LPNORM Function

Returns the Lp norm of the second argument and subsequent non-missing arguments.

Category:

Descriptive Statistics

Syntax

LPNORM(p, value-1 <,value-2 …> )

Required Arguments

p

specifies a numeric constant, variable, or expression that is greater than or equal to 1, which is used as the power for computing the L_p norm.

value

specifies a numeric constant, variable, or expression.

Details

If all arguments have missing values, then the result is a missing value. Otherwise, the result is the L_p norm of the non-missing values of the second and subsequent arguments.

In the following example, p is the value of the first argument, and

x 1, x 2, . . ., x n

are the values of the other non-missing arguments.

\begin{matrix} L P N O R M (p, x 1, x 2, . . ., x n) = {(a b s {(x 1)}^{p} + a b s {(x 2)}^{p} + . . . + a b s {(x n)}^{p})}^{1 / p} \end{matrix}

Examples

Example 1: Calculating the Lp Norm

The following example returns the L_p norm of the second and subsequent non-missing arguments.

data _null_;
   x1 = lpnorm(1, ., 3, 0, .q, -4);
   x2 = lpnorm(2, ., 3, 0, .q, -4);
   x3 = lpnorm(3, ., 3, 0, .q, -4);
   x999 = lpnorm(999, ., 3, 0, .q, -4);
   put x1= / x2= / x3= / x999=;
run;

SAS writes the following output to the log:

x1=7
x2=5
x3=4.4979414453
x999=4

Example 2: Calculating the Lp Norm When You Use a Variable List

The following example uses a variable list and returns the L_p norm.

data _null_;
   x1 = 1;
   x2 = 3;
   x3 = 4;
   x4 = 3;
   x5 = 1;
   x = lpnorm(of x1-x5);
   put x=;
run;