Hi. I’ve been trying out LinearSolve.jl for a bit, and I happened to notice that this package is generally for
\min \| \mathbf{Ax} - \mathbf{b} \|_2^2
where \mathbf{b},\mathbf{x} are vectors. My problem, on the other hand, is a matrix least-squares
\min \| \mathbf{AX} - \mathbf{B} \|_F^2
which can be solved using \. I also know I can simply solve the least-squares for each columns of \mathbf{X}. But I’m curious to know if there’s a nice memory and time efficient way to solve the matrix least-squares using LinearSolve.jl.
A simple example:
# Backslash
using LinearAlgebra
A = rand(10,5)
B = rand(10,3)
sol1 = A \ B
# LinearSolve.jl (does not work)
using LinearSolve
prob = LinearSolve.LinearProblem(A, B)
sol2 = LinearSolve.solve(prob)
where I’m met with the error message
ERROR: MethodError: no method matching ldiv!(::Vector{Float64}, ::LinearAlgebra.QRCompactWY{Float64, Matrix{Float64}, Matrix{Float64}}, ::Matrix{Float64})
The function `ldiv!` exists, but no method is defined for this combination of argument types.
Closest candidates are:
ldiv!(::AbstractVecOrMat, ::IdentityOperator, ::AbstractVecOrMat)
@ SciMLOperators C:\Users\anon\.julia\packages\SciMLOperators\KVzmP\src\basic.jl:62
ldiv!(::AbstractVecOrMat, ::Bidiagonal, ::AbstractVecOrMat)
@ LinearAlgebra C:\Users\anon\.julia\juliaup\julia-1.11.3+0.x64.w64.mingw32\share\julia\stdlib\v1.11\LinearAlgebra\src\bidiag.jl:834
ldiv!(::AbstractVecOrMat, ::InvertibleOperator, ::AbstractVecOrMat)
@ SciMLOperators C:\Users\anon\.julia\packages\SciMLOperators\KVzmP\src\matrix.jl:384
Any advice would be great. Thanks!