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scalation/scalation/scalation.calculus/DFourier

DFourier

scalation.calculus.DFourier
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.

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

Graph
Supertypes
class Fourier
class Object
trait Matchable
class Any
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Members list

Value members

Concrete methods

def dnbf(n: Int)(m: Int)(j: Int)(t: Double): Double

Obtain the value of nth derivative of the m-th order 'j'-th basis function at time 't'. Or alternatively, obtain the nth derivative basis function by calling dnbf(n)(m)(j) only. Ex: val x = dnbf(n)(m)(j)(t) retrieves the nth derivative value of the j-th basis function at 't'. val f = dnbf(n)(m)(j) retrieves the nth derivative of the j-th basis function.

Obtain the value of nth derivative of the m-th order 'j'-th basis function at time 't'. Or alternatively, obtain the nth derivative basis function by calling dnbf(n)(m)(j) only. Ex: val x = dnbf(n)(m)(j)(t) retrieves the nth derivative value of the j-th basis function at 't'. val f = dnbf(n)(m)(j) retrieves the nth derivative of the j-th basis function.

Value parameters

j

indicates which basis function

m

the order of the basis function

n

the order of the derivative

t

the time parameter

Attributes

Inherited methods

def abf(m: Int)(t: VectorD): MatrixD

Obtain the value of the m-th order basis functions (all) at time 't'. Or alternatively, obtain the basis function by calling bf(m)(j) only. Ex: val x = bf(m)(t) retrieves the value of all the basis functions at 't'. val f = bf(m) retrieves all the basis functions.

Obtain the value of the m-th order basis functions (all) at time 't'. Or alternatively, obtain the basis function by calling bf(m)(j) only. Ex: val x = bf(m)(t) retrieves the value of all the basis functions at 't'. val f = bf(m) retrieves all the basis functions.

Value parameters

m

the order of all the basis function

t

the time parameter

Attributes

Inherited from:
BasisFunction
def abf_(m: Int)(t: Double): VectorD

Obtain the value of the m-th order basis functions (all) at time 't'. Or alternatively, obtain the basis function by calling bf(m)(j) only. Ex: val x = bf(m)(t) retrieves the value of all the basis functions at 't'. val f = bf(m) retrieves all the basis functions.

Obtain the value of the m-th order basis functions (all) at time 't'. Or alternatively, obtain the basis function by calling bf(m)(j) only. Ex: val x = bf(m)(t) retrieves the value of all the basis functions at 't'. val f = bf(m) retrieves all the basis functions.

Value parameters

m

the order of all the basis function

t

the time parameter

Attributes

Inherited from:
BasisFunction
def apply(m: Int)(j: Int)(t: Double): Double

Obtain the value of the m-th order 'j'-th basis function at time 't'. Or alternatively, obtain the basis function by calling bf(m)(j) only. Ex: val x = bf(m)(j)(t) retrieves the value of the j-th basis function at 't'. val f = bf(m)(j) retrieves the j-th basis function.

Obtain the value of the m-th order 'j'-th basis function at time 't'. Or alternatively, obtain the basis function by calling bf(m)(j) only. Ex: val x = bf(m)(j)(t) retrieves the value of the j-th basis function at 't'. val f = bf(m)(j) retrieves the j-th basis function.

Value parameters

j

indicates which basis function

m

the order of the basis function

t

the time parameter

Attributes

Inherited from:
BasisFunction
def bf(m: Int)(j: Int)(t: Double): Double

Obtain the value of the m-th order j-th basis function at time t. Or alternatively, obtain the basis function by calling bf(m)(j) only.

Obtain the value of the m-th order j-th basis function at time t. Or alternatively, obtain the basis function by calling bf(m)(j) only.

Value parameters

j

indicates which basis function

m

the order of the basis function

t

the time parameter

Attributes

Inherited from:
Fourier
def bf1(j: Int)(t: Double): Double

Obtain the value of the 1st order 'j'-th basis function at time 't'. Or alternatively, obtain the basis function by calling bf1(j) only. Ex: val x = bf1(j)(t) retrieves the value of the j-th basis function at 't'. val f = bf1(j) retrieves the j-th basis function.

Obtain the value of the 1st order 'j'-th basis function at time 't'. Or alternatively, obtain the basis function by calling bf1(j) only. Ex: val x = bf1(j)(t) retrieves the value of the j-th basis function at 't'. val f = bf1(j) retrieves the j-th basis function.

Value parameters

j

indicates which basis function

t

the time parameter

Attributes

Inherited from:
BasisFunction
def bf2(j: Int)(t: Double): Double

Obtain the value of the 2nd order 'j'-th basis function at time 't'. Or alternatively, obtain the basis function by calling bf2(j) only. Ex: val x = bf2(j)(t) retrieves the value of the j-th basis function at 't'. val f = bf2(j) retrieves the j-th basis function.

Obtain the value of the 2nd order 'j'-th basis function at time 't'. Or alternatively, obtain the basis function by calling bf2(j) only. Ex: val x = bf2(j)(t) retrieves the value of the j-th basis function at 't'. val f = bf2(j) retrieves the j-th basis function.

Value parameters

j

indicates which basis function

t

the time parameter

Attributes

Inherited from:
BasisFunction
def bf3(j: Int)(t: Double): Double

Obtain the value of the 3rd order 'j'-th basis function at time 't'. Or alternatively, obtain the basis function by calling bf3(j) only. Ex: val x = bf3(j)(t) retrieves the value of the j-th basis function at 't'. val f = bf3(j) retrieves the j-th basis function.

Obtain the value of the 3rd order 'j'-th basis function at time 't'. Or alternatively, obtain the basis function by calling bf3(j) only. Ex: val x = bf3(j)(t) retrieves the value of the j-th basis function at 't'. val f = bf3(j) retrieves the j-th basis function.

Value parameters

j

indicates which basis function

t

the time parameter

Attributes

Inherited from:
BasisFunction
def bf4(j: Int)(t: Double): Double

Obtain the value of the 4th order 'j'-th basis function at time 't'. Or alternatively, obtain the basis function by calling bf4(j) only. Ex: val x = bf4(j)(t) retrieves the value of the j-th basis function at 't'. val f = bf4(j) retrieves the j-th basis function.

Obtain the value of the 4th order 'j'-th basis function at time 't'. Or alternatively, obtain the basis function by calling bf4(j) only. Ex: val x = bf4(j)(t) retrieves the value of the j-th basis function at 't'. val f = bf4(j) retrieves the j-th basis function.

Value parameters

j

indicates which basis function

t

the time parameter

Attributes

Inherited from:
BasisFunction
def count(m: Int): Int

The number of basis functions for a specified order.

The number of basis functions for a specified order.

Value parameters

m

the order of the basis function

Attributes

Inherited from:
BasisFunction
def d1bf(m: Int)(j: Int)(t: Double): Double

Obtain the value of 1st derivative of the m-th order 'j'-th basis function at time 't'. Or alternatively, obtain the 1st derivative basis function by calling d1bf(m)(j) only. Ex: val x = d1bf(m)(j)(t) retrieves the 1st derivative value of the j-th basis function at 't'. val f = d1bf(m)(j) retrieves the 1st derivative of the j-th basis function.

Obtain the value of 1st derivative of the m-th order 'j'-th basis function at time 't'. Or alternatively, obtain the 1st derivative basis function by calling d1bf(m)(j) only. Ex: val x = d1bf(m)(j)(t) retrieves the 1st derivative value of the j-th basis function at 't'. val f = d1bf(m)(j) retrieves the 1st derivative of the j-th basis function.

Value parameters

j

indicates which basis function

m

the order of the basis function

t

the time parameter

Attributes

Inherited from:
DBasisFunction
def d2bf(m: Int)(j: Int)(t: Double): Double

Obtain the value of 2nd derivative of the m-th order 'j'-th basis function at time 't'. Or alternatively, obtain the 2nd derivative basis function by calling d2bf(m)(j) only. Ex: val x = d2bf(m)(j)(t) retrieves the 2nd derivative value of the j-th basis function at 't'. val f = d2bf(m)(j) retrieves the 2nd derivative of the j-th basis function.

Obtain the value of 2nd derivative of the m-th order 'j'-th basis function at time 't'. Or alternatively, obtain the 2nd derivative basis function by calling d2bf(m)(j) only. Ex: val x = d2bf(m)(j)(t) retrieves the 2nd derivative value of the j-th basis function at 't'. val f = d2bf(m)(j) retrieves the 2nd derivative of the j-th basis function.

Value parameters

j

indicates which basis function

m

the order of the basis function

t

the time parameter

Attributes

Inherited from:
DBasisFunction
def dnabf(n: Int)(m: Int)(t: VectorD): MatrixD

Obtain the value of nth derivative of the m-th order basis functions (all) at time 't'. Or alternatively, obtain the basis function by calling dnabf(m)(j) only. Ex: val x = dnabf(n)(m)(t) retrieves the nth derivative value of the value of all the basis functions at 't'. val f = dnabf(n)(m) retrieves the nth derivative value of all the basis functions.

Obtain the value of nth derivative of the m-th order basis functions (all) at time 't'. Or alternatively, obtain the basis function by calling dnabf(m)(j) only. Ex: val x = dnabf(n)(m)(t) retrieves the nth derivative value of the value of all the basis functions at 't'. val f = dnabf(n)(m) retrieves the nth derivative value of all the basis functions.

Value parameters

m

the order of all the basis function

n

the order of the derivative

t

the time parameter

Attributes

Inherited from:
DBasisFunction
def dnabf_(n: Int)(m: Int)(t: Double): VectorD

Obtain the value of nth derivative of the m-th order basis functions (all) at time 't'. Or alternatively, obtain the basis function by calling dnabf(m)(j) only. Ex: val x = dnabf(n)(m)(t) retrieves the nth derivative value of the value of all the basis functions at 't'. val f = dnabf(n)(m) retrieves the nth derivative value of all the basis functions.

Obtain the value of nth derivative of the m-th order basis functions (all) at time 't'. Or alternatively, obtain the basis function by calling dnabf(m)(j) only. Ex: val x = dnabf(n)(m)(t) retrieves the nth derivative value of the value of all the basis functions at 't'. val f = dnabf(n)(m) retrieves the nth derivative value of all the basis functions.

Value parameters

m

the order of all the basis function

n

the order of the derivative

t

the time parameter

Attributes

Inherited from:
DBasisFunction
def dot_(n: Int)(m: Int)(i: Int, j: Int)(g: DBasisFunction, a: Double, b: Double): Double

Compute the dot/inner product of nth derivative of 'this' basis function and that of basis function 'g'.

Compute the dot/inner product of nth derivative of 'this' basis function and that of basis function 'g'.

Value parameters

a

the start of the interval

b

the end of the interval

g

the other function

j

indicates which basis function

m

the order of the basis function

n

the order of the derivative

Attributes

Inherited from:
DBasisFunction
def dot_(m: Int)(i: Int, j: Int)(g: BasisFunction, a: Double, b: Double): Double

Compute the dot/inner product of 'this' basis function object and basis function 'g'.

Compute the dot/inner product of 'this' basis function object and basis function 'g'.

Value parameters

a

the start of the interval

b

the end of the interval

g

the other function

i

indicates which basis function of 'this'

j

indicates which basis function of 'g'

m

the order of the basis function

Attributes

Inherited from:
BasisFunction
override def getCache(m: Int, t: VectorD): Array[MatrixD]

Retrieves the cached design matrices and penalty matrices

Retrieves the cached design matrices and penalty matrices

Value parameters

m

the order of all the basis function

t

the time parameter

Attributes

Definition Classes
Inherited from:
DBasisFunction
def getOrder: Int

Retrieves the order of the this Fourier basis function

Retrieves the order of the this Fourier basis function

Attributes

Inherited from:
Fourier
def range(m: Int): Range

The range for the Fourier basis functions.

The range for the Fourier basis functions.

Value parameters

m

the order of the spline

Attributes

Inherited from:
Fourier
def recomputeCache: Unit

Recompute cached matrices.

Recompute cached matrices.

Attributes

Inherited from:
BasisFunction
def size(m: Int): Int

The number of usable Fourier basis functions for a specified order, including one constant term and 'm' sin/cos terms.

The number of usable Fourier basis functions for a specified order, including one constant term and 'm' sin/cos terms.

Value parameters

m

the order of the spline

Attributes

Inherited from:
Fourier
override def toString: String

String representation of the Fourier Basis Functions

String representation of the Fourier Basis Functions

Attributes

Definition Classes
Fourier -> Any
Inherited from:
Fourier
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