jsat.linear.solvers

Class ConjugateGradient

java.lang.Object

jsat.linear.solvers.ConjugateGradient

public class ConjugateGradient
extends Object

Provides an iterative implementation of the COnjugate Gradient Method.

The Conjugate method, if using exact arithmetic, produces the exact result after a finite number of iterations that is no more then the number of rows in the matrix. Because of this, no max iteration parameter is given.

Author:

Edward Raff

Constructor Summary

Constructors

Constructor and Description
ConjugateGradient()

Method Summary

Modifier and Type	Method and Description
static Vec	solve(double eps, Matrix A, Vec x, Vec b) Uses the Conjugate Gradient method to solve a linear system of equations involving a symmetric positive definite matrix. A symmetric positive definite matrix is a matrix A such that: AT = A xT * A * x > 0 for all x != 0 NOTE: No checks will be performed to confirm these properties of the given matrix.
static Vec	solve(double eps, Matrix A, Vec x, Vec b, Matrix Minv) Uses the Conjugate Gradient method to solve a linear system of equations involving a symmetric positive definite matrix. A symmetric positive definite matrix is a matrix A such that: AT = A xT * A * x > 0 for all x != 0 NOTE: No checks will be performed to confirm these properties of the given matrix.
static Vec	solve(Matrix A, Vec b)
static Vec	solveCGNR(double eps, Matrix A, Vec x, Vec b) Uses the Conjugate Gradient method to compute the least squares solution to a system of linear equations. Computes the least squares solution to A x = b.
static Vec	solveCGNR(Matrix A, Vec b)

Methods inherited from class java.lang.Object

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

Constructor Detail

ConjugateGradient

public ConjugateGradient()

Method Detail

solve

public static Vec solve(double eps,
                        Matrix A,
                        Vec x,
                        Vec b)

Uses the Conjugate Gradient method to solve a linear system of equations involving a symmetric positive definite matrix.

A symmetric positive definite matrix is a matrix A such that:

• A^T = A
• x^T * A * x > 0 for all x != 0

NOTE: No checks will be performed to confirm these properties of the given matrix. If a matrix is given that does not meet this requirements, invalid results may be returned.

Parameters:

eps - the precision of the desired result.

A - the symmetric positive definite matrix

x - an initial guess for x, can be all zeros. This vector will be altered

b - the target values

Returns:

the approximate solution to the equation A x = b

solve

public static Vec solve(Matrix A,
                        Vec b)

solve

public static Vec solve(double eps,
                        Matrix A,
                        Vec x,
                        Vec b,
                        Matrix Minv)

Uses the Conjugate Gradient method to solve a linear system of equations involving a symmetric positive definite matrix.

A symmetric positive definite matrix is a matrix A such that:

• A^T = A
• x^T * A * x > 0 for all x != 0

NOTE: No checks will be performed to confirm these properties of the given matrix. If a matrix is given that does not meet this requirements, invalid results may be returned.

Parameters:

eps - the precision of the desired result.

A - the symmetric positive definite matrix

x - an initial guess for x, can be all zeros. This vector will be altered

b - the target values

Minv - the of a matric M, such that M is a symmetric positive definite matrix. Is applied as M^-1( A x - b = 0) to increase convergence and stability. These increases are soley a property of M^-1

Returns:

the approximate solution to the equation A x = b

solveCGNR

public static Vec solveCGNR(double eps,
                            Matrix A,
                            Vec x,
                            Vec b)

Uses the Conjugate Gradient method to compute the least squares solution to a system of linear equations.
Computes the least squares solution to A x = b. Where A is an m x n matrix and b is a vector of length m and x is a vector of length n

NOTE: Unlike solve(double, jsat.linear.Matrix, jsat.linear.Vec, jsat.linear.Vec), the CGNR method does not need any special properties of the matrix. Because of this, slower convergence or numerical error can occur.

Parameters:

eps - the desired precision for the result

A - any m x n matrix

x - the initial guess for x, can be all zeros. This vector will be altered

b - the target values

Returns:

the least squares solution to A x = b

solveCGNR

public static Vec solveCGNR(Matrix A,
                            Vec b)