qr

Perform QR decomposition. More...

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

\(A = Q * R\)

\(Q * Q^T = I\)

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.

        af::array q, r, tau;
        af::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.

        af::array re = af::matmul(q, r);

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

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

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Function Documentation

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

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

AFAPI void af::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

Examples:

lin_algebra/qr.cpp.

AFAPI void af::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

AFAPI void af::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

Examples:

lin_algebra/qr.cpp.