LegendreJacobiMatrix

Legendre matrix for Jacobi polynomials.

Examples

܀ Interface
️܀ See example
↢

INTERFACE
  MODULE PURE SUBROUTINE LegendreJacobiMatrix(n, D, E, alphaCoeff, betaCoeff)
    INTEGER(I4B), INTENT(IN) :: n
    !! n should be greater than or equal to 1
    REAL(DFP), INTENT(OUT) :: D(:)
    !! the size should be 1:n
    REAL(DFP), INTENT(OUT) :: E(:)
    !! the size should be 1:n-1
    REAL(DFP), OPTIONAL, INTENT(OUT) :: alphaCoeff(0:)
    !! recurrence coefficient of monic legendre polynomial, from 0 to n-1
    REAL(DFP), OPTIONAL, INTENT(OUT) :: betaCoeff(0:)
    !! recurrence coefficient of monic legendre polynomial, from 0 to n-1
  END SUBROUTINE LegendreJacobiMatrix
END INTERFACE

program main
use easifemBase
implicit none

INTEGER( I4B ), parameter :: n = 5
REAL( DFP ) :: D(n), E(n), alphaCoeff(n), betaCoeff(n)
CALL JacobiJacobiMatrix(n, 0.0_DFP, 0.0_DFP, D, E, alphaCoeff, betaCoeff)
CALL Display(D, "D: ")
CALL Display(E, "E: ")
CALL Display(alphaCoeff, "alphaCoeff: ")
CALL Display(betaCoeff, "betaCoeff: ")
end program main

See results

results
  D:   
-------
0.00000
0.00000
0.00000
0.00000
0.00000

  E:   
-------
0.57735
0.51640
0.50709
0.50395
0.00000

alphaCoeff: 
------------
  0.00000   
  0.00000   
  0.00000   
  0.00000   
  0.00000   

betaCoeff: 
-----------
  2.00000  
  0.33333  
  0.26667  
  0.25714  
  0.25397

Examples​

Examples