qr

Syntax

[Q,R] = qr(A)

[Q,R] = qr(A,econ)

Inputs

A: The matrix to decompose.; Dimension: matrix
econ: Economy decomposition flag. Set to 0.; Type: integer; Dimension: scalar

Outputs

Q: Orthonormal matrix.; Dimension: matrix
R: Upper triangular matrix.; Dimension: matrix

Example

Matrix input:

[Q,R] = qr([1,2,3;4,5,6;7,8,10;11,12,15],0)

Q = [Matrix] 4 x 3
-0.073127 -0.8104  0.56383
-0.29251  -0.46944 -0.78362
-0.51189  -0.12848 -0.038225
-0.8044   0.32614  0.25802
R = [Matrix] 3 x 3
-13.675 -15.357 -19.159
0       -1.0822 -1.6406
0       0       0.47782

Comments

[Q,R] = qr(A) computes matrices Q and R such that A = QR.

QR decomposition is often used for solving over-determined linear least squares equations Ax = b. For the economy decomposition of an MxN matrix A with m>n, Q is MxN and R is NxN.

qr uses the LAPACK routines 'dgeqrf' for real matrices and 'zgeqrf' for complex matrices.