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CFunctions.py
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Sun, Nov 17, 15:51

CFunctions.py
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import numba as nb
from math import log, exp
@nb.njit(nogil=True, parallel=True)
def newpos(ii, r0, ds, uu, um):
"""
Compute new position along self.ijk direction
um: flux entering the cell
uu: flux exiting the cell
"""
if um != uu:
Du = uu - um
mDu = um / Du
# eq. 7.8 Doos et al 2013
return (r0 - ii + mDu) * exp(Du * ds) + ii - mDu
else:
return r0 + uu * ds
@nb.njit(nogil=True, parallel=True)
def cross(ijk, ia, ja, ka, i_futr, i_past, r0, flux):
"""
Compute crossing times
"""
# um: flux entering the cell
# uu: flux exiting the cell
# i_futr: interpolation coefficient for "future" GCM data
# i_past: interpolation coefficient for "past" GCM data
uu, um, ba, sp, sn, Du, ii = 0, 0, 0, 0, 0, 0, 0
UNDEF = 1.0e20
um = (i_futr * flux[1, ka, ja, ia] +
i_past * flux[0, ka, ja, ia])
if ijk == 1:
ii = ia
uu = (i_futr * flux[1, ka, ja, ia + 1] +
i_past * flux[0, ka, ja, ia + 1])
elif ijk == 2:
ii = ja
uu = (i_futr * flux[1, ka, ja + 1, ia] +
i_past * flux[0, ka, ja + 1, ia])
elif ijk == 3:
ii = ka
uu = (i_futr * flux[1, ka + 1, ja, ia] +
i_past * flux[0, ka + 1, ja, ia])
# east, north or upward crossing
if uu > 0 and (r0 != (ii + 1)):
if um != uu:
Du = (uu - um)
ba = (r0 - ii) * Du + um
if ba > 0:
# eq. 7.9 & 7.6 Doos et al. 2013
sp = (log(uu) - log(ba)) / Du
# It can still be that there is a
# zero flux somewhere between r0 and
# the face
if (sp <= 0.0):
sp = UNDEF
else:
sp = UNDEF
else:
sp = (1.0 + ii - r0) / uu
else:
sp = UNDEF
# west, south or downward crossing
if um < 0 and r0 != ii:
if um != uu:
# negative velocity, so we go from exit (uu)
# to enter (um)
Du = (um - uu)
# (ii)-----(r0)---(ii+1)
# (um)-----(ba)---(uu)
ba = (1 + ii - r0) * Du + uu
if ba < 0:
sn = (log(-ba) - log(-um)) / Du
# It can still be that there is a
# zero flux somewhere between r0 and
# the face
if sn <= 0:
sn = UNDEF
else:
sn = UNDEF
else:
sn = (ii - r0) / uu
else:
sn = UNDEF
return uu, um, sp, sn
@nb.njit(nogil=True, parallel=True)
def transform(ii, jj, kk, stxyz, CS, SN, dX, dY, xG, yG, Z):
for m in range(ii.size):
transform_one(ii[m], jj[m], kk[m], stxyz[m, :], CS, SN, dX, dY, xG, yG, Z)
@nb.njit(nogil=True, parallel=True)
def transform_one(i, j, k, stxyz, CS, SN, dX, dY, xG, yG, Z): # nogil
ii = int(i)
jj = int(j)
kk = int(k)
nx = i % 1
ny = j % 1
nz = k % 1
# inside the cell
if (nx >= 1e-9) & (ny >= 1e-9):
cosij = CS[jj, ii]
sinij = SN[jj, ii]
dxij = dX[jj, ii]
dyij = dY[jj, ii]
# x
stxyz[0] = xG[jj, ii] + \
cosij * dxij * nx - sinij * dyij * ny
# y
stxyz[1] = yG[jj, ii] + \
sinij * dxij * nx + cosij * dyij * ny
# z
if nz >= 1e-9:
stxyz[2] = (1.0 - nz) * Z[kk, jj, ii] + \
nz * Z[kk + 1, jj, ii]
else:
stxyz[2] = Z[kk, jj, ii]
# at the SW corner
elif (nx < 1e-9) & (ny < 1e-9):
# x
stxyz[0] = xG[jj, ii]
# y
stxyz[1] = yG[jj, ii]
# z
if nz >= 1e-9:
stxyz[2] = (1.0 - nz) * Z[kk, jj, ii] + \
nz * Z[kk + 1, jj, ii]
else:
stxyz[2] = Z[kk, jj, ii]
# on W face
elif nx < 1e-9:
cosij = CS[jj, ii]
sinij = SN[jj, ii]
dyij = dY[jj, ii]
# x
stxyz[0] = xG[jj, ii] - sinij * dyij * ny
# y
stxyz[1] = yG[jj, ii] + cosij * dyij * ny
# z
if nz >= 1e-9:
stxyz[2] = (1.0 - nz) * Z[kk, jj, ii] + \
nz * Z[kk + 1, jj, ii]
else:
stxyz[2] = Z[kk, jj, ii]
# on S face
else:
cosij = CS[jj, ii]
sinij = SN[jj, ii]
dxij = dX[jj, ii]
# x
stxyz[0] = xG[jj, ii] + cosij * dxij * nx
# y
stxyz[1] = yG[jj, ii] + sinij * dxij * nx
# z
if nz >= 1e-9:
stxyz[2] = (1.0 - nz) * Z[kk, jj, ii] + \
nz * Z[kk + 1, jj, ii]
else:
stxyz[2] = Z[kk, jj, ii]
@nb.njit(nogil=True, parallel=True)
def ext_loop(nvals, ntact,
xyz, ijk, out_xyz, out_tijk,
out_dt, outfreq,
nend, iendw, iende, jendn, jends,
imax, jmax, kmax, Adsmax, Adxyz, dtmax, dstep,
CS, SN, dX, dY, xG, yG, Z,
uflux, vflux, wflux, out_code):
ds, dse, dsw, dsn, dss, dsu, dsd = 0, 0, 0, 0, 0, 0, 0
for ntrac in range(ntact):
# initialize stuff
ts = 0.0 # normalised time between two GCM time steps
tt = 0.0 # time in seconds between two GCM time steps
# output init
for kk in range(nvals):
out_tijk[ntrac, kk, 0] = -1e20
rec_out = 0
# take coord
# the coordinate system is as follows:
# cell i
# |---------------------|
# i i <= x < i+1 i+1
x1 = xyz[ntrac, 0]
y1 = xyz[ntrac, 1]
z1 = xyz[ntrac, 2]
ib = ijk[ntrac, 0]
jb = ijk[ntrac, 1]
kb = ijk[ntrac, 2]
while True:
# time interpolation constants
i_futr = ts % 1.0
i_past = 1.0 - i_futr
x0 = x1
y0 = y1
z0 = z1
ia = ib
ja = jb
ka = kb
dsmax = Adsmax[kb, jb, ib]
dxyz = Adxyz[kb, jb, ib]
# make sure we do not start from land
# TODO do we still need this?
if dxyz == 0.0:
print("\nx0: %f\n", x0)
print("y0: %f\n", y0)
print("z0: %f\n", z0)
print("ia: %d\n", ia)
print("ja: %d\n", ja)
print("ka: %d\n", ka)
print("x1: %f\n", x1)
print("y1: %f\n", y1)
print("z1: %f\n", z1)
print("ib: %d\n", ib)
print("jb: %d\n", jb)
print("kb: %d\n", kb)
print("ds: %f\n", ds)
print("dsmax: %f\n", dsmax)
print("dxyz: %f\n", dxyz)
print("dsn: %f\n", dsn)
print("dss: %f\n", dss)
print("dse: %f\n", dse)
print("dsw: %f\n", dsw)
print("dsu: %f\n", dsu)
print("dsd: %f\n", dsd)
raise ValueError("Particule on land")
#
# calculate the 3 crossing times over the box
# choose the shortest time and calculate the
# new positions
#
# solving the differential equations
# note:
# space variables (x,...) are dimensionless
# time variables (ds,...) are in seconds/m^3
#
uu1, um1, dse, dsw = \
cross(1, ia, ja, ka, i_futr, i_past, x0, uflux)
vu1, vm1, dsn, dss = \
cross(2, ia, ja, ka, i_futr, i_past, y0, vflux)
wu1, wm1, dsu, dsd = \
cross(3, ia, ja, ka, i_futr, i_past, z0, wflux)
ds = min(min(min(min(min(min(dse, dsw), dsn), dss),
dsd), dsu), dsmax)
if (ds == 0.0) or (ds == 1e20):
print("\nx0: %f\n", x0)
print("y0: %f\n", y0)
print("z0: %f\n", z0)
print("ia: %d\n", ia)
print("ja: %d\n", ja)
print("ka: %d\n", ka)
print("x1: %f\n", x1)
print("y1: %f\n", y1)
print("z1: %f\n", z1)
print("ib: %d\n", ib)
print("jb: %d\n", jb)
print("kb: %d\n", kb)
print("ds: %f\n", ds)
print("dsmax: %f\n", dsmax)
print("dxyz: %f\n", dxyz)
print("dsn: %f\n", dsn)
print("dss: %f\n", dss)
print("dse: %f\n", dse)
print("dsw: %f\n", dsw)
print("dsu: %f\n", dsu)
print("dsd: %f\n", dsd)
raise ValueError("Cannot integrate track for unknown reasons\n")
# now update the time
dt = ds * dxyz
# if time step makes the integration time
# very close to the GCM output
if (tt + dt) >= out_dt:
dt = out_dt - tt
tt = out_dt
ts = 1.0
ds = dt / dxyz
end_loop = True
else:
end_loop = False
tt += dt
if dt == dtmax:
ts += dstep
else:
ts += dt / out_dt
# compute new time interpolation constant
in_futr = ts % 1.0
in_past = 1.0 - in_futr
# now we actually compute the new position
# eastward grid-cell exit
if ds == dse:
scrivi = 1
# if at the "new time" the flow at the cell
# face is positive the particle will exit
uu = (in_futr * uflux[1, ka, ja, ia + 1] +
in_past * uflux[0, ka, ja, ia + 1])
if uu > 0.0:
ib = ia + 1
x1 = float(ia + 1)
y1 = newpos(ja, y0, ds, vu1, vm1)
z1 = newpos(ka, z0, ds, wu1, wm1)
# deal with corner cases (including rounding error)
# TODO: corner cases are extremely rare, but
# may happen. Is there a better way to deal with them?
if (y1 - ja) >= 1: # y
uu = (in_futr * vflux[1, ka, ja + 1, ia] +
in_past * vflux[0, ka, ja + 1, ia])
if uu > 0.0:
jb = ja + 1
y1 = float(ja + 1)
elif (y1 - ja) <= 0:
uu = (in_futr * vflux[1, ka, ja, ia] +
in_past * vflux[0, ka, ja, ia])
if uu < 0.0:
jb = ja - 1
y1 = float(ja)
if (z1 - ka) >= 1: # z
uu = (in_futr * wflux[1, ka + 1, ja, ia] +
in_past * wflux[0, ka + 1, ja, ia])
if uu > 0.0:
kb = ka + 1
z1 = float(ka + 1)
elif (z1 - ka) <= 0:
uu = (in_futr * wflux[1, ka, ja, ia] +
in_past * wflux[0, ka, ja, ia])
if uu < 0.0:
kb = ka - 1
z1 = float(ka)
# westward grid-cell exit
elif ds == dsw:
scrivi = 1
uu = (in_futr * uflux[1, ka, ja, ia] +
in_past * uflux[0, ka, ja, ia])
if uu < 0.0:
ib = ia - 1
x1 = float(ia)
y1 = newpos(ja, y0, ds, vu1, vm1)
z1 = newpos(ka, z0, ds, wu1, wm1)
# deal with corner cases (including rounding error)
if (y1 - ja) >= 1: # y
uu = (in_futr * vflux[1, ka, ja + 1, ia] +
in_past * vflux[0, ka, ja + 1, ia])
if uu > 0.0:
jb = ja + 1
y1 = float(ja + 1)
elif (y1 - ja) <= 0:
uu = (in_futr * vflux[1, ka, ja, ia] +
in_past * vflux[0, ka, ja, ia])
if uu < 0.0:
jb = ja - 1
y1 = float(ja)
if (z1 - ka) >= 1: # z
uu = (in_futr * wflux[1, ka + 1, ja, ia] +
in_past * wflux[0, ka + 1, ja, ia])
if uu > 0.0:
kb = ka + 1
z1 = float(ka + 1)
elif (z1 - ka) <= 0:
uu = (in_futr * wflux[1, ka, ja, ia] +
in_past * wflux[0, ka, ja, ia])
if uu < 0.0:
kb = ka - 1
z1 = float(ka)
# northward grid-cell exit
elif ds == dsn:
scrivi = 1
uu = (in_futr * vflux[1, ka, ja + 1, ia] +
in_past * vflux[0, ka, ja + 1, ia])
if uu > 0.0:
jb = ja + 1
x1 = newpos(ia, x0, ds, uu1, um1)
y1 = float(ja + 1)
z1 = newpos(ka, z0, ds, wu1, wm1)
# deal with corner cases (including rounding error)
if (x1 - ia) >= 1: # x
uu = (in_futr * uflux[1, ka, ja, ia + 1] +
in_past * uflux[0, ka, ja, ia + 1])
if uu > 0.0:
ib = ia + 1
x1 = float(ia + 1)
elif (x1 - ia) <= 0:
uu = (in_futr * uflux[1, ka, ja, ia] +
in_past * uflux[0, ka, ja, ia])
if uu < 0.0:
ib = ia - 1
x1 = float(ia)
if (z1 - ka) >= 1: # z
uu = (in_futr * wflux[1, ka + 1, ja, ia] +
in_past * wflux[0, ka + 1, ja, ia])
if uu > 0.0:
kb = ka + 1
z1 = float(ka + 1)
elif (z1 - ka) <= 0:
uu = (in_futr * wflux[1, ka, ja, ia] +
in_past * wflux[0, ka, ja, ia])
if uu < 0.0:
kb = ka - 1
z1 = float(ka)
# southward grid-cell exit
elif ds == dss:
scrivi = 1
uu = (in_futr * vflux[1, ka, ja, ia] +
in_past * vflux[0, ka, ja, ia])
if uu < 0.0:
jb = ja - 1
x1 = newpos(ia, x0, ds, uu1, um1)
y1 = float(ja)
z1 = newpos(ka, z0, ds, wu1, wm1)
# deal with corner cases (including rounding error)
if (x1 - ia) >= 1: # x
uu = (in_futr * uflux[1, ka, ja, ia + 1] +
in_past * uflux[0, ka, ja, ia + 1])
if uu > 0.0:
ib = ia + 1
x1 = float(ia + 1)
elif (x1 - ia) <= 0:
uu = (in_futr * uflux[1, ka, ja, ia] +
in_past * uflux[0, ka, ja, ia])
if uu < 0.0:
ib = ia - 1
x1 = float(ia)
if (z1 - ka) >= 1: # z
uu = (in_futr * wflux[1, ka + 1, ja, ia] +
in_past * wflux[0, ka + 1, ja, ia])
if uu > 0.0:
kb = ka + 1
z1 = float(ka + 1)
elif (z1 - ka) <= 0:
uu = (in_futr * wflux[1, ka, ja, ia] +
in_past * wflux[0, ka, ja, ia])
if uu < 0.0:
kb = ka - 1
z1 = float(ka)
# upward grid-cell exit
elif ds == dsu:
scrivi = 1
uu = (in_futr * wflux[1, ka + 1, ja, ia] +
in_past * wflux[0, ka + 1, ja, ia])
if uu > 0.0:
kb = ka + 1
x1 = newpos(ia, x0, ds, uu1, um1)
y1 = newpos(ja, y0, ds, vu1, vm1)
z1 = float(ka + 1)
# deal with corner cases (including rounding error)
if (x1 - ia) >= 1: # x
uu = (in_futr * uflux[1, ka, ja, ia + 1] +
in_past * uflux[0, ka, ja, ia + 1])
if uu > 0.0:
ib = ia + 1
x1 = float(ia + 1)
elif (x1 - ia) <= 0:
uu = (in_futr * uflux[1, ka, ja, ia] +
in_past * uflux[0, ka, ja, ia])
if uu < 0.0:
ib = ia - 1
x1 = float(ia)
if (y1 - ja) >= 1: # y
uu = (in_futr * vflux[1, ka, ja + 1, ia] +
in_past * vflux[0, ka, ja + 1, ia])
if uu > 0.0:
jb = ja + 1
y1 = float(ja + 1)
elif (y1 - ja) <= 0:
uu = (in_futr * vflux[1, ka, ja, ia] +
in_past * vflux[0, ka, ja, ia])
if uu < 0.0:
jb = ja - 1
y1 = float(ja)
# downward grid-cell exit
elif ds == dsd:
scrivi = 1
uu = (in_futr * wflux[1, ka, ja, ia] +
in_past * wflux[0, ka, ja, ia])
if uu < 0.0:
kb = ka - 1
x1 = newpos(ia, x0, ds, uu1, um1)
y1 = newpos(ja, y0, ds, vu1, vm1)
z1 = float(ka)
# deal with corner cases (including rounding error)
if (x1 - ia) >= 1: # x
uu = (in_futr * uflux[1, ka, ja, ia + 1] +
in_past * uflux[0, ka, ja, ia + 1])
if uu > 0.0:
ib = ia + 1
x1 = float(ia + 1)
elif (x1 - ia) <= 0:
uu = (in_futr * uflux[1, ka, ja, ia] +
in_past * uflux[0, ka, ja, ia])
if uu < 0.0:
ib = ia - 1
x1 = float(ia)
if (y1 - ja) >= 1: # y
uu = (in_futr * vflux[1, ka, ja + 1, ia] +
in_past * vflux[0, ka, ja + 1, ia])
if uu > 0.0:
jb = ja + 1
y1 = float(ja + 1)
elif (y1 - ja) <= 0:
uu = (in_futr * vflux[1, ka, ja, ia] +
in_past * vflux[0, ka, ja, ia])
if uu < 0.0:
jb = ja - 1
y1 = float(ja)
elif end_loop or (ds == dsmax):
scrivi = 1
x1 = newpos(ia, x0, ds, uu1, um1)
y1 = newpos(ja, y0, ds, vu1, vm1)
z1 = newpos(ka, z0, ds, wu1, wm1)
# TODO for 2D advection we will need to include
# the check for convergence/divergence zones
else:
print("\nUnrecognised ds\n")
print("ds: %f\n", ds)
print("dsmax: %f\n", dsmax)
print("dxyz: %f\n", dxyz)
print("dsn: %f\n", dsn)
print("dss: %f\n", dss)
print("dse: %f\n", dse)
print("dsw: %f\n", dsw)
print("dsu: %f\n", dsu)
print("dsd: %f\n", dsd)
raise ValueError("\nUnrecognised ds\n")
# check if particle entered a kill area
kill_area = 0
for kk in range(nend):
if (iendw[kk] <= x1) and \
(x1 <= iende[kk]) and \
(jends[kk] <= y1) and \
(y1 <= jendn[kk]):
# we store the region where it was killed
kill_area = 10 + kk
break # break the for loop over kill areas
if kill_area > 0:
# write to buffer
if rec_out >= nvals:
raise ValueError("Kill region: buffer finished, make it larger!")
out_tijk[ntrac, rec_out, 0] = tt
out_tijk[ntrac, rec_out, 1] = x1
out_tijk[ntrac, rec_out, 2] = y1
out_tijk[ntrac, rec_out, 3] = z1
out_code[ntrac] = kill_area
transform_one(x1, y1, z1, out_xyz[ntrac, rec_out, :], CS, SN, dX, dY, xG, yG, Z)
rec_out += 1
break # break particle loop
# check if the particle is still
# inside the domain
if (ib > imax) or (ib < 0) or \
(jb > jmax) or (jb < 0):
# write to buffer
if rec_out >= nvals:
raise ValueError("Exit domain: buffer finished, make it larger!")
out_tijk[ntrac, rec_out, 0] = tt
out_tijk[ntrac, rec_out, 1] = x1
out_tijk[ntrac, rec_out, 2] = y1
out_tijk[ntrac, rec_out, 3] = z1
out_code[ntrac] = 1
transform_one(x1, y1, z1, out_xyz[ntrac, rec_out, :], CS, SN, dX, dY, xG, yG, Z)
rec_out += 1
break
# check if the particle exited through the top
if kb >= kmax:
# write to buffer
# TODO there should be a better way to deal with the
# top boundary condition
if rec_out >= nvals:
raise ValueError("Airborne: buffer finished, make it larger!")
out_tijk[ntrac, rec_out, 0] = tt
out_tijk[ntrac, rec_out, 1] = x1
out_tijk[ntrac, rec_out, 2] = y1
out_tijk[ntrac, rec_out, 3] = z1
out_code[ntrac] = 2
transform_one(x1, y1, z1, out_xyz[ntrac, rec_out, :], CS, SN, dX, dY, xG, yG, Z)
rec_out += 1
break
# At the end of the cycle we can write the
# position of the particle in buffer
# gcmstep => outfreq == 1
# always => outfreq == 2
# cross => outfreq == 3
if ((tt == out_dt) and (outfreq == 1)) \
or ((outfreq == 3) and (scrivi == 1)) \
or ((outfreq == 2) and (ts > 0.0)):
# write to buffer
if rec_out >= nvals:
raise ValueError("Normal write: buffer finished, make it larger!")
out_tijk[ntrac, rec_out, 0] = tt
out_tijk[ntrac, rec_out, 1] = x1
out_tijk[ntrac, rec_out, 2] = y1
out_tijk[ntrac, rec_out, 3] = z1
transform_one(x1, y1, z1, out_xyz[ntrac, rec_out, :], CS, SN, dX, dY, xG, yG, Z)
xyz[ntrac, 0] = x1
xyz[ntrac, 1] = y1
xyz[ntrac, 2] = z1
ijk[ntrac, 0] = ib
ijk[ntrac, 1] = jb
ijk[ntrac, 2] = kb
rec_out += 1
break
@nb.njit(nogil=True, parallel=True)
def loc_time_fast(timeax, N, time, is_monotonic):
loc_time = -9999999
# We go backwards since the time we are looking for
# is usually towards the end
for ii in range(N - 1, -1, -1):
if abs(timeax[ii] - time) <= 1.0e-9: # we found it
return ii
# the axis is monotonic, so if we find a value
# smaller than time, it means there is no time in
# the axis
elif is_monotonic and (timeax[ii] < time):
return loc_time
return loc_time

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