LobattoGradientEval

Evaluate gradient of Lobatto polynomials.

Interface 1

܀ Interface

INTERFACE
  MODULE PURE FUNCTION LobattoGradientEval(n, x) RESULT(ans)
    INTEGER(I4B), INTENT(IN) :: n
    REAL(DFP), INTENT(IN) :: x
    REAL(DFP) :: ans
  END FUNCTION LobattoGradientEval
END INTERFACE

️܀ See example

This example shows the usage of LobattoGradientEval method.

This routine evaluates gradient of Lobatto polynomial of order n, at single point

program main
  use easifembase
  implicit none
  integer( i4b ) :: n
  real( dfp ) :: ans, x, exact
  real( dfp ), parameter :: tol=1.0E-8
  n = 5
  x = -1.0_DFP; call callme
  exact = SQRT(9.0_DFP/2.0_DFP)*(35.0*x**4 - 30.0*x**2 + 3.0)/8.0
  call ok( SOFTEQ(ans, exact, tol ))
  x = 0.0_DFP; call callme
  exact = SQRT(9.0_DFP/2.0_DFP)*(35.0*x**4 - 30.0*x**2 + 3.0)/8.0
  call ok( SOFTEQ(ans, exact, tol ))
  x = +1.0_DFP; call callme
  exact = SQRT(9.0_DFP/2.0_DFP)*(35.0*x**4 - 30.0*x**2 + 3.0)/8.0
  contains
  subroutine callme
    ans= LobattoGradientEval( n=n, x=x )
  end subroutine callme
end program main

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Interface 2

܀ Interface

INTERFACE
  MODULE PURE FUNCTION LobattoGradientEval(n, x) RESULT(ans)
    INTEGER(I4B), INTENT(IN) :: n
    REAL(DFP), INTENT(IN) :: x(:)
    REAL(DFP) :: ans(1:SIZE(x))
  END FUNCTION LobattoGradientEval
END INTERFACE

️܀ See example

This example shows the usage of LobattoEvalAll method.

This routine evaluates Lobatto polynomial upto order n, for many points.

program main
  use easifembase
  implicit none
  integer( i4b ) :: n
  real( dfp ), allocatable :: ans( : ), x
  type(string) :: astr

  x = -1.0_DFP
  n = 5; call callme

l0	l1	l2	l3	l4	l5
1	0	0	0	0	0

  x = 1.0_DFP
  n = 5; call callme

l0	l1	l2	l3	l4	l5
0	1	0	0	0	0

  x = 0.5_DFP
  n = 5; call callme

l0	l1	l2	l3	l4	l5
0.25	0.75	-0.45928	-0.29646	-4.38475E-02	0.1243

  contains
  subroutine callme
    ans= LobattoEvalAll( n=n, x=x )
    astr = MdEncode( ans )
    call display( astr%chars(), "" )
  end subroutine callme

end program main

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