Chapter 1, Problem 18C

Explanation of Solution

Implementation of norm(v):

The norm() method takes the input parameter of “vec” to return the Euclidean norm of “vec” array of coordinates.

//Function definition

public static double norm(double[ ] vec)      

{

/*Call the norm() by passing the “vec” and “2” and return the result of computed value. */

return norm(vec,2);

}

Explanation:

In norm() method,

• It takes the input parameter of “vec”.
• Call the norm() method by passing the “vec” and “2” and return the result of computed value of p-norm value of “vec” array of coordinates.

Implementation of norm(v, p):

The norm() method takes the input parameter of “vec” and “pow” to return the p-norm value of “vec” array of coordinates.

//Function definition

public static double norm(double[ ] vec, int pow)

{

//Declare the variables

int sum = 0;

double exp = 1.0/pow;

//Loop executes until from “i” to "vec"

for (double i : vec)

//Add the "sum" and the power of number

sum += Math.pow(i,pow);

//Return the return

return Math.pow(sum, exp);

}

Explanation:

In norm() method,

• It takes the input parameter of “vec” and “pow”.
• Loop executes until the “vec” to add the sum and power of input.
• Return the computed p-norm value of “vec” array of coordinates.

Complete Program:

/**********************************************************

* Program demonstrates how to determine the Euclidean norm*

* for two-dimensional vectors...