def test_simple_withB(self):
x_vars = ['N', 'R']
b_vars = ['W']
x_truth = pn.Series([300., 60.], index=x_vars)
x_a = pn.Series([200., 50.], index=x_vars)
x_cov = pn.DataFrame(
[[200.**2, 0.], [0., 50.**2]],
index=x_vars,
columns=x_vars,
)
b_vars = ['W']
b_param = pn.Series(15, index=b_vars)
b_cov = pn.DataFrame([[5**2]], index=b_vars, columns=b_vars)
y_vars = ['z%02i' % i for i in range(50)]
y_cov = pn.DataFrame(np.identity(50) * 100**2,
index=y_vars,
columns=y_vars)
np.random.seed(1)
y_obs = forward_simple(pn.concat((x_truth, b_param))) + \
np.random.normal(loc=0, scale=100, size=50)
oe = pyOE.optimalEstimation(
x_vars,
x_a,
x_cov,
y_vars,
y_obs,
y_cov,
forward_simple,
forwardKwArgs={},
x_truth=x_truth,
b_vars=b_vars,
b_p=b_param,
S_b=b_cov,
)
oe.doRetrieval()
oe.chiSquareTest()
oe.linearityTest()
assert np.all(
np.isclose(oe.x_op.values, np.array([242.23058144, 58.80698325])))
assert np.all(
np.isclose(oe.x_op_err.values, np.array([38.45975929,
2.11433569])))
assert np.all(
np.isclose(
oe.y_op.values,
np.array([
8.59387481e-05, 2.35930374e-04, 6.25082165e-04,
1.59826496e-03, 3.94383617e-03, 9.39176836e-03,
2.15841176e-02, 4.78717872e-02, 1.02466854e-01,
2.11663310e-01, 4.21955044e-01, 8.11792809e-01,
1.50724078e+00, 2.70071334e+00, 4.67017078e+00,
7.79373174e+00, 1.25521050e+01, 1.95094978e+01,
2.92640235e+01, 4.23623849e+01, 5.91813932e+01,
7.97899855e+01, 1.03817366e+02, 1.30361709e+02,
1.57975050e+02, 1.84750395e+02, 2.08516617e+02,
2.27119478e+02, 2.38740727e+02, 2.42190476e+02,
2.37107902e+02, 2.24023415e+02, 2.04267474e+02,
1.79747741e+02, 1.52646230e+02, 1.25102832e+02,
9.89479086e+01, 7.55273967e+01, 5.56366318e+01,
3.95526479e+01, 2.71361802e+01, 1.79671951e+01,
1.14807503e+01, 7.07976235e+00, 4.21333028e+00,
2.41986283e+00, 1.34126444e+00, 7.17458014e-01,
3.70371013e-01, 1.84516797e-01
])))
assert np.isclose(oe.dgf, 1.9612330067312422)
assert np.all(
np.isclose(
oe.chi2Results['chi2value'].values,
np.array([47.36895951, 32.34974831, 0.21562209, 0.07752859])))
assert np.isclose(oe.trueLinearity, 0.04230584990874298)
assert np.all(
np.isclose(oe.linearity,
np.array([0.029214156840052827,
0.0065951044149309464])))
N = N0 * np.exp(-lam * D**mu)
Z = 1e18 * np.sum(N*D**6)
return [10*np.log10(Z)]
#define names for X and Y
x_vars = ["N0log","lam"]
y_vars = ["Ze"]
#prior knowledge. Note that the provided numbers do not have any scientific meaning.
#first guess for X
x_ap = [3,4100]
#covariance matrix for X
x_cov = np.array([[1,0],[0,10]])
#covariance matrix for Y
y_cov = np.array([[1]])
#measured observation of Y
y_obs = [10]
#additional data to forward function
forwardKwArgs = {"D":np.logspace(-4,-2,50)}
#create optimal estimation object
oe = pyOE.optimalEstimation(x_vars, x_ap, x_cov, y_vars, y_cov, y_obs, forward,forwardKwArgs=forwardKwArgs)
#run the retrieval
oe.doRetrieval( maxIter=10, maxTime=10000000.0)
#plot the result
oe.plotIterations()
plt.savefig("oe_result.png")
def test_simple(self):
x_vars = ['N', 'R', 'W']
x_truth = pn.Series([300., 60., 10.], index=x_vars)
x_a = pn.Series([200., 50., 15.], index=x_vars)
x_cov = pn.DataFrame(
[[200.**2, 0., 0.], [0., 50.**2, 0.], [0., 0., 5.**2]],
index=x_vars,
columns=x_vars,
)
y_vars = ['z%02i' % i for i in range(50)]
y_cov = pn.DataFrame(np.identity(50) * 100**2,
index=y_vars,
columns=y_vars)
np.random.seed(1)
y_obs = forward_simple(x_truth) + np.random.normal(
loc=0, scale=100, size=50)
oe = pyOE.optimalEstimation(
x_vars,
x_a,
x_cov,
y_vars,
y_obs,
y_cov,
forward_simple,
forwardKwArgs={},
x_truth=x_truth,
)
oe.doRetrieval()
oe.chiSquareTest()
oe.linearityTest()
assert np.all(
np.isclose(oe.x_op.values,
np.array([213.51862975, 57.92756234, 13.40863054])))
assert np.all(
np.isclose(oe.x_op_err.values,
np.array([40.63426603, 2.29118537, 2.6609677])))
assert np.all(
np.isclose(
oe.y_op.values,
np.array([
3.17145649e-06, 1.10062999e-05, 3.65341959e-05,
1.15993429e-04, 3.52243388e-04, 1.02312321e-03,
2.84242260e-03, 7.55309564e-03, 1.91971583e-02,
4.66685743e-02, 1.08514493e-01, 2.41338486e-01,
5.13382485e-01, 1.04455458e+00, 2.03281029e+00,
3.78388728e+00, 6.73682327e+00, 1.14722273e+01,
1.86859835e+01, 2.91111794e+01, 4.33789731e+01,
6.18264567e+01, 8.42839875e+01, 1.09898412e+02,
1.37060838e+02, 1.63497447e+02, 1.86545249e+02,
2.03579028e+02, 2.12499301e+02, 2.12157114e+02,
2.02597144e+02, 1.85048114e+02, 1.61663372e+02,
1.35087208e+02, 1.07967351e+02, 8.25365465e+01,
6.03497901e+01, 4.22066478e+01, 2.82332960e+01,
1.80641665e+01, 1.10547748e+01, 6.47079287e+00,
3.62276965e+00, 1.93999035e+00, 9.93651387e-01,
4.86792795e-01, 2.28102406e-01, 1.02233026e-01,
4.38256322e-02, 1.79696985e-02
])))
assert np.isclose(oe.dgf, (2.6733916350055233))
assert np.isclose(oe.trueLinearity, 1.1025635773075495)
assert np.all(
np.isclose(
oe.linearity,
np.array([
0.04508784837582387, 0.02804107536933482,
0.0191628880252254
])))
assert np.all(
np.isclose(oe.chi2Results['chi2value'],
np.array([67.748733, 41.148962, 2.908089, 0.176378])))
#prior knowledge. Note that the provided numbers do not have any scientific meaning.
#first guess for X
x_ap = [3, 4100]
#covariance matrix for X
x_cov = np.array([[1, 0], [0, 10]])
#covariance matrix for Y
y_cov = np.array([[1]])
#measured observation of Y
y_obs = [10]
#additional data to forward function
forwardKwArgs = {"D": np.logspace(-4, -2, 50)}
#create optimal estimation object
oe = pyOE.optimalEstimation(x_vars,
x_ap,
x_cov,
y_vars,
y_cov,
y_obs,
forward,
forwardKwArgs=forwardKwArgs)
#run the retrieval
oe.doRetrieval(maxIter=10, maxTime=10000000.0)
#plot the result
oe.plotIterations()
plt.savefig("oe_result.png")
def test_simple_withB(self):
x_vars = ['N', 'R']
b_vars = ['W']
x_truth = pn.Series([300., 60.], index=x_vars)
x_a = pn.Series([200., 50.], index=x_vars)
x_cov = pn.DataFrame(
[[200.**2, 0.], [0., 50.**2]],
index=x_vars,
columns=x_vars,
)
b_vars = ['W']
b_param = pn.Series(15, index=b_vars)
b_cov = pn.DataFrame([[5**2]], index=b_vars, columns=b_vars)
y_vars = ['z%02i' % i for i in range(50)]
y_cov = pn.DataFrame(np.identity(50) * 100**2,
index=y_vars,
columns=y_vars)
np.random.seed(1)
y_obs = forward_simple(pn.concat((x_truth, b_param))) + \
np.random.normal(loc=0, scale=100, size=50)
oe = pyOE.optimalEstimation(
x_vars,
x_a,
x_cov,
y_vars,
y_obs,
y_cov,
forward_simple,
forwardKwArgs={},
x_truth=x_truth,
b_vars=b_vars,
b_p=b_param,
S_b=b_cov,
)
oe.doRetrieval()
chi2passed, chi2value, chi2critical = oe.chiSquareTest()
linearity, trueLinearityChi2, trueLinearityChi2Critical = oe.linearityTest(
)
print('np', np.__version__)
print('pn', pn.__version__)
print('pyOE', pyOE.__version__)
print('scipy', scipy.__version__)
assert np.all(
np.isclose(oe.x_op.values, np.array([255.30992222, 58.68130862])))
assert np.all(
np.isclose(oe.x_op_err.values, np.array([38.59979542, 2.0071929])))
assert np.all(
np.isclose(
oe.y_op.values,
np.array([
9.66145500e-05, 2.64647052e-04, 6.99600329e-04,
1.78480744e-03, 4.39431462e-03, 1.04411743e-02,
2.39423053e-02, 5.29835436e-02, 1.13155184e-01,
2.33220288e-01, 4.63891718e-01, 8.90482377e-01,
1.64965245e+00, 2.94929357e+00, 5.08864283e+00,
8.47313942e+00, 1.36158624e+01, 2.11156461e+01,
3.16025417e+01, 4.56455107e+01, 6.36256959e+01,
8.55904756e+01, 1.11116039e+02, 1.39215145e+02,
1.68327329e+02, 1.96417962e+02, 2.21190355e+02,
2.40386232e+02, 2.52122389e+02, 2.55194702e+02,
2.49281652e+02, 2.34999746e+02, 2.13797631e+02,
1.87714060e+02, 1.59055663e+02, 1.30064833e+02,
1.02642934e+02, 7.81729764e+01, 5.74569615e+01,
4.07555802e+01, 2.78990827e+01, 1.84310971e+01,
1.17508929e+01, 7.23017763e+00, 4.29324314e+00,
2.46025669e+00, 1.36061037e+00, 7.26182114e-01,
3.74038011e-01, 1.85927808e-01
])))
assert np.isclose(oe.dgf, 1.9611398655015124)
assert np.isclose(oe.trueLinearity, 0.039634853402863594)
assert np.all(np.array(oe.linearity) < 1)
assert np.all(chi2passed)
def test_simple(self):
x_vars = ['N', 'R', 'W']
x_truth = pn.Series([300., 60., 10.], index=x_vars)
x_a = pn.Series([200., 50., 15.], index=x_vars)
x_cov = pn.DataFrame(
[[200.**2, 0., 0.], [0., 50.**2, 0.], [0., 0., 5.**2]],
index=x_vars,
columns=x_vars,
)
y_vars = ['z%02i' % i for i in range(50)]
y_cov = pn.DataFrame(np.identity(50) * 100**2,
index=y_vars,
columns=y_vars)
np.random.seed(1)
y_obs = forward_simple(x_truth) + \
np.random.normal(loc=0, scale=100, size=50)
oe = pyOE.optimalEstimation(
x_vars,
x_a,
x_cov,
y_vars,
y_obs,
y_cov,
forward_simple,
forwardKwArgs={},
x_truth=x_truth,
)
oe.doRetrieval()
chi2passed, chi2value, chi2critical = oe.chiSquareTest()
linearity, trueLinearityChi2, trueLinearityChi2Critical = oe.linearityTest(
)
print('np', np.__version__)
print('pn', pn.__version__)
print('pyOE', pyOE.__version__)
print('scipy', scipy.__version__)
assert np.all(
np.isclose(oe.x_op.values,
np.array([230.75639479, 58.49351178, 12.32118448])))
assert np.all(
np.isclose(oe.x_op_err.values,
np.array([42.940902, 2.05667214, 2.4442318])))
assert np.all(
np.isclose(
oe.y_op.values,
np.array([
8.07132255e-08, 3.57601384e-07, 1.50303019e-06,
5.99308237e-06, 2.26697545e-05, 8.13499728e-05,
2.76937671e-04, 8.94377132e-04, 2.74014386e-03,
7.96416170e-03, 2.19594168e-02, 5.74401494e-02,
1.42535928e-01, 3.35542210e-01, 7.49348775e-01,
1.58757726e+00, 3.19080133e+00, 6.08385266e+00,
1.10045335e+01, 1.88833313e+01, 3.07396995e+01,
4.74716852e+01, 6.95478498e+01, 9.66600005e+01,
1.27445324e+02, 1.59409810e+02, 1.89156040e+02,
2.12931252e+02, 2.27390663e+02, 2.30366793e+02,
2.21401803e+02, 2.01862876e+02, 1.74600622e+02,
1.43267982e+02, 1.11523535e+02, 8.23565110e+01,
5.76956909e+01, 3.83444793e+01, 2.41755486e+01,
1.44598524e+01, 8.20475101e+00, 4.41652793e+00,
2.25533253e+00, 1.09258243e+00, 5.02125028e-01,
2.18919049e-01, 9.05459987e-02, 3.55278561e-02,
1.32246067e-02, 4.66993202e-03
])))
assert np.isclose(oe.dgf, (2.7132392503933556))
assert np.isclose(oe.trueLinearity, 0.41529831393972894)
assert np.all(np.array(oe.linearity) < 1)
assert np.all(chi2passed)
def test_simple_withB(self):
x_vars = ['N', 'R']
b_vars = ['W']
x_truth = pn.Series([300., 60.], index=x_vars)
x_a = pn.Series([200., 50.], index=x_vars)
x_cov = pn.DataFrame([[200.**2, 0.],
[0., 50.**2]],
index=x_vars,
columns=x_vars,
)
b_vars = ['W']
b_param = pn.Series(15, index=b_vars)
b_cov = pn.DataFrame([[5**2]], index=b_vars, columns=b_vars)
y_vars = ['z%02i' % i for i in range(50)]
y_cov = pn.DataFrame(np.identity(50) * 100**2,
index=y_vars,
columns=y_vars)
np.random.seed(1)
y_obs = forward_simple(pn.concat((x_truth, b_param))) + \
np.random.normal(loc=0, scale=100, size=50)
oe = pyOE.optimalEstimation(
x_vars,
x_a,
x_cov,
y_vars,
y_obs,
y_cov,
forward_simple,
forwardKwArgs={},
x_truth=x_truth,
b_vars=b_vars,
b_p=b_param,
S_b=b_cov,
)
oe.doRetrieval()
oe.chiSquareTest()
oe.linearityTest()
assert np.all(np.isclose(oe.x_op.values, np.array(
[252.7093795, 58.47319368])))
assert np.all(np.isclose(oe.x_op_err.values, np.array(
[37.6333103, 1.93583752])))
assert np.all(
np.isclose(
oe.y_op.values,
np.array([1.06378560e-04, 2.90316569e-04,
7.64624051e-04, 1.94349087e-03,
4.76733284e-03, 1.12856574e-02,
2.57831911e-02, 5.68466519e-02,
1.20957147e-01, 2.48379984e-01,
4.92220927e-01, 9.41373507e-01,
1.73748990e+00, 3.09486011e+00,
5.32008016e+00, 8.82579321e+00,
1.41301814e+01, 2.18323330e+01,
3.25544958e+01, 4.68468310e+01,
6.50590746e+01, 8.71954782e+01,
1.12781655e+02, 1.40780137e+02,
1.69590969e+02, 1.97161665e+02,
2.21207909e+02, 2.39517496e+02,
2.50283520e+02, 2.52397869e+02,
2.45639119e+02, 2.30710732e+02,
2.09120439e+02, 1.82929432e+02,
1.54429088e+02, 1.25815181e+02,
9.89225733e+01, 7.50613173e+01,
5.49661574e+01, 3.88448091e+01,
2.64928709e+01, 1.74374700e+01,
1.10763416e+01, 6.78996647e+00,
4.01695841e+00, 2.29342984e+00,
1.26366513e+00, 6.71950008e-01,
3.44826269e-01, 1.70774153e-01])
)
)
assert np.isclose(oe.dgf, 1.9630943621484518)
assert np.isclose(oe.chi2, 60.41671208566697)
assert np.isclose(oe.trueNonlinearity, 0.02364625922873849)
assert np.all(
np.isclose(
oe.nonlinearity, np.array([1.93185672e-05, 6.04938579e-03])
)
)
def test_simple(self):
x_vars = ['N', 'R', 'W']
x_truth = pn.Series([300., 60., 10.], index=x_vars)
x_a = pn.Series([200., 50., 15.], index=x_vars)
x_cov = pn.DataFrame([[200.**2, 0., 0.],
[0., 50.**2, 0.],
[0., 0., 5.**2]],
index=x_vars,
columns=x_vars,
)
y_vars = ['z%02i' % i for i in range(50)]
y_cov = pn.DataFrame(np.identity(50) * 100**2,
index=y_vars,
columns=y_vars)
np.random.seed(1)
y_obs = forward_simple(x_truth) + np.random.normal(loc=0, scale=100, size=50)
oe = pyOE.optimalEstimation(
x_vars,
x_a,
x_cov,
y_vars,
y_obs,
y_cov,
forward_simple,
forwardKwArgs={},
x_truth=x_truth,
)
oe.doRetrieval()
oe.chiSquareTest()
oe.linearityTest()
assert np.all(np.isclose(oe.x_op.values, np.array(
[216.67732376, 58.16498463, 12.62412649])))
assert np.all(np.isclose(oe.x_op_err.values, np.array(
[40.71776776, 2.07152667, 2.51450318])))
assert np.all(
np.isclose(
oe.y_op.values,
np.array([2.69557604e-07, 1.10375135e-06,
4.29823492e-06, 1.59187253e-05,
5.60693694e-05, 1.87820198e-04,
5.98353942e-04, 1.81289754e-03,
5.22381278e-03, 1.43153242e-02,
3.73090348e-02, 9.24753702e-02,
2.17990408e-01, 4.88706293e-01,
1.04197601e+00, 2.11284066e+00,
4.07450649e+00, 7.47278561e+00,
1.30343468e+01, 2.16219701e+01,
3.41114745e+01, 5.11805517e+01,
7.30312399e+01, 9.91086650e+01,
1.27912745e+02, 1.57005639e+02,
1.83280358e+02, 2.03477240e+02,
2.14839926e+02, 2.15731413e+02,
2.06020779e+02, 1.87114697e+02,
1.61623318e+02, 1.32769822e+02,
1.03727515e+02, 7.70704350e+01,
5.44604078e+01, 3.65993362e+01,
2.33918607e+01, 1.42185585e+01,
8.21950397e+00, 4.51892248e+00,
2.36278069e+00, 1.17492779e+00,
5.55645982e-01, 2.49910453e-01,
1.06898080e-01, 4.34865176e-02,
1.68243617e-02, 6.19044403e-03])
)
)
assert np.isclose(oe.dgf, 2.7039260453696317)
assert np.isclose(oe.trueNonlinearity, 0.5892181071502255)
assert np.all(
np.isclose(
oe.nonlinearity, np.array([0.0172169, 0.01304629, 0.01061978])
)
)
assert np.isclose(oe.chi2, 64.21108547675885)