p-norm of a Vector
DESCRIPTION:
Computes the p-norm of a vector.
USAGE: 
vecnorm(x, p = 2)

REQUIRED ARGUMENTS:
x:
the vector whose norm is sought (either numeric or complex).
OPTIONAL ARGUMENTS:
p:
a number or character string indicating the type of norm desired. Possible values include real number greater or equal to 1, Inf, or character strings "euclidean" or "maximum".
VALUE:
the p-norm of x. This is defined as: [(x1)**p + (x2)**p + ....+(xn)**p]***(1/p) for p greater than or equal to 1.
METHOD:
Computation of the 2 norm is based on the function dnrm2 Linpack BLAS (Dongarra et al. 1979). For 1 < p < Inf, p-norms are computed so as to avoid overflow and underflow.

The numerical value of a norm may differ for vectors which have the same elements appearing in a different order. Sorting a vector so that the elements of smallest modulus appear first may help reduce this roundoff error.

REFERENCES:
Dongarra, J. J., Bunch, J. R., Moler, C. B., and Stewart, G. W. (1979). Linpack User's Guide. SIAM, Philadelphia.
SEE ALSO:
dist , max , rep , rnorm , sqrt , sum .
EXAMPLES: 
x <-  rnorm(100)


sqrt(sum(x*x))
vecnorm(x)


x <- rep(sqrt(.Machine$double.xmax), 4)
sqrt(sum(x*x))
vecnorm(x)


sum(abs(x))
vecnorm(x, p = 1)


max(abs(x))
vecnorm(x, p = Inf)