edu.rit.numeric

Class Tridiagonal

java.lang.Object

edu.rit.numeric.Tridiagonal

public class Tridiagonal
extends java.lang.Object

Class Tridiagonal provides static methods for solving tridiagonal systems of linear equations.

The Java code was translated from routines gsl_linalg_solve_tridiag(), gsl_linalg_solve_symm_tridiag(), gsl_linalg_solve_cyc_tridiag(), and gsl_linalg_solve_symm_cyc_tridiag() in the GNU Scientific Library Version 1.9.

Method Summary

Modifier and Type	Method and Description
static void	solve(double[] d, double[] e, double[] f, double[] b, double[] x) Solve the given tridiagonal system of linear equations.
static void	solveCyclic(double[] d, double[] e, double[] f, double[] b, double[] x) Solve the given cyclic tridiagonal system of linear equations.
static void	solveSymmetric(double[] d, double[] e, double[] b, double[] x) Solve the given symmetric tridiagonal system of linear equations.
static void	solveSymmetricCyclic(double[] d, double[] e, double[] b, double[] x) Solve the given symmetric cyclic tridiagonal system of linear equations.

Methods inherited from class java.lang.Object

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

Method Detail

solve

public static void solve(double[] d,
                         double[] e,
                         double[] f,
                         double[] b,
                         double[] x)

Solve the given tridiagonal system of linear equations. This method solves the general N-by-N system Ax = b where A is tridiagonal (N >= 2). The form of A for the 4-by-4 case is:

     [ d0  e0  0   0  ]
 A = [ f0  d1  e1  0  ]
     [ 0   f1  d2  e2 ]
     [ 0   0   f2  d3 ]
 

Parameters:

d - (input) Vector of diagonal elements. Length N must be >= 2.

e - (input) Vector of super-diagonal elements. Length must be N-1.

f - (input) Vector of sub-diagonal elements. Length must be N-1.

b - (input) Vector of right hand side elements. Length must be N.

x - (output) Solution vector. Length must be N.

Throws:

java.lang.NullPointerException - (unchecked exception) Thrown if any argument is null.

java.lang.IllegalArgumentException - (unchecked exception) Thrown if any argument is the wrong length.

DomainException - (unchecked exception) Thrown if the linear system cannot be solved.

solveSymmetric

public static void solveSymmetric(double[] d,
                                  double[] e,
                                  double[] b,
                                  double[] x)

Solve the given symmetric tridiagonal system of linear equations. This method solves the general N-by-N system Ax = b where A is symmetric tridiagonal (N >= 2). The form of A for the 4-by-4 case is:

     [ d0  e0  0   0  ]
 A = [ e0  d1  e1  0  ]
     [ 0   e1  d2  e2 ]
     [ 0   0   e2  d3 ]
 

Parameters:

d - (input) Vector of diagonal elements. Length N must be >= 2.

e - (input) Vector of off-diagonal elements. Length must be N-1.

b - (input) Vector of right hand side elements. Length must be N.

x - (output) Solution vector. Length must be N.

Throws:

java.lang.NullPointerException - (unchecked exception) Thrown if any argument is null.

java.lang.IllegalArgumentException - (unchecked exception) Thrown if any argument is the wrong length.

DomainException - (unchecked exception) Thrown if the linear system cannot be solved.

solveCyclic

public static void solveCyclic(double[] d,
                               double[] e,
                               double[] f,
                               double[] b,
                               double[] x)

Solve the given cyclic tridiagonal system of linear equations. This method solves the general N-by-N system Ax = b where A is cyclic tridiagonal (N >= 3). The form of A for the 4-by-4 case is:

     [ d0  e0  0   f3 ]
 A = [ f0  d1  e1  0  ]
     [ 0   f1  d2  e2 ]
     [ e3  0   f2  d3 ]
 

Parameters:

d - (input) Vector of diagonal elements. Length N must be >= 3.

e - (input) Vector of super-diagonal elements. Length must be N.

f - (input) Vector of sub-diagonal elements. Length must be N.

b - (input) Vector of right hand side elements. Length must be N.

x - (output) Solution vector. Length must be N.

Throws:

java.lang.NullPointerException - (unchecked exception) Thrown if any argument is null.

java.lang.IllegalArgumentException - (unchecked exception) Thrown if any argument is the wrong length.

DomainException - (unchecked exception) Thrown if the linear system cannot be solved.

solveSymmetricCyclic

public static void solveSymmetricCyclic(double[] d,
                                        double[] e,
                                        double[] b,
                                        double[] x)

Solve the given symmetric cyclic tridiagonal system of linear equations. This method solves the general N-by-N system Ax = b where A is symmetric cyclic tridiagonal (N >= 3). The form of A for the 4-by-4 case is:

     [ d0  e0  0   e3 ]
 A = [ e0  d1  e1  0  ]
     [ 0   e1  d2  e2 ]
     [ e3  0   e2  d3 ]
 

Parameters:

d - (input) Vector of diagonal elements. Length N must be >= 3.

e - (input) Vector of off-diagonal elements. Length must be N.

b - (input) Vector of right hand side elements. Length must be N.

x - (output) Solution vector. Length must be N.

Throws:

java.lang.NullPointerException - (unchecked exception) Thrown if any argument is null.

java.lang.IllegalArgumentException - (unchecked exception) Thrown if any argument is the wrong length.

DomainException - (unchecked exception) Thrown if the linear system cannot be solved.