LaguerreSolver (Apache Commons Math 3.6.1 API)

org.apache.commons.math3.analysis.solvers

## Class LaguerreSolver

- java.lang.Object
- - org.apache.commons.math3.analysis.solvers.BaseAbstractUnivariateSolver<PolynomialFunction>
  - - org.apache.commons.math3.analysis.solvers.AbstractPolynomialSolver
    - - org.apache.commons.math3.analysis.solvers.LaguerreSolver

- All Implemented Interfaces:
    BaseUnivariateSolver<PolynomialFunction>, PolynomialSolver

      public class LaguerreSolver
      extends AbstractPolynomialSolver

  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. The algorithm requires a bracketing condition.
  Since:
    1.2

- - ### Constructor Summary

    Constructors
    Constructor and Description
    `LaguerreSolver()` Construct a solver with default accuracy (1e-6).
    `LaguerreSolver(double absoluteAccuracy)` Construct a solver.
    `LaguerreSolver(double relativeAccuracy, double absoluteAccuracy)` Construct a solver.
    `LaguerreSolver(double relativeAccuracy, double absoluteAccuracy, double functionValueAccuracy)` Construct a solver.

  - ### Method Summary

    Methods
    Modifier and Type | Method and Description
    --- | ---
    `double` | `doSolve()` Method for implementing actual optimization algorithms in derived classes.
    `double` | `laguerre(double lo, double hi, double fLo, double fHi)` Deprecated. This method should not be part of the public API: It will be made private in version 4.0.
    `Complex[]` | `solveAllComplex(double[] coefficients, double initial)` Find all complex roots for the polynomial with the given coefficients, starting from the given initial value.
    `Complex[]` | `solveAllComplex(double[] coefficients, double initial, int maxEval)` Find all complex roots for the polynomial with the given coefficients, starting from the given initial value.
    `Complex` | `solveComplex(double[] coefficients, double initial)` Find a complex root for the polynomial with the given coefficients, starting from the given initial value.
    `Complex` | `solveComplex(double[] coefficients, double initial, int maxEval)` Find a complex root for the polynomial with the given coefficients, starting from the given initial value.

    - ### Methods inherited from class org.apache.commons.math3.analysis.solvers.AbstractPolynomialSolver

      `getCoefficients, setup`

    - ### Methods inherited from class org.apache.commons.math3.analysis.solvers.BaseAbstractUnivariateSolver

      `computeObjectiveValue, getAbsoluteAccuracy, getEvaluations, getFunctionValueAccuracy, getMax, getMaxEvaluations, getMin, getRelativeAccuracy, getStartValue, incrementEvaluationCount, isBracketing, isSequence, solve, solve, solve, verifyBracketing, verifyInterval, verifySequence`

    - ### Methods inherited from class java.lang.Object

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

    - ### Methods inherited from interface org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver

      `getAbsoluteAccuracy, getEvaluations, getFunctionValueAccuracy, getMaxEvaluations, getRelativeAccuracy, solve, solve, solve`

- - ### Constructor Detail

    - #### LaguerreSolver

          public LaguerreSolver()

      Construct a solver with default accuracy (1e-6).

    - #### LaguerreSolver

          public LaguerreSolver(double absoluteAccuracy)

      Construct a solver.
      Parameters:
        `absoluteAccuracy` - Absolute accuracy.

    - #### LaguerreSolver

          public LaguerreSolver(double relativeAccuracy,
                        double absoluteAccuracy)

      Construct a solver.
      Parameters:
        `relativeAccuracy` - Relative accuracy.
        `absoluteAccuracy` - Absolute accuracy.

    - #### LaguerreSolver

          public LaguerreSolver(double relativeAccuracy,
                        double absoluteAccuracy,
                        double functionValueAccuracy)

      Construct a solver.
      Parameters:
        `relativeAccuracy` - Relative accuracy.
        `absoluteAccuracy` - Absolute accuracy.
        `functionValueAccuracy` - Function value accuracy.

  - ### Method Detail

    - #### doSolve

          public double doSolve()
                         throws TooManyEvaluationsException,
                                NumberIsTooLargeException,
                                NoBracketingException

      Method for implementing actual optimization algorithms in derived classes.
      Specified by:
        `doSolve` in class `BaseAbstractUnivariateSolver<PolynomialFunction>`
      Returns:
        the root.
      Throws:
        `TooManyEvaluationsException` - if the maximal number of evaluations is exceeded.
        `NoBracketingException` - if the initial search interval does not bracket a root and the solver requires it.
        `NumberIsTooLargeException`

    - #### laguerre

          @Deprecated
          public double laguerre(double lo,
                                   double hi,
                                   double fLo,
                                   double fHi)

      Deprecated. This method should not be part of the public API: It will be made private in version 4.0.
      Find a real root in the given interval. Despite the bracketing condition, the root returned by `LaguerreSolver.ComplexSolver.solve(Complex[],Complex)` may not be a real zero inside `[min, max]`. For example, `p(x) = x3 + 1,` with `min = -2`, `max = 2`, `initial = 0`. When it occurs, this code calls `LaguerreSolver.ComplexSolver.solveAll(Complex[],Complex)` in order to obtain all roots and picks up one real root.
      Parameters:
        `lo` - Lower bound of the search interval.
        `hi` - Higher bound of the search interval.
        `fLo` - Function value at the lower bound of the search interval.
        `fHi` - Function value at the higher bound of the search interval.
      Returns:
        the point at which the function value is zero.

    - #### solveAllComplex

          public Complex[] solveAllComplex(double[] coefficients,
                                  double initial)
                                    throws NullArgumentException,
                                           NoDataException,
                                           TooManyEvaluationsException

      Find all complex roots for the polynomial with the given coefficients, starting from the given initial value.

      Note: This method is not part of the API of `BaseUnivariateSolver`.

      Parameters:
        `coefficients` - Polynomial coefficients.
        `initial` - Start value.
      Returns:
        the full set of complex roots of the polynomial
      Throws:
        `TooManyEvaluationsException` - if the maximum number of evaluations is exceeded when solving for one of the roots
        `NullArgumentException` - if the `coefficients` is `null`.
        `NoDataException` - if the `coefficients` array is empty.
      Since:
        3.1

    - #### solveAllComplex

          public Complex[] solveAllComplex(double[] coefficients,
                                  double initial,
                                  int maxEval)
                                    throws NullArgumentException,
                                           NoDataException,
                                           TooManyEvaluationsException

      Find all complex roots for the polynomial with the given coefficients, starting from the given initial value.

      Note: This method is not part of the API of `BaseUnivariateSolver`.

      Parameters:
        `coefficients` - polynomial coefficients
        `initial` - start value
        `maxEval` - maximum number of evaluations
      Returns:
        the full set of complex roots of the polynomial
      Throws:
        `TooManyEvaluationsException` - if the maximum number of evaluations is exceeded when solving for one of the roots
        `NullArgumentException` - if the `coefficients` is `null`
        `NoDataException` - if the `coefficients` array is empty
      Since:
        3.5

    - #### solveComplex

          public Complex solveComplex(double[] coefficients,
                             double initial)
                               throws NullArgumentException,
                                      NoDataException,
                                      TooManyEvaluationsException

      Find a complex root for the polynomial with the given coefficients, starting from the given initial value.

      Note: This method is not part of the API of `BaseUnivariateSolver`.

      Parameters:
        `coefficients` - Polynomial coefficients.
        `initial` - Start value.
      Returns:
        a complex root of the polynomial
      Throws:
        `TooManyEvaluationsException` - if the maximum number of evaluations is exceeded.
        `NullArgumentException` - if the `coefficients` is `null`.
        `NoDataException` - if the `coefficients` array is empty.
      Since:
        3.1

    - #### solveComplex

          public Complex solveComplex(double[] coefficients,
                             double initial,
                             int maxEval)
                               throws NullArgumentException,
                                      NoDataException,
                                      TooManyEvaluationsException

      Find a complex root for the polynomial with the given coefficients, starting from the given initial value.

      Note: This method is not part of the API of `BaseUnivariateSolver`.

      Parameters:
        `coefficients` - polynomial coefficients
        `initial` - start value
        `maxEval` - maximum number of evaluations
      Returns:
        a complex root of the polynomial
      Throws:
        `TooManyEvaluationsException` - if the maximum number of evaluations is exceeded
        `NullArgumentException` - if the `coefficients` is `null`
        `NoDataException` - if the `coefficients` array is empty
      Since:
        3.1

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