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

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Vocabulary
math.matrices

Inputs

m	a matrix
p	a positive real number
q	a positive real number

Outputs

n	a non-negative real number

Word description
Find the norm (size) of a matrix in L^p,q vector space.

This is the matrix norm for any p, q ∈ ℝ. It is still an entry-wise norm, like matrix-p-norm-entrywise, and is not an induced or Schatten norm.

Examples
Equivalent to l2-norm for p = q = 2 :

USING: math.matrices prettyprint ; { { 1 1 } { 1 1 } } 2 2 matrix-p-q-norm .
2.0

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

Definition

USING: kernel math math.functions sequences ;

IN: math.matrices

:: matrix-p-q-norm ( m p q -- n )
    m dup zero-matrix?
    [ drop 0 ] [ [ [ sq ] map-sum q p / ^ ] map-sum q recip ^ ]
    if ; inline foldable flushable