Modules
	norm
	Calculate the norm of a vector.

Functions
array	inverse (const array &in)
	Matrix inversion. More...

array	matpow (const array &base, double exponent)
	Matrix power. More...

unsigned	rank (const array &in, double tolerance=1e-5)
	Rank of matrix. More...

template<typename T >
T	det (const array &in)
	Matrix determinant. More...

Detailed Description

Function Documentation

array af::inverse ( const array & in )

Matrix inversion.

For a square matrix A, this function returns the regular inverse IA of the same size as A, such that the following relationship is valid:

matmul(A, IA) = I

where I is an identity matrix of the same dimensions as A and IA.

If the input matrix is not square, the inverse operation swaps the rows and columns of the matrix and calculates what is sometimes called the pseudo-inverse.

matrix	rows	columns
input matrix	m	n
inverse matrix	n	m

Further, for non-square input matrices, it is always a multiplication of the flat matrix (m < n) and the tall matrix (m > n) that gives the identity matrix, as illustrated below for a flat matrix A of size 2 x 6 and a tall matrix B of size 6 x 2. The size of the (square) identity matrix is the minimum of m and n, which in the figure below is 2.

So depending on the orientation (tall or flat) of the input matrix, we either pre-multiply or post-multiply the (pseudo) inverse matrix to get the identity matrix.

Double-precision or complex input requires ArrayFire Pro.

array A = randu(5, 5);
array B = randu(5, 4);
array IA = inverse(A); // Regular inverse
array IB = inverse(B); // Psuedo inverse

Parameters

[in] in square system matrix

Returns: inverse system

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

Matrix power.

Calculates the input array (typically a 2D matrix) raised to the specified exponent.

Double-precision or complex input requires ArrayFire Pro.

// matrix^3
array in = randu(5, 5);
array out = matpow(in, 3);  // in x in x in

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

Modules

Functions

Detailed Description

Function Documentation