topic Re: Doing a partial echelon using IML in SAS Studio

Doing a partial echelon using IML

Daniel_MM — Wed, 17 May 2023 02:12:37 GMT

I have a data set that has the form:

a=N x M data set (N>M)

and

b=NxP data set

which forms an equation

aX=b,

to solve this I am using the IML echelon function, but unfortunately my data does not seem to be perfect (possible rounding errors) as the echelon over solves my matrix [a|b] and row reduces too far, is there a possible way to identify what rows to pick so that I could do an inversion solve or to truncate the variables to ensure rounding errors are not an issue?

Re: Doing a partial echelon using IML

Ksharp — Wed, 17 May 2023 12:50:51 GMT

Why not post it at IML forum? @Rick_SAS might give you a hand .

Re: Doing a partial echelon using IML

Ksharp — Wed, 17 May 2023 13:10:48 GMT

Could post a real example ,include the data you have and the answer you want to see ?

Re: Doing a partial echelon using IML

Rick_SAS — Wed, 17 May 2023 13:44:44 GMT

If N > M (more rows than columns), then the system is almost surely overdetermined and you need to compute a least squares solution.

There are many ways to solve least squares systems. A few are discussed here:
On solving rank-deficient systems of equations in SAS - The DO Loop

Re: Doing a partial echelon using IML

Rick_SAS — Wed, 17 May 2023 14:48:42 GMT

PS: If your data matrix really does have a unique solution to Ax=b, then you can use ANY set of M rows to find x.

Re: Doing a partial echelon using IML

Daniel_MM — Wed, 17 May 2023 22:47:22 GMT

I have verified that the equations have a unique solution, but unfortunately some variables only have a few entries in the entire system so I cant just take a random set of rows, I am attempting to use a Moore-Penrose generalised inverse to solve the system which seems to be working, thanks for the swift reply though, great to see the community so active.