Talk:QR decomposition

usage?

What does "and the usage for linear least squares problems on the example from Polynomial_regression" mean, specifically, as a task requirement? --Rdm 16:02, 17 June 2011 (UTC)

It means that there already is a existing task on RC (Polynomial regression) which requires linear least squares, and since LLS is one use case for QR, that task can be used here as an example. The Go and R solutions of the Polynomial regression already used QR instead of the normal equations approach. --Avi 20:52, 17 June 2011 (UTC)

According to the wikipedia page on least squares, QR reduction is supposed to be more numerically stable than faster approaches. But we can solve the Polynomial regression example exactly, so I am not sure that that example is a good one for QR reduction least squares fitting. --Rdm 16:34, 17 June 2011 (UTC)

The advantage is that it is already existing, has many solutions and can be used as a comparison. --Avi 20:52, 17 June 2011 (UTC)

C example

The code does do the job, but is quite ugly, and overly long. Much improvement is needed, and all the matrix_delete() calls would make you appreciate garbage collection that much more. --Ledrug 01:26, 29 June 2011

Is the D version (that is a port of the Common Lisp version) any better?

Common Lisp example

What is eye in make-householder? In array-range m and n seem useless.

Thanks for pointing this out. (eye n) returns a nxn identity matrix. I overlooked that. (identity) is an already taken Common Lisp function, so I couldnt use that. The terminology is following matlab/octave's naming. Your second point is also correct, and these two local bindings can be removed. Thanks. --Avi 16:21, 12 July 2011 (UTC)

Description flow

In response to [1], I find the task description difficult to follow, as its narrative form interleaves mathematical formulae and expressions with English text. I tried splitting it up as I did in Gauss-Legendre_Quadrature, but I was unable to. If someone could organize the task description to visually separate the formulas from the written text, that'd be great. --Michael Mol 15:34, 4 July 2011 (UTC)

The narative interleaves formulas and text since this is how most papers are written. The formulas are not meant to be a pseudocode in mathematical notation which can then be reimplemented line by line, I have given a non-optimized Common Lisp version which follows the steps and should be easy to follow and can be used as a reference. --Avi 16:25, 12 July 2011 (UTC)

Draft status

Also in response to [2], the simplest way to get a task from draft to non-draft status is to leave a note here asking if there are any further issues that people would like resolved. So I'll ask it; are there any issues or points of confusion in this task that people would like to see resolved? --Michael Mol 15:34, 4 July 2011 (UTC)

Please fix the CommonLisp version.

I did now. Thanks for your hints. Are there any other objections? --Avi 17:02, 12 July 2011 (UTC)

What is this line of make-householder doing? (beta (/ 2 (mmul (mtp v) v))))

It creates a local variable $\beta$ (which is often used in articles about the QR decomposition) with the value ${\frac {2}{v^{T}v}}$, and is used to create the Householder matrix $H=I-\beta \,vv^{T}$. I also could have written the first formula directly instead of that. --Avi 18:18, 13 July 2011 (UTC)

<lang lisp>(m- (eye m)

   (.* (/ 2 (mmul (mtp v) v)))
       (mmul v (mtp v))))</lang>

$\beta$ is a scalar value (since $v^{T}v$ is a doct product), not a matrix, so making it a array will cause a type error. --Avi 16:07, 14 July 2011 (UTC)

What you have reverted breaks the code to me. Maybe I am using a different Common Lisp compiler? http://ideone.com/UUsVG