smile.math.matrix

Class BiconjugateGradient

java.lang.Object

smile.math.matrix.BiconjugateGradient

public class BiconjugateGradient
extends java.lang.Object

The biconjugate gradient method is an algorithm to solve systems of linear equations.

Constructor Summary

Constructors

Constructor and Description
BiconjugateGradient() Constructor with itol = 1 and tol = 1E-10.
BiconjugateGradient(double tol, int itol, int maxIter) Constructor.

Method Summary

Modifier and Type	Method and Description
static BiconjugateGradient	getInstance() Returns the instance with default settings.
BiconjugateGradient	setConvergenceTest(int itol) Sets which convergence test is applied.
BiconjugateGradient	setMaxIter(int maxIter) Sets the maximum number of allowed iterations.
BiconjugateGradient	setPreconditioner(Preconditioner preconditioner) Sets the preconditioner matrix.
BiconjugateGradient	setTolerance(double tol) Sets the desired convergence tolerance.
double	solve(Matrix A, double[] b, double[] x) Solves A * x = b by iterative biconjugate gradient method.

Methods inherited from class java.lang.Object

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

Constructor Detail

BiconjugateGradient

public BiconjugateGradient()

Constructor with itol = 1 and tol = 1E-10. The maximum number of iterations will be determined by the size of matrix. The preconditioner will be a trivial diagonal part of input matrix if not set.

BiconjugateGradient

public BiconjugateGradient(double tol,
                           int itol,
                           int maxIter)

Constructor.

Method Detail

getInstance

public static BiconjugateGradient getInstance()

Returns the instance with default settings.

setTolerance

public BiconjugateGradient setTolerance(double tol)

Sets the desired convergence tolerance.

Returns:

return this object.

setConvergenceTest

public BiconjugateGradient setConvergenceTest(int itol)

Sets which convergence test is applied. If itol = 1, iteration stops when |Ax - b| / |b| is less than the parameter tolerance. If itol = 2, the stop criterion is |A^-1 (Ax - b)| / |A^-1b| is less than tolerance. If tol = 3, |x_k+1 - x_k|₂ is less than tolerance. The setting of tol = 4 is same as tol = 3 except that the L_∞ norm instead of L₂.

Returns:

return this object.

setMaxIter

public BiconjugateGradient setMaxIter(int maxIter)

Sets the maximum number of allowed iterations.

Returns:

return this object.

setPreconditioner

public BiconjugateGradient setPreconditioner(Preconditioner preconditioner)

Sets the preconditioner matrix.

Returns:

return this object.

solve

public double solve(Matrix A,
                    double[] b,
                    double[] x)

Solves A * x = b by iterative biconjugate gradient method.

Parameters:

b - the right hand side of linear equations.

x - on input, x should be set to an initial guess of the solution (or all zeros). On output, x is reset to the improved solution.

Returns:

the estimated error.