# Determinant of CUDA matrix?
**URL:** https://discourse.julialang.org/t/determinant-of-cuda-matrix/77245
**Category:** GPU
**Tags:** cuda, linearalgebra
**Created:** [March 1, 2022, 2:54pm UTC](https://discourse.julialang.org/t/determinant-of-cuda-matrix/77245 "2022-03-01T14:54:03Z")
**Posts on this page:** 9
**Page:** 1
### Author:  [@HenriDeh](https://discourse.julialang.org/u/HenriDeh)
#### Post date: [March 1, 2022, 2:54pm UTC](https://discourse.julialang.org/t/determinant-of-cuda-matrix/77245/1 "2022-03-01T14:54:03Z")
Hello,
I have so far been able to use CUDA without having to dig into the actual package api (besides `cu(m)`) just thanks to multiple dispatch. Today I need to compute the determinant of a matrix and I would like my code to work both on the GPU and the CPU. However, the `det` function from LinearAlgebra is not specialized for `CuArray` and throws a CPU address error. I guess this is because `det` calls a function from a `C` library (BLAS ?).
I have been searching for a bit now and I just can’t find a CUDA implementation of det. So, I’d like to know if there exists a linear algebra package for CUDA that I don’t know of, or if I’ll have to learn how to efficiently compute a determinant to implement it myself and learn the internals of CUDA.jl.
I’m not sure I have the skills to do that.
MWE:
```julia
using CUDA
m = rand(10,10) |> cu
det(m)
```
---
### Author:  [@carstenbauer](https://discourse.julialang.org/u/carstenbauer)
#### Post date: [March 1, 2022, 3:27pm UTC](https://discourse.julialang.org/t/determinant-of-cuda-matrix/77245/2 "2022-03-01T15:27:25Z")
You can try computing the LU factorization and then taking the product of the diagonal elements:
```julia
julia> M = rand(10,10);
julia> Mgpu = cu(M);
julia> det(M) # cpu
-0.10243723110926993
julia> prod(diag(LinearAlgebra.LAPACK.getrf!(M)[1])) # cpu
-0.10243723110926993
julia> prod(diag(CUSOLVER.getrf!(Mgpu)[1])) # gpu
-0.10243723f0
```
(Might be necessary to think more carefully about the sign though!)
---
### Author:  [@carstenbauer](https://discourse.julialang.org/u/carstenbauer)
#### Post date: [March 1, 2022, 3:32pm UTC](https://discourse.julialang.org/t/determinant-of-cuda-matrix/77245/3 "2022-03-01T15:32:25Z")
Also, there is an open issue about determinant calculation on GPU here: [https://github.com/JuliaGPU/CUDA.jl/issues/110](https://github.com/JuliaGPU/CUDA.jl/issues/110)
Perhaps worth figuring out the details and making a PR.
---
### Author:  [@HenriDeh](https://discourse.julialang.org/u/HenriDeh)
#### Post date: [March 1, 2022, 4:34pm UTC](https://discourse.julialang.org/t/determinant-of-cuda-matrix/77245/4 "2022-03-01T16:34:42Z")
> [@carstenbauer](#):
>
> `prod(diag(CUSOLVER.getrf!(Mgpu)[1]))`
> (Might be necessary to think more carefully about the sign though!)
Thanks, that’s what I was hoping for!
Seems to work as far as I can tell. What sign issue are you referring to?
I could open a PR in CUDA.jl, if this implementation suffice, so I won’t have to commit type piracy 😬
---
### Author:  [@stevengj](https://discourse.julialang.org/u/stevengj)
#### Post date: [March 1, 2022, 5:50pm UTC](https://discourse.julialang.org/t/determinant-of-cuda-matrix/77245/5 "2022-03-01T17:50:03Z")
> [@HenriDeh](#):
>
> Today I need to compute the determinant of a matrix
Out of curiosity, for what application do you need the determinant?
(Note, by the way, that for a large matrix the determinant can easily overflow the maximum floating-point value; you might consider using `logdet` instead.)
---
### Author:  [@HenriDeh](https://discourse.julialang.org/u/HenriDeh)
#### Post date: [March 1, 2022, 6:36pm UTC](https://discourse.julialang.org/t/determinant-of-cuda-matrix/77245/6 "2022-03-01T18:36:19Z")
I’m trying to implement a multivariate gaussian neural network for a deep reinforcement learning algorithm. It will output a mean vector and a vector containing the elements of a lower triangular Cholesky decomposition. I then reconstruct the covariance matrix from the latter vector.
During training I need to take the gradient of the `logpdf` of the approximated MvNormal, which requires the `logdet` indeed. The sign issue is not a problem for me since the covariance matrix is PSD so I can simply take the `abs` of the implementation proposed by @carstenbauer.
Since it’s for a deep learning application, I need the `logpdf` function to be differentiable and preferably gpu compatible. It’s unfortunately not the case with `Distributions.jl` so I have to implement it from scratch. I’m making progress but now my next issue is that `CUSOLVER.getrf!` has no adjoint for Zygote to differentiate - that’s a problem for another post.
---
### Author:  [@stevengj](https://discourse.julialang.org/u/stevengj)
#### Post date: [March 1, 2022, 7:34pm UTC](https://discourse.julialang.org/t/determinant-of-cuda-matrix/77245/7 "2022-03-01T19:34:08Z")
> [@HenriDeh](#):
>
> I’m making progress but now my next issue is that `CUSOLVER.getrf!` has no adjoint for Zygote to differentiate - that’s a problem for another post.
You can easily differentiate the determinant (or log determinant) directly. See [these slides](https://rawcdn.githack.com/mitmath/matrixcalc/c97512521a9ff63802454ee258f1759c45f7d8b6/determinant_and_inverse.html) from our [matrix calculus course](https://github.com/mitmath/matrixcalc).
---
### Author:  [@rejuvyesh](https://discourse.julialang.org/u/rejuvyesh)
#### Post date: [March 1, 2022, 7:42pm UTC](https://discourse.julialang.org/t/determinant-of-cuda-matrix/77245/8 "2022-03-01T19:42:57Z")
Should probably also checkout [TuringLang/DistributionsAD.jl: Automatic differentiation of Distributions using Tracker, Zygote, ForwardDiff and ReverseDiff (github.com)](https://github.com/TuringLang/DistributionsAD.jl)
---
### Author:  [@HenriDeh](https://discourse.julialang.org/u/HenriDeh)
#### Post date: [March 1, 2022, 8:38pm UTC](https://discourse.julialang.org/t/determinant-of-cuda-matrix/77245/9 "2022-03-01T20:38:36Z")
Oh, glad I didn’t go all the way through the trouble before knowing about this, thanks!
@stevengj Thank you for the resources, I sure could use a more advanced Linear Algebra / Matrix Calculus course some time soon.