com.imsl.test.example.math

Class GenMinResEx2

java.lang.Object

com.imsl.test.example.math.GenMinResEx2

All Implemented Interfaces:

GenMinRes.Function, GenMinRes.Norm, GenMinRes.VectorProducts

public class GenMinResEx2
extends Object
implements GenMinRes.Function, GenMinRes.Norm

Solves a small linear system with user supplied inner product.

A solution to a small linear system is found. The coefficient matrix is stored as a full matrix and no preconditioning is used. Typically, preconditioning is required to achieve convergence in a reasonable number of iterations. The user supplies a function to compute the inner product and norm within the Gram-Schmidt implementation.

See Also:

Code, Output

Constructor Summary

Constructors

Constructor and Description
GenMinResEx2()

Method Summary

Modifier and Type	Method and Description
void	amultp(double[] p, double[] z) Multiplies the matrix a and the input vector p.
double	innerproduct(double[] x, double[] y) Computes the inner product of x and y.
static void	main(String[] args)
double	norm(double[] x) Computes the Euclidean norm of x.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

GenMinResEx2

public GenMinResEx2()

Method Detail

amultp

public void amultp(double[] p,
                   double[] z)

Multiplies the matrix a and the input vector p. The result is returned in z.

Specified by:

amultp in interface GenMinRes.Function

Parameters:

p - a double array with p.length=a[0].length

z - a double array

innerproduct

public double innerproduct(double[] x,
                           double[] y)

Computes the inner product of x and y. The inner product \( < x, y > \) = \( \sum_{i=1}^{x.length} x[i]*y[i] \), where x.length \( \le \) y.length.

Specified by:

innerproduct in interface GenMinRes.VectorProducts

Parameters:

x - a double array with x.length \( \le \) y.length

y - a double array

Returns:

the inner product

norm

public double norm(double[] x)

Computes the Euclidean norm of x. The Euclidean norm of a vector, \(x \) is defined as \(\sqrt{\sum_{i=1}^{n} x_i*x_i} = \sqrt{ < x , x >} \) where \( < \cdot,\cdot > \) denotes the inner product operation.

Specified by:

norm in interface GenMinRes.Norm

Parameters:

x - a double array

Returns:

a double, the Euclidean norm of x

main

public static void main(String[] args)
                 throws Exception

Throws:

Exception