 A high-performance general-purpose compute library

Perform QR decomposition. More...

## Functions

AFAPI void qr (array &out, array &tau, const array &in)
C++ Interface for QR decomposition in packed format.

AFAPI void qr (array &q, array &r, array &tau, const array &in)
C++ Interface for QR decomposition.

AFAPI void qrInPlace (array &tau, array &in)
C++ Interface for QR decomposition.

AFAPI af_err af_qr (af_array *q, af_array *r, af_array *tau, const af_array in)
C Interface for QR decomposition.

AFAPI af_err af_qr_inplace (af_array *tau, af_array in)
C Interface for QR decomposition.

## Detailed Description

Perform QR decomposition.

This function decomposes input matrix A into an orthogonal matrix Q and an upper triangular matrix R such that

 \f$A = Q * R\f$

\f$Q * Q^T = I\f$


Where I is an identity matrix. The matrix Q is a square matrix of size max(M, N) where M and N are rows and columns of A respectively. The matrix R is the same size as **A*.

This operation can be performed in ArrayFire using the following code snippet.

array q, r, tau;
qr(q, r, tau, in);

The additional parameter Tau can be used to speed up solving over and under determined system of equations.

The original matrix can be reconstructed using the following code snippet.

array re = matmul(q, r);

When memory is a concern, users can perform QR decomposition in place as shown below.

array out = in.copy();
array tau2;
qrInPlace(tau2, out);

## ◆ af_qr()

 AFAPI af_err af_qr ( af_array * q, af_array * r, af_array * tau, const af_array in )

C Interface for QR decomposition.

Parameters
 [out] q is the orthogonal matrix from QR decomposition [out] r is the upper triangular matrix from QR decomposition [out] tau will contain additional information needed for solving a least squares problem using q and r [in] in is the input matrix

## ◆ af_qr_inplace()

 AFAPI af_err af_qr_inplace ( af_array * tau, af_array in )

C Interface for QR decomposition.

Parameters
 [out] tau will contain additional information needed for unpacking the data [in,out] in is the input matrix on entry. It contains packed QR decomposition on exit

## ◆ qr() [1/2]

 AFAPI void qr ( array & out, array & tau, const array & in )

C++ Interface for QR decomposition in packed format.

Parameters
 [out] out is the output array containing the packed QR decomposition [out] tau will contain additional information needed for unpacking the data [in] in is the input matrix
Note
This function is not supported in GFOR

## ◆ qr() [2/2]

 AFAPI void qr ( array & q, array & r, array & tau, const array & in )

C++ Interface for QR decomposition.

Parameters
 [out] q is the orthogonal matrix from QR decomposition [out] r is the upper triangular matrix from QR decomposition [out] tau will contain additional information needed for solving a least squares problem using q and r [in] in is the input matrix
Note
This function is not supported in GFOR

## ◆ qrInPlace()

 AFAPI void qrInPlace ( array & tau, array & in )

C++ Interface for QR decomposition.

Parameters
 [out] tau will contain additional information needed for unpacking the data [in,out] in is the input matrix on entry. It contains packed QR decomposition on exit
Note
This function is not supported in GFOR