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

Matrix operations

Matrix operations

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Next: | matrix-p-q-norm ( m p q -- n ) |

Vocabulary

math.matrices

Inputs

Outputs

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

Examples

Calls l1-norm:

Falls back to matrix-p-norm-entrywise:

See also

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

Definition

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

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

t

See also

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

Definition

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