org.apache.commons.math.analysis.solvers

## Class LaguerreSolver

• All Implemented Interfaces:
UnivariateRealSolver, ConvergingAlgorithm

public class LaguerreSolver
extends UnivariateRealSolverImpl
Implements the Laguerre's Method for root finding of real coefficient polynomials. For reference, see A First Course in Numerical Analysis, ISBN 048641454X, chapter 8.

Laguerre's method is global in the sense that it can start with any initial approximation and be able to solve all roots from that point.

Since:
1.2
• ### Method Detail

• #### getPolynomialFunction

@Deprecated
public PolynomialFunction getPolynomialFunction()
Deprecated. as of 2.0 the function is not stored anymore within the instance.
Returns a copy of the polynomial function.
Returns:
a fresh copy of the polynomial function
• #### solve

@Deprecated
public double solve(double min,
double max)
throws ConvergenceException,
FunctionEvaluationException
Deprecated.
Solve for a zero root in the given interval.

A solver may require that the interval brackets a single zero root. Solvers that do require bracketing should be able to handle the case where one of the endpoints is itself a root.

Parameters:
min - the lower bound for the interval.
max - the upper bound for the interval.
Returns:
a value where the function is zero
Throws:
ConvergenceException - if the maximum iteration count is exceeded or the solver detects convergence problems otherwise.
FunctionEvaluationException - if an error occurs evaluating the function
• #### solve

@Deprecated
public double solve(double min,
double max,
double initial)
throws ConvergenceException,
FunctionEvaluationException
Deprecated.
Solve for a zero in the given interval, start at startValue.

A solver may require that the interval brackets a single zero root. Solvers that do require bracketing should be able to handle the case where one of the endpoints is itself a root.

Parameters:
min - the lower bound for the interval.
max - the upper bound for the interval.
initial - the start value to use
Returns:
a value where the function is zero
Throws:
ConvergenceException - if the maximum iteration count is exceeded or the solver detects convergence problems otherwise.
FunctionEvaluationException - if an error occurs evaluating the function
• #### solve

public double solve(int maxEval,
UnivariateRealFunction f,
double min,
double max,
double initial)
throws ConvergenceException,
FunctionEvaluationException
Find a real root in the given interval with initial value.

Requires bracketing condition.

Overrides:
solve in class UnivariateRealSolverImpl
Parameters:
f - function to solve (must be polynomial)
min - the lower bound for the interval
max - the upper bound for the interval
initial - the start value to use
maxEval - Maximum number of evaluations.
Returns:
the point at which the function value is zero
Throws:
ConvergenceException - if the maximum iteration count is exceeded or the solver detects convergence problems otherwise
FunctionEvaluationException - if an error occurs evaluating the function
java.lang.IllegalArgumentException - if any parameters are invalid
• #### solve

@Deprecated
public double solve(UnivariateRealFunction f,
double min,
double max,
double initial)
throws ConvergenceException,
FunctionEvaluationException
Deprecated. in 2.2 (to be removed in 3.0).
Find a real root in the given interval with initial value.

Requires bracketing condition.

Parameters:
f - function to solve (must be polynomial)
min - the lower bound for the interval
max - the upper bound for the interval
initial - the start value to use
Returns:
the point at which the function value is zero
Throws:
ConvergenceException - if the maximum iteration count is exceeded or the solver detects convergence problems otherwise
FunctionEvaluationException - if an error occurs evaluating the function
java.lang.IllegalArgumentException - if any parameters are invalid
• #### solve

public double solve(int maxEval,
UnivariateRealFunction f,
double min,
double max)
throws ConvergenceException,
FunctionEvaluationException
Find a real root in the given interval.

Despite the bracketing condition, the root returned by solve(Complex[], Complex) may not be a real zero inside [min, max]. For example, p(x) = x^3 + 1, min = -2, max = 2, initial = 0. We can either try another initial value, or, as we did here, call solveAll() to obtain all roots and pick up the one that we're looking for.

Overrides:
solve in class UnivariateRealSolverImpl
Parameters:
f - the function to solve
min - the lower bound for the interval
max - the upper bound for the interval
maxEval - Maximum number of evaluations.
Returns:
the point at which the function value is zero
Throws:
ConvergenceException - if the maximum iteration count is exceeded or the solver detects convergence problems otherwise
FunctionEvaluationException - if an error occurs evaluating the function
java.lang.IllegalArgumentException - if any parameters are invalid
• #### solve

@Deprecated
public double solve(UnivariateRealFunction f,
double min,
double max)
throws ConvergenceException,
FunctionEvaluationException
Deprecated. in 2.2 (to be removed in 3.0).
Find a real root in the given interval.

Despite the bracketing condition, the root returned by solve(Complex[], Complex) may not be a real zero inside [min, max]. For example, p(x) = x^3 + 1, min = -2, max = 2, initial = 0. We can either try another initial value, or, as we did here, call solveAll() to obtain all roots and pick up the one that we're looking for.

Parameters:
f - the function to solve
min - the lower bound for the interval
max - the upper bound for the interval
Returns:
the point at which the function value is zero
Throws:
ConvergenceException - if the maximum iteration count is exceeded or the solver detects convergence problems otherwise
FunctionEvaluationException - if an error occurs evaluating the function
java.lang.IllegalArgumentException - if any parameters are invalid
• #### solveAll

@Deprecated
public Complex[] solveAll(double[] coefficients,
double initial)
throws ConvergenceException,
FunctionEvaluationException
Deprecated. in 2.2.
Find all complex roots for the polynomial with the given coefficients, starting from the given initial value.
Parameters:
coefficients - the polynomial coefficients array
initial - the start value to use
Returns:
the point at which the function value is zero
Throws:
ConvergenceException - if the maximum iteration count is exceeded or the solver detects convergence problems otherwise
FunctionEvaluationException - if an error occurs evaluating the function
java.lang.IllegalArgumentException - if any parameters are invalid
• #### solveAll

@Deprecated
public Complex[] solveAll(Complex[] coefficients,
Complex initial)
throws MaxIterationsExceededException,
FunctionEvaluationException
Deprecated. in 2.2.
Find all complex roots for the polynomial with the given coefficients, starting from the given initial value.
Parameters:
coefficients - the polynomial coefficients array
initial - the start value to use
Returns:
the point at which the function value is zero
Throws:
MaxIterationsExceededException - if the maximum iteration count is exceeded or the solver detects convergence problems otherwise
FunctionEvaluationException - if an error occurs evaluating the function
java.lang.IllegalArgumentException - if any parameters are invalid
• #### solve

@Deprecated
public Complex solve(Complex[] coefficients,
Complex initial)
throws MaxIterationsExceededException,
FunctionEvaluationException
Deprecated. in 2.2.
Find a complex root for the polynomial with the given coefficients, starting from the given initial value.
Parameters:
coefficients - the polynomial coefficients array
initial - the start value to use
Returns:
the point at which the function value is zero
Throws:
MaxIterationsExceededException - if the maximum iteration count is exceeded or the solver detects convergence problems otherwise
FunctionEvaluationException - if an error occurs evaluating the function
java.lang.IllegalArgumentException - if any parameters are invalid