Matrix ops: inverse, power, determinant, norm, rank

Functions
template<typename ty >
ty	norm (const array &in, float p=af::nan)
	Matrix or vector norm.
array	inv (const array &in)
	Matrix inversion.
array	pinv (const array &in)
	Pseudo inverse.
array	mpow (const array &base, double exponent)
	Matrix power.
unsigned	rank (const array &in, double tolerance=1e-5)
	Rank of matrix.
template<typename T >
T	det (const array &in)
	Matrix determinant.

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Function Documentation

ty af::norm	(	const array &	in,
		float	p = af::nan
	)

Matrix or vector norm.

Some options require ArrayFire Pro.

Parameters:

[in]	in
[in]	p	type of norm: p == inf returns max(abs(in)) for vectors, infinity norm for matrices p == -inf returns min(abs(in)) for vectors, not supported for matrices p == nan (default) returns Euclidean norm for both vectors and matrices p (anything else) returns p norm of the input

Note:

if p is 2 and the input is vector, ArrayFire Pro license is required.

array af::inv

(

const array &

in

)

Matrix inversion.

Double-precision or complex input requires ArrayFire Pro.

Parameters:

[in]

in

square system matrix

Returns:

inverse system

array af::pinv

(

const array &

in

)

Pseudo inverse.

Double-precision or complex input requires ArrayFire Pro.

Parameters:

[in]

in

system matrix (possibly nonsquare)

Returns:

pseudo inverse of the input

array af::mpow	(	const array &	base,
		double	exponent
	)

Matrix power.

Double-precision or complex input requires ArrayFire Pro.

Parameters:

[in]	base	square
[in]	exponent

Returns:

base raised to exponent

unsigned af::rank	(	const array &	in,
		double	tolerance = 1e-5
	)

Rank of matrix.

Double-precision or complex input requires ArrayFire Pro.

Parameters:

[in]	in
[in]	tolerance	only consider singular values greater than this

Returns:

maximum of linearly independent column vectors

T af::det

(

const array &

in

)

Matrix determinant.

Double-precision or complex input requires ArrayFire Pro.

Parameters:

[in]

in

square

Returns:

scalar determinant