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Last active Aug 29, 2015

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Fortran implementation of the Generalized Lomb-Scargle (GLS) periodogram
f2py --quiet --f90flags="-fopenmp" --opt="-O3" -lgomp -m glombscargle -c lombscargle_generalized.f90
GLS periodogram
SUBROUTINE GLOMBSCARGLE(T, Y, SIG, W, NCPU, P, M, NT, NW)
!f2py threadsafe
!f2py intent(in) T(NT)
!f2py intent(in) Y(NT)
!f2py intent(in) SIG(NT)
!f2py intent(in) W(NW)
!f2py integer intent(in), optional :: NCPU = -1
!f2py intent(out) P(NW)
!f2py intent(out) M
!f2py intent(hide) NT
!f2py intent(hide) NW
use omp_lib
IMPLICIT NONE
!* Input arguments
INTEGER NT, NW, M
INTEGER,optional :: NCPU
REAL (KIND=8) T(NT), Y(NT), SIG(NT)
REAL (KIND=8) W(NW), P(NW)
!* Calculate the Generalized Lomb-Scargle (GLS) periodogram as defined by
!* Zechmeister, M. & Kürster, M., A&A 496, 577-584, 2009 (ZK2009)
!*
!* Arguments
!* =========
!*
!* T (input) REAL (KIND=8) array, dimension (NT)
!* Sample times
!*
!* Y (input) REAL (KIND=8) array, dimension (NT)
!* Measurement values
!*
!* SIG (input) REAL (KIND=8) array, dimension (NT)
!* Measured uncertainties
!*
!* W (input) REAL (KIND=8) array, dimension (NW)
!* Angular frequencies for output periodogram
!*
!* NCPU (input) INTEGER, OPTIONAL
!* Number of CPUs to distribute calculation
!*
!* P (output) REAL (KIND=8) array, dimension (NW)
!* Lomb-Scargle periodogram
!*
!* NT (input) integer
!* Dimension of input arrays
!*
!* NW (output) integer
!* Dimension of frequency and output arrays
!* Local variables
INTEGER I, J
REAL (KIND=8) sig2(NT), ww(NT), th(NT), yh(NT)
REAL (KIND=8) upow(NW), a(NW), b(NW), off(NW)
REAL (KIND=8) pi, pi2, pi4
REAL (KIND=8) Y_, YY, C, S, YC, YS, CCh, CSh, SSh, CC, SS, CS, D
REAL (KIND=8) x(NT), cosx(NT), sinx(NT), wcosx(NT), wsinx(NT)
pi2 = 6.2831853071795862d0
pi4 = 12.566370614359172d0
th = T
sig2 = sig*sig
ww = (1.d0 / sum(1.d0/sig2)) / sig2 ! w of ZK2009, the normalized weights
Y_ = sum(ww*Y) ! Eq. (7)
yh = Y - Y_ ! Subtract weighted mean
YY = sum(ww * yh**2) ! Eq. (16)
! Unnormalized power
upow = 0.d0
a = 0.d0
b = 0.d0
off = 0.d0
! If NCPU is present, distribute the calculation using OpenMP
if (present(NCPU).and.(.not.(NCPU.eq.-1))) then
call OMP_SET_NUM_THREADS(NCPU)
else
call OMP_SET_NUM_THREADS(1)
endif
!$OMP PARALLEL DO &
!$OMP PRIVATE(x,cosx,sinx,wcosx,wsinx,C,S,YC,YS,CCh,CSh,SSh,CC,SS,CS,D)
do I=1,NW
x = W(I) * th
cosx = cos(x)
sinx = sin(x)
wcosx = ww*cosx ! attach weights
wsinx = ww*sinx ! attach weights
C = sum(wcosx) ! Eq. (8)
S = sum(wsinx) ! Eq. (9)
YC = sum(yh*wcosx) ! Eq. (17)
YS = sum(yh*wsinx) ! Eq. (18)
CCh = sum(wcosx*cosx) ! Eq. (13)
CSh = sum(wcosx*sinx) ! Eq. (15)
SSh = 1.d0 - CCh
CC = CCh - C*C ! Eq. (13)
SS = SSh - S*S ! Eq. (14)
CS = CSh - C*S ! Eq. (15)
D = CC*SS - CS*CS ! Eq. (6)
a(I) = (YC*SS-YS*CS) / D
b(I) = (YS*CC-YC*CS) / D
off(I) = -a(I)*C - b(I)*S
upow(I) = (SS*YC*YC + CC*YS*YS - 2.d0*CS*YC*YS) / (YY*D) ! Eq. (5)
end do
!$OMP END PARALLEL DO
! An ad-hoc estimate of the number of independent frequencies
! see discussion following Eq. (24)
M = (maxval(W/pi2) - minval(W/pi2)) * (maxval(th) - minval(th))
P = upow
END SUBROUTINE GLOMBSCARGLE
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