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scalation/scalation/scalation.calculus/DBasisFunction

DBasisFunction

scalation.calculus.DBasisFunction
See theDBasisFunction companion object
trait DBasisFunction extends BasisFunction

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

Attributes

Companion
object
Graph
Supertypes
class Object
trait Matchable
class Any
Known subtypes
class DB_Spline
class DFourier
class DRadial

Members list

Value members

Abstract 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

Concrete methods

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

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

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

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

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

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 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 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 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
def recomputeCache: Unit

Recompute cached matrices.

Recompute cached matrices.

Attributes

Inherited from:
BasisFunction

Inherited and Abstract methods

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. 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 getOrder: Int

Retrieve the order of the Basis function.

Retrieve the order of the Basis function.

Attributes

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

The range of basis functions for a specified order.

The range of basis functions for a specified order.

Value parameters

m

the order of the basis function

Attributes

Inherited from:
BasisFunction
def size(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
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