * F[2, 1, a, b]) / J[a, b]
            Finv[0, 2, a, b] += (-F[0, 2, a, b] * F[1, 1, a, b] +
                                F[0, 1, a, b] * F[1, 2, a, b]) / J[a, b]
            Finv[1, 2, a, b] += (F[0, 2, a, b] * F[1, 0, a, b] -
                                F[0, 0, a, b] * F[1, 2, a, b]) / J[a, b]
            Finv[2, 2, a, b] += (-F[0, 1, a, b] * F[1, 0, a, b] +
                                F[0, 0, a, b] * F[1, 1, a, b]) / J[a, b]
    return Finv

%timeit vinv(F)
  69.3 µs ± 1.56 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)

vs your code

julia> @btime many3x3inverts!($Barray, $Aarray)
  10.399 μs (0 allocations: 0 bytes)

It’s notoriously fast. Thanks for such an enlightening discussion.

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