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AbstractOrthopol1D

AbstractOrthopol1D is an abstract class for orthogonal polynomials in one dimension.

info

AbstractOrthopol1D It is a child of AbstractBasis1D.

Structure​

TYPE, ABSTRACT,  EXTENDS( AbstractBasis1D_ ) :: &
  & AbstractOrthopol1D_
  PRIVATE
  INTEGER( I4B ) :: n = 0
    !! order of orthogonal polynomial
  REAL( DFP ) :: an_1= 0.0_DFP
    !! $\alpha_{n-1}$
  REAL( DFP ) :: bn_1 = 0.0_DFP
    !! $\beta_{n-1}$
  REAL( DFP ) :: sn_1 = 1.0_DFP
    !! scale for $Orthopol_{n-1}$
  REAL( DFP ) :: sn_2 = 1.0_DFP
    !! scale for $Orthopol_{n-2}$
  CLASS( AbstractOrthopol1D_ ), POINTER :: Jn_1 => NULL()
    !! Jacobi polynomial of order n-1
  CLASS( AbstractOrthopol1D_ ), POINTER :: Jn_2 => NULL()
    !! Jacobi polynomial of order n-2

ConstructorMethods​

Initiate​

Deallocate​

isInitiated​

IOMethods​

Display​

GetMethods​

GetJ1Pointer​

GetJn2Pointer​

GetOrder​

Eval​

Evaluate the polynomial at given point xx. If xx is a vector, the result will also be a vector. The interface is given below.

MODULE ELEMENTAL FUNCTION Eval( obj, x ) RESULT( ans )
  CLASS( AbstractOrthopol1D_ ), INTENT( IN ) :: obj
  REAL( DFP ), INTENT( IN ) :: x
  REAL( DFP ) :: ans
END FUNCTION Eval

P0​

Pm1​

dP0​

dPm1​

EvalGradient​

Evaluate the gradient of the polynomial at a given point. If the input argument is a vector then output argument will also be a vector. The interface is given below.

INTERFACE
MODULE ELEMENTAL FUNCTION EvalGradient( obj, x ) &
  & RESULT( ans )
  CLASS( AbstractOrthopol1D_ ), INTENT( IN ) :: obj
  REAL( DFP ), INTENT( IN ) :: x
  REAL( DFP ) :: ans
END FUNCTION EvalGradient
END INTERFACE

BasisEval​

BasisEvalGradient​

GetStringToDisplay​

GetStringForUID​

Weight​

GetRecurrenceCoeff​

GetCoeffScale​

Zeros​

GaussQuadrature​

GaussLegendreQuadrature​

GaussLobattoQuadrature​

SetMethods​

SetParam​