def vtem(time, levi, lat, vzm, vthzm, thzm):
ntime = len(time)
levi100 = 100.0 * levi
vtem = numpy.zeros(vzm.shape, dtype="d")
for itime in range(ntime):
dthdp = deriv(levi100, thzm[itime, ...])
psieddy = vthzm[itime, ...] / dthdp
dpsidp = deriv(levi100, psieddy)
vtem[itime, ...] = vzm[itime, ...] - dpsidp
return vtem
def _init_epfy(time, levi, lat, uzm, uvzm, vthzm, thzm):
ntime = len(time)
latrad = (lat / 180.0) * numpy.pi
coslat = numpy.cos(latrad)
levi100 = 100.0 * levi
epfy = numpy.zeros(uzm.shape, dtype='d')
for itime in range(ntime):
dthdp = deriv(levi100, thzm[itime, ...])
dudp = deriv(levi100, uzm[itime, ...])
psieddy = vthzm[itime, ...] / dthdp
epfy[itime, ...] = a * numpy.einsum('j,ij...->ij...', coslat, (dudp * psieddy - uvzm[itime, ...]))
return epfy
def test_deriv_array(self):
x = np.array([2.0, 5.0, 7.0, 3.0, 4.0])
y = np.array([3.0, 5.0, 4.0, 7.0, 8.0])
actual = deriv(x, y)
expected = np.array(
[1.3666666, -0.033333302, -0.25000000, 1.5833340, 0.41666698])
np.testing.assert_array_almost_equal(actual, expected, 6)
def psitem(time, levi, lat, vzm, vthzm, thzm):
ntime = len(time)
nlevi = len(levi)
latrad = (lat / 180.0) * numpy.pi
coslat = numpy.cos(latrad)
levi100 = levi * 100.0
psitem = numpy.zeros(vzm.shape, dtype="d")
vzm_shape_1 = list(vzm.shape[1:])
vzm_shape_1[0] += 1
vzmwithzero = numpy.zeros(vzm_shape_1, dtype="d")
levi100withzero = numpy.zeros((nlevi + 1, ), dtype="d")
levi100withzero[1:] = levi100
for itime in range(ntime):
dthdp = deriv(levi100, thzm[itime, ...])
psieddy = vthzm[itime, ...] / dthdp
vzmwithzero[1:, ...] = vzm[itime, ...]
for ilev in range(1, nlevi + 1):
result = int_tabulated(levi100withzero[0:ilev + 1],
vzmwithzero[0:ilev + 1, ...])
tmp1 = (2 * numpy.pi * a * coslat) / g0
tmp2 = result - psieddy[ilev - 1, ...]
psitem[itime, ilev - 1,
...] = numpy.einsum("i,i...->i...", tmp1, tmp2)
return psitem
def test_deriv_list(self):
x = [2.0, 5.0, 7.0, 3.0, 4.0]
y = [3.0, 5.0, 4.0, 7.0, 8.0]
actual = deriv(x, y)
expected = [
1.3666666, -0.033333302, -0.25000000, 1.5833340, 0.41666698
]
np.testing.assert_array_almost_equal(actual, expected, 6)
def _init_wtem(time, levi, lat, wzm, vthzm, thzm):
ntime = len(time)
latrad = (lat / 180.0) * numpy.pi
coslat = numpy.cos(latrad)
levi100 = 100.0 * levi
_wzm = -1.0 * numpy.einsum('ij...,j->ij...', wzm, levi100) / H
wtem = numpy.zeros(wzm.shape, dtype='d')
for itime in range(ntime):
dthdp = deriv(levi100, thzm[itime, ...])
psieddy = vthzm[itime, ...] / dthdp
tmp = numpy.einsum('ij...,j->ij...', psieddy, coslat)
dpsidy = numpy.einsum('ij...,j->ij...', deriv(latrad, tmp, axis=1), 1.0 / (a * coslat))
wtem[itime, ...] = _wzm[itime, ...] + dpsidy
return wtem
def utendepfd(time, levi, lat, uzm, uvzm, uwzm, vthzm, thzm):
ntime = len(time)
latrad = (lat / 180.0) * numpy.pi
coslat = numpy.cos(latrad)
levi100 = 100.0 * levi
iacoslat = 1.0 / (a * coslat)
epfy = _init_epfy(time, levi, lat, uzm, uvzm, vthzm, thzm)
epfz = _init_epfz(time, levi, lat, uzm, uwzm, vthzm, thzm)
utendepfd = numpy.zeros(uzm.shape, dtype='d')
for itime in range(ntime):
tmp = numpy.einsum('ij...,j->ij...', epfy[itime, ...], coslat)
depfydphi = numpy.einsum('ij...,j->ij...', deriv(latrad, tmp, axis=1), iacoslat)
depfzdp = deriv(levi100, epfz[itime, ...])
utendepfd[itime, ...] = numpy.einsum('ij...,j->ij...', depfydphi + depfzdp, iacoslat)
return utendepfd
def _init_epfz(time, levi, lat, uzm, uwzm, vthzm, thzm):
ntime = len(time)
latrad = (lat / 180.0) * numpy.pi
coslat = numpy.cos(latrad)
fshape = (1, len(lat)) + tuple([1] * (uzm.ndim - 3))
f = 2 * om * numpy.sin(latrad).reshape(fshape)
levi100 = 100.0 * levi
_uwzm = -1.0 * numpy.einsum('ij...,j->ij...', uwzm, levi100) / H
epfz = numpy.zeros(uzm.shape, dtype='d')
for itime in range(ntime):
ucos = numpy.einsum('ij...,j->ij...', uzm[itime, ...], coslat)
dudphi = deriv(latrad, ucos, axis=1) / a
dthdp = deriv(levi100, thzm[itime, ...])
psieddy = vthzm[itime, ...] / dthdp
epfz[itime, ...] = a * numpy.einsum('j,ij...->ij...', coslat, (f - dudphi) * psieddy - _uwzm[itime, ...])
return epfz
def utendwtem(time, levi, lat, uzm, wzm, vthzm, thzm):
ntime = len(time)
levi100 = 100.0 * levi
wtem = _init_wtem(time, levi, lat, wzm, vthzm, thzm)
utendwtem = numpy.zeros(uzm.shape, dtype="d")
for itime in range(ntime):
dudp = deriv(levi100, uzm[itime, ...])
utendwtem[itime, ...] = -1.0 * wtem[itime, ...] * dudp
return utendwtem
def utendvtem(time, levi, lat, uzm, vzm, vthzm, thzm):
ntime = len(time)
latrad = (lat / 180.0) * numpy.pi
coslat = numpy.cos(latrad)
fshape = (1, len(lat)) + tuple([1] * (uzm.ndim - 3))
f = 2 * om * numpy.sin(latrad).reshape(fshape)
_vtem = vtem(time, levi, lat, vzm, vthzm, thzm)
utendvtem = numpy.zeros(uzm.shape, dtype="d")
for itime in range(ntime):
ucos = numpy.einsum("ij...,j->ij...", uzm[itime, ...], coslat)
dudphi = deriv(latrad, ucos, axis=1) / a
utendvtem[itime, ...] = _vtem[itime, ...] * (f - dudphi)
return utendvtem
def test_deriv_list_no_y(self):
x = [1.2345, 2.34567, 3.45678, 4.56789, 5.678901]
actual = deriv(x)
expected = [1.11120, 1.11114, 1.11111, 1.11106, 1.11096]
np.testing.assert_array_almost_equal(actual, expected, 6)
