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mo_specan.f90
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mo_specan.f90
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MODULE mo_specan
! This module provides routines for spectral analysis
! using routines from fftpack http://orion.math.iastate.edu/burkardt/f_src/fftpack/fftpack.html
! License
! -------
! This file is part of the JAMS Fortran package, distributed under the MIT License.
!
! Copyright (c) 2013 Philipp Bosecker
!
! Permission is hereby granted, free of charge, to any person obtaining a copy
! of this software and associated documentation files (the "Software"), to deal
! in the Software without restriction, including without limitation the rights
! to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
! copies of the Software, and to permit persons to whom the Software is
! furnished to do so, subject to the following conditions:
!
! The above copyright notice and this permission notice shall be included in all
! copies or substantial portions of the Software.
!
! THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
! IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
! FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
! AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
! LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
! OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
! SOFTWARE.
USE mo_kind, ONLY: i4, sp, spc, dp, dpc
USE mo_constants, ONLY: PI_sp, PI_dp
USE mo_nelmin, ONLY: nelminrange
IMPLICIT NONE
PUBLIC :: cost ! Cost function for fitting linear reservoir model
PUBLIC :: linres ! Fitting linear reservoir model
PUBLIC :: periodogram ! Periodogram of given dataset using FFT
PUBLIC :: setmeas ! Set measurement as module variable
! ------------------------------------------------------------------
! NAME
! cost
! PURPOSE
! Define objective function to fit linear reservoir model linres to data.
! CALLING SEQUENCE
! func = cost(para)
! INTENT(IN)
! real(sp/dp) :: para(:) parameter of function
! INTENT(INOUT)
! None
! INTENT(OUT)
! None
! INTENT(IN), OPTIONAL
! None
! INTENT(INOUT), OPTIONAL
! None
! INTENT(OUT), OPTIONAL
! None
! RESTRICTIONS
! None
! EXAMPLE
! see test example test_mo_specan
! LITERATURE
! None
! HISTORY
! Written, December 2013, Philipp Bosecker
! ------------------------------------------------------------------
INTERFACE cost
MODULE PROCEDURE cost_sp, cost_dp
END INTERFACE cost
! ------------------------------------------------------------------
! NAME
! linres
! PURPOSE
! Fitting a linear reservoir model f dependent on the frequency w
! f(w)=1/(a(1+tc^2w^2))
! introduced by Gelhar et. al (1974) to the double logarithmic periodogram of a time series.
! The time series is for example groundwater fluctuations.
! The periodogram can be determined using the subroutine periodogram.
! The best fitting parameters a and tc are returned.
! In the linear reservoir model a is a discharge constant and
! tc is the characteristic respond time.
! CALLING SEQUENCE
! call linres(data,bestpara,a_min,a_max,tc_min,tc_max,initial_a,initial_tc)
! INTENT(IN)
! real(sp/dp) :: data(:) Time series
! real(sp/dp) :: a_min minimum of first parameter
! real(sp/dp) :: a_max maximum of first parameter
! real(sp/dp) :: tc_min minimum of second parameter
! real(sp/dp) :: tc_max maximum of second parameter
! real(sp/dp) :: initial_a first initial parameter
! real(sp/dp) :: initial_tc second initial parameter
! INTENT(INOUT)
! None
! INTENT(OUT)
! real(sp(dp) :: bestpara(2) best fitting parameter a and tc found for linear reservoir model
! INTENT(IN), OPTIONAL
! None
! INTENT(INOUT), OPTIONAL
! None
! INTENT(OUT), OPTIONAL
! None
! RESTRICTIONS
! None
! EXAMPLE
! see test example test_mo_specan
! LITERATURE
! Lynn W. Gelhar and John L. Wilson,
! Ground-Water Quality Modeling,
! Ground Water, 1974
! HISTORY
! Written, December 2013, Philipp Bosecker
! ------------------------------------------------------------------
INTERFACE linres
MODULE PROCEDURE linres_sp, linres_dp
END INTERFACE linres
! ------------------------------------------------------------------
! NAME
! periodogram
! PURPOSE
! Computes the periodogram of given dataset using FFT. The periodogram
! is calculated as the square of the absolut value of the discrete complex
! Fourier transformation. The output periodogram has the size of N/2.
! CALLING SEQUENCE
! call periodogram(data,output)
! INTENT(IN)
! real(sp/dp) :: data(:) Time series
! INTENT(INOUT)
! NONE
! INTENT(OUT)
! real(sp/dp) :: output(:,2) frequency, power
! INTENT(IN), OPTIONAL
! None
! INTENT(INOUT), OPTIONAL
! None
! INTENT(OUT), OPTIONAL
! None
! RESTRICTIONS
! None
! EXAMPLE
! see test example test_mo_specan
! LITERATURE
! P.N. Swarztrauber,
! Vectorizing the FFTs, in Parallel Computations (G. Rodrigue, ed.),
! Academic Press, 1982, pp. 51--83
! HISTORY
! Written, December 2013, Philipp Bosecker
! ------------------------------------------------------------------
INTERFACE periodogram
MODULE PROCEDURE periodogram_sp, periodogram_dp
END INTERFACE periodogram
! ------------------------------------------------------------------
! NAME
! setmeas
! PURPOSE
! Read in data/measurements and store them as global module variable meas.
! Global module variable is needed since optimization only allows for a single argument
! (which is parameter set) of the objective function.
! CALLING SEQUENCE
! call setmeas(data)
! INTENT(IN)
! real(sp/dp) :: data(:) data/measurements
! INTENT(INOUT)
! None
! INTENT(OUT)
! None
! INTENT(IN), OPTIONAL
! None
! INTENT(INOUT), OPTIONAL
! None
! INTENT(OUT), OPTIONAL
! None
! RESTRICTIONS
! None
! EXAMPLE
! see test example test_mo_specan
! LITERATURE
! None
! HISTORY
! Written, December 2013, Philipp Bosecker
! ------------------------------------------------------------------
INTERFACE setmeas
MODULE PROCEDURE setmeas_dp, setmeas_sp
END INTERFACE setmeas
! ------------------------------------------------------------------
PRIVATE
! ------------------------------------------------------------------
REAL(dp), DIMENSION(:), ALLOCATABLE :: meas_dp ! data/measurement
REAL(sp), DIMENSION(:), ALLOCATABLE :: meas_sp ! data/measurement
!**************************************************
!
! Changes that have been done in FFTPACK routines:
!
! - Declaration of data type
! - single and double precision versions
! - fixed that wrong data types were overgiven
!
!**************************************************
! Private routines, mostly from fftpack
INTERFACE cfftf
MODULE PROCEDURE cfftf_sp, cfftf_dp
END INTERFACE cfftf
INTERFACE cfftf1
MODULE PROCEDURE cfftf1_sp, cfftf1_dp
END INTERFACE cfftf1
INTERFACE cffti
MODULE PROCEDURE cffti_sp, cffti_dp
END INTERFACE cffti
INTERFACE cffti1
MODULE PROCEDURE cffti1_sp, cffti1_dp
END INTERFACE cffti1
INTERFACE i_factor
MODULE PROCEDURE i_factor
END INTERFACE i_factor
! INTERFACE passf
! MODULE PROCEDURE passf_sp, passf_dp
! END INTERFACE passf
! INTERFACE passf2
! MODULE PROCEDURE passf2_sp, passf2_dp
! END INTERFACE passf2
! INTERFACE passf3
! MODULE PROCEDURE passf3_sp, passf3_dp
! END INTERFACE passf3
! INTERFACE passf4
! MODULE PROCEDURE passf4_sp, passf4_dp
! END INTERFACE passf4
! INTERFACE passf5
! MODULE PROCEDURE passf5_sp, passf5_dp
! END INTERFACE passf5
! ------------------------------------------------------------------
CONTAINS
! ------------------------------------------------------------------
FUNCTION cost_sp(para)
IMPLICIT NONE
REAL(sp), DIMENSION(:), INTENT(IN) :: para
REAL(sp) :: cost_sp
! local variables
INTEGER(i4) :: n
INTEGER(i4) :: i
REAL(sp), DIMENSION(:), ALLOCATABLE :: model
n = size(meas_sp,1)
allocate(model(n))
do i = 1, n
model(i) = 1._sp/(para(1)**2*(1._sp+para(2)**2*real(meas_sp(i),sp)))
end do
cost_sp = 0._sp
do i = 1, n
cost_sp = cost_sp + abs(log(model(i))-log(real(meas_sp(i),sp)))
end do
END FUNCTION cost_sp
FUNCTION cost_dp(para)
IMPLICIT NONE
REAL(dp), DIMENSION(:), INTENT(IN) :: para
REAL(dp) :: cost_dp
! local variables
INTEGER(i4) :: n
INTEGER(i4) :: i
REAL(dp), DIMENSION(:), ALLOCATABLE :: model
n = size(meas_dp,1)
allocate(model(n))
do i = 1, n
model(i) = 1._dp/(para(1)**2*(1._dp+para(2)**2*real(meas_dp(i),dp)))
end do
cost_dp = 0._dp
do i = 1, n
cost_dp = cost_dp + abs(log(model(i))-log(real(meas_dp(i),dp)))
end do
END FUNCTION cost_dp
! ------------------------------------------------------------------
SUBROUTINE linres_sp(data,a_min,a_max,tc_min,tc_max,initial_a,initial_tc, bestpara)
IMPLICIT NONE
REAL(sp), DIMENSION(:), INTENT(IN) :: data
REAL(sp), DIMENSION(2), INTENT(OUT) :: bestpara
REAL(sp), INTENT(IN) :: a_min
REAL(sp), INTENT(IN) :: a_max
REAL(sp), INTENT(IN) :: tc_min
REAL(sp), INTENT(IN) :: tc_max
REAL(sp), INTENT(IN) :: initial_a
REAL(sp), INTENT(IN) :: initial_tc
! local variables
REAL(sp), DIMENSION(2,2) :: pararanges
REAL(sp), DIMENSION(2) :: initial
! REAL(sp), DIMENSION(2) :: para
initial(1) = initial_a
initial(2) = initial_tc
pararanges(1,1) = a_min
pararanges(1,2) = a_max
pararanges(2,1) = tc_min
pararanges(2,2) = tc_max
call setmeas(data)
bestpara = nelminrange(cost_sp, initial, pararanges)
END SUBROUTINE linres_sp
SUBROUTINE linres_dp(data,a_min,a_max,tc_min,tc_max,initial_a,initial_tc, bestpara)
IMPLICIT NONE
REAL(dp), DIMENSION(:), INTENT(IN) :: data
REAL(dp), DIMENSION(2), INTENT(OUT) :: bestpara
REAL(dp), INTENT(IN) :: a_min
REAL(dp), INTENT(IN) :: a_max
REAL(dp), INTENT(IN) :: tc_min
REAL(dp), INTENT(IN) :: tc_max
REAL(dp), INTENT(IN) :: initial_a
REAL(dp), INTENT(IN) :: initial_tc
! local variables
REAL(dp), DIMENSION(2,2) :: pararanges
REAL(dp), DIMENSION(2) :: initial
! REAL(dp), DIMENSION(2) :: para
initial(1) = initial_a
initial(2) = initial_tc
pararanges(1,1) = a_min
pararanges(1,2) = a_max
pararanges(2,1) = tc_min
pararanges(2,2) = tc_max
call setmeas(data)
bestpara = nelminrange(cost_dp, initial, pararanges)
END SUBROUTINE linres_dp
! ------------------------------------------------------------------
SUBROUTINE periodogram_sp(data,output)
IMPLICIT NONE
REAL(sp), DIMENSION(:), INTENT(IN) :: data
REAL(sp), DIMENSION(:,:), INTENT(OUT) :: output
! local variables
INTEGER(i4) :: N, i
COMPLEX(spc), DIMENSION(:), ALLOCATABLE :: c_data
! REAL(sp) :: mean_data
REAL(sp), DIMENSION(:), ALLOCATABLE :: wsave
REAL(sp), DIMENSION(:), ALLOCATABLE :: Iw
REAL(sp), DIMENSION(:), ALLOCATABLE :: w
N = size(data)
allocate(c_data(N))
allocate(wsave(4*N+15))
do i = 1, N
c_data(i) = cmplx(data(i), 0.0_sp,kind=sp) !- mean_data
end do
call cffti(N,wsave)
call cfftf(N,c_data,wsave)
allocate(Iw(N))
allocate(w(N))
do i = 1, N/2
Iw(i) = 2*(abs(c_data(i))**2.0_sp)/real(N,sp)
output(i,2) = Iw(i)
end do
do i = 1, N/2
w(i) = 2*PI_sp*real(i,sp)/real(N,sp)
output(i,1) = w(i)
end do
END SUBROUTINE periodogram_sp
SUBROUTINE periodogram_dp(data,output)
IMPLICIT NONE
REAL(dp), DIMENSION(:), INTENT(IN) :: data
REAL(dp), DIMENSION(:,:), INTENT(OUT) :: output
! local variables
INTEGER(i4) :: N, i
COMPLEX(dpc), DIMENSION(:), ALLOCATABLE :: c_data
! REAL(dp) :: mean_data
REAL(dp), DIMENSION(:), ALLOCATABLE :: wsave
REAL(dp), DIMENSION(:), ALLOCATABLE :: Iw
REAL(dp), DIMENSION(:), ALLOCATABLE :: w
N = size(data)
allocate(c_data(N))
allocate(wsave(4*N+15))
do i = 1, N
c_data(i) = cmplx(data(i), 0.0_dp,kind=dp)
end do
call cffti(N,wsave)
call cfftf(N,c_data,wsave)
allocate(Iw(N))
allocate(w(N))
do i = 1, N/2
Iw(i) = (abs(c_data(i))**2.0_dp)/real(N,dp)
output(i,2) = Iw(i)
end do
do i = 1, N/2
w(i) = 2*PI_dp*real(i,dp)/real(N,dp)
output(i,1) = w(i)
end do
END SUBROUTINE periodogram_dp
! ------------------------------------------------------------------
SUBROUTINE setmeas_dp(data)
REAL(dp), DIMENSION(:), INTENT(IN) :: data
allocate(meas_dp(size(data)))
meas_dp(:) = data(:)
END SUBROUTINE setmeas_dp
SUBROUTINE setmeas_sp(data)
REAL(sp), DIMENSION(:), INTENT(IN) :: data
allocate(meas_sp(size(data)))
meas_sp(:) = data(:)
END SUBROUTINE setmeas_sp
! ------------------------------------------------------------------
! PRIVATE ROUTINES
! ------------------------------------------------------------------
SUBROUTINE cfftf_sp ( n, c, wsave )
!
!*******************************************************************************
!
!! CFFTF computes the forward complex discrete Fourier transform.
!
!
! Discussion:
!
! This process is sometimes called Fourier analysis.
!
! CFFTF computes the Fourier coefficients of a complex periodic sequence.
!
! The transform is not normalized. To obtain a normalized transform,
! the output must be divided by N. Otherwise a call of CFFTF
! followed by a call of CFFTB will multiply the sequence by N.
!
! The array WSAVE must be initialized by calling CFFTI.
!
! The transform is defined by:
!
! C_out(J) = sum ( 1 <= K <= N )
! C_in(K) * exp ( - sqrt ( -1 ) * ( J - 1 ) * ( K - 1 ) * 2 * PI / N )
!
! Modified:
!
! 09 March 2001
!
! Author:
!
! Paul Swarztrauber,
! National Center for Atmospheric Research
!
! Reference:
!
! David Kahaner, Clever Moler, Steven Nash,
! Numerical Methods and Software,
! Prentice Hall, 1988.
!
! P N Swarztrauber,
! Vectorizing the FFT's,
! in Parallel Computations,
! G. Rodrigue, editor,
! Academic Press, 1982, pages 51-83.
!
! B L Buzbee,
! The SLATEC Common Math Library,
! in Sources and Development of Mathematical Software,
! W. Cowell, editor,
! Prentice Hall, 1984, pages 302-318.
!
! Parameters:
!
! Input, integer N, the length of the sequence to be transformed.
! The method is more efficient when N is the product of small primes.
!
! Input/output, complex C(N).
! On input, the data sequence to be transformed.
! On output, the Fourier coefficients.
!
! Input, real WSAVE(4*N+15). The array must be initialized by calling
! CFFTI. A different WSAVE array must be used for each different
! value of N.
!
implicit none
!
integer(i4), intent(in) :: n
!
complex(spc), intent(inout) :: c(n)
real(sp), intent(in) :: wsave(4*n+15)
!********************
integer(i4) :: i
integer(i4) :: wsave_int(4*n+15)
complex(spc) :: wsave_complex(4*n+15)
do i = 1, 4*n+15
wsave_complex(i) = cmplx(wsave(i),0.0_sp,kind=sp)
wsave_int(i) = int(wsave(i))
end do
!********************
!
if ( n <= 1 ) then
return
end if
!call cfftf1 ( n, c, wsave(1), wsave(2*n+1), wsave(4*n+1) )
call cfftf1_sp ( n, c, wsave_complex(1), wsave(2*n+1), wsave_int(4*n+1) )
return
END SUBROUTINE cfftf_sp
SUBROUTINE cfftf_dp ( n, c, wsave )
!
implicit none
!
integer(i4), intent(in) :: n
!
complex(dpc), intent(inout) :: c(n)
real(dp), intent(in) :: wsave(4*n+15)
!********************
integer(i4) :: i
integer(i4) :: wsave_int(4*n+15)
complex(dpc) :: wsave_complex(4*n+15)
do i = 1, 4*n+15
wsave_complex(i) = cmplx(wsave(i),0.0_dp,kind=dp)
wsave_int(i) = int(wsave(i))
end do
!********************
!
if ( n <= 1 ) then
return
end if
!call cfftf1 ( n, c, wsave(1), wsave(2*n+1), wsave(4*n+1) )
call cfftf1_dp ( n, c, wsave_complex(1), wsave(2*n+1), wsave_int(4*n+1) )
return
END SUBROUTINE cfftf_dp
! ------------------------------------------------------------------
SUBROUTINE cfftf1_sp ( n, c, ch, wa, ifac )
!
!*******************************************************************************
!
!! CFFTF1 is a lower level routine used by CFFTF.
!
!
! Modified:
!
! 09 March 2001
!
! Author:
!
! Paul Swarztrauber,
! National Center for Atmospheric Research
!
! Parameters:
!
! Input, integer N, the length of the sequence to be transformed.
!
! Input/output, complex C(N).
! On input, the data sequence to be transformed.
! On output, the Fourier coefficients.
!
! Input, complex CH(N).
!
! Input, real WA(2*N).
!
! Input, integer IFAC(15).
! IFAC(1) = N, the number that was factored.
! IFAC(2) = NF, the number of factors.
! IFAC(3:2+NF), the factors.
!
implicit none
!
integer(i4) :: n
!
complex(spc) :: c(n)
complex(spc) :: ch(n)
integer(i4) :: idl1
integer(i4) :: ido
integer(i4) :: ifac(15)
integer(i4) :: ip
integer(i4) :: iw
integer(i4) :: ix2
integer(i4) :: ix3
integer(i4) :: ix4
integer(i4) :: k1
integer(i4) :: l1
integer(i4) :: l2
integer(i4) :: na
integer(i4) :: nac
integer(i4) :: nf
real(sp) :: wa(2*n)
!***************
real(sp) :: c_r(n*2)
real(sp) :: ch_r(n*2)
integer(i4) :: i, ii
ii = 1
do i = 1, n
c_r(ii) = real(real(c(i),sp),sp)
ch_r(ii) = real(real(ch(i),sp),sp)
ii = ii + 1
c_r(ii) = real(aimag(c(i)),sp)
ch_r(ii) = real(aimag(ch(i)),sp)
ii = ii + 1
end do
!***************
!
nf = ifac(2)
na = 0
l1 = 1
iw = 1
do k1 = 1, nf
ip = ifac(k1+2)
l2 = ip * l1
ido = n / l2
idl1 = 2 * ido * l1
if ( ip == 4 ) then
ix2 = iw + 2 * ido
ix3 = ix2 + 2 * ido
if ( na == 0 ) then
!call passf4 ( 2*ido, l1, c, ch, wa(iw), wa(ix2), wa(ix3) )
call passf4_sp ( 2*ido, l1, c_r, ch_r, wa(iw), wa(ix2), wa(ix3) )
else
!call passf4 ( 2*ido, l1, c, ch, wa(iw), wa(ix2), wa(ix3) )
call passf4_sp ( 2*ido, l1, ch_r, c_r, wa(iw), wa(ix2), wa(ix3) )
end if
na = 1 - na
else if ( ip == 2 ) then
if ( na == 0 ) then
!call passf2 ( 2*ido, l1, c, ch, wa(iw) )
call passf2_sp ( 2*ido, l1, c_r, ch_r, wa(iw) )
else
!call passf2 ( 2*ido, l1, ch, c, wa(iw) )
call passf2_sp ( 2*ido, l1, ch_r, c_r, wa(iw) )
end if
na = 1 - na
else if ( ip == 3 ) then
ix2 = iw + 2 * ido
if ( na == 0 ) then
!call passf3 ( 2*ido, l1, c, ch, wa(iw), wa(ix2) )
call passf3_sp ( 2*ido, l1, c_r, ch_r, wa(iw), wa(ix2) )
else
!call passf3 ( 2*ido, l1, ch, c, wa(iw), wa(ix2) )
call passf3_sp ( 2*ido, l1, ch_r, c_r, wa(iw), wa(ix2) )
end if
na = 1 - na
else if ( ip == 5 ) then
ix2 = iw + 2 * ido
ix3 = ix2 + 2 * ido
ix4 = ix3 + 2 * ido
if ( na == 0 ) then
!call passf5 ( 2*ido, l1, c, ch, wa(iw), wa(ix2), wa(ix3), wa(ix4) )
call passf5_sp ( 2*ido, l1, c_r, ch_r, wa(iw), wa(ix2), wa(ix3), wa(ix4) )
else
!call passf5 ( 2*ido, l1, ch, c, wa(iw), wa(ix2), wa(ix3), wa(ix4) )
call passf5_sp ( 2*ido, l1, ch_r, c_r, wa(iw), wa(ix2), wa(ix3), wa(ix4) )
end if
na = 1 - na
else
if ( na == 0 ) then
!call passf ( nac, 2*ido, ip, l1, idl1, c, c, c, ch, ch, wa(iw) )
call passf_sp ( nac, 2*ido, ip, l1, idl1, c_r, c_r, c_r, ch_r, ch_r, wa(iw) )
else
!call passf ( nac, 2*ido, ip, l1, idl1, ch, ch, ch, c, c, wa(iw) )
call passf_sp ( nac, 2*ido, ip, l1, idl1, ch_r, ch_r, ch_r, c_r, c_r, wa(iw) )
end if
if ( nac /= 0 ) then
na = 1 - na
end if
end if
l1 = l2
iw = iw + ( ip - 1 ) * 2 * ido
end do
!*********************
ii = 1
do i = 1, n
c(i) = cmplx(c_r(ii), c_r(ii+1),kind=sp)
ch(i) = cmplx(ch_r(ii), ch_r(ii+1),kind=sp)
ii = ii + 2
end do
!*********************
if ( na /= 0 ) then
c(1:n) = ch(1:n)
end if
return
END SUBROUTINE cfftf1_sp
SUBROUTINE cfftf1_dp ( n, c, ch, wa, ifac )
!
implicit none
!
integer(i4) :: n
!
complex(dpc) :: c(n)
complex(dpc) :: ch(n)
integer(i4) :: idl1
integer(i4) :: ido
integer(i4) :: ifac(15)
integer(i4) :: ip
integer(i4) :: iw
integer(i4) :: ix2
integer(i4) :: ix3
integer(i4) :: ix4
integer(i4) :: k1
integer(i4) :: l1
integer(i4) :: l2
integer(i4) :: na
integer(i4) :: nac
integer(i4) :: nf
real(dp) :: wa(2*n)
!***************
real(dp) :: c_r(n*2)
real(dp) :: ch_r(n*2)
integer(i4) :: i, ii
ii = 1
do i = 1, n
c_r(ii) = real(real(c(i),dp),dp)
ch_r(ii) = real(real(ch(i),dp),dp)
ii = ii + 1
c_r(ii) = real(aimag(c(i)),dp)
ch_r(ii) = real(aimag(ch(i)),dp)
ii = ii + 1
end do
!***************
!
nf = ifac(2)
na = 0
l1 = 1
iw = 1
do k1 = 1, nf
ip = ifac(k1+2)
l2 = ip * l1
ido = n / l2
idl1 = 2 * ido * l1
if ( ip == 4 ) then
ix2 = iw + 2 * ido
ix3 = ix2 + 2 * ido
if ( na == 0 ) then
!call passf4 ( 2*ido, l1, c, ch, wa(iw), wa(ix2), wa(ix3) )
call passf4_dp ( 2*ido, l1, c_r, ch_r, wa(iw), wa(ix2), wa(ix3) )
else
!call passf4 ( 2*ido, l1, c, ch, wa(iw), wa(ix2), wa(ix3) )
call passf4_dp ( 2*ido, l1, ch_r, c_r, wa(iw), wa(ix2), wa(ix3) )
end if
na = 1 - na
else if ( ip == 2 ) then
if ( na == 0 ) then
!call passf2 ( 2*ido, l1, c, ch, wa(iw) )
call passf2_dp ( 2*ido, l1, c_r, ch_r, wa(iw) )
else
!call passf2 ( 2*ido, l1, ch, c, wa(iw) )
call passf2_dp ( 2*ido, l1, ch_r, c_r, wa(iw) )
end if
na = 1 - na
else if ( ip == 3 ) then
ix2 = iw + 2 * ido
if ( na == 0 ) then
!call passf3 ( 2*ido, l1, c, ch, wa(iw), wa(ix2) )
call passf3_dp ( 2*ido, l1, c_r, ch_r, wa(iw), wa(ix2) )
else
!call passf3 ( 2*ido, l1, ch, c, wa(iw), wa(ix2) )
call passf3_dp ( 2*ido, l1, ch_r, c_r, wa(iw), wa(ix2) )
end if
na = 1 - na
else if ( ip == 5 ) then
ix2 = iw + 2 * ido
ix3 = ix2 + 2 * ido
ix4 = ix3 + 2 * ido
if ( na == 0 ) then
!call passf5 ( 2*ido, l1, c, ch, wa(iw), wa(ix2), wa(ix3), wa(ix4) )
call passf5_dp ( 2*ido, l1, c_r, ch_r, wa(iw), wa(ix2), wa(ix3), wa(ix4) )
else
!call passf5 ( 2*ido, l1, ch, c, wa(iw), wa(ix2), wa(ix3), wa(ix4) )
call passf5_dp ( 2*ido, l1, ch_r, c_r, wa(iw), wa(ix2), wa(ix3), wa(ix4) )
end if
na = 1 - na
else
if ( na == 0 ) then
!call passf ( nac, 2*ido, ip, l1, idl1, c, c, c, ch, ch, wa(iw) )
call passf_dp ( nac, 2*ido, ip, l1, idl1, c_r, c_r, c_r, ch_r, ch_r, wa(iw) )
else
!call passf ( nac, 2*ido, ip, l1, idl1, ch, ch, ch, c, c, wa(iw) )
call passf_dp ( nac, 2*ido, ip, l1, idl1, ch_r, ch_r, ch_r, c_r, c_r, wa(iw) )
end if
if ( nac /= 0 ) then
na = 1 - na
end if
end if
l1 = l2
iw = iw + ( ip - 1 ) * 2 * ido
end do
!*********************
ii = 1
do i = 1, n
c(i) = cmplx(c_r(ii), c_r(ii+1),kind=dp)
ch(i) = cmplx(ch_r(ii), ch_r(ii+1),kind=dp)
ii = ii + 2
end do
!*********************
if ( na /= 0 ) then
c(1:n) = ch(1:n)
end if
return
END SUBROUTINE cfftf1_dp
! ------------------------------------------------------------------
SUBROUTINE cffti_sp ( n, wsave )
!
!*******************************************************************************
!
!! CFFTI initializes WSAVE, used in CFFTF and CFFTB.
!
!
! Discussion:
!
! The prime factorization of N together with a tabulation of the
! trigonometric functions are computed and stored in WSAVE.
!
! Modified:
!
! 09 March 2001
!
! Author:
!
! Paul Swarztrauber,
! National Center for Atmospheric Research
!
! Reference:
!
! David Kahaner, Clever Moler, Steven Nash,