Packages

  • package root
    Definition Classes
    root
  • package scalation
    Definition Classes
    root
  • package activity

    The activity package contains classes, traits and objects for activity-oriented simulation models (for example, Petri Nets).

    The activity package contains classes, traits and objects for activity-oriented simulation models (for example, Petri Nets).

    Definition Classes
    scalation
  • package analytics

    The analytics package contains classes, traits and objects for analytics.

    The analytics package contains classes, traits and objects for analytics.

    Definition Classes
    scalation
  • package animation

    The animation package contains classes, traits and objects for 2D animation of simulation objects.

    The animation package contains classes, traits and objects for 2D animation of simulation objects.

    Definition Classes
    scalation
  • package calculus

    The calculus package contains classes with methods for computing derivatives, gradient vectors, Jacobian matrices, integrals and basic operators in Functional Analysis.

    The calculus package contains classes with methods for computing derivatives, gradient vectors, Jacobian matrices, integrals and basic operators in Functional Analysis.

    Definition Classes
    scalation
  • B_Spline
  • B_SplineTest
  • B_SplineTest2
  • B_SplineTest3
  • B_SplineTest4
  • BasisFunction
  • DB_Spline
  • DB_SplineTest
  • DB_SplineTest2
  • DBasisFunction
  • DFourier
  • DFourierTest
  • DRadial
  • DRadialTest
  • Differential
  • DifferentialTest
  • DifferentialTest2
  • FFT
  • FFTTest
  • Fourier
  • FourierTest
  • GaussianFunc
  • Hilbert
  • HilbertTest
  • Integral
  • IntegralTest
  • IntegralTest2
  • Poly
  • PolyTest
  • Radial
  • RadialTest
  • RadialType
  • package dynamics

    The dynamics package contains classes, traits and objects for system dynamics simulations using Ordinary Differential Equations (ODEs).

    The dynamics package contains classes, traits and objects for system dynamics simulations using Ordinary Differential Equations (ODEs).

    Definition Classes
    scalation
  • package dynamics_pde

    The dynamics_pde package contains classes, traits and objects for system dynamics simulations using Partial Differential Equations 'PDE's.

    The dynamics_pde package contains classes, traits and objects for system dynamics simulations using Partial Differential Equations 'PDE's.

    Definition Classes
    scalation
  • package event

    The event package contains classes, traits and objects for event oriented simulation models (for example, event scheduling or event graphs).

    The event package contains classes, traits and objects for event oriented simulation models (for example, event scheduling or event graphs).

    Definition Classes
    scalation
  • package maxima

    The maxima package contains classes, traits and objects for optimization to find maxima.

    The maxima package contains classes, traits and objects for optimization to find maxima.

    Definition Classes
    scalation
  • package minima

    The minima package contains classes, traits and objects for optimization to find minima.

    The minima package contains classes, traits and objects for optimization to find minima.

    Definition Classes
    scalation
  • package model

    The model package contains a trait giving a template for models to follow.

    The model package contains a trait giving a template for models to follow.

    Definition Classes
    scalation
  • package process

    The process package contains classes, traits and objects for process-oriented simulation models (for example, process-interaction).

    The process package contains classes, traits and objects for process-oriented simulation models (for example, process-interaction).

    Definition Classes
    scalation
  • package queueingnet

    The queueingnet package contains classes, traits and objects for solving simple queueing network problems.

    The queueingnet package contains classes, traits and objects for solving simple queueing network problems.

    Definition Classes
    scalation
  • package state

    The state package contains classes, traits and objects for state-oriented simulation models (for example, Markov Chains).

    The state package contains classes, traits and objects for state-oriented simulation models (for example, Markov Chains).

    Definition Classes
    scalation
  • package tableau

    The tableau package contains classes for tableau oriented simulation models (similar to spreadsheet simulations).

    The tableau package contains classes for tableau oriented simulation models (similar to spreadsheet simulations).

    Definition Classes
    scalation
p

scalation

calculus

package calculus

The calculus package contains classes with methods for computing derivatives, gradient vectors, Jacobian matrices, integrals and basic operators in Functional Analysis.

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Type Members

  1. class B_Spline extends BasisFunction with Error

    The B_Spline class provides B-Spline basis functions for various orders 'm', where the order is one more than the degree.

    The B_Spline class provides B-Spline basis functions for various orders 'm', where the order is one more than the degree. A spline function is a piecewise polynomial function where the pieces are stitched together at knots with the goal of maintaining continuity and differentiability. B-Spline basis functions form a popular form of basis functions used in Functional Data Analysis.

    See also

    http://web.mit.edu/hyperbook/Patrikalakis-Maekawa-Cho/node17.html -----------------------------------------------------------------------------

  2. trait BasisFunction extends AnyRef

    The BasisFunction trait provides a common framework for various Basis Functions.

    The BasisFunction trait provides a common framework for various Basis Functions. They are a set of functions forming a basis whose orthogonal components form a function space. Two functions 'f' and 'g' are orthogonal if their inner product is 0, meaning <f, g> = 0.

  3. class DB_Spline extends B_Spline with DBasisFunction

    The DB_Spline class provides B-Spline basis functions with derivatives for various orders 'm', where the order is one more than the degree.

    The DB_Spline class provides B-Spline basis functions with derivatives for various orders 'm', where the order is one more than the degree. A spline function is a piecewise polynomial function where the pieces are stitched together at knots with the goal of maintaining continuity and differentability. B-Spline basis functions form a popular form of basis functions used in Functional Data Analysis.

    See also

    http://web.mit.edu/hyperbook/Patrikalakis-Maekawa-Cho/node17.html -----------------------------------------------------------------------------

  4. trait DBasisFunction extends BasisFunction

    The DBasisFunction trait provides a common framework for the derivatives of various Basis Functions.

  5. class DFourier extends Fourier with DBasisFunction

    The DFourier class provides Fourier basis functions with derivatives.

    The DFourier class provides Fourier basis functions with derivatives. Such basis functions are useful are useful for fitting periodic data in Functional Data Analysis.

    See also

    en.wikipedia.org/wiki/Fourier_series

  6. class DRadial extends Radial with DBasisFunction

    The DRadial class provides Radial basis functions with derivatives.

    The DRadial class provides Radial basis functions with derivatives. Such basis functions are useful are useful in Neural Networks and Support Vector Classification.

  7. class Fourier extends BasisFunction with Error

    The Fourier class provides Fourier basis functions.

    The Fourier class provides Fourier basis functions. Such basis functions are useful are useful for fitting periodic data in Functional Data Analysis.

    See also

    en.wikipedia.org/wiki/Fourier_series

  8. class GaussianFunc extends AnyRef

    The GaussianFunc class implements the Gaussian function, a generalization of the Gaussian/Normal distribution density function.

    The GaussianFunc class implements the Gaussian function, a generalization of the Gaussian/Normal distribution density function.

    See also

    en.wikipedia.org/wiki/Gaussian_function

  9. class Hilbert extends AnyRef

    The Hilbert class provides operators to add, subtract, mutiply, divide and raise functions.

    The Hilbert class provides operators to add, subtract, mutiply, divide and raise functions. Given two functions, 'f' and 'g', a new function is created. It also provides methods for computing dot/inner products, norms and distances for functions defined in Hilbert Space. On interval [a, b]

    Lp-norm (f) = [ ∫f(t)p dt ]1/p

    See also

    implicit conversion 'functionS2S2Hilbert' in package.scala

  10. type Interval = (Double, Double)

    Type definition for an interval [a, b]

  11. case class Poly(c: VectorD, x: String = "x") extends Product with Serializable

    The Poly class provides operations on univariate polynomials.

    The Poly class provides operations on univariate polynomials.

    Poly (2, 3) => 3 x + 2

    Note, reverse order of coefficients, i.e., coefficients for smallest terms first.

    c

    the coefficients of the polynomial

    x

    the variable/indeterminate of the polynomial

    See also

    MPoly' for multivariate polynomials.

  12. class Radial extends BasisFunction with Error

    The Radial class provides Radial basis functions.

    The Radial class provides Radial basis functions. Such basis functions are useful are useful in Neural Networks and Support Vector Classification. -----------------------------------------------------------------------------

Value Members

  1. def _0f(x: Double): Double

    Zero function.

  2. def _1f(x: Double): Double

    One function.

  3. implicit def functionS2S2Hilbert(f: FunctionS2S): Hilbert

    Implicit conversion from 'FunctionS2S' to 'Hilbert', which supports functional operators.

    Implicit conversion from 'FunctionS2S' to 'Hilbert', which supports functional operators.

    f

    the function to turn into a Hilbert function

  4. object B_Spline

    Companion object for B_Spline class provides functions for clamping the the ends of a spline and running timing benchmarks.

  5. object B_SplineTest extends App

    The B_SplineTest object is used to test the B_Spline class.

    The B_SplineTest object is used to test the B_Spline class. It tests the B-Spline functions using the general recurrence. > runMain scalation.calculus.B_SplineTest

  6. object B_SplineTest2 extends App

    The B_SplineTest2 object is used to test the B_Spline class.

    The B_SplineTest2 object is used to test the B_Spline class. It tests the B-Spline functions using the general recurrence and plots several basis functions using PlotM. > runMain scalation.calculus.B_SplineTest2

  7. object B_SplineTest3 extends App

    The B_SplineTest3 object is used to test the B_Spline class.

    The B_SplineTest3 object is used to test the B_Spline class. It tests the B-Spline functions using the general recurrence. > runMain scalation.calculus.B_SplineTest3

  8. object B_SplineTest4 extends App

    The B_SplineTest4 object is used to test the B_Spline class.

    The B_SplineTest4 object is used to test the B_Spline class. It tests the B-Spline functions using the general recurrence. > runMain scalation.calculus.B_SplineTest4

  9. object BasisFunction

    The BasisFunction object provides utility functions related to basis functions.

  10. object DB_SplineTest extends App

    The DB_SplineTest object is used to test the DB_Spline class.

    The DB_SplineTest object is used to test the DB_Spline class. Here, we compute the penalty matrix for a ridge regression. > runMain scalation.caculus.DB_SplineTest

  11. object DB_SplineTest2 extends App

    The DB_SplineTest2 object is used to test the DB_Spline class.

    The DB_SplineTest2 object is used to test the DB_Spline class. Here, we smooth functional data manually with a roughness penalty.

    See also

    Ramsay et al. page 86 > runMain scalation.caculus.DB_SplineTest2

  12. object DBasisFunction

    The DBasisFunction object provides utility functions related to derivatives of basis functions.

  13. object DFourierTest extends App

    The DFourierTest object is used to test the DFourier class.

    The DFourierTest object is used to test the DFourier class. > runMain scalation.calculus.DFourierTest

  14. object DRadialTest extends App

    The DRadialTest object is used to test the DRadial class.

    The DRadialTest object is used to test the DRadial class. > runMain scalation.calculus.DRadialTest

  15. object Differential

    The Differential object contains functions for computing derivatives, partial derivatives, Laplacians, gradient vectors, Hessian matrices and Jacobian matrices.

  16. object DifferentialTest extends App

    The DifferentialTest object is used to test the Differential object.

    The DifferentialTest object is used to test the Differential object. > runMain scalation.calculus.DifferentialTest

  17. object DifferentialTest2 extends App

    The DifferentialTest2 object is used to test the Differential object showing trade-offs of using 1-sided and 2-sided derivative approximations as well as different values for h.

    The DifferentialTest2 object is used to test the Differential object showing trade-offs of using 1-sided and 2-sided derivative approximations as well as different values for h.

    See also

    www.rose-hulman.edu/~bryan/lottamath/diffgrad.pdf > runMain scalation.calculus.DifferentialTest2

  18. object FFT

    The FFT object provides a method to transform a signal in the time domain (e.g., a times series) in its representation in the frequency domain.

    The FFT object provides a method to transform a signal in the time domain (e.g., a times series) in its representation in the frequency domain. The inverse transform is also provided.

  19. object FFTTest extends App

    The FFTTest is used to test the FFT object by starting with a signal in th4e time domain, converting it to its frequency domain representation and the converting it back to the time domain.

    The FFTTest is used to test the FFT object by starting with a signal in th4e time domain, converting it to its frequency domain representation and the converting it back to the time domain. > runMain scalation.calculus.FFTTest

  20. object FourierTest extends App

    The FourierTest object is used to test the Fourier class.

    The FourierTest object is used to test the Fourier class. > runMain scalation.calculus.FourierTest

  21. object HilbertTest extends App

    The HilbertTest object is used to test the Hilbert class.

    The HilbertTest object is used to test the Hilbert class. > runMain scalation.calculus.HilbertTest

  22. object Integral

    The Integral object provides implementations for five basic integration methods:

    The Integral object provides implementations for five basic integration methods:

    ∫f(x)dx on interval [a, b]

    trap - trapezoidal method - linear simpson - Simpson method - quadratic simpson38 - 3/8 Simpson method - cubic boole - Boole Method - quartic romberg - Romberg method - recursive, uses trap

    The first four are Composite Newton-Coates type integrators.

    See also

    en.wikipedia.org/wiki/Newton%E2%80%93Cotes_formulas

  23. object IntegralTest extends App

    The IntegralTest2 object tests the numerical integrators on simple problems.

    The IntegralTest2 object tests the numerical integrators on simple problems. Easy problems. > runMain scalation.calculus.IntegralTest

  24. object IntegralTest2 extends App

    The IntegralTest2 object tests the numerical integrators using the Gauss function that has no analytic solution.

    The IntegralTest2 object tests the numerical integrators using the Gauss function that has no analytic solution. Hard problem. > runMain scalation.calculus.IntegralTest2

  25. object Poly extends Serializable

    The Poly companion object provides factory methods for the 'Poly' class.

  26. object PolyTest extends App

    The PolyTest object is used to test the Poly class.

    The PolyTest object is used to test the Poly class. > runMain scalation.calculus.PolyTest

  27. object RadialTest extends App

    The RadialTest object is used to test the Radial class.

    The RadialTest object is used to test the Radial class. > runMain scalation.calculus.RadialTest

  28. object RadialType extends Enumeration

    Enumerations defining various Basis Functions to be used

Inherited from AnyRef

Inherited from Any

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