Package com.irurueta.numerical

Class ExponentialMatrixEstimator

java.lang.Object
com.irurueta.numerical.ExponentialMatrixEstimator
public class ExponentialMatrixEstimator extends Object
Estimates exponential of a square matrix. This is based on Gene H. Golub and Charles F. Van Loan. Matrix Computations. 3rd ed. 1996. p. 572

  • Field Summary

    Fields
    Modifier and Type
    Field
    Description
    private com.irurueta.algebra.Matrix
    as
    Scaled version of provided input matrix.
    private com.irurueta.algebra.Matrix
    cX
    Internal matrix reused for efficiency while provided input matrices keep the same size.
    private com.irurueta.algebra.Matrix
    d
    Denominator of Padé approximant.
    private com.irurueta.algebra.Matrix
    f
    Contains copy of estimated result.
    private final DoubleFactorialEstimator
    factorialEstimator
    Estimates factorial values.
    private com.irurueta.algebra.Matrix
    n
    Numerator of Padé approximant.
    private int
    rows
    Number of rows of matrix to be estimated.
    private com.irurueta.algebra.Matrix
    tmp
    Internal matrix reused for efficiency while provided input matrices keep the same size.
    static final double
    TOLERANCE
    Default error tolerance of estimated result element-wise.
    private com.irurueta.algebra.Matrix
    x
    Internal matrix reused for efficiency while provided input matrices keep the same size.

  • Constructor Summary

    Constructors
    Constructor
    Description
    ExponentialMatrixEstimator()
     

  • Method Summary

    Modifier and Type
    Method
    Description
    com.irurueta.algebra.Matrix
    exponential(com.irurueta.algebra.Matrix a)
    Estimates exponential of provided matrix with default error tolerance.
    com.irurueta.algebra.Matrix
    exponential(com.irurueta.algebra.Matrix a, double tolerance)
    Estimates exponential of provided matrix.
    void
    exponential(com.irurueta.algebra.Matrix a, com.irurueta.algebra.Matrix result)
    Estimates exponential of provided matrix with default error tolerance.
    void
    exponential(com.irurueta.algebra.Matrix a, com.irurueta.algebra.Matrix result, double tolerance)
    Estimates exponential of provided matrix.
    private int
    findQForRelativeError(double maxRelativeError)
    Finds required order of Padé approximant for provided maximum allowed relative error to be achieved.
    private int
    findQForTolerance(double tolerance, double normA)
    Finds required order of Padé approximant for provided absolute error tolerance to be achieved.
    private void
    initialize(int rows)
    Initializes matrices being reused as long as number of rows is preserved for multiple provided input matrices for efficiency purposes.
    private static double
    normmax(com.irurueta.algebra.Matrix a)
    Estimates infinite norm of provided matrix.
    private double
    relativeError(int p, int q)
    Estimates relative error achieved by this algorithm for provided input values.

    Methods inherited from class java.lang.Object

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

  • Field Details

    • TOLERANCE

      public static final double TOLERANCE
      Default error tolerance of estimated result element-wise. When this tolerance is used, algorithm achieves an error close to machine precision, but might be slightly larger than this value (which is about 1.1e-16).

    • factorialEstimator

      private final DoubleFactorialEstimator factorialEstimator
      Estimates factorial values.

    • rows

      private int rows
      Number of rows of matrix to be estimated. Every time the number of rows change, reused matrices are re-instantiated for computational efficiency.

    • as

      private com.irurueta.algebra.Matrix as
      Scaled version of provided input matrix. This instance is reused as long as provided input matrices keep the same size.

    • d

      private com.irurueta.algebra.Matrix d
      Denominator of Padé approximant. This is reused for efficiency while provided input matrices keep the same size.

    • n

      private com.irurueta.algebra.Matrix n
      Numerator of Padé approximant. This is reused for efficiency while provided input matrices keep the same size.

    • x

      private com.irurueta.algebra.Matrix x
      Internal matrix reused for efficiency while provided input matrices keep the same size.

    • tmp

      private com.irurueta.algebra.Matrix tmp
      Internal matrix reused for efficiency while provided input matrices keep the same size.

    • cX

      private com.irurueta.algebra.Matrix cX
      Internal matrix reused for efficiency while provided input matrices keep the same size.

    • f

      private com.irurueta.algebra.Matrix f
      Contains copy of estimated result. This is reused for efficiency while provided input matrices keep the same size.

  • Constructor Details

    • ExponentialMatrixEstimator

      public ExponentialMatrixEstimator()

  • Method Details

    • exponential

      public com.irurueta.algebra.Matrix exponential(com.irurueta.algebra.Matrix a) throws com.irurueta.algebra.AlgebraException
      Estimates exponential of provided matrix with default error tolerance. When this tolerance is used, algorithm achieves an error close to machine precision, but might be slightly larger than this value (which is about 1.1e-6).
      Parameters:
      a - matrix to be used for exponential estimation.
      Returns:
      estimated exponential matrix.
      Throws:
      com.irurueta.algebra.AlgebraException - if there are numerical errors.

    • exponential

      public com.irurueta.algebra.Matrix exponential(com.irurueta.algebra.Matrix a, double tolerance) throws com.irurueta.algebra.AlgebraException
      Estimates exponential of provided matrix. Larger tolerance than default one can be used to reduce computational complexity if less accuracy is required.
      Parameters:
      a - matrix to be used for exponential estimation.
      tolerance - maximum allowed absolute error tolerance element-wise.
      Returns:
      estimated exponential matrix.
      Throws:
      com.irurueta.algebra.AlgebraException - if there are numerical errors.

    • exponential

      public void exponential(com.irurueta.algebra.Matrix a, com.irurueta.algebra.Matrix result) throws com.irurueta.algebra.AlgebraException
      Estimates exponential of provided matrix with default error tolerance. When this tolerance is used, algorithm achieves an error close to machine precision, but might be slightly larger than this value (which is about 1.1e-6).
      Parameters:
      a - matrix to be used for exponential estimation.
      result - instance where result will be stored.
      Throws:
      com.irurueta.algebra.AlgebraException - if there are numerical errors.

    • exponential

      public void exponential(com.irurueta.algebra.Matrix a, com.irurueta.algebra.Matrix result, double tolerance) throws com.irurueta.algebra.AlgebraException
      Estimates exponential of provided matrix. Larger tolerance than default one can be used to reduce computational complexity if less accuracy is required.
      Parameters:
      a - matrix to be used for exponential estimation.
      result - instance where result will be stored.
      tolerance - maximum allowed absolute error tolerance element-wise.
      Throws:
      com.irurueta.algebra.AlgebraException - if there are numerical errors.

    • initialize

      private void initialize(int rows) throws com.irurueta.algebra.AlgebraException
      Initializes matrices being reused as long as number of rows is preserved for multiple provided input matrices for efficiency purposes.
      Parameters:
      rows - number of rows.
      Throws:
      com.irurueta.algebra.AlgebraException - if an error occurs during instantiation.

    • relativeError

      private double relativeError(int p, int q)
      Estimates relative error achieved by this algorithm for provided input values.
      Parameters:
      p - Padé approximant order of numerator.
      q - Padé approximant order of denominator.
      Returns:
      estimated relative error.

    • findQForRelativeError

      private int findQForRelativeError(double maxRelativeError)
      Finds required order of Padé approximant for provided maximum allowed relative error to be achieved.
      Parameters:
      maxRelativeError - maximum allowed relative error.
      Returns:
      Padé approximant order.

    • findQForTolerance

      private int findQForTolerance(double tolerance, double normA)
      Finds required order of Padé approximant for provided absolute error tolerance to be achieved.
      Parameters:
      tolerance - maximum allowed absolute error tolerance.
      normA - infinite norm (maximum absolute value) of provided matrix.
      Returns:
      Padé approximant order.

    • normmax

      private static double normmax(com.irurueta.algebra.Matrix a)
      Estimates infinite norm of provided matrix. Infinite norm is equivalent to the maximum absolute value of all matrix elements.
      Parameters:
      a - matrix to compute infinite norm for.
      Returns:
      estimated infinite norm.