Chebyshev1Transform

Discrete Chebyshev1 transform.

Interface 1

܀ Interface

INTERFACE
  MODULE PURE FUNCTION Chebyshev1Transform(n, coeff, x, w, &
    &  quadType) RESULT(ans)
    INTEGER(I4B), INTENT(IN) :: n
    !! order of jacobi polynomial
    REAL(DFP), INTENT(IN) :: coeff(0:n)
    !! nodal value (at quad points)
    REAL(DFP), INTENT(IN) :: x(0:n)
    !! quadrature points
    REAL(DFP), INTENT(IN) :: w(0:n)
    !! weights
    INTEGER(I4B), INTENT(IN) :: quadType
    !! Quadrature type, Gauss, GaussLobatto, GaussRadau, GaussRadauLeft
    !! GaussRadauRight
    REAL(DFP) :: ans(0:n)
    !! modal values  or coefficients
  END FUNCTION Chebyshev1Transform
END INTERFACE

️܀ See example

• This example shows the usage of Chebyshev1Transform method.
• This routine performs the forward Chebyshev1 transform.

program main
  use easifembase
  implicit none
  integer( i4b ) :: n
  real(dfp), allocatable :: uhat(:), u( : ), pt( : ), &
    & wt(:), exact(:), error(:,:)
  real( dfp ), parameter :: tol=1.0E-10
  type(string) :: astr
  integer( i4b ), parameter :: quadType = GaussLobatto
  n = 10
  call reallocate( pt, n+1, wt, n+1 )
  call Chebyshev1Quadrature( n=n+1, pt=pt, wt=wt, &
    & quadType=quadType )
  u = Chebyshev1Eval(n=5_I4B, x=pt)
  uhat = Chebyshev1Transform(n=n, coeff=u, x=pt, w=wt, &
    & quadType=quadType)
  uhat( 6 ) = uhat( 6 ) - 1.0_dFP
  CALL ok( SOFTEQ( NORM2(uhat), 0.0_DFP, tol), "test"  )
  n = 10
  call reallocate( pt, n+1, wt, n+1, exact, n+1 )
  call Chebyshev1Quadrature( n=n+1, &
    & pt=pt, wt=wt, quadType=quadType )
  !u = 1.0 / (1.0 + 16.0*pt**2)
  u = 1.0*pt + 2.0*pt**2
  uhat = Chebyshev1Transform(n=n, &
    & coeff=u, x=pt, w=wt, quadType=quadType)
  exact(1:3) = 1.0_DFP
  call ok( ALL(SOFTEQ(exact, uhat, tol)), "n=10 "//CHAR_LF)
end program main

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Interface 2

܀ Interface

INTERFACE
  MODULE PURE FUNCTION Chebyshev1Transform(n, coeff, x, w, &
    & quadType) RESULT(ans)
    INTEGER(I4B), INTENT(IN) :: n
    !! order of polynomial
    REAL(DFP), INTENT(IN) :: coeff(0:, 1:)
    !! nodal value (at quad points)
    REAL(DFP), INTENT(IN) :: x(0:n)
    !! quadrature points
    REAL(DFP), INTENT(IN) :: w(0:n)
    !! weights
    INTEGER(I4B), INTENT(IN) :: quadType
    !! Quadrature type, Gauss, GaussLobatto, GaussRadau, GaussRadauLeft
    !! GaussRadauRight
    REAL(DFP) :: ans(0:n, 1:SIZE(coeff, 2))
    !! modal values  or coefficients for each column of val
  END FUNCTION Chebyshev1Transform
END INTERFACE

️܀ See example

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Interface 3

܀ Interface

INTERFACE
  MODULE FUNCTION Chebyshev1Transform(n, f, quadType) &
    & RESULT(ans)
    INTEGER(I4B), INTENT(IN) :: n
    !! order of jacobi polynomial
    PROCEDURE(iface_1DFunction), POINTER, INTENT(IN) :: f
    !! 1D space function
    INTEGER(I4B), INTENT(IN) :: quadType
    !! Quadrature type, Gauss, GaussLobatto, GaussRadau, GaussRadauLeft
    !! GaussRadauRight
    REAL(DFP) :: ans(0:n)
    !! modal values  or coefficients
  END FUNCTION Chebyshev1Transform
END INTERFACE

️܀ See example

• This example shows the usage of Chebyshev1Transform method.
• This routine performs the forward Chebyshev1 transform.

program main
  use easifembase
  implicit none
  integer( i4b ) :: n
  real(dfp), allocatable :: uhat(:), u( : ), pt( : ), &
    & wt(:), exact(:), error(:,:)
  real( dfp ), parameter :: tol=1.0E-10
  type(string) :: astr
  integer( i4b ), parameter :: quadType = Gauss
  n = 10
  call reallocate( pt, n+1, wt, n+1 )
  call Chebyshev1Quadrature( n=n+1, pt=pt, wt=wt, &
    & quadType=quadType )
  u = Chebyshev1Eval(n=5_I4B, x=pt)
  uhat = Chebyshev1Transform(n=n, coeff=u, x=pt, w=wt, &
    & quadType=quadType)
  uhat( 6 ) = uhat( 6 ) - 1.0_dFP
  CALL ok( SOFTEQ( NORM2(uhat), 0.0_DFP, tol), "test"  )
  n = 10
  call reallocate( pt, n+1, wt, n+1, exact, n+1 )
  call Chebyshev1Quadrature( n=n+1, &
    & pt=pt, wt=wt, quadType=quadType )
  !u = 1.0 / (1.0 + 16.0*pt**2)
  u = 1.0*pt + 2.0*pt**2
  uhat = Chebyshev1Transform(n=n, &
    & coeff=u, x=pt, w=wt, quadType=quadType)
  exact(1:3) = 1.0_DFP
  call ok( ALL(SOFTEQ(exact, uhat, tol)), "n=10 "//CHAR_LF)
end program main

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