How to find the permutation matrix for the qr decomposition?

How to find the permutation matrix for the qr decomposition without using the function "[q,r,e]=qr(A)"?

Answer 1

[Christine Tobler]

You need to compute all three matrices together: Q and R are different if the third output e is also returned.

For an algorithm, search for "qr with column pivoting" or consult Golub and Van Loan, "Matrix Computations", 3rd edition, section 5.4.1 "Rank Deficiency: QR with Column Pivoting".

As I remember, the trick is to permute the columns of A to move the column of largest norm to the left, in every step of the algorithm.

[Sergey Solovev]

Thanks, I'll take a look

Answer 2

[Christine Tobler]

I'm afraid using the three-output syntax is the only way. You can use

 [~, ~, p] = qr(A);

but Q and R are still computed, just not returned. Could you tell us some more about why you need the permutation matrix only?

[Sergey Solovev]

To solve an equation of type Ax=B, when A[2x7], B[2x1]. I know that equation can be solved with "mldivid" functions, but I need to know how it calculates. I know how to calculate Q and R matrix.

[John D'Errico]

So you know how to compute a basic QR, but are not sure how the pivoting was done inside QR?

[Sergey Solovev]

I dont know why and how the permutation matrix is formed. By what criterion is it formed?