qr (MathScript RT Module Function)

LabVIEW 2012 MathScript RT Module Help

Edition Date: June 2012

Part Number: 373123C-01

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Owning Class: linalgebra

Requires: MathScript RT Module

Syntax

r = qr(a)

r = qr(a, 0)

[q, r] = qr(a)

[q, r] = qr(a, 0)

[q, r, pm] = qr(a)

[q, r, pv] = qr(a, 0)

Description

Performs the QR decomposition of an input matrix with or without column pivoting.

Details

Examples

Inputs

Name Description
a Specifies a matrix.
0 Specifies that LabVIEW computes the economy size QR decomposition such that the size of q is m-by-min(m, n) and the size of r is min(m, n)-by-n, where a is an m-by-n matrix.

Outputs

Name Description
q Returns the orthogonal or unitary matrix of the QR decomposition of a.
r Returns the upper triangular matrix of the QR decomposition of a.
pm Returns the pivot matrix of the QR decomposition of a. pm is a matrix of 32-bit signed integers.
pv Returns the pivot vector of the QR decomposition of a. pv is a row vector of 32-bit signed integers.

Details

The QR decomposition of a matrix a without column pivoting computes matrices q and r such that q*r = a, where q is an orthogonal or unitary matrix and r is an upper triangular matrix.

The QR decomposition of a matrix a with column pivoting computes matrices q and r and the pivot matrix pm or the pivot vector pv such that q*r = a*pm or q*r = a(pv). LabVIEW performs column pivoting on a such that the diagonal elements of r are in decreasing order.

The following table lists the support characteristics of this function.

 Supported in the LabVIEW Run-Time Engine Yes Supported on RT targets Yes Suitable for bounded execution times on RT Not characterized

Examples

A = rand(2)
[Q, R, P] = qr(A)