norm {Matrix}R Documentation

Matrix Norms

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", "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

For dense matrices, the methods eventually call 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 0.999375-29 Index]