474 lines
17 KiB
Python
474 lines
17 KiB
Python
# SciPy imports.
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import numpy as np
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from numpy import pi
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from numpy.testing import (assert_array_almost_equal,
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assert_equal, assert_warns)
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from pytest import raises as assert_raises
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from scipy.odr import (Data, Model, ODR, RealData, OdrStop, OdrWarning,
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multilinear, exponential, unilinear, quadratic,
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polynomial)
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class TestODR(object):
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# Bad Data for 'x'
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def test_bad_data(self):
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assert_raises(ValueError, Data, 2, 1)
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assert_raises(ValueError, RealData, 2, 1)
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# Empty Data for 'x'
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def empty_data_func(self, B, x):
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return B[0]*x + B[1]
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def test_empty_data(self):
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beta0 = [0.02, 0.0]
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linear = Model(self.empty_data_func)
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empty_dat = Data([], [])
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assert_warns(OdrWarning, ODR,
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empty_dat, linear, beta0=beta0)
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empty_dat = RealData([], [])
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assert_warns(OdrWarning, ODR,
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empty_dat, linear, beta0=beta0)
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# Explicit Example
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def explicit_fcn(self, B, x):
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ret = B[0] + B[1] * np.power(np.exp(B[2]*x) - 1.0, 2)
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return ret
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def explicit_fjd(self, B, x):
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eBx = np.exp(B[2]*x)
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ret = B[1] * 2.0 * (eBx-1.0) * B[2] * eBx
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return ret
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def explicit_fjb(self, B, x):
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eBx = np.exp(B[2]*x)
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res = np.vstack([np.ones(x.shape[-1]),
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np.power(eBx-1.0, 2),
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B[1]*2.0*(eBx-1.0)*eBx*x])
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return res
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def test_explicit(self):
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explicit_mod = Model(
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self.explicit_fcn,
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fjacb=self.explicit_fjb,
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fjacd=self.explicit_fjd,
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meta=dict(name='Sample Explicit Model',
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ref='ODRPACK UG, pg. 39'),
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)
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explicit_dat = Data([0.,0.,5.,7.,7.5,10.,16.,26.,30.,34.,34.5,100.],
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[1265.,1263.6,1258.,1254.,1253.,1249.8,1237.,1218.,1220.6,
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1213.8,1215.5,1212.])
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explicit_odr = ODR(explicit_dat, explicit_mod, beta0=[1500.0, -50.0, -0.1],
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ifixx=[0,0,1,1,1,1,1,1,1,1,1,0])
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explicit_odr.set_job(deriv=2)
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explicit_odr.set_iprint(init=0, iter=0, final=0)
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out = explicit_odr.run()
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assert_array_almost_equal(
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out.beta,
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np.array([1.2646548050648876e+03, -5.4018409956678255e+01,
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-8.7849712165253724e-02]),
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)
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assert_array_almost_equal(
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out.sd_beta,
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np.array([1.0349270280543437, 1.583997785262061, 0.0063321988657267]),
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)
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assert_array_almost_equal(
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out.cov_beta,
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np.array([[4.4949592379003039e-01, -3.7421976890364739e-01,
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-8.0978217468468912e-04],
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[-3.7421976890364739e-01, 1.0529686462751804e+00,
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-1.9453521827942002e-03],
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[-8.0978217468468912e-04, -1.9453521827942002e-03,
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1.6827336938454476e-05]]),
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)
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# Implicit Example
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def implicit_fcn(self, B, x):
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return (B[2]*np.power(x[0]-B[0], 2) +
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2.0*B[3]*(x[0]-B[0])*(x[1]-B[1]) +
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B[4]*np.power(x[1]-B[1], 2) - 1.0)
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def test_implicit(self):
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implicit_mod = Model(
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self.implicit_fcn,
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implicit=1,
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meta=dict(name='Sample Implicit Model',
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ref='ODRPACK UG, pg. 49'),
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)
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implicit_dat = Data([
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[0.5,1.2,1.6,1.86,2.12,2.36,2.44,2.36,2.06,1.74,1.34,0.9,-0.28,
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-0.78,-1.36,-1.9,-2.5,-2.88,-3.18,-3.44],
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[-0.12,-0.6,-1.,-1.4,-2.54,-3.36,-4.,-4.75,-5.25,-5.64,-5.97,-6.32,
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-6.44,-6.44,-6.41,-6.25,-5.88,-5.5,-5.24,-4.86]],
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1,
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)
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implicit_odr = ODR(implicit_dat, implicit_mod,
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beta0=[-1.0, -3.0, 0.09, 0.02, 0.08])
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out = implicit_odr.run()
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assert_array_almost_equal(
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out.beta,
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np.array([-0.9993809167281279, -2.9310484652026476, 0.0875730502693354,
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0.0162299708984738, 0.0797537982976416]),
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)
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assert_array_almost_equal(
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out.sd_beta,
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np.array([0.1113840353364371, 0.1097673310686467, 0.0041060738314314,
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0.0027500347539902, 0.0034962501532468]),
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)
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assert_array_almost_equal(
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out.cov_beta,
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np.array([[2.1089274602333052e+00, -1.9437686411979040e+00,
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7.0263550868344446e-02, -4.7175267373474862e-02,
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5.2515575927380355e-02],
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[-1.9437686411979040e+00, 2.0481509222414456e+00,
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-6.1600515853057307e-02, 4.6268827806232933e-02,
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-5.8822307501391467e-02],
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[7.0263550868344446e-02, -6.1600515853057307e-02,
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2.8659542561579308e-03, -1.4628662260014491e-03,
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1.4528860663055824e-03],
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[-4.7175267373474862e-02, 4.6268827806232933e-02,
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-1.4628662260014491e-03, 1.2855592885514335e-03,
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-1.2692942951415293e-03],
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[5.2515575927380355e-02, -5.8822307501391467e-02,
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1.4528860663055824e-03, -1.2692942951415293e-03,
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2.0778813389755596e-03]]),
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)
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# Multi-variable Example
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def multi_fcn(self, B, x):
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if (x < 0.0).any():
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raise OdrStop
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theta = pi*B[3]/2.
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ctheta = np.cos(theta)
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stheta = np.sin(theta)
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omega = np.power(2.*pi*x*np.exp(-B[2]), B[3])
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phi = np.arctan2((omega*stheta), (1.0 + omega*ctheta))
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r = (B[0] - B[1]) * np.power(np.sqrt(np.power(1.0 + omega*ctheta, 2) +
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np.power(omega*stheta, 2)), -B[4])
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ret = np.vstack([B[1] + r*np.cos(B[4]*phi),
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r*np.sin(B[4]*phi)])
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return ret
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def test_multi(self):
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multi_mod = Model(
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self.multi_fcn,
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meta=dict(name='Sample Multi-Response Model',
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ref='ODRPACK UG, pg. 56'),
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)
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multi_x = np.array([30.0, 50.0, 70.0, 100.0, 150.0, 200.0, 300.0, 500.0,
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700.0, 1000.0, 1500.0, 2000.0, 3000.0, 5000.0, 7000.0, 10000.0,
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15000.0, 20000.0, 30000.0, 50000.0, 70000.0, 100000.0, 150000.0])
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multi_y = np.array([
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[4.22, 4.167, 4.132, 4.038, 4.019, 3.956, 3.884, 3.784, 3.713,
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3.633, 3.54, 3.433, 3.358, 3.258, 3.193, 3.128, 3.059, 2.984,
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2.934, 2.876, 2.838, 2.798, 2.759],
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[0.136, 0.167, 0.188, 0.212, 0.236, 0.257, 0.276, 0.297, 0.309,
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0.311, 0.314, 0.311, 0.305, 0.289, 0.277, 0.255, 0.24, 0.218,
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0.202, 0.182, 0.168, 0.153, 0.139],
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])
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n = len(multi_x)
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multi_we = np.zeros((2, 2, n), dtype=float)
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multi_ifixx = np.ones(n, dtype=int)
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multi_delta = np.zeros(n, dtype=float)
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multi_we[0,0,:] = 559.6
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multi_we[1,0,:] = multi_we[0,1,:] = -1634.0
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multi_we[1,1,:] = 8397.0
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for i in range(n):
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if multi_x[i] < 100.0:
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multi_ifixx[i] = 0
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elif multi_x[i] <= 150.0:
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pass # defaults are fine
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elif multi_x[i] <= 1000.0:
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multi_delta[i] = 25.0
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elif multi_x[i] <= 10000.0:
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multi_delta[i] = 560.0
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elif multi_x[i] <= 100000.0:
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multi_delta[i] = 9500.0
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else:
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multi_delta[i] = 144000.0
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if multi_x[i] == 100.0 or multi_x[i] == 150.0:
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multi_we[:,:,i] = 0.0
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multi_dat = Data(multi_x, multi_y, wd=1e-4/np.power(multi_x, 2),
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we=multi_we)
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multi_odr = ODR(multi_dat, multi_mod, beta0=[4.,2.,7.,.4,.5],
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delta0=multi_delta, ifixx=multi_ifixx)
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multi_odr.set_job(deriv=1, del_init=1)
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out = multi_odr.run()
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assert_array_almost_equal(
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out.beta,
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np.array([4.3799880305938963, 2.4333057577497703, 8.0028845899503978,
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0.5101147161764654, 0.5173902330489161]),
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)
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assert_array_almost_equal(
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out.sd_beta,
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np.array([0.0130625231081944, 0.0130499785273277, 0.1167085962217757,
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0.0132642749596149, 0.0288529201353984]),
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)
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assert_array_almost_equal(
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out.cov_beta,
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np.array([[0.0064918418231375, 0.0036159705923791, 0.0438637051470406,
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-0.0058700836512467, 0.011281212888768],
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[0.0036159705923791, 0.0064793789429006, 0.0517610978353126,
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-0.0051181304940204, 0.0130726943624117],
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[0.0438637051470406, 0.0517610978353126, 0.5182263323095322,
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-0.0563083340093696, 0.1269490939468611],
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[-0.0058700836512467, -0.0051181304940204, -0.0563083340093696,
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0.0066939246261263, -0.0140184391377962],
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[0.011281212888768, 0.0130726943624117, 0.1269490939468611,
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-0.0140184391377962, 0.0316733013820852]]),
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)
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# Pearson's Data
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# K. Pearson, Philosophical Magazine, 2, 559 (1901)
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def pearson_fcn(self, B, x):
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return B[0] + B[1]*x
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def test_pearson(self):
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p_x = np.array([0.,.9,1.8,2.6,3.3,4.4,5.2,6.1,6.5,7.4])
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p_y = np.array([5.9,5.4,4.4,4.6,3.5,3.7,2.8,2.8,2.4,1.5])
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p_sx = np.array([.03,.03,.04,.035,.07,.11,.13,.22,.74,1.])
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p_sy = np.array([1.,.74,.5,.35,.22,.22,.12,.12,.1,.04])
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p_dat = RealData(p_x, p_y, sx=p_sx, sy=p_sy)
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# Reverse the data to test invariance of results
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pr_dat = RealData(p_y, p_x, sx=p_sy, sy=p_sx)
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p_mod = Model(self.pearson_fcn, meta=dict(name='Uni-linear Fit'))
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p_odr = ODR(p_dat, p_mod, beta0=[1.,1.])
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pr_odr = ODR(pr_dat, p_mod, beta0=[1.,1.])
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out = p_odr.run()
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assert_array_almost_equal(
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out.beta,
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np.array([5.4767400299231674, -0.4796082367610305]),
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)
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assert_array_almost_equal(
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out.sd_beta,
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np.array([0.3590121690702467, 0.0706291186037444]),
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)
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assert_array_almost_equal(
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out.cov_beta,
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np.array([[0.0854275622946333, -0.0161807025443155],
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[-0.0161807025443155, 0.003306337993922]]),
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)
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rout = pr_odr.run()
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assert_array_almost_equal(
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rout.beta,
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np.array([11.4192022410781231, -2.0850374506165474]),
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)
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assert_array_almost_equal(
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rout.sd_beta,
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np.array([0.9820231665657161, 0.3070515616198911]),
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)
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assert_array_almost_equal(
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rout.cov_beta,
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np.array([[0.6391799462548782, -0.1955657291119177],
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[-0.1955657291119177, 0.0624888159223392]]),
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)
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# Lorentz Peak
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# The data is taken from one of the undergraduate physics labs I performed.
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def lorentz(self, beta, x):
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return (beta[0]*beta[1]*beta[2] / np.sqrt(np.power(x*x -
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beta[2]*beta[2], 2.0) + np.power(beta[1]*x, 2.0)))
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def test_lorentz(self):
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l_sy = np.array([.29]*18)
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l_sx = np.array([.000972971,.000948268,.000707632,.000706679,
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.000706074, .000703918,.000698955,.000456856,
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.000455207,.000662717,.000654619,.000652694,
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.000000859202,.00106589,.00106378,.00125483, .00140818,.00241839])
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l_dat = RealData(
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[3.9094, 3.85945, 3.84976, 3.84716, 3.84551, 3.83964, 3.82608,
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3.78847, 3.78163, 3.72558, 3.70274, 3.6973, 3.67373, 3.65982,
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3.6562, 3.62498, 3.55525, 3.41886],
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[652, 910.5, 984, 1000, 1007.5, 1053, 1160.5, 1409.5, 1430, 1122,
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957.5, 920, 777.5, 709.5, 698, 578.5, 418.5, 275.5],
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sx=l_sx,
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sy=l_sy,
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)
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l_mod = Model(self.lorentz, meta=dict(name='Lorentz Peak'))
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l_odr = ODR(l_dat, l_mod, beta0=(1000., .1, 3.8))
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out = l_odr.run()
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assert_array_almost_equal(
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out.beta,
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np.array([1.4306780846149925e+03, 1.3390509034538309e-01,
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3.7798193600109009e+00]),
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)
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assert_array_almost_equal(
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out.sd_beta,
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np.array([7.3621186811330963e-01, 3.5068899941471650e-04,
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2.4451209281408992e-04]),
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)
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assert_array_almost_equal(
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out.cov_beta,
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np.array([[2.4714409064597873e-01, -6.9067261911110836e-05,
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-3.1236953270424990e-05],
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[-6.9067261911110836e-05, 5.6077531517333009e-08,
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3.6133261832722601e-08],
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[-3.1236953270424990e-05, 3.6133261832722601e-08,
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2.7261220025171730e-08]]),
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)
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def test_ticket_1253(self):
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def linear(c, x):
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return c[0]*x+c[1]
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c = [2.0, 3.0]
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x = np.linspace(0, 10)
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y = linear(c, x)
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model = Model(linear)
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data = Data(x, y, wd=1.0, we=1.0)
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job = ODR(data, model, beta0=[1.0, 1.0])
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result = job.run()
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assert_equal(result.info, 2)
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# Verify fix for gh-9140
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def test_ifixx(self):
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x1 = [-2.01, -0.99, -0.001, 1.02, 1.98]
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x2 = [3.98, 1.01, 0.001, 0.998, 4.01]
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fix = np.vstack((np.zeros_like(x1, dtype=int), np.ones_like(x2, dtype=int)))
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data = Data(np.vstack((x1, x2)), y=1, fix=fix)
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model = Model(lambda beta, x: x[1, :] - beta[0] * x[0, :]**2., implicit=True)
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odr1 = ODR(data, model, beta0=np.array([1.]))
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sol1 = odr1.run()
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odr2 = ODR(data, model, beta0=np.array([1.]), ifixx=fix)
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sol2 = odr2.run()
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assert_equal(sol1.beta, sol2.beta)
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# verify bugfix for #11800 in #11802
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def test_ticket_11800(self):
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# parameters
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beta_true = np.array([1.0, 2.3, 1.1, -1.0, 1.3, 0.5])
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nr_measurements = 10
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std_dev_x = 0.01
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x_error = np.array([[0.00063445, 0.00515731, 0.00162719, 0.01022866,
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-0.01624845, 0.00482652, 0.00275988, -0.00714734, -0.00929201, -0.00687301],
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[-0.00831623, -0.00821211, -0.00203459, 0.00938266, -0.00701829,
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0.0032169, 0.00259194, -0.00581017, -0.0030283, 0.01014164]])
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std_dev_y = 0.05
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y_error = np.array([[0.05275304, 0.04519563, -0.07524086, 0.03575642,
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0.04745194, 0.03806645, 0.07061601, -0.00753604, -0.02592543, -0.02394929],
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[0.03632366, 0.06642266, 0.08373122, 0.03988822, -0.0092536,
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-0.03750469, -0.03198903, 0.01642066, 0.01293648, -0.05627085]])
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beta_solution = np.array([
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2.62920235756665876536e+00, -1.26608484996299608838e+02, 1.29703572775403074502e+02,
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-1.88560985401185465804e+00, 7.83834160771274923718e+01, -7.64124076838087091801e+01])
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# model's function and Jacobians
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def func(beta, x):
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y0 = beta[0] + beta[1] * x[0, :] + beta[2] * x[1, :]
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y1 = beta[3] + beta[4] * x[0, :] + beta[5] * x[1, :]
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return np.vstack((y0, y1))
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def df_dbeta_odr(beta, x):
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nr_meas = np.shape(x)[1]
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zeros = np.zeros(nr_meas)
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ones = np.ones(nr_meas)
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|
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dy0 = np.array([ones, x[0, :], x[1, :], zeros, zeros, zeros])
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dy1 = np.array([zeros, zeros, zeros, ones, x[0, :], x[1, :]])
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|
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return np.stack((dy0, dy1))
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|
|
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def df_dx_odr(beta, x):
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nr_meas = np.shape(x)[1]
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ones = np.ones(nr_meas)
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|
|
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dy0 = np.array([beta[1] * ones, beta[2] * ones])
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dy1 = np.array([beta[4] * ones, beta[5] * ones])
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return np.stack((dy0, dy1))
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|
|
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# do measurements with errors in independent and dependent variables
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x0_true = np.linspace(1, 10, nr_measurements)
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x1_true = np.linspace(1, 10, nr_measurements)
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x_true = np.array([x0_true, x1_true])
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|
|
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y_true = func(beta_true, x_true)
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|
|
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x_meas = x_true + x_error
|
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y_meas = y_true + y_error
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|
|
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# estimate model's parameters
|
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model_f = Model(func, fjacb=df_dbeta_odr, fjacd=df_dx_odr)
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|
|
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data = RealData(x_meas, y_meas, sx=std_dev_x, sy=std_dev_y)
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|
|
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odr_obj = ODR(data, model_f, beta0=0.9 * beta_true, maxit=100)
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#odr_obj.set_iprint(init=2, iter=0, iter_step=1, final=1)
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odr_obj.set_job(deriv=3)
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|
|
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odr_out = odr_obj.run()
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|
|
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# check results
|
|
assert_equal(odr_out.info, 1)
|
|
assert_array_almost_equal(odr_out.beta, beta_solution)
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|
|
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def test_multilinear_model(self):
|
|
x = np.linspace(0.0, 5.0)
|
|
y = 10.0 + 5.0 * x
|
|
data = Data(x, y)
|
|
odr_obj = ODR(data, multilinear)
|
|
output = odr_obj.run()
|
|
assert_array_almost_equal(output.beta, [10.0, 5.0])
|
|
|
|
def test_exponential_model(self):
|
|
x = np.linspace(0.0, 5.0)
|
|
y = -10.0 + np.exp(0.5*x)
|
|
data = Data(x, y)
|
|
odr_obj = ODR(data, exponential)
|
|
output = odr_obj.run()
|
|
assert_array_almost_equal(output.beta, [-10.0, 0.5])
|
|
|
|
def test_polynomial_model(self):
|
|
x = np.linspace(0.0, 5.0)
|
|
y = 1.0 + 2.0 * x + 3.0 * x ** 2 + 4.0 * x ** 3
|
|
poly_model = polynomial(3)
|
|
data = Data(x, y)
|
|
odr_obj = ODR(data, poly_model)
|
|
output = odr_obj.run()
|
|
assert_array_almost_equal(output.beta, [1.0, 2.0, 3.0, 4.0])
|
|
|
|
def test_unilinear_model(self):
|
|
x = np.linspace(0.0, 5.0)
|
|
y = 1.0 * x + 2.0
|
|
data = Data(x, y)
|
|
odr_obj = ODR(data, unilinear)
|
|
output = odr_obj.run()
|
|
assert_array_almost_equal(output.beta, [1.0, 2.0])
|
|
|
|
def test_quadratic_model(self):
|
|
x = np.linspace(0.0, 5.0)
|
|
y = 1.0 * x ** 2 + 2.0 * x + 3.0
|
|
data = Data(x, y)
|
|
odr_obj = ODR(data, quadratic)
|
|
output = odr_obj.run()
|
|
assert_array_almost_equal(output.beta, [1.0, 2.0, 3.0])
|
|
|