matrix-l1-norm ( m -- n )
Matrix operations

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Vocabulary
math.matrices

Inputs

m

a matrix

Outputs

n

a number

Word description
Find the norm (size) of a matrix in 𝑙₁ (L^₁) vector space, usually written ∥･∥₁.

This is the matrix norm when p=1, and is the overall maximum of the sums of the columns.

Notes

•	User code should call the generic l1-norm instead.
•	This word is the matrix-specific variant of l1-norm.
•	This word is the p = 1 variant of matrix-p-norm.
•	This word is the transpose variant of matrix-l-infinity-norm.
•	This word is intended for use with "flat" (2-dimensional) matrices.

Examples

USING: math.matrices prettyprint ; { { 2 -2 1 } { 1 3 -1 } { 2 -4 2 } } matrix-l1-norm .
9

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

Definition

USING: kernel sequences ;

IN: math.matrices

: matrix-l1-norm ( m -- n )
    dup zero-matrix?
    [ drop 0 ] [ flip matrix-l-infinity-norm ] if ; inline
    foldable flushable