module fftpack
use fftpack_kind
implicit none
private
public :: zffti, zfftf, zfftb
public :: fft, ifft
public :: fftshift, ifftshift
public :: fftfreq, rfftfreq
public :: dffti, dfftf, dfftb
public :: rfft, irfft
public :: dzffti, dzfftf, dzfftb
public :: dcosqi, dcosqf, dcosqb
public :: dcosti, dcost
public :: dct, idct
public :: dct_t1i, dct_t1
public :: dct_t23i, dct_t2, dct_t3
public :: rk
interface
!> Version: experimental
!>
!> Initialize `zfftf` and `zfftb`.
!> ([Specification](../page/specs/fftpack.html#zffti))
pure subroutine zffti(n, wsave)
import rk
integer, intent(in) :: n
real(kind=rk), intent(out) :: wsave(*)
end subroutine zffti
!> Version: experimental
!>
!> Forward transform of a complex periodic sequence.
!> ([Specification](../page/specs/fftpack.html#zfftf))
pure subroutine zfftf(n, c, wsave)
import rk
integer, intent(in) :: n
complex(kind=rk), intent(inout) :: c(*)
real(kind=rk), intent(in) :: wsave(*)
end subroutine zfftf
!> Version: experimental
!>
!> Unnormalized inverse of `zfftf`.
!> ([Specification](../page/specs/fftpack.html#zfftb))
pure subroutine zfftb(n, c, wsave)
import rk
integer, intent(in) :: n
complex(kind=rk), intent(inout) :: c(*)
real(kind=rk), intent(in) :: wsave(*)
end subroutine zfftb
!> Version: experimental
!>
!> Initialize `dfftf` and `dfftb`.
!> ([Specification](../page/specs/fftpack.html#dffti))
pure subroutine dffti(n, wsave)
import rk
integer, intent(in) :: n
real(kind=rk), intent(out) :: wsave(*)
end subroutine dffti
!> Version: experimental
!>
!> Forward transform of a real periodic sequence.
!> ([Specification](../page/specs/fftpack.html#dfftf))
pure subroutine dfftf(n, r, wsave)
import rk
integer, intent(in) :: n
real(kind=rk), intent(inout) :: r(*)
real(kind=rk), intent(in) :: wsave(*)
end subroutine dfftf
!> Version: experimental
!>
!> Unnormalized inverse of `dfftf`.
!> ([Specification](../page/specs/fftpack.html#dfftb))
pure subroutine dfftb(n, r, wsave)
import rk
integer, intent(in) :: n
real(kind=rk), intent(inout) :: r(*)
real(kind=rk), intent(in) :: wsave(*)
end subroutine dfftb
!> Version: experimental
!>
!> Initialize `dzfftf` and `dzfftb`.
!> ([Specification](../page/specs/fftpack.html#dzffti))
pure subroutine dzffti(n, wsave)
import rk
integer, intent(in) :: n
real(kind=rk), intent(out) :: wsave(*)
end subroutine dzffti
!> Version: experimental
!>
!> Simplified forward transform of a real periodic sequence.
!> ([Specification](../page/specs/fftpack.html#dzfftf))
pure subroutine dzfftf(n, r, azero, a, b, wsave)
import rk
integer, intent(in) :: n
real(kind=rk), intent(in) :: r(*)
real(kind=rk), intent(out) :: azero
real(kind=rk), intent(out) :: a(*), b(*)
real(kind=rk), intent(in) :: wsave(*)
end subroutine dzfftf
!> Version: experimental
!>
!> Unnormalized inverse of `dzfftf`.
!> ([Specification](../page/specs/fftpack.html#dzfftb))
pure subroutine dzfftb(n, r, azero, a, b, wsave)
import rk
integer, intent(in) :: n
real(kind=rk), intent(out) :: r(*)
real(kind=rk), intent(in) :: azero
real(kind=rk), intent(in) :: a(*), b(*)
real(kind=rk), intent(in) :: wsave(*)
end subroutine dzfftb
!> Version: experimental
!>
!> Initialize `dcosqf` and `dcosqb`.
!> ([Specification](../page/specs/fftpack.html#initialize-dct-2-3-dcosqi-or-dct_t23i))
pure subroutine dcosqi(n, wsave)
import rk
integer, intent(in) :: n
real(kind=rk), intent(out) :: wsave(*)
end subroutine dcosqi
!> Version: experimental
!>
!> Forward transform of quarter wave data.
!> ([Specification](../page/specs/fftpack.html#compute-dct-3-dcosqf-or-dct_t3))
pure subroutine dcosqf(n, x, wsave)
import rk
integer, intent(in) :: n
real(kind=rk), intent(inout) :: x(*)
real(kind=rk), intent(in) :: wsave(*)
end subroutine dcosqf
!> Version: experimental
!>
!> Unnormalized inverse of `dcosqf`.
!> ([Specification](../page/specs/fftpack.html#compute-dct-2-dcosqb-or-dct_t2))
pure subroutine dcosqb(n, x, wsave)
import rk
integer, intent(in) :: n
real(kind=rk), intent(inout) :: x(*)
real(kind=rk), intent(in) :: wsave(*)
end subroutine dcosqb
!> Version: experimental
!>
!> Initialize `dcost`.
!> ([Specification](../page/specs/fftpack.html#initialize-dct-1-dcosti-or-dct_t1i))
pure subroutine dcosti(n, wsave)
import rk
integer, intent(in) :: n
real(kind=rk), intent(out) :: wsave(*)
end subroutine dcosti
!> Version: experimental
!>
!> Discrete fourier cosine transform of an even sequence.
!> ([Specification](../page/specs/fftpack.html#compute-dct-1-dcost-or-dct_t1))
pure subroutine dcost(n, x, wsave)
import rk
integer, intent(in) :: n
real(kind=rk), intent(inout) :: x(*)
real(kind=rk), intent(in) :: wsave(*)
end subroutine dcost
!> Version: experimental
!>
!> Integer frequency values involved in complex FFT.
!> ([Specifiction](../page/specs/fftpack.html#fftfreq))
pure module function fftfreq(n) result(out)
integer, intent(in) :: n
integer, dimension(n) :: out
end function fftfreq
!> Version: experimental
!>
!> Integer frequency values involved in real FFT.
!> ([Specifiction](../page/specs/fftpack.html#rfftfreq))
pure module function rfftfreq(n) result(out)
integer, intent(in) :: n
integer, dimension(n) :: out
end function rfftfreq
end interface
!> Version: experimental
!>
!> Forward transform of a complex periodic sequence.
!> ([Specifiction](../page/specs/fftpack.html#fft))
interface fft
pure module function fft_rk(x, n) result(result)
complex(kind=rk), intent(in) :: x(:)
integer, intent(in), optional :: n
complex(kind=rk), allocatable :: result(:)
end function fft_rk
end interface fft
!> Version: experimental
!>
!> Backward transform of a complex periodic sequence.
!> ([Specifiction](../page/specs/fftpack.html#ifft))
interface ifft
pure module function ifft_rk(x, n) result(result)
complex(kind=rk), intent(in) :: x(:)
integer, intent(in), optional :: n
complex(kind=rk), allocatable :: result(:)
end function ifft_rk
end interface ifft
!> Version: experimental
!>
!> Forward transform of a real periodic sequence.
!> ([Specifiction](../page/specs/fftpack.html#rfft))
interface rfft
pure module function rfft_rk(x, n) result(result)
real(kind=rk), intent(in) :: x(:)
integer, intent(in), optional :: n
real(kind=rk), allocatable :: result(:)
end function rfft_rk
end interface rfft
!> Version: experimental
!>
!> Backward transform of a real periodic sequence.
!> ([Specifiction](../page/specs/fftpack.html#irfft))
interface irfft
pure module function irfft_rk(x, n) result(result)
real(kind=rk), intent(in) :: x(:)
integer, intent(in), optional :: n
real(kind=rk), allocatable :: result(:)
end function irfft_rk
end interface irfft
!> Version: experimental
!>
!> Dsicrete cosine transforms.
!> ([Specification](../page/specs/fftpack.html#simplified-dct-of-types-1-2-3-dct))
interface dct
pure module function dct_rk(x, n, type) result(result)
real(kind=rk), intent(in) :: x(:)
integer, intent(in), optional :: n
integer, intent(in), optional :: type
real(kind=rk), allocatable :: result(:)
end function dct_rk
end interface dct
!> Version: experimental
!>
!> Inverse discrete cosine transforms.
!> ([Specification](../page/specs/fftpack.html#simplified-inverse-dct-of-types-1-2-3-idct))
interface idct
pure module function idct_rk(x, n, type) result(result)
real(kind=rk), intent(in) :: x(:)
integer, intent(in), optional :: n
integer, intent(in), optional :: type
real(kind=rk), allocatable :: result(:)
end function idct_rk
end interface idct
!> Version: experimental
!>
!> Initialize DCT type-1
!> ([Specification](../page/specs/fftpack.html#initialize-dct-1-dcosti-or-dct_t1i))
interface dct_t1i
procedure :: dcosti
end interface dct_t1i
!> Version: experimental
!>
!> Perform DCT type-1
!> ([Specification](../page/specs/fftpack.html#compute-dct-1-dcost-or-dct_t1))
interface dct_t1
procedure :: dcost
end interface dct_t1
!> Version: experimental
!>
!> Initialize DCT types 2, 3
!> ([Specification](../page/specs/fftpack.html#initialize-dct-2-3-dcosqi-or-dct_t23i))
interface dct_t23i
procedure :: dcosqi
end interface dct_t23i
!> Version: experimental
!>
!> Perform DCT type-2
!> ([Specification](../page/specs/fftpack.html#compute-dct-2-dcosqb-or-dct_t2))
interface dct_t2
procedure :: dcosqb
end interface dct_t2
!> Version: experimental
!>
!> Perform DCT type-3
!> ([Specification](../page/specs/fftpack.html#compute-dct-3-dcosqf-or-dct_t3))
interface dct_t3
procedure :: dcosqf
end interface dct_t3
!> Version: experimental
!>
!> Shifts zero-frequency component to center of spectrum.
!> ([Specifiction](../page/specs/fftpack.html#fftshift))
interface fftshift
pure module function fftshift_crk(x) result(result)
complex(kind=rk), intent(in) :: x(:)
complex(kind=rk), dimension(size(x)) :: result
end function fftshift_crk
pure module function fftshift_rrk(x) result(result)
real(kind=rk), intent(in) :: x(:)
real(kind=rk), dimension(size(x)) :: result
end function fftshift_rrk
end interface fftshift
!> Version: experimental
!>
!> Shifts zero-frequency component to beginning of spectrum.
!> ([Specifiction](../page/specs/fftpack.html#ifftshift))
interface ifftshift
pure module function ifftshift_crk(x) result(result)
complex(kind=rk), intent(in) :: x(:)
complex(kind=rk), dimension(size(x)) :: result
end function ifftshift_crk
pure module function ifftshift_rrk(x) result(result)
real(kind=rk), intent(in) :: x(:)
real(kind=rk), dimension(size(x)) :: result
end function ifftshift_rrk
end interface ifftshift
end module fftpack
