norm {madness}

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]