I'm doing some coordinate transformation stuff that requires the solution of a 2 by 3 system. Right now, all rectangular SMatrix systems are done by LinearAlgebra and the allocations mean I can't run this on the GPU. I coded this version which seems to be working and non-allocating.
@inline function (\)(a::SMatrix{2,3}, b::SVector{2})
# columns of a'
a1,a2 = a[1,:],a[2,:]
# Q,R decomposition
r11 = norm(a1)
q1 = a1/r11
r12 = q1'*a2
p = a2-r12*q1
r22 = norm(p) < eps(r11) ? one(r11) : norm(p)
q2 = p/r22
# forward substitution to solve R'v = b
v1 = b[1]/r11
v2 = (b[2]-r12*v1)/r22
# return solution x = Qv
return q1*v1+q2*v2
endI'm happy to add this to solve.jl and do a PR if it would be helpful.
I'm doing some coordinate transformation stuff that requires the solution of a 2 by 3 system. Right now, all rectangular
SMatrixsystems are done byLinearAlgebraand the allocations mean I can't run this on the GPU. I coded this version which seems to be working and non-allocating.I'm happy to add this to
solve.jland do a PR if it would be helpful.