qr

QR decomposition.

Syntax

[Q, R]    = qr(A)
[Q, R, E] = qr(A)        % with column pivoting
Y         = qr(A)        % packed form

Description

Decomposes A into an orthogonal/unitary Q and upper-triangular R such that A = Q*R. With three outputs, applies column pivoting and returns the permutation E such that A*E = Q*R with R having descending diagonal magnitudes — useful for rank-revealing QR.

For non-square A: with two outputs, Q is full size (m×m); pass an additional 0 argument or use the economy form for the thinner m×n Q.

Examples

[Q, R] = qr(magic(4));
norm(Q*R - magic(4))     % near-zero
Q' * Q                   % I (within eps)

See also

• lu — LU decomposition (with partial pivoting).
• chol — Cholesky factorization of a Hermitian positive-definite matrix.
• svd — Singular value decomposition.
• linsolve — Solve a linear system with optional structure hints.