scalation
API
Generated with
scalation/scalation/scalation.calculus

scalation.calculus

package scalation.calculus

Members list

Type members

Classlikes

class AutoDiff(y: MatrixD)

The AutoDiff class supports Automatic Differentiation.

The AutoDiff class supports Automatic Differentiation.

Attributes

Supertypes
class Object
trait Matchable
class Any
class B_Spline(ττ: VectorD, mMax: Int, clamp: Boolean) extends BasisFunction

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.

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.

Value parameters

clamp

flag for augmenting ττ

mMax

the maximum order, allowing splines orders from 1 to mMax

ττ

the time-points of the original knots in the time dimension

Attributes

See also
Companion
object
Supertypes
class Object
trait Matchable
class Any
Known subtypes
class DB_Spline
object B_Spline

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

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

Attributes

Companion
class
Supertypes
class Object
trait Matchable
class Any
Self type
B_Spline.type
object BasisFunction

The BasisFunction object provides utility functions related to basis functions.

The BasisFunction object provides utility functions related to basis functions.

Attributes

Companion
trait
Supertypes
class Object
trait Matchable
class Any
Self type
trait BasisFunction

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.

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.

Attributes

Companion
object
Supertypes
class Object
trait Matchable
class Any
Known subtypes
class B_Spline
class DB_Spline
class DFourier
class DRadial
class Fourier
class Radial
Show all
class DB_Spline(ττ: VectorD, mMax: Int, clamp: Boolean) extends B_Spline, 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. 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.

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.

Value parameters

clamp

whether or not to clamp the ends of the knot vector using B_Spline.clamp

mMax

the maximum order, allowing splines orders from 1 to mMax

ττ

the time-points of the original knots in the time dimension

Attributes

See also
Supertypes
class B_Spline
class Object
trait Matchable
class Any
Show all
object DBasisFunction

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

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

Attributes

Companion
trait
Supertypes
class Object
trait Matchable
class Any
Self type
trait DBasisFunction extends BasisFunction

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

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

Attributes

Companion
object
Supertypes
class Object
trait Matchable
class Any
Known subtypes
class DB_Spline
class DFourier
class DRadial
class DFourier(w: Double, mMax: Int) extends Fourier, DBasisFunction

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

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

Value parameters

mMax

the number of sin/cos pairs to be used in the basis function

w

the fundamental frequency parameter

Attributes

See also

en.wikipedia.org/wiki/Fourier_series

Supertypes
class Fourier
class Object
trait Matchable
class Any
Show all
class DRadial(centers: VectorD, radialType_: RadialType, `γ_`: Double, k_: Int) extends Radial, DBasisFunction

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

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

Value parameters

centers

a list of centers

k_

the polynomial power of the radius used in Poly Harmonic Spline

radialType_

the type of the Radial Basis Function to be used

γ_

shape parameter

Attributes

Supertypes
class Radial
class Object
trait Matchable
class Any
Show all
object Differential

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

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

Attributes

Supertypes
class Object
trait Matchable
class Any
Self type
class Fourier(w: Double, mMax: Int) extends BasisFunction

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

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

Value parameters

mMax

the number of sin/cos pairs to be used in the basis function

w

the fundamental frequency parameter

Attributes

See also

en.wikipedia.org/wiki/Fourier_series

Supertypes
class Object
trait Matchable
class Any
Known subtypes
class DFourier
class GaussianFunc(a: Double, b: Double, c: Double)

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.

Value parameters

a

the height parameter of the Gaussian function

b

the position parameter of the Gaussian function

c

the width parameter of the Gaussian function

Attributes

See also

en.wikipedia.org/wiki/Gaussian_function

Supertypes
class Object
trait Matchable
class Any
case class Hilbert(f: FunctionS2S)

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

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

Value parameters

f

the function to convert into a Hilbert function

Attributes

Supertypes
trait Serializable
trait Product
trait Equals
class Object
trait Matchable
class Any
Show all
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.

Attributes

See also

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

Supertypes
class Object
trait Matchable
class Any
Self type
Integral.type
case class Node(v_dim2: Int, b: MatrixD, u: MatrixD, f: AFF)

The Node case class maintains information about a node in a Computation Graph.

The Node case class maintains information about a node in a Computation Graph.

Value parameters

b

the parameter matrix (weight => multiply, bias => add)

f

the activation function family or null for none

u

the input vector

v_dim2

the output second dimension

Attributes

Supertypes
trait Serializable
trait Product
trait Equals
class Object
trait Matchable
class Any
Show all
case class Poly(c: VectorD, x: String)

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.

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.

Value parameters

c

the coefficients of the polynomial

x

the variable/indeterminate of the polynomial

Attributes

See also

`MPoly' for multivariate polynomials.

Companion
object
Supertypes
trait Serializable
trait Product
trait Equals
class Object
trait Matchable
class Any
Show all
object Poly

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

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

Attributes

Companion
class
Supertypes
trait Product
trait Mirror
class Object
trait Matchable
class Any
Self type
Poly.type
class Radial(centers: VectorD, var radialType: RadialType, var γ: Double, var k: Int) extends BasisFunction

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

Value parameters

centers

a list of centers

k

the polynomial power of the radius used in Poly Harmonic Spline

radialType

the type of the Radial Basis Function to be used

γ

shape parameter

Attributes

Supertypes
class Object
trait Matchable
class Any
Known subtypes
class DRadial
enum RadialType

Enumerations defining various Basis Functions to be used

Enumerations defining various Basis Functions to be used

Attributes

Supertypes
trait Enum
trait Serializable
trait Product
trait Equals
class Object
trait Matchable
class Any
Show all
final class autoDiffTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class autoDiffTest2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class b_SplineTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class b_SplineTest2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class b_SplineTest3

Attributes

Supertypes
class Object
trait Matchable
class Any
final class b_SplineTest4

Attributes

Supertypes
class Object
trait Matchable
class Any
final class dB_SplineTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class dB_SplineTest2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class dFourierTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class dRadialTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class differentialTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class differentialTest2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class fourierTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class hilbertTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class integralTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class integralTest2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class polyTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class radialTest

Attributes

Supertypes
class Object
trait Matchable
class Any

Value members

Concrete methods

def autoDiffTest(): Unit

The autoDiffTest main function tests the AutoDiff class. Compare to the step-by-step results for Perceptron.

The autoDiffTest main function tests the AutoDiff class. Compare to the step-by-step results for Perceptron.

Attributes

See also

scalation.modeling.neuralnet.neuralNet_3LTest

runMain scalation.calculus.autoDiffTest

def autoDiffTest2(): Unit

The autoDiffTest2 main function tests the AutoDiff class. Compare to the step-by-step results for NeuralNet_3L.

The autoDiffTest2 main function tests the AutoDiff class. Compare to the step-by-step results for NeuralNet_3L.

Attributes

See also

scalation.modeling.neuralnet.neuralNet_3LTest11 FIX: values up to delta0 are correct, delta0 has one column in AutoDiff, but 2 in NeuralNet_3L

runMain scalation.calculus.autoDiffTest2

def b_SplineTest(): Unit

The b_SplineTest object is used to test the B_Spline class. It tests the B-Spline functions using the general recurrence.

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

Attributes

def b_SplineTest2(): Unit

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.

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

Attributes

def b_SplineTest3(): Unit

The b_SplineTest3 object is used to test the B_Spline class. It tests the B-Spline functions using the general recurrence.

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

Attributes

def b_SplineTest4(): Unit

The b_SplineTest4 object is used to test the B_Spline class. It tests the B-Spline functions using the general recurrence.

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

Attributes

def dB_SplineTest(): Unit

The dB_SplineTest main function is used to test the DB_Spline class. Here, we compute the penalty matrix for a ridge regression.

The dB_SplineTest main function is used to test the DB_Spline class. Here, we compute the penalty matrix for a ridge regression.

runMain scalation.caculus.dB_SplineTest

Attributes

def dB_SplineTest2(): Unit

The dB_SplineTest2 main function is used to test the DB_Spline class. Here, we smooth functional data manually with a roughness penalty.

The dB_SplineTest2 main function is used to test the DB_Spline class. Here, we smooth functional data manually with a roughness penalty.

Attributes

See also

Ramsay et al. page 86

runMain scalation.caculus.dB_SplineTest2

def dFourierTest(): Unit

The dFourierTest object is used to test the DFourier class.

The dFourierTest object is used to test the DFourier class.

runMain scalation.calculus.dFourierTest

Attributes

def dRadialTest(): Unit

The dRadialTest main function is used to test the DRadial class.

The dRadialTest main function is used to test the DRadial class.

runMain scalation.calculus.dRadialTest

Attributes

def differentialTest(): Unit

The differentialTest main function is used to test the Differential object.

The differentialTest main function is used to test the Differential object.

runMain scalation.calculus.differentialTest

Attributes

def differentialTest2(): Unit

The differentialTest2 main function 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 main function 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.

Attributes

See also

www.rose-hulman.edu/~bryan/lottamath/diffgrad.pdf

runMain scalation.calculus.differentialTest2

def fourierTest(): Unit

The fourierTest main function is used to test the Fourier class.

The fourierTest main function is used to test the Fourier class.

runMain scalation.calculus.fourierTest

Attributes

def functionS2S2Hilbert(f: FunctionS2S): Hilbert

Convert a function from FunctionS2S to Hilbert, which supports functional operators.

Convert a function from FunctionS2S to Hilbert, which supports functional operators.

Value parameters

f

the function to turn into a Hilbert function

Attributes

def hilbertTest(): Unit

The hilbertTest main function is used to test the Hilbert class.

The hilbertTest main function is used to test the Hilbert class.

runMain scalation.calculus.hilbertTest

Attributes

def integralTest(): Unit

The integralTest2 main function tests the numerical integrators on simple problems. Easy problems.

The integralTest2 main function tests the numerical integrators on simple problems. Easy problems.

runMain scalation.calculus.integralTest

Attributes

def integralTest2(): Unit

The integralTest2 main function tests the numerical integrators using the Gauss function that has no analytic solution. Hard problem.

The integralTest2 main function tests the numerical integrators using the Gauss function that has no analytic solution. Hard problem.

runMain scalation.calculus.integralTest2

Attributes

def polyTest(): Unit

The polyTest main function is used to test the Poly class.

The polyTest main function is used to test the Poly class.

runMain scalation.calculus.polyTest

Attributes

def radialTest(): Unit

The radialTest main function is used to test the Radial class.

The radialTest main function is used to test the Radial class.

runMain scalation.calculus.radialTest

Attributes

Generated with