def test_parseval(self, rtol=1.0e-15):
""" Make sure 2D fft satisfies Parseval's relation
within machine double precision """
# set random stream function
p1 = np.random.randn(self.m.nz, self.m.ny, self.m.nx)
p1 -= p1.mean(axis=(-2, -1))[:, np.newaxis, np.newaxis]
ph1 = self.m.fft(p1)
# var(P) from Fourier coefficients
P_var_spec = spec_var(self.m, ph1)
# print "Variance from spectrum: %5.16f" % P_var_spec
# var(P) in physical space
P_var_phys = p1.var(axis=(-2, -1))
# print "Variance in physical space: %5.16f" %P_var_phys
# relative error
error = np.abs((P_var_phys - P_var_spec) / P_var_phys).sum()
print "error = %5.16f" % error
self.assertTrue(error < rtol, "fft does not satisfy Parseval's relation")
def test_parseval(self, rtol=1.e-15):
""" Make sure 2D fft satisfies Parseval's relation
within machine double precision """
# set random stream function
p1 = np.random.randn(self.m.nz, self.m.ny, self.m.nx)
p1 -= p1.mean(axis=(-2, -1))[:, np.newaxis, np.newaxis]
ph1 = self.m.fft(p1)
# var(P) from Fourier coefficients
P_var_spec = spec_var(self.m, ph1)
#print "Variance from spectrum: %5.16f" % P_var_spec
# var(P) in physical space
P_var_phys = p1.var(axis=(-2, -1))
#print "Variance in physical space: %5.16f" %P_var_phys
# relative error
error = np.abs((P_var_phys - P_var_spec) / P_var_phys).sum()
print "error = %5.16f" % error
self.assertTrue(error < rtol,
"fft does not satisfy Parseval's relation")
ntd=1)
# McWilliams 84 IC condition
fk = m.wv != 0
ckappa = np.zeros_like(m.wv2)
ckappa[fk] = np.sqrt(m.wv2[fk] * (1. + (m.wv2[fk] / 36.)**2))**-1
nhx, nhy = m.wv2.shape
Pi_hat = np.random.randn(nhx, nhy) * ckappa + 1j * np.random.randn(
nhx, nhy) * ckappa
Pi = m.ifft(Pi_hat[np.newaxis])
Pi = Pi - Pi.mean()
Pi_hat = m.fft(Pi)
KEaux = spec_var(m, m.filtr * m.wv * Pi_hat)
pih = (Pi_hat * np.sqrt(0.5 / KEaux))
qih = -m.wv2 * pih
qi = m.ifft(qih)
m.set_q(qi)
t = time.time()
# run the model
m.run()
elapsed = (time.time() - t) / nsteps * 1000
print('Time per time-step: %.3f ms' % elapsed)
# import matplotlib.pyplot as plt
# plt.figure(figsize=(10, 4))
qh = snap['qh'][:]
ph = qh2ph(m.a,qh)
pph, pth = psi_tau_h(ph)
# calculates the thickness flux
prod = calc_tfh(pph,pth,m.U[0],m.k)
ki, prod = diagnostic_tools.calc_ispec(m,prod)
try:
prod_k = np.vstack([prod_k,prod])
except:
prod_k = prod
Ebt = np.hstack([Ebt, diagnostic_tools.spec_var(m,m.wv*pph)/2.])
Ebc = np.hstack([Ebc, diagnostic_tools.spec_var(m,m.wv*pth)/2.])
Epe = np.hstack([Epe, diagnostic_tools.spec_var(m,(1./m.rd)*pth)/2.])
nlh = pth.conj()*jacob_h(m,pph,-m.wv2*pth)
E_bt_bc = np.hstack([E_bt_bc, nlh.real.sum()])
E_ek_bt = np.hstack([E_ek_bt, diagnostic_tools.spec_var(m,m.wv*pth)])
ki, ti = np.meshgrid(ki,kefile['t'])
prod_k = np.ma.masked_array(prod_k, prod_k<=.0)
# the fractional energy production at deformation radius scales
plt.rc('xtick', labelsize=20)
plt.rc('ytick', labelsize=20)
beta = 0., H = 1., rek = 0., rd = None, dt = 0.005,
taveint=year, ntd=2)
# McWilliams 84 IC condition
fk = m.wv != 0
ckappa = np.zeros_like(m.wv2)
ckappa[fk] = np.sqrt( m.wv2[fk]*(1. + (m.wv2[fk]/36.)**2) )**-1
nhx,nhy = m.wv2.shape
Pi_hat = np.random.randn(nhx,nhy)*ckappa +1j*np.random.randn(nhx,nhy)*ckappa
Pi = m.ifft( Pi_hat[np.newaxis] )
Pi = Pi - Pi.mean()
Pi_hat = m.fft( Pi )
KEaux = spec_var( m, m.filtr*m.wv*Pi_hat )
pih = ( Pi_hat/np.sqrt(KEaux) )
qih = -m.wv2*pih
qi = m.ifft(qih)
m.set_q(qi)
# run the model and plot some figs
plt.rcParams['image.cmap'] = 'RdBu_r'
plt.ion()
for snapshot in m.run_with_snapshots(tsnapstart=0, tsnapint=15*m.dt):
plt.clf()
p1 = plt.imshow(m.q[0] + m.beta * m.y)
