matrix-p-norm ( m p -- n )
Matrix operations

Prev:	matrix-l-infinity-norm ( m -- n )
Next:	matrix-p-q-norm ( m p q -- n )

Vocabulary
math.matrices

Inputs

m	a matrix
p	a positive real number

Outputs

n	a non-negative real number

Word description
Find the norm (size) of a matrix in 𝑙ₚ (L^p) vector space, usually written ∥･∥ₚ. For p ≠ 1, 2, ∞, this is an "entry-wise" norm.

Notes

•	User code should call the generic p-norm instead.
•	This word is the matrix-specific variant of p-norm.
•	This word is the p = q variant of matrix-p-q-norm.
•	This word is intended for use with "flat" (2-dimensional) matrices.

Examples
Calls l1-norm:

USING: math.matrices prettyprint ; 4 4 1 <matrix> 1 matrix-p-norm .
4

Falls back to matrix-p-norm-entrywise:

USING: math.functions math.matrices prettyprint ; 2 2 3 <matrix> 1.5 matrix-p-norm 7.559 10e-4 ~ .
t

See also
matrix-l1-norm, matrix-l2-norm, matrix-l-infinity-norm, matrix-p-q-norm

Definition

USING: combinators kernel math ;

IN: math.matrices

: matrix-p-norm ( m p -- n )
    over zero-matrix?
    [ 2drop 0 ] [
        {
            { [ dup 1 number= ] [ drop matrix-l1-norm ] }
            { [ dup 2 number= ] [ drop matrix-l2-norm ] }
            {
                [ dup fp-infinity? ]
                [ drop matrix-l-infinity-norm ]
            }
            [ matrix-p-norm-entrywise ]
        } cond
    ] if ; inline foldable flushable