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eig_project.f90
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eig_project.f90
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!-------------------------------------------------------------------------------------
! eigvec_projection
!-------------------------------------------------------------------------------------
! Copyright (c) 2017 Daniel C. Elton
!
! This software is licensed under The MIT License (MIT)
! 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.
!-------------------------------------------------------------------------------------
module eig_project
use main_vars
implicit none
contains
!-----------------------------------------------------------------------
!----------------- project velocities onto eigenvector k --------------
!-----------------------------------------------------------------------
subroutine calculate_frequencies_and_smoothing
implicit none
integer :: PointsAvailable
real(8) :: MaxFreqPossible
length = Ntimesteps
!------------ figure out variables for smoothing --------------
!for fft - has to be power of 2
trun = 2**( floor( dlog( dble(Ntimesteps) )/dlog(2d0) ) + 1 )
!MinFreqOut = 1/(timestep*trun*Cspeed*ps2s) !smallest possible frequency
!MaxFreqPossible = 1/(2*timestep) !largest frequency
PointsAvailable = trun/2 !spectrum will be folded over this point
if (PointsAvailable .lt. NPointsOut) NPointsOut = PointsAvailable
BlockSize = floor(real(PointsAvailable/NPointsOut))
!------------ allocations --------------
allocate(freqs_smoothed(NPointsOut))
allocate(all_SED_smoothed(Nk, Neig, NPointsOut))
if (BTEMD) allocate(all_corr_fns(Nk, Neig, Ncorrptsout))
!------------ find frequencies for smoothed data ---------------
do i = 0, NPointsOut-1
freqs_smoothed(i+1) = ( floor((i+.5)*BlockSize) )/(timestep*trun) !use central frequency
enddo
freqs_smoothed = freqs_smoothed/(Cspeed*ps2s) !convert to 1/cm
!------------ create exponential window function ---------------
!------------ in case we want to use windowing later -----------
!tau_window = 0.01*Ntimesteps
!tau_window = 8.69*Ntimesteps/(2*Decibels_reduced)
!allocate(window_fn(Ntimesteps))
!do i = 1, Ntimesteps!
! window_fn(i) = dexp( - abs(i - (Ntimesteps-1)/2) /tau_window)
!enddo
end subroutine calculate_frequencies_and_smoothing
!-----------------------------------------------------------------------
!----------------- project velocities onto eigenvector k --------------
!----------------- frequency domain method ---------------------------
!-----------------------------------------------------------------------
subroutine eigen_projection_and_SED(eig, SED_smoothed, ik)
implicit none
integer, intent(in) :: ik
double complex, dimension(Natoms, 3), intent(in) :: eig !!Eigenvector to project onto
real(8), dimension(NpointsOut), intent(out) :: SED_smoothed
real(8), dimension(trun) :: SED
double complex :: part1
!-------- projection
do t = 1, Ntimesteps
qdot(t) = 0
do ix = 1,3
do ia = 1, Natoms
part1 = MassPrefac(ia)*velocities(t, ia, ix)*conjg(eig(ia, ix))
qdot(t) = qdot(t) + part1*exp( dcmplx(0, 1)*dot_product(k_vectors(ik, :), r(ia, :)) )
enddo
enddo
enddo
!------ (optional and typically not needed) apply window function
!SED = SED*window_fn
!--------- calculate Spectral Energy Density
call calc_DFT_squared(qdot, SED, length, trun)
SED = (1d0/3.14159d0)*SED/timestep !!*(1d0/(2*length) ) division performed in DFT routine
!------- block averaging / smoothing
do i = 1, NPointsOut
SED_smoothed(i) = sum(SED((i-1)*BlockSize+1:i*BlockSize) ) /BlockSize
enddo
end subroutine eigen_projection_and_SED
!------------------------------------------------------------------------------
!- Time domain (energy autocorrelation) method -----------------------------
!------------------------------------------------------------------------------
subroutine BTE_MD(eig, SED_smoothed, ik, ie, BTEMD_corr_fun_out)
implicit none
integer, intent(in) :: ik, ie
double complex, dimension(Natoms, 3), intent(in) :: eig !!Eigenvector to project onto
real(8), dimension(NpointsOut), intent(out) :: SED_smoothed
real(8), dimension(Ncorrptsout), intent(out) :: BTEMD_corr_fun_out
real(8), dimension(Ntimesteps) :: Ekw, SED, BTEMD_corr_fun
double complex :: exppart, q1, qdot
!-------- projection
do t = 1, Ntimesteps
qdot = dcmplx(0, 0)
q1 = dcmplx(0, 0)
do ia = 1, Natoms
exppart = exp( dcmplx(0, 1)*dot_product(k_vectors(ik, :), r_eq(ia, :)) )
qdot = qdot + MassPrefac(ia)*dot_product(velocities(t, ia, :), conjg(eig(ia, :)))*exppart
!q1 = q1 + MassPrefac(ia)*dot_product(coordinates(t, ia, :) - r_eq(ia, :), eig(ia, :))*exppart
enddo
Ekw(t) = qdot !qdot*conjg(qdot)/2d0 !+ (freqs(ik, ie)**2)*q1*conjg(q1)/2d0
enddo
!--------- calculate correlation function
call calc_corr_function2(Ekw, BTEMD_corr_fun, Ntimesteps)
BTEMD_corr_fun_out = BTEMD_corr_fun(1:Ncorrptsout)/BTEMD_corr_fun(1) !normalize
!--------- calculate Spectral Energy Density for the mode
call calc_DFT(dcmplx(BTEMD_corr_fun), SED, length, trun)
SED = (1d0/3.14159d0)*SED/timestep !!*(1d0/(2*length) ) division performed in DFT routine
!------- block averaging / smoothing
do i = 1, NPointsOut
SED_smoothed(i) = sum(SED((i-1)*BlockSize+1:i*BlockSize) ) /BlockSize
enddo
end subroutine BTE_MD
!------------------------------------------------------------------------
!------- Compute DFT squared (discrete Fourier transform) using four1.f
!------------------------------------------------------------------------
subroutine calc_DFT_squared(input, output, tread, trun)
Implicit none
integer, intent(in) :: tread, trun
double complex, dimension(tread), intent(in) :: input
double precision, dimension(trun), intent(out) :: output
complex, dimension(:), allocatable :: transformed
if (.not. allocated(transformed)) then
allocate(transformed(0:trun-1))
elseif (.not. (trun .eq. size(transformed))) then
deallocate(transformed)
allocate(transformed(0:trun-1))
endif
transformed = 0
transformed(0:tread-1) = input
call four1(transformed, trun, 1)
output=dble(transformed(0:trun-1)*CONJG(transformed(0:trun-1)))/(trun)
end subroutine calc_DFT_squared
!------------------------------------------------------------------------
!---------------- Compute AUTOcorrelation function using four1.f-------
!------------------------------------------------------------------------
subroutine calc_corr_function2(input,output,N)
Implicit none
double precision, dimension(N), intent(in) :: input
real(8), dimension(N), intent(out) :: output
integer, intent(in) :: N
double complex, dimension(:), allocatable :: input_padded, output_padded
complex, dimension(:), allocatable :: transformed
integer*8 :: plan=0, i, trun
if (.not.(allocated(input_padded))) then
!find closest power of 2 greater than number of steps
trun = 2**( floor( dlog( dble(N) )/dlog(2d0) ) + 1 )
allocate(input_padded(2*trun))
allocate(output_padded(2*trun))
allocate(transformed(2*trun))
endif
input_padded = 0
input_padded(1:N) = cmplx(input)
transformed = real(input_padded)
call four1(transformed,2*trun,1)
transformed = transformed*conjg(transformed)
call four1(transformed,2*trun,-1)
output = dble(transformed(1:N))/N
!normalization 1
do i = 1, N-1
output(i) = output(i)/(N-i)
enddo
end subroutine calc_corr_function2
!------------------------------------------------------------------------
!------- Compute DFT (discrete Fourier transform) using four1.f
!------------------------------------------------------------------------
subroutine calc_DFT(input, output, tread, trun)
Implicit none
integer, intent(in) :: tread, trun
double complex, dimension(tread), intent(in) :: input
double precision, dimension(trun), intent(out) :: output
complex, dimension(:), allocatable :: transformed
if (.not. allocated(transformed)) then
allocate(transformed(0:trun-1))
elseif (.not. (trun .eq. size(transformed))) then
deallocate(transformed)
allocate(transformed(0:trun-1))
endif
transformed = 0
transformed(0:tread-1) = input
call four1(transformed, trun, 1)
output=dble(transformed(0:trun-1))/trun
end subroutine calc_DFT
end module eig_project