norm {Matrix}R Documentation

Norm of a Matrix

Description

Computes a matrix norm of x using Lapack. The norm can be the one norm, the infinity norm, the Frobenius norm, or the maximum modulus among elements of a matrix, as determined by the value of type.

Usage

norm(x, type, ...) 

Arguments

x a real or complex matrix.
type A character indicating the type of norm desired. "O" or "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); and "M" or "m" specifies the maximum modulus of all the elements in x. The default is "O".
Only the first character of type[1] is used.
... further arguments passed to or from other methods.

Details

Based on the Lapack functions dlange, dlansy, dlantr, zlange, zlansy, and zlantr.

Value

A numeric value of class "norm", representing the quantity chosen according to type.

References

Anderson, E., et al. (1994). LAPACK User's Guide, 2nd edition, SIAM, Philadelphia.

Examples

x <- Hilbert(9)
norm(x, "1")
norm(x, "I")
norm(x, "F")
norm(x, "M")

[Package Matrix version 0.9975-6 Index]