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AA
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@inline function triSolve!(x,tri,b)
# Thomas algorithm, b and x used as intermediate storage
# b is destroyed after the elemination
n = size(tri,2)
x[1] = tri[2,1]
for i=1:n-1
x[i+1] = tri[2,i+1]-tri[3,i]/x[i]*tri[1,i+1]
b[i+1] = b[i+1]-tri[3,i]/x[i]*b[i]
end
x[n] = b[n]/x[n]
for i=n-1:-1:1
x[i]=(b[i] - tri[1,i+1]*x[i+1])/x[i]
end
end
@inline function mulUL!(tri,biU,biL)
n = size(biL,2)
tri[2,1] = tri[2,1] - biU[2,1]*biL[1,1] - biU[1,1]*biL[2,1]
tri[3,1] = tri[3,1] - biU[2,2]*biL[2,1]
for i=2:n-1
tri[1,i] = tri[1,i] - biU[1,i-1]*biL[1,i]
tri[2,i] = tri[2,i] - biU[2,i]*biL[1,i] - biU[1,i]*biL[2,i]
tri[3,i] = tri[3,i] - biU[2,i+1]*biL[2,i]
end
tri[1,n] = tri[1,n] - biU[1,n-1]*biL[1,n]
tri[2,n] = tri[2,n] - biU[2,n]*biL[1,n] - biU[1,n]*biL[2,n]
end
@inline function mulbiUv!(u,biU,v)
n = size(biU,2)
for i=1:n
u[i] = u[i] + biU[2,i]*v[i] + biU[1,i]*v[i+1]
end
end
@inline function mulbiLv!(u,biL,v)
n = size(biL,2)
u[1] = u[1] + biL[1,1]*v[1]
for i=2:n
u[i] = u[i] + biL[2,i-1]*v[i-1] + biL[1,i]*v[i]
end
u[n+1] = u[n+1] + biL[2,n]*v[n]
end
@kernel inbounds = true function TriDiagKernel!(tri,@Const(JRhoW),@Const(JWRho),@Const(JWRhoTh),@Const(JRhoThW),fac)
Iz,IC, = @index(Global, NTuple)
NumG = @uniform @ndrange()[2]
Nz = @uniform @ndrange()[1]
invfac = eltype(tri)(1) / fac
invfac2 = invfac / fac
if IC <= NumG
if Iz == 1
tri[1,Iz,IC] = eltype(tri)(0)
tri[2,Iz,IC] = invfac2 - JWRho[2,Iz,IC] * JRhoW[1,Iz,IC] - JWRho[1,Iz,IC] * JRhoW[2,Iz,IC] -
JWRhoTh[2,Iz,IC] * JRhoThW[1,Iz,IC] - JWRhoTh[1,Iz,IC] * JRhoThW[2,Iz,IC]
tri[3,Iz,IC] = - JWRho[2,Iz+1,IC] * JRhoW[2,Iz,IC] -
JWRhoTh[2,Iz+1,IC] * JRhoThW[2,Iz,IC]
elseif Iz == Nz
tri[1,Iz,IC] = - JWRho[1,Iz-1,IC] * JRhoW[1,Iz,IC] -
JWRhoTh[1,Iz-1,IC] * JRhoThW[1,Iz,IC]
tri[2,Iz,IC] = invfac2 - JWRho[2,Iz,IC] * JRhoW[1,Iz,IC] - JWRho[1,Iz,IC] * JRhoW[2,Iz,IC] -
JWRhoTh[2,Iz,IC] * JRhoThW[1,Iz,IC] - JWRhoTh[1,Iz,IC] * JRhoThW[2,Iz,IC]
tri[3,Iz,IC] = eltype(tri)(0)
else
tri[1,Iz,IC] = - JWRho[1,Iz-1,IC] * JRhoW[1,Iz,IC] -
JWRhoTh[1,Iz-1,IC] * JRhoThW[1,Iz,IC]
tri[2,Iz,IC] = invfac2 - JWRho[2,Iz,IC] * JRhoW[1,Iz,IC] - JWRho[1,Iz,IC] * JRhoW[2,Iz,IC] -
JWRhoTh[2,Iz,IC] * JRhoThW[1,Iz,IC] - JWRhoTh[1,Iz,IC] * JRhoThW[2,Iz,IC]
tri[3,Iz,IC] = - JWRho[2,Iz+1,IC] * JRhoW[2,Iz,IC] -
JWRhoTh[2,Iz+1,IC] * JRhoThW[2,Iz,IC]
end
end
end
@kernel inbounds = true function SchurSolveFKernel!(k,v,@Const(JWRho),@Const(JWRhoTh),fac)
Iz,IC, = @index(Global, NTuple)
NumG = @uniform @ndrange()[2]
Nz = @uniform @ndrange()[1]
if IC <= NumG
if Iz < Nz
v[Iz,IC,4] = v[Iz,IC,4] / fac + JWRho[2,Iz,IC] * v[Iz,IC,1] + JWRho[1,Iz,IC] * v[Iz+1,IC,1] +
JWRhoTh[2,Iz,IC] * v[Iz,IC,5] + JWRhoTh[1,Iz,IC] * v[Iz+1,IC,5]
else
k[Iz,IC,4] = 0
end
end
end
@kernel inbounds = true function SchurSolveBKernel!(NumVTr,k,v,@Const(JRhoW),@Const(JRhoThW),fac)
Iz,IC, = @index(Global, NTuple)
NumG = @uniform @ndrange()[2]
Nz = @uniform @ndrange()[1]
if IC <= NumG
if Iz == 1
v[Iz,IC,1] += JRhoW[1,Iz,IC] * k[Iz,IC,4]
v[Iz,IC,5] += JRhoThW[1,Iz,IC] * k[Iz,IC,4]
elseif Iz == Nz
v[Iz,IC,1] += JRhoW[2,Iz-1,IC] * k[Iz-1,IC,4]
v[Iz,IC,5] += JRhoThW[2,Iz-1,IC] * k[Iz-1,IC,4]
else
v[Iz,IC,1] += JRhoW[1,Iz,IC] * k[Iz,IC,4] + JRhoW[2,Iz-1,IC] * k[Iz-1,IC,4]
v[Iz,IC,5] += JRhoThW[1,Iz,IC] * k[Iz,IC,4] + JRhoThW[2,Iz-1,IC] * k[Iz-1,IC,4]
end
k[Iz,IC,1] = fac * v[Iz,IC,1]
k[Iz,IC,2] = fac * v[Iz,IC,2]
k[Iz,IC,3] = fac * v[Iz,IC,3]
k[Iz,IC,5] = fac * v[Iz,IC,5]
for iT = 6 : NumVTr
k[Iz,IC,iT] = fac * v[Iz,IC,iT]
end
end
end
@kernel inbounds = true function SchurSolveTriKernel!(Nz,k,v,@Const(tri))
IG = @index(Local, NTuple)
IC, = @index(Global, NTuple)
NumG = @uniform @ndrange()[1]
triCol = @localmem eltype(F) (3,Nz,NumG)
vCol = @localmem eltype(F) (Nz,NumG)
kCol = @localmem eltype(F) (Nz,NumG)
if IC <= NumG
@. @views triCol[:,:,IG] = tri[:,:,IC]
@. @views vCol[:,:,IG] = v[:,IC,4]
end
if IC <= NumG
@views triSolve!(kCol[:,iG],triCol[:,:,IC],v[1:Nz-1,IC,4])
end
if IC <= NumG
@. @views k[:,IC,4] = vCol[:,IG]
end
end
NVTX.@annotate function SchurSolveGPU!(k,v,J,fac,Cache,Global)
backend = get_backend(k)
FT = eltype(k)
Nz = size(k,1)
NumG = size(k,2)
NumVTr = size(k,3)
group = (Nz,10)
ndrange = (Nz,NumG)
groupTriDiag = (Nz-1,10)
ndrangeTriDiag = (Nz-1,NumG)
# group = (1024)
groupTri = (64)
ndrangeTri = (NumG)
if J.CompTri
KTriDiagKernel! = TriDiagKernel!(backend,groupTriDiag)
KTriDiagKernel!(J.tri,J.JRhoW,J.JWRho,J.JWRhoTh,J.JRhoThW,fac,ndrange=ndrangeTriDiag)
J.CompTri = false
end
KSchurSolveFKernel! = SchurSolveFKernel!(backend,group)
KSchurSolveFKernel!(k,v,J.JWRho,J.JWRhoTh,fac,ndrange=ndrange)
KSchurSolveTriKernel! = SchurSolveTriKernel!(backend,groupTri)
KSchurSolveTriKernel!(Nz,k,v,J.tri,ndrange=ndrangeTri)
KSchurSolveBKernel! = SchurSolveBKernel!(backend,group)
KSchurSolveBKernel!(NumVTr,k,v,J.JRhoW,J.JRhoThW,fac,ndrange=ndrange)
end
function SchurSolve!(k,v,J,fac,Cache,Global)
# sw=(spdiags(repmat(invfac2,n,1),0,n,n)-invfac*JWW-JWRho*JRhoW-JWRhoTh*JRhoThW)\
# (invfac*rw+JWRho*rRho+JWRhoTh*rTh)
n1 = size(v,1)
n2 = size(v,2)
n = n1 * n2
tri = J.tri
JWRho = J.JWRho
JRhoW = J.JRhoW
JWRhoTh = J.JWRhoTh
JRhoThW=J.JRhoThW
JTrW=J.JTrW
JWW=J.JWW
JDiff = J.JDiff
JAdvC = J.JAdvC
JAdvF = J.JAdvF
@views CdTh = Cache.Aux2DG[:,:,1]
@views CdTr = Cache.Aux2DG[:,:,2:end]
NumV = Global.Model.NumV
if size(k,3) > Global.Model.NumV
NumTr = Global.Model.NumTr
else
NumTr = 0
end
invfac=1/fac
invfac2=invfac/fac
if Global.Model.JacVerticalDiffusion && Global.Model.JacVerticalAdvection
for in2=1:n2
if J.CompTri
@views @. JAdvC[2,:,in2] += invfac
@views @. JAdvF[2,:,in2] += invfac
@views @. JDiff[:,:,in2] += JAdvC[:,:,in2]
end
JDiff[2,1,in2] += CdTh[1,in2]
@views rTh = v[:,in2,5]
@views sTh = k[:,in2,5]
@views triSolve!(sTh,JDiff[:,:,in2],rTh)
@. rTh = invfac * sTh
JDiff[2,1,in2] -= CdTh[1,in2]
@views rTh = v[:,in2,2]
@views sTh = k[:,in2,2]
@views triSolve!(sTh,JAdvC[:,:,in2],rTh)
@. rTh = invfac * sTh
@views rTh=v[:,in2,3]
@views sTh=k[:,in2,3]
@views triSolve!(sTh,JAdvC[:,:,in2],rTh)
@. rTh = invfac * sTh
@views rTh=v[1:n1-1,in2,4]
@views sTh=k[1:n1-1,in2,4]
@views triSolve!(sTh,JAdvF[:,:,in2],rTh)
@. rTh = invfac * sTh
end
if Global.Model.Equation == "CompressibleMoist"
for in2=1:n2
JDiff[2,1,in2] += CdTr[1,in2,1]
@views rTh=v[:,in2,NumV+1]
@views sTh=k[:,in2,NumV+1]
@views triSolve!(sTh,JDiff[:,:,in2],rTh)
@. rTh = invfac * sTh
JDiff[2,1,in2] -= CdTr[1,in2,1]
end
end
elseif Global.Model.JacVerticalAdvection
for in2=1:n2
if J.CompTri
@views @. JAdvC[2,:,in2] += invfac
@views @. JAdvF[2,:,in2] += invfac
end
@views rTh = v[:,in2,1]
@views sTh = k[:,in2,1]
@views triSolve!(sTh,JAdvC[:,:,in2],rTh)
@. rTh = invfac * sTh
@views rTh = v[:,in2,2]
@views rTh = v[:,in2,5]
@views sTh = k[:,in2,5]
@views triSolve!(sTh,JAdvC[:,:,in2],rTh)
@. rTh = invfac * sTh
@views rTh = v[:,in2,2]
@views sTh = k[:,in2,2]
@views triSolve!(sTh,JAdvC[:,:,in2],rTh)
@. rTh = invfac * sTh
@views rTh=v[:,in2,3]
@views sTh=k[:,in2,3]
@views triSolve!(sTh,JAdvC[:,:,in2],rTh)
@. rTh = invfac * sTh
@views rTh=v[1:n1-1,in2,4]
@views sTh=k[1:n1-1,in2,4]
@views triSolve!(sTh,JAdvF[:,:,in2],rTh)
@. rTh = invfac * sTh
end
if Global.Model.Equation == "CompressibleMoist"
for in2=1:n2
@views rTh=v[:,in2,NumV+1]
@views sTh=k[:,in2,NumV+1]
@views triSolve!(sTh,JAdvC[:,:,in2],rTh)
@. rTh = invfac * sTh
end
end
end
if Global.Model.Equation == "Compressible"
for in2=1:n2
@views rRho=v[:,in2,1]
@views rTh=v[:,in2,5]
@views rw=v[1:n1-1,in2,4]
@views sw=k[1:n1-1,in2,4]
k[n1,in2,4] = 0
if Global.Model.Damping
if J.CompTri
@views @. tri[1,:,in2] = 0
@views @. tri[2,:,in2] = invfac2 - invfac * JWW[1,:,in2]
@views @. tri[3,:,in2] = 0
@views mulUL!(tri[:,:,in2],JWRho[:,:,in2],JRhoW[:,:,in2])
@views mulUL!(tri[:,:,in2],JWRhoTh[:,:,in2],JRhoThW[:,:,in2])
end
@. rw = invfac * rw
@views mulbiUv!(rw,JWRho[:,:,in2],rRho)
@views mulbiUv!(rw,JWRhoTh[:,:,in2],rTh)
@views triSolve!(sw,tri[:,:,in2],rw)
else
if J.CompTri
@views @. tri[1,:,in2] = 0
@views @. tri[2,:,in2] = invfac2
@views @. tri[3,:,in2] = 0
@views mulUL!(tri[:,:,in2],JWRho[:,:,in2],JRhoW[:,:,in2])
@views mulUL!(tri[:,:,in2],JWRhoTh[:,:,in2],JRhoThW[:,:,in2])
end
@. rw = invfac * rw
@views mulbiUv!(rw,JWRho[:,:,in2],rRho)
@views mulbiUv!(rw,JWRhoTh[:,:,in2],rTh)
@views triSolve!(sw,tri[:,:,in2],rw)
end
@views mulbiLv!(rRho,JRhoW[:,:,in2],sw)
@views mulbiLv!(rTh,JRhoThW[:,:,in2],sw)
@views @. k[:,in2,1] = fac * rRho
@views @. k[:,in2,2:3] = fac * v[:,in2,2:3]
@views @. k[:,in2,5] = fac * rTh
for iT = 1 : NumTr
@views mulbiLv!(v[:,in2,5+iT],JTrW[:,:,in2,iT],sw)
@views @. k[:,in2,5+iT] = fac * v[:,in2,5+iT]
end
if Global.Model.Damping
@views @. sw = sw / (1.0 - invfac * JWW[1,:,in2])
end
end
elseif Global.Model.Equation == "CompressibleMoist"
RhoVPos = Global.Model.RhoVPos
JWRhoV=J.JWRhoV
for in2=1:n2
@views rRho=v[:,in2,1]
@views rTh=v[:,in2,5]
@views rRhoV=v[:,in2,RhoVPos]
@views rw=v[:,in2,4]
@views sw=k[:,in2,4]
invfac=1/fac
invfac2=invfac/fac
if Global.Model.Damping
if J.CompTri
@views @. tri[1,:,in2] = 0
@views @. tri[2,:,in2] = invfac2 - invfac * JWW[1,:,in2]
@views @. tri[3,:,in2] = 0
@views mulUL!(tri[:,:,in2],JWRho[:,:,in2],JRhoW[:,:,in2])
@views mulUL!(tri[:,:,in2],JWRhoTh[:,:,in2],JRhoThW[:,:,in2])
@views mulUL!(tri[:,:,in2],JWRhoV[:,:,in2],JTrW[:,:,in2,RhoVPos])
end
@. rw = invfac * rw
@views mulbiUv!(rw,JWRho[:,:,in2],rRho)
@views mulbiUv!(rw,JWRhoV[:,:,in2],rRhoV)
@views mulbiUv!(rw,JWRhoTh[:,:,in2],rTh)
@views triSolve!(sw,tri[:,:,in2],rw)
else
if J.CompTri
@views @. tri[1,:,in2] = 0
@views @. tri[2,:,in2] = invfac2
@views @. tri[3,:,in2] = 0
@views mulUL!(tri[:,:,in2],JWRho[:,:,in2],JRhoW[:,:,in2])
@views mulUL!(tri[:,:,in2],JWRhoTh[:,:,in2],JRhoThW[:,:,in2])
@views mulUL!(tri[:,:,in2],JWRhoV[:,:,in2],JTrW[:,:,in2,RhoVPos])
end
@. rw = invfac * rw
@views mulbiUv!(rw,JWRho[:,:,in2],rRho)
@views mulbiUv!(rw,JWRhoV[:,:,in2],rRhoV)
@views mulbiUv!(rw,JWRhoTh[:,:,in2],rTh)
@views triSolve!(sw,tri[:,:,in2],rw)
end
@views mulbiLv!(rRho,JRhoW[:,:,in2],sw)
@views mulbiLv!(rTh,JRhoThW[:,:,in2],sw)
@views @. k[:,in2,1] = fac * rRho
@views @. k[:,in2,2:3] = fac * v[:,in2,2:3]
@views @. k[:,in2,5] = fac * rTh
for iT = 1 : NumTr
@views mulbiLv!(v[:,in2,5+iT],JTrW[:,:,in2,iT],sw)
@views @. k[:,in2,5+iT] = fac * v[:,in2,5+iT]
end
if Global.Model.Damping
@views @. sw = sw / (1.0 - invfac * JWW[1,:,in2])
end
end
end
J.CompTri=false
end