norm: Matrix and vector norms.

In madness: Automatic Differentiation of Multivariate Operations

Matrix and vector norms.

Description

Compute the norm of a vector or matrix, as determined by the type.

Usage

maxeig(x)

## S4 method for signature 'madness'
maxeig(x)

## S4 method for signature 'madness,missing'
norm(x)

## S4 method for signature 'madness,ANY'
norm(x, type = "One")

Arguments

x

madness object.

type

character string, specifying the type of matrix norm to be computed. A character indicating the type of norm desired. "O", "o" or "1" specifies the one norm, (maximum absolute column sum); "I" or "i" specifies the infinity norm (maximum absolute row sum); "F" or "f" specifies the Frobenius norm (the Euclidean norm of x treated as if it were a vector); "M" or "m" specifies the maximum modulus of all the elements in x; and "2" specifies the “spectral” or 2-norm, which is the largest singular value (svd) of x. The default is "O". Only the first character of type[1] is used.

Value

the matrix norm, a non-negative number.

Note

This should probably be fixed to return a scalar, not a 1 by 1 matrix?

Author(s)

Steven E. Pav [e-mail]

madness documentation built on Aug. 21, 2023, 9:07 a.m.