Class ThomasSolver

java.lang.Object

net.finmath.finitedifference.solvers.ThomasSolver

public final class ThomasSolver
extends Object

Utility class providing an implementation of the Thomas algorithm for solving a tridiagonal linear system.

The method solves a system of the form

[ d0  u0   0   ...                ] [x0]   [r0]
[ l1  d1  u1   0   ...            ] [x1] = [r1]
[  0  l2  d2  u2   0   ...        ] [x2]   [r2]
[              ...                ] [...]  [...]
[          ... l(n-1) d(n-1)      ] [xn]   [rn]

where:

• lower[i] contains the sub-diagonal entry for row i,
• diag[i] contains the main diagonal entry for row i,
• upper[i] contains the super-diagonal entry for row i,
• rhs[i] contains the right-hand side entry for row i.

By convention, lower[0] is unused and may be set to any value, and upper[n-1] is unused by the backward substitution step.

This solver runs in linear time and is intended for non-singular tridiagonal systems. No validation of input sizes or pivot values is performed.

Author:

Alessandro Gnoatto

Method Summary

Modifier and Type	Method	Description
static double[]	solve(double[] lower, double[] diag, double[] upper, double[] rhs)	Solves a tridiagonal linear system using the Thomas algorithm.

Methods inherited from class Object

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

Method Details

solve

public static double[] solve(double[] lower,
 double[] diag,
 double[] upper,
 double[] rhs)

Solves a tridiagonal linear system using the Thomas algorithm.

The input arrays represent the three diagonals of the tridiagonal matrix and the right-hand side vector. All arrays are expected to have identical length n, where n >= 1.

The algorithm consists of a forward elimination phase followed by a backward substitution phase.

Note: The caller must provide arrays of consistent length and a non-singular tridiagonal system.

Parameters:

lower - The lower diagonal of the system matrix. Entry lower[i] represents the coefficient below the main diagonal in row i. The value lower[0] is not used.

diag - The main diagonal of the system matrix. Entry diag[i] represents the diagonal coefficient in row i.

upper - The upper diagonal of the system matrix. Entry upper[i] represents the coefficient above the main diagonal in row i. The value upper[n-1] is not used in the final row.

rhs - The right-hand side vector of the linear system.

Returns:

The solution vector x satisfying the tridiagonal system.