def plotcostone_opt(vect=1):
"""Using test_cost plots convergance of cost fn gradient for decreasing
value of alpha.
"""
sns.set_context('poster',
font_scale=1.5,
rc={
'lines.linewidth': 1,
'lines.markersize': 6
})
fig, ax = plt.subplots(
nrows=1,
ncols=1,
) #figsize=(10,10))
sns.set_style('ticks')
power = np.arange(1, 14, 1)
xlist = [10**(-x) for x in power]
d = dC.DalecData(
1999,
2000,
'nee_day',
nc_file='../../alice_holt_data/ah_data_daily_test_nee3.nc',
scale_nee=1)
m = mc.DalecModel(d)
tstlist = [test_cost_opt(m, x, vect) for x in xlist]
ax.semilogx(xlist, tstlist, 'k', marker='x', mew=1, ms=8)
#ax.semilogx(xlist, tstlist, 'k', 'x')
plt.xlabel(r'$\alpha$')
plt.ylabel(r'$f(\alpha)$')
#plt.title('test of the gradient of the cost function')
print tstlist
return ax, fig
def plotcostone_ens(vect=1, sizee=20):
"""Using test_cost plots convergance of cost fn gradient for decreasing
value of alpha.
"""
sns.set_context('poster',
font_scale=1.5,
rc={
'lines.linewidth': 1,
'lines.markersize': 6
})
fig, ax = plt.subplots(
nrows=1,
ncols=1,
) #figsize=(10,10))
sns.set_style('ticks')
power = np.arange(1, 14, 1)
xlist = [10**(-x) for x in power]
xb_opt = np.array([60.3, 149.17, 276.1])
d = dC.DalecDataTwin(1999, 2000, 'nee_day', err_scale=0.25)
d.xb = cp.copy(d.x_truth)
d.xb[d.params4opt] = xb_opt
d.opt_xb = xb_opt
m = mc.DalecModel(d, size_ens=sizee)
m.run_ensemble(xb_opt)
tstlist = [abs(test_cost_ens(m, x, vect)) for x in xlist]
ax.semilogx(xlist, tstlist, 'k', marker='x', mew=1, ms=8)
#ax.semilogx(xlist, tstlist, 'k', 'x')
plt.xlabel(r'$\alpha$')
plt.ylabel(r'$f(\alpha)$')
#plt.title('test of the gradient of the cost function')
print tstlist
return ax, fig
def test_cost_cvt(alph=1e-8, vect=0):
"""Test for cost and gradcost functions.
"""
d = dC.DalecDataTwin(
1999,
2000,
'nee',
nc_file='../../alice_holt_data/ah_data_daily_test_nee3.nc',
scale_nee=1)
m = mc.DalecModel(d, size_ens=1)
pvals = d.edinburgh_mean
zvals = m.pvals2zvals(pvals)
gradj = m.gradcost_cvt(zvals)
print gradj.shape
if vect == 0:
h = zvals * (np.linalg.norm(zvals))**(-1)
elif vect == 1:
h = gradj * (np.linalg.norm(gradj))**(-1)
elif vect == 2:
h = np.ones(23) * (np.sqrt(23)**-1)
j = m.cost_cvt(zvals)
jalph = m.cost_cvt(zvals + alph * h)
print jalph - j
print np.dot(alph * h, gradj)
print(jalph - j) / (np.dot(alph * h, gradj))
return abs(jalph - j) / (np.dot(alph * h, gradj))
def test_costfn(alph=1e-9):
"""Test for cost and gradcost functions.
"""
d = dC.DalecData(50, 'nee')
m = mc.DalecModel(d)
gradj = m.gradcost(d.pvals)
h = gradj * (np.linalg.norm(gradj))**(-1)
j = m.cost(d.pvals)
jalph = m.cost(d.pvals + alph * h)
print(jalph - j) / (np.dot(alph * h, gradj))
assert (jalph - j) / (np.dot(alph * h, gradj)) < 1.0001
def test_linmod(gamma=1e1):
""" Test from TLM to check it converges.
"""
d = dC.DalecData(731, 'nee')
pvals = d.pvals
m = mc.DalecModel(d)
cx, matlist = m.linmod_list(pvals)
pvals2 = pvals * (1 + 0.3 * gamma)
cxdx = m.mod_list(pvals2)[-1]
pvals3 = pvals * (0.3 * gamma)
dxl = np.linalg.norm(np.dot(m.mfac(matlist, 730), pvals3.T))
dxn = np.linalg.norm(cxdx - cx - dxl)
return dxl / dxn
def test_cost(alph=1e-8, vect=0):
"""Test for cost and gradcost functions.
"""
d = dC.DalecData(365, 'nee')
m = mc.DalecModel(d)
pvals = d.edinburghmean
gradj = m.gradcost2(pvals)
if vect == True:
h = pvals * (np.linalg.norm(pvals))**(-1)
else:
h = gradj * (np.linalg.norm(gradj))**(-1)
j = m.cost(pvals)
jalph = m.cost(pvals + alph * h)
print jalph - j
print np.dot(alph * h, gradj)
return (jalph - j) / (np.dot(alph * h, gradj))