Dear all, I might be wrong, but in the plethora of BLAS and LAPACK functions, I was not able to find a function of the type inv(dest, X) where X is the matrix to invert and dest is the destination. Any suggestion?

[image] stevengj: Don’t do this. I am doing a weighted linear least squares regression and need to compute error bars. Unfortunately at some point there is a tridiagonal matrix that needs to be inverted (and I don’t see a way around this inversion).

[image] e3c6: I don’t see a way around this inversion Unless you are using A^{-1} directly, any A^{-1}b or similar is best implemented as A \ b. Calculating an inverse of a matrix is the numerical equivalent of code smell emanating from a medium-size trout that has been under the sofa for tw…

[image] Tamas_Papp: Unless you are using A^{-1} directly I am. If you are interested, this is what I’m trying to do: Weighted least squares - Wikipedia

Never use OLS formulas for computation. For WLS, there are much better options, eg premultiplying by the relevant Cholesky factor or its inverse (depending on details and how you obtain W).

[image] Tamas_Papp: (depending on details and how you obtain W) W is the inverse of the covariance matrix of observation errors (errors are not independent). How you suggest I compute the covariance matrix of the parameters (denoted M^\beta in the Wikipedia link)? (I only need the variances). …

[image] e3c6: How you suggest I compute the covariance matrix of the parameters (denoted M^\beta in the Wikipedia link)? Don’t — computer the Cholesky factor of M^\beta. If you have W=LL', it is fairly simple matrix algebra to work it out, but it may be better to start with the QR decompositi…

I have read many times the recommendation to avoid matrix inversion and use LU instead (or whatever factorization is applicable). However in the particular case of linear regression, it is always pointed out that if parameter errors are variances, the inversion is generally unavoidable. For example…

[image] e3c6: at some point there is a tridiagonal matrix I think it would help if you could write down your whole regression problem in mathematical form, including the form of the error you’re trying to compute. At this stage it seems people are guessing at what you’re trying to do :wink: P…

[image] e3c6: inv!(dest, A) could be useful […] and I suspect it should not be so hard to have? There is a trade-off between the maintenance cost of supporting in-place variants vs their usefulness (recall that these are generic functions, and need to work for many types). Given that most peo…

The cost of creating the array should in most cases be completely dwarfed by the cost of doing the factorization.

Inverse with destination?

General Usage

Tamas_Papp May 18, 2019, 2:01pm 19

Don’t — computer the Cholesky factor of M^\beta. If you have W=LL', it is fairly simple matrix algebra to work it out, but it may be better to start with the QR decomposition of the demeaned observations.

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Inverse with destination?

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