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[FIX] cosmui, sinmu have wrong normalization factors for lasym=T #22

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merged 12 commits into from
Jul 5, 2023
Merged

[FIX] cosmui, sinmu have wrong normalization factors for lasym=T #22

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fcf3121
add dnorm3 in fixaray; adjust computation of dnorm and cosmui3
jonathanschilling Mar 9, 2022
8a1ed23
use ntheta2-1 for dnorm3 instead of ntheta3(==ntheta2 in lasym=F case)
jonathanschilling Mar 9, 2022
a8d3857
tcon profile does not need to be scaled down by 0.5 in asymmetric mod…
jonathanschilling Mar 15, 2022
3515dc0
also comment out tcon*=0.5 in PARVMEC=F branch
jonathanschilling Mar 15, 2022
e1fac5e
add comments for dnorm, dnorm3
jonathanschilling Mar 17, 2022
82f401b
cosmui, sinmui-induced changes in jxbforce, wrout
jonathanschilling Mar 17, 2022
05e2f16
Add test for asymmetric cases.
cianciosa Apr 3, 2023
38732f2
Fix test and file names.
cianciosa Apr 3, 2023
99dab86
Force symmetry in the theta angles and special case the Pi value for …
cianciosa Jun 23, 2023
e16ceb7
Relax test tolarance since wint is causing rounding errors.
cianciosa Jun 23, 2023
59fcb42
Add just test tolarance.
cianciosa Jul 5, 2023
0c0893d
Adjust test tolarance.
cianciosa Jul 5, 2023
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8 changes: 4 additions & 4 deletions Sources/General/bcovar.f
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Original file line number Diff line number Diff line change
Expand Up @@ -447,9 +447,9 @@ SUBROUTINE bcovar_par(lu, lv, tpxc, ier_flag)
1 ABS(azd(js,1)/aznorm))*tcon_mul*(32*hs)**2
END DO
tcon(ns) = p5*tcon(ns - 1)
IF (lasym) THEN
tcon = p5*tcon
END IF
! IF (lasym) THEN
! tcon = p5*tcon
! END IF
#endif
ENDIF

Expand Down Expand Up @@ -878,7 +878,7 @@ SUBROUTINE bcovar (lu, lv)
& ABS(azd(js,1)/aznorm))*tcon_mul*(32*hs)**2
END DO
tcon(ns) = p5*tcon(ns-1)
IF (lasym) tcon = p5*tcon
!IF (lasym) tcon = p5*tcon
#endif
ENDIF

Expand Down
89 changes: 72 additions & 17 deletions Sources/Initialization_Cleanup/fixaray.f
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Original file line number Diff line number Diff line change
@@ -1,6 +1,6 @@
SUBROUTINE fixaray
USE vmec_main, p5 => cp5
USE vmec_params, ONLY: jmin2, mscale, nscale,
USE vmec_params, ONLY: jmin2, mscale, nscale,
& mnyq, nnyq, signgs
#ifdef _HBANGLE
USE angle_constraints, ONLY: init_multipliers
Expand All @@ -15,7 +15,7 @@ SUBROUTINE fixaray
C-----------------------------------------------
INTEGER :: i, m, j, n, mn, mn1, nmin0, istat1, istat2
INTEGER :: mnyq0, nnyq0
REAL(dp) :: argi, arg, argj, dnorm, tfixon, tfixoff
REAL(dp) :: argi, arg, argj, dnorm, dnorm3, tfixon, tfixoff
C-----------------------------------------------
!
! INDEX OF LOCAL VARIABLES
Expand All @@ -27,11 +27,11 @@ SUBROUTINE fixaray
!
! COMPUTE TRIGONOMETRIC FUNCTION ARRAYS
! NOTE: ARRAYS ALLOCATED HERE ARE GLOBAL AND ARE DEALLOCATED IN FILEOUT
! NOTE: NEED 2 X NYQUIST FOR FAST HESSIAN CALCULATIONS
! NOTE: NEED 2 X NYQUIST FOR FAST HESSIAN CALCULATIONS
!
mnyq0 = ntheta1/2
nnyq0 = nzeta/2

mnyq = MAX(0, 2*mnyq0, 2*mpol1)
nnyq = MAX(0, 2*nnyq0, 2*ntor)

Expand All @@ -56,12 +56,48 @@ SUBROUTINE fixaray
STOP 'allocation error in fixaray: istat2'
END IF

dnorm = one/(nzeta*(ntheta2 - 1))
IF (lasym) THEN
dnorm = one/(nzeta*ntheta3) !Fix, SPH012314
END IF

mscale(0) = 1; nscale(0) = 1
! dnorm is the normalization factor for Fourier integrals
! on the reduced poloidal interval [0, pi].
!
! All forward Fourier transforms in VMEC are performed as follows:
! 1. Decompose the function to be transformed into
! an even-parity contribution and an odd-parity contribution (symforce).
! 2. Fourier-transform the two definite-parity contributions
! separately over the reduced poloidal interval [0, pi] (tomnsp*).
!
! Inverse Fourier transforms are performed as follows:
! 1. Inverse-Fourier-transform the even-parity and odd-parity
! contributions separately (totzsp*)
! into the reduced poloidal interval [0, pi].
! 2. Combine the definite-parity contributions into
! the full poloidal interval [0, 2 pi[ (symrzl).
!
! In the symmetric case, only contributions with that parity
! which a given quantity has under the assumption of symmetry,
! are transformed. This allows to skip the sym* routines
! in the symmetric case.
dnorm = one/(nzeta*(ntheta2 - 1))

! dnorm3 is the normalization factor for the surface-averaging integrals.
! These integrals are always performed in realspace
! and thus, they need to adapt to the number of poloidal grid points.
! In the asymmetric case, there are ntheta1 grid points spanning [0, 2 pi[.
! In the symmetric case, there are ntheta2 grid points spanning [0, pi].
!
! In the asymmetric case, the integral is performed
! over the full period of the poloidal interval.
! Thus, the trapezoidal rule applied here does not need
! the factors of 1/2 at the endpoints.
! In the symmetric case, the integral is performed
! over the reduced poloidal interval, which is not a periodic domain anymore.
! Thus, the factors 1/2 have to be taken into account at the endpoints.
if (lasym) then
dnorm3 = one/(nzeta*ntheta1)
else
dnorm3 = one/(nzeta*(ntheta2 - 1))
end if

mscale(0) = 1; nscale(0) = 1
! mscale(0) = osqrt2; nscale(0) = osqrt2 !versions < 6.9, incorrectly used osqrt2

mscale(1:mnyq) = mscale(0)/osqrt2
Expand All @@ -75,17 +111,36 @@ SUBROUTINE fixaray
argi = twopi*(i - 1)/ntheta1
DO m = 0, mnyq
arg = argi*m
cosmu(i,m) = COS(arg)*mscale(m)
sinmu(i,m) = SIN(arg)*mscale(m)

! Special case the Pi angle.
IF (i .eq. ntheta2) THEN
IF (MOD(m, 2) .eq. 0) THEN
cosmu(i,m) = mscale(m)
ELSE
cosmu(i,m) = -mscale(m)
END IF
sinmu(i,m) = 0
ELSE IF (i .gt. ntheta2) THEN
! Force symmetry for angles indices over ntheta2
cosmu(i,m) = cosmu(2*ntheta2 - i,m)
sinmu(i,m) = -sinmu(2*ntheta2 - i,m)
ELSE
cosmu(i,m) = COS(arg)*mscale(m)
sinmu(i,m) = SIN(arg)*mscale(m)
END IF

cosmui(i,m) = dnorm*cosmu(i,m)
cosmui3(i,m) = cosmui(i,m) !Use this if integration over FULL 1,ntheta3 interval
sinmui(i,m) = dnorm*sinmu(i,m)
IF (i.EQ.1 .OR. i.EQ.ntheta2) THEN
cosmui(i,m) = cosmui(i,m)/2
END IF
IF (ntheta2 .EQ. ntheta3) THEN
cosmui3(i,m) = cosmui(i,m)
END IF

! Use this if integration over FULL 1,ntheta3 interval
cosmui3(i,m) = dnorm3*cosmu(i,m)
if (.not.lasym .and. (i.EQ.1 .OR. i.EQ.ntheta2)) then
cosmui3(i,m) = cosmui3(i,m)/2
end if

cosmum(i,m) = cosmu(i,m)*(m)
sinmum(i,m) = -sinmu(i,m)*(m)
cosmumi(i,m) = cosmui(i,m)*(m)
Expand All @@ -97,7 +152,7 @@ SUBROUTINE fixaray
DO j = 1, nzeta
argj = twopi*(j - 1)/nzeta
DO n = 0, nnyq
arg = argj*(n)
arg = argj*n
cosnv(j,n) = COS(arg)*nscale(n)
sinnv(j,n) = SIN(arg)*nscale(n)
cosnvn(j,n) = cosnv(j,n)*(n*nfp)
Expand Down
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