A high-performance general-purpose compute library

Perform QR decomposition. More...

Functions

AFAPI void qr (array &out, array &tau, const array &in)
 C++ Interface to perform QR decomposition in packed format. More...
 
AFAPI void qr (array &q, array &r, array &tau, const array &in)
 C++ Interface to perform QR decomposition. More...
 
AFAPI void qrInPlace (array &tau, array &in)
 C++ Interface to perform QR decomposition. More...
 
AFAPI af_err af_qr (af_array *q, af_array *r, af_array *tau, const af_array in)
 C Interface to perform QR decomposition. More...
 
AFAPI af_err af_qr_inplace (af_array *tau, af_array in)
 C Interface to perform QR decomposition. More...
 

Detailed Description

Perform QR decomposition.

This function decomposes input matrix \(A\) into an orthogonal matrix \(Q\) and an upper triangular matrix \(R\) such that, \(A = Q * R\) and \(Q * Q^T = I\), 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 systems 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);

Function Documentation

◆ af_qr()

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

C Interface to perform QR decomposition.

This function is not supported in GFOR.

Parameters
[out]qorthogonal matrix from QR decomposition
[out]rupper triangular matrix from QR decomposition
[out]tauadditional information needed for solving a least-squares problem using q and r
[in]ininput array
Returns
AF_SUCCESS, if function returns successfully, else an af_err code is given

◆ af_qr_inplace()

AFAPI af_err af_qr_inplace ( af_array tau,
af_array  in 
)

C Interface to perform QR decomposition.

This function is not supported in GFOR.

Parameters
[out]tauadditional information needed for unpacking the data
[in,out]ininput array on entry; packed QR decomposition on exit
Returns
AF_SUCCESS, if function returns successfully, else an af_err code is given

◆ qr() [1/2]

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

C++ Interface to perform QR decomposition in packed format.

This function is not supported in GFOR.

Parameters
[out]outpacked QR decomposition
[out]tauadditional information needed for unpacking the data
[in]ininput array

◆ qr() [2/2]

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

C++ Interface to perform QR decomposition.

This function is not supported in GFOR.

Parameters
[out]qorthogonal matrix from QR decomposition
[out]rupper triangular matrix from QR decomposition
[out]tauadditional information needed for solving a least-squares problem using q and r
[in]ininput array

◆ qrInPlace()

AFAPI void qrInPlace ( array tau,
array in 
)

C++ Interface to perform QR decomposition.

This function is not supported in GFOR.

Parameters
[out]tauadditional information needed for unpacking the data
[in,out]ininput array on entry; packed QR decomposition on exit