# Choleski Factorization transpose

I have a Matlab code like this:

``````

T = 0.5;
NbPas=100;
DeltaT=T/NbPas;
rho=-0.2;

L = chol([DeltaT,rho*DeltaT;rho*DeltaT,DeltaT])’;
``````

I tried to translate it into Julia code:

``````
T = 0.5
NbPas=100
DeltaT=T/NbPas
rho=-0.2

L = cholfact([DeltaT rho*DeltaT;rho*DeltaT DeltaT])’
``````

but got an error message

``````
ctranspose not implemented for Base.LinAlg.Cholesky{Float64,Array{Float64,2}}
``````

Either:

``````L = chol([DeltaT rho*DeltaT;rho*DeltaT DeltaT])’
L = cholfact([DeltaT rho*DeltaT;rho*DeltaT DeltaT], :L)
``````
2 Likes

Thanks so much!

The latter returns a cholesky factor object (which is not a subtype of abstract array), instead of a lower triangular matrix. You can extract it with

``````L = cholfact([DeltaT rho*DeltaT;rho*DeltaT DeltaT], :L)
Lmatrix = L[:L]
``````

Alternatively, these work:

``````L = cholfact([DeltaT rho*DeltaT;rho*DeltaT DeltaT])[:L]
L = cholfact([DeltaT rho*DeltaT;rho*DeltaT DeltaT], :L)[:L]
``````

If performance matters, go with the latter of these two. The former computes the upper triangular, and then transposes it while the latter gets the lower triangular directly.

For a 4000x4000 matrix, this makes the difference between 262/315 and 185/187 ms minimum/median on my computer.
Extra allocations of non-lazy tranpose on 0.6.2 is why the minimum/median gap is so big for calculating the upper triangle and transposing.

On 0.7 it was 270/271 and 203/204, respectively.
Syntax was updated to `cholfact(Hermitian(X, :L)).L`.
Memory requirements did not go down because `.L` still transposed the data when using `cholfact(Hermitian(X)).L`.

3 Likes

Hi Maybe cholfact has been deprecated, but I keep getting cholfact not found. What package is it in? Has it been subsumed into cholesky()? If not, what are the differences?

You can search through History.md to find these sorts of deprecations. Looks like it was a .7 / 1.0 breaking change here.

2 Likes

Thanks! Exactly what I needed