Chebyshev1EvalAll

Evaluate Chebyshev1 polynomials from order = 0 to n at single or several points.

Interface 1

܀ Interface

INTERFACE
  MODULE PURE FUNCTION Chebyshev1EvalAll(n, x) RESULT(ans)
    INTEGER(I4B), INTENT(IN) :: n
    !! Highest order of polynomial.
    !! Polynomials from 0 to n will be computed.
    REAL(DFP), INTENT(IN) :: x
    !! Point of evaluation, $x \in [-1, 1]$
    REAL(DFP) :: ans(n + 1)
    !! Evaluate Chebyshev1 polynomial of order = 0 to n (total n+1)
    !! at point x
  END FUNCTION Chebyshev1EvalAll
END INTERFACE

️܀ See example

program main
  use easifembase
  implicit none
  integer( i4b ) :: n
  real( dfp ), allocatable :: ans( : ), x
  type(string) :: astr
  x = 0.0_DFP
  n = 5
  ans= Chebyshev1EvalAll( n=n, x=x )
  astr = MdEncode( ans )
  call display( astr%chars(), "" )
end program main

P0	P1	P2	P3	P4	P5
1	0	-1	-0	1	0

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Interface 2

܀ Interface

INTERFACE
  MODULE PURE FUNCTION Chebyshev1EvalAll(n, x) RESULT(ans)
    INTEGER(I4B), INTENT(IN) :: n
    !! Highest order of polynomial.
    !! Polynomials from 0 to n will be computed.
    REAL(DFP), INTENT(IN) :: x(:)
    !! number of points, SIZE(x)=M
    REAL(DFP) :: ans(SIZE(x), n + 1)
    !! shape (M,N+1)
  END FUNCTION Chebyshev1EvalAll
END INTERFACE

️܀ See example

program main
  use easifembase
  implicit none
  integer( i4b ) :: n
  real( dfp ), allocatable :: ans( :, : ), x( : )
  type(string) :: astr
  x = [-1.0, -0.5, 0.0, 0.5, 1.0]
  n = 5
  ans= Chebyshev1EvalAll( n=n, x=x )
  astr = MdEncode( ans )
  call display( astr%chars(), "" )
end program main

P0	P1	P2	P3	P4	P5
1	-1	1	-1	1	-1
1	-0.5	-0.5	1	-0.5	-0.5
1	0	-1	-0	1	0
1	0.5	-0.5	-1	-0.5	0.5
1	1	1	1	1	1

↢