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()

Method Summary

Modifier and Type	Method and Description
static double	solve(Matrix A, double[] b, double[] x) Solves A * x = b by iterative biconjugate gradient method.
static double	solve(Matrix A, double[] b, double[] x, double tol) Solves A * x = b by iterative biconjugate gradient method.
static double	solve(Matrix A, double[] b, double[] x, double tol, int itol) Solves A * x = b by iterative biconjugate gradient method.
static double	solve(Matrix A, double[] b, double[] x, double tol, int itol, int maxIter) Solves A * x = b by iterative biconjugate gradient method.
static double	solve(Matrix A, Preconditioner Ap, double[] b, double[] x) Solves A * x = b by iterative biconjugate gradient method.
static double	solve(Matrix A, Preconditioner Ap, double[] b, double[] x, double tol) Solves A * x = b by iterative biconjugate gradient method.
static double	solve(Matrix A, Preconditioner Ap, double[] b, double[] x, double tol, int itol) Solves A * x = b by iterative biconjugate gradient method.
static double	solve(Matrix A, Preconditioner Ap, double[] b, double[] x, double tol, int itol, int maxIter) 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()

Method Detail

solve

public static 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.

solve

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

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

Parameters:

Ap - the preconditioned matrix of A.

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.

solve

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

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.

tol - the desired convergence tolerance.

Returns:

the estimated error.

solve

public static double solve(Matrix A,
                           Preconditioner Ap,
                           double[] b,
                           double[] x,
                           double tol)

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

Parameters:

Ap - the preconditioned matrix of A.

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.

tol - the desired convergence tolerance.

Returns:

the estimated error.

solve

public static double solve(Matrix A,
                           double[] b,
                           double[] x,
                           double tol,
                           int itol)

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.

itol - specify 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.

tol - the desired convergence tolerance.

Returns:

the estimated error.

solve

public static double solve(Matrix A,
                           Preconditioner Ap,
                           double[] b,
                           double[] x,
                           double tol,
                           int itol)

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

Parameters:

Ap - the preconditioned matrix of A.

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.

itol - specify 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.

tol - the desired convergence tolerance.

Returns:

the estimated error.

solve

public static double solve(Matrix A,
                           double[] b,
                           double[] x,
                           double tol,
                           int itol,
                           int maxIter)

Solves A * x = b by iterative biconjugate gradient method. This method can be called repeatedly, with maxIter < n, to monitor how error decreases.

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.

itol - specify 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.

tol - the desired convergence tolerance.

maxIter - the maximum number of allowed iterations.

Returns:

the estimated error.

solve

public static double solve(Matrix A,
                           Preconditioner Ap,
                           double[] b,
                           double[] x,
                           double tol,
                           int itol,
                           int maxIter)

Solves A * x = b by iterative biconjugate gradient method. This method can be called repeatedly, with maxIter < n, to monitor how error decreases.

Parameters:

Ap - the preconditioned matrix of A.

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.

itol - specify 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.

tol - the desired convergence tolerance.

maxIter - the maximum number of allowed iterations.

Returns:

the estimated error.