add exercise05 with julia without for/if

[Shunsuke-Hori]

It is not exactly what is asked for because I don't use for/if

[vikjam]

Hi @Shunsuke-Hori, I added the loops as the exercise mentions. Do you have any thoughts on the differences in computing time?

[Shunsuke-Hori]

@vikjam Now, loop version is using dense matrix while vectorized one is using sparse matrix. Let's use the same one and compare them again.

Also, we should try with huge data as well.

(Having said that, I am not sure if the performance is a serious concern for HP filter because we don't iterate filtering. Typically, we use it just once, right?)

[Shunsuke-Hori]

@vikjam OK, I figured out. My code with sparse matrix is performing very poorly now because it is type unstable.

H = zeros(N, N) in your code implicitly assumes that every computation is operated with Float64, which is almost surely appropriate for HP filter.

H in my code can have either Int or Float depending on the input λ. If I pass 1600. instead of 1600, my code with vectorized sparse matrix is by far the fastest no matter how large the sample size is.

I'll fix it and push.

[Shunsuke-Hori]

Fixed. Now, even with 1600 as input, sparse matrix without loop is the best

[Shunsuke-Hori]

One more note: the vectorized dense matrix code is not so efficient. I am creating a bunch of garbage by diagm. If we really want to use dense matrix, loop would be better.

[vikjam]

Hi @Shunsuke-Hori, could you explain this cell? I wanted to add a bit more explanation to the notebook:

abstract type MatrixType end
struct Dense <: MatrixType end
struct Sparse <: MatrixType end
abstract type AssignMethod end
struct Loop <: AssignMethod end
struct Vectorized <: AssignMethod end

[Shunsuke-Hori]

@vikjam I am making use of multiple dispatch. I wanted to avoid repeating the same code for loop/vectorize/dense/sparse but if/else makes code slow and ugly.

Thanks to multiple dispatch, Julia recognizes functions differently if input types are different. So, by defining those types, I let julia to construct four functions with same name and same first two arguments but different 3rd and 4th arguments.