Chebyshev1EvalSum

Evaluate the finite sum of Chebyshev1 polynomials at point x.

Interface 1

܀ Interface

INTERFACE
  MODULE PURE FUNCTION Chebyshev1EvalSum(n, x, coeff) &
    & RESULT(ans)
    INTEGER(I4B), INTENT(IN) :: n
    !! order of polynomial
    REAL(DFP), INTENT(IN) :: x
    !! point
    REAL(DFP), INTENT(IN) :: coeff(0:n)
    !! Coefficient of finite sum, size = n+1
    REAL(DFP) :: ans
    !! Evaluate Chebyshev1 polynomial of order n at point x
  END FUNCTION Chebyshev1EvalSum
END INTERFACE

️܀ See example

program main
  use easifembase
  implicit none
  integer( i4b ) :: n
  real( dfp ), allocatable :: ans(:), x(:), exact(:), &
    & coeff(:)
  real( dfp ), parameter :: tol=1.0E-10
  type(string) :: astr
  n = 3
  x = [-0.5, 0.5, 0.25]
  coeff = [1, 0, 0, 0]
  ans = Chebyshev1EvalSum( n=n, x=x, coeff=coeff )
  exact = Chebyshev1Eval( n=0_I4B, x=x )
  call ok( ALL(SOFTEQ(ans, exact, tol )))
  n = 3
  x = [-0.5, 0.5, 0.25]
  coeff = [0, 0, 0, 1]
  ans = Chebyshev1EvalSum( n=n, x=x, coeff=coeff )
  exact = Chebyshev1Eval( n=3_I4B, x=x)
  call ok( ALL(SOFTEQ(ans, exact, tol )))
  n = 100
  x = [-0.5, 0.5, 0.25]
  coeff = zeros(n+1, 0.0_DFP)
  coeff( n+1 ) = 1.0_DFP
  ans = Chebyshev1EvalSum( n=n, x=x, coeff=coeff )
  exact = Chebyshev1Eval( n=n, x=x )
  call ok( ALL(SOFTEQ(ans, exact, tol )))
end program main

↢

Interface 2

܀ Interface

INTERFACE
  MODULE PURE FUNCTION Chebyshev1EvalSum(n, x, coeff) RESULT(ans)
    INTEGER(I4B), INTENT(IN) :: n
    !! order of polynomial
    REAL(DFP), INTENT(IN) :: x(:)
    !! point
    REAL(DFP), INTENT(IN) :: coeff(0:n)
    !! Coefficient of finite sum, size = n+1
    REAL(DFP) :: ans(SIZE(x))
    !! Evaluate Chebyshev1 polynomial of order n at point x
  END FUNCTION Chebyshev1EvalSum
END INTERFACE

️܀ See example

See above example.

↢