Factorizations: LU, QR, Cholesky, singular values, eigenvalues, Hessenberg

Functions
array	lu (const array &in)
	LU factorization (packed)
void	lu (array &lower, array &upper, const array &in)
	LU factorization.
void	lu (array &lower, array &upper, array &pivot, const array &in)
	LU factorization (with pivoting)
array	qr (const array &in)
	QR factorization (packed).
void	qr (array &q, array &r, const array &in)
	QR factorization.
void	qr (array &q, array &r, array &tau, const array &in)
	QR factorization with tau.
array	cholesky (unsigned &info, const array &X, bool is_upper=true)
	Cholesky decomposition ("Y^T * Y == X").
array	hessenberg (const array &in)
	Hessenberg matrix form.
void	hessenberg (array &h, array &q, const array &in)
	Hessenberg matrix h with unitary permutation matrix q.
array	eigen (const array &in, bool is_diag=false)
	Eigenvalues.
void	eigen (array &values, array &vectors, const array &in)
	Eigenvalues and eigenvectors.
array	svd (const array &in, bool is_diag=false)
	Singular values.
void	svd (array &s, array &u, array &v, const array &in)
	Singular values with unitary bases: in = u * s * v.

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Function Documentation

array af::lu

(

const array &

in

)

LU factorization (packed)

Parameters:

[in]

in

Returns:

lower and upper matrix combined (getrf)

Examples:

examples/misc/lin_algebra.cpp.

void af::lu	(	array &	lower,
		array &	upper,
		const array &	in
	)

LU factorization.

Parameters:

[out]	lower	triangular matrix
[out]	upper	triangular matrix
[in]	in

void af::lu	(	array &	lower,
		array &	upper,
		array &	pivot,
		const array &	in
	)

LU factorization (with pivoting)

Parameters:

[out]	lower	triangular matrix
[out]	upper	triangular matrix
[out]	pivot	indices
[in]	in

array af::qr

(

const array &

in

)

QR factorization (packed).

Parameters:

[in]

in

Returns:

Q,R factors (geqrf)

void af::qr	(	array &	q,
		array &	r,
		const array &	in
	)

QR factorization.

Parameters:

[out]	q	unitary rotation matrix
[out]	r	upper triangular
[in]	in

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

QR factorization with tau.

Parameters:

[out]	q	orthogonal matrix
[out]	r	upper triangular matrix
[out]	tau	Additional information about q
[in]	in

array af::cholesky	(	unsigned &	info,
		const array &	X,
		bool	is_upper = true
	)

Cholesky decomposition ("Y^T * Y == X").

Parameters:

[out]	info	details on result of decomposition
[in]	X
[in]	is_upper	true for upper triangular solution, false for lower triangular solution

Returns:

upper or lower triangular factor

array af::hessenberg

(

const array &

in

)

Hessenberg matrix form.

Parameters:

[in]

in

Returns:

Hessenberg form

void af::hessenberg	(	array &	h,
		array &	q,
		const array &	in
	)

Hessenberg matrix h with unitary permutation matrix q.

such that in = q * h * q^T. Requires ArrayFire Pro.

Parameters:

[out]	h	Hessenberg matrix
[out]	q	unitary matrix
[in]	in

array af::eigen	(	const array &	in,
		bool	is_diag = false
	)

Eigenvalues.

Requires ArrayFire Pro.

Parameters:

[in]	in
[in]	is_diag	true then produce diagonal matrix of eigenvalues, false then vector of eigenvalues

Returns:

eigenvalues

Examples:

examples/misc/lin_algebra.cpp.

void af::eigen	(	array &	values,
		array &	vectors,
		const array &	in
	)

Eigenvalues and eigenvectors.

Requires ArrayFire Pro.

Parameters:

[out]	values
[out]	vectors
[in]	in

array af::svd	(	const array &	in,
		bool	is_diag = false
	)

Singular values.

Double-precision or complex values require ArrayFire Pro.

Parameters:

[in]	in
[in]	is_diag	true then produce diagonal matrix of eigenvalues, false then vector of eigenvalues

Returns:

singular values

void af::svd	(	array &	s,
		array &	u,
		array &	v,
		const array &	in
	)

Singular values with unitary bases: in = u * s * v.

Parameters:

[out]	s	singular values
[out]	u	left unitary matrix
[out]	v	right unitary matrix
[in]	in	The input matrix.