vector_norm

Computes various norms of a vector or the difference of two vectors.

Synopsis

#include <imsl.h>

float imsl_f_vector_norm (int n, float *x, …., 0)

The type double function is imsl_d_vector_norm.

Required Arguments

int n (Input)
The length of the input vector(s).

float *x (Input)
Input vector for which the norm is to be computed

Return Value

The requested norm of the input vector. If the norm cannot be computed, NaN is returned. By default, the two norm of x, , is computed.

Synopsis with Optional Arguments

#include <imsl.h>

float imsl_f_vector_norm (int n, float *x,

IMSL_ONE_NORM,

IMSL_INF_NORM, int *index,

IMSL_SECOND_VECTOR, float *y,0)

Optional Arguments

IMSL_ONE_NORM
Compute the one norm,

 

IMSL_INF_NORM, int *index (Output)
Compute the infinity norm,

 

IMSL_SECOND_VECTOR, float *y (Input)
Compute the norm of x minus y,

∥x - y∥, instead of ∥x∥

 

Description

By default, imsl_f_vector_norm computes the Euclidean norm

 

If the option IMSL_ONE_NORM is selected, the 1-norm

 

is returned. If the option IMSL_INF_NORM is selected, the infinity norm

max ∣xi∣

is returned. In the case of the infinity norm, the program also returns the index of the element with maximum modulus. If IMSL_SECOND_VECTOR is selected, then the norm of x −y is computed.

Examples

 

Example 1

In this example, the Euclidean norm of an input vector is computed.

 

#include <stdio.h>

#include <imsl.h>

 

int main()

{

float x[] = {1.0, 3.0, -2.0, 4.0};

float norm;

int n;

 

n = sizeof(x)/sizeof(*x);

norm = imsl_f_vector_norm (n, x, 0);

 

printf("Euclidean norm of x = %f\n", norm);

}

Output

 

Euclidean norm of x = 5.477226

Example 2

This example computes max |xi − yi| and prints the norm and index.

 

#include <stdio.h>

#include <imsl.h>

 

int main()

{

float x[] = {1.0, 3.0, -2.0, 4.0};

float y[] = {4.0, 2.0, -1.0, -5.0};

float norm;

int index;

int n;

 

n = sizeof(x)/sizeof(*x);

norm = imsl_f_vector_norm (n, x,

IMSL_SECOND_VECTOR, y,

IMSL_INF_NORM, &index, 0);

 

printf("Infinity norm of x-y = %f ", norm);

printf("at location %d\n", index);

}

Output

 

Infinity norm of x-y = 9.000000 at location 3