Function norm

pub fn norm<'a>(
    array: impl AsRef<Array>,
    ord: impl IntoOption<Ord<'a>>,
    axes: impl IntoOption<&'a [i32]>,
    keep_dims: impl Into<Option<bool>>,
) -> Result<Array>

Matrix or vector norm.

For values of ord < 1, the result is, strictly speaking, not a mathematical norm, but it may still be useful for various numerical purposes.

The following norms can be calculated:

ord	norm for matrices	norm for vectors
None	Frobenius norm	2-norm
‘fro’	Frobenius norm	–
inf	max(sum(abs(x), axis-1))	max(abs(x))
-inf	min(sum(abs(x), axis-1))	min(abs(x))
0	–	sum(x !- 0)
1	max(sum(abs(x), axis-0))	as below
-1	min(sum(abs(x), axis-0))	as below
2	2-norm (largest sing. value)	as below
-2	smallest singular value	as below
other	–	sum(abs(x)ord)(1./ord)

Nuclear norm and norms based on singular values are not yet implemented.

The Frobenius norm is given by G. H. Golub and C. F. Van Loan, Matrix Computations, Baltimore, MD, Johns Hopkins University Press, 1985, pg. 15

The nuclear norm is the sum of the singular values.

Both the Frobenius and nuclear norm orders are only defined for matrices and produce a fatal error when array.ndim != 2

Params

• array: input array
• ord: order of the norm, see table
• axes: axes that hold 2d matrices
• keep_dims: if true the axes which are normed over are left in the result as dimensions with size one