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import pickle |
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import tempfile |
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import shutil |
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import os |
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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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assert_allclose) |
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import pytest |
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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: |
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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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def empty_data_func(self, B, x): |
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return B[0]*x + B[1] |
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@pytest.mark.thread_unsafe |
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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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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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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_allclose( |
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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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rtol=1e-6, atol=2e-6, |
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) |
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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 |
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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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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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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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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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|
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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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|
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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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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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|
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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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|
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|
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def test_ticket_11800(self): |
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|
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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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|
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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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|
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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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|
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beta_solution = np.array([ |
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2.62920235756665876536e+00, -1.26608484996299608838e+02, |
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1.29703572775403074502e+02, -1.88560985401185465804e+00, |
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7.83834160771274923718e+01, -7.64124076838087091801e+01]) |
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|
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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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|
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return np.vstack((y0, y1)) |
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|
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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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|
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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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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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|
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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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|
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assert_equal(odr_out.info, 1) |
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assert_array_almost_equal(odr_out.beta, beta_solution) |
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|
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def test_multilinear_model(self): |
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x = np.linspace(0.0, 5.0) |
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y = 10.0 + 5.0 * x |
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data = Data(x, y) |
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odr_obj = ODR(data, multilinear) |
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output = odr_obj.run() |
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assert_array_almost_equal(output.beta, [10.0, 5.0]) |
|
|
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def test_exponential_model(self): |
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x = np.linspace(0.0, 5.0) |
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y = -10.0 + np.exp(0.5*x) |
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data = Data(x, y) |
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odr_obj = ODR(data, exponential) |
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output = odr_obj.run() |
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assert_array_almost_equal(output.beta, [-10.0, 0.5]) |
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|
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def test_polynomial_model(self): |
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x = np.linspace(0.0, 5.0) |
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y = 1.0 + 2.0 * x + 3.0 * x ** 2 + 4.0 * x ** 3 |
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poly_model = polynomial(3) |
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data = Data(x, y) |
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odr_obj = ODR(data, poly_model) |
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output = odr_obj.run() |
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assert_array_almost_equal(output.beta, [1.0, 2.0, 3.0, 4.0]) |
|
|
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def test_unilinear_model(self): |
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x = np.linspace(0.0, 5.0) |
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y = 1.0 * x + 2.0 |
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data = Data(x, y) |
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odr_obj = ODR(data, unilinear) |
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output = odr_obj.run() |
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assert_array_almost_equal(output.beta, [1.0, 2.0]) |
|
|
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def test_quadratic_model(self): |
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x = np.linspace(0.0, 5.0) |
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y = 1.0 * x ** 2 + 2.0 * x + 3.0 |
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data = Data(x, y) |
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odr_obj = ODR(data, quadratic) |
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output = odr_obj.run() |
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assert_array_almost_equal(output.beta, [1.0, 2.0, 3.0]) |
|
|
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def test_work_ind(self): |
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|
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def func(par, x): |
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b0, b1 = par |
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return b0 + b1 * x |
|
|
|
|
|
n_data = 4 |
|
x = np.arange(n_data) |
|
y = np.where(x % 2, x + 0.1, x - 0.1) |
|
x_err = np.full(n_data, 0.1) |
|
y_err = np.full(n_data, 0.1) |
|
|
|
|
|
linear_model = Model(func) |
|
real_data = RealData(x, y, sx=x_err, sy=y_err) |
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odr_obj = ODR(real_data, linear_model, beta0=[0.4, 0.4]) |
|
odr_obj.set_job(fit_type=0) |
|
out = odr_obj.run() |
|
|
|
sd_ind = out.work_ind['sd'] |
|
assert_array_almost_equal(out.sd_beta, |
|
out.work[sd_ind:sd_ind + len(out.sd_beta)]) |
|
|
|
@pytest.mark.skipif(True, reason="Fortran I/O prone to crashing so better " |
|
"not to run this test, see gh-13127") |
|
def test_output_file_overwrite(self): |
|
""" |
|
Verify fix for gh-1892 |
|
""" |
|
def func(b, x): |
|
return b[0] + b[1] * x |
|
|
|
p = Model(func) |
|
data = Data(np.arange(10), 12 * np.arange(10)) |
|
tmp_dir = tempfile.mkdtemp() |
|
error_file_path = os.path.join(tmp_dir, "error.dat") |
|
report_file_path = os.path.join(tmp_dir, "report.dat") |
|
try: |
|
ODR(data, p, beta0=[0.1, 13], errfile=error_file_path, |
|
rptfile=report_file_path).run() |
|
ODR(data, p, beta0=[0.1, 13], errfile=error_file_path, |
|
rptfile=report_file_path, overwrite=True).run() |
|
finally: |
|
|
|
shutil.rmtree(tmp_dir) |
|
|
|
def test_odr_model_default_meta(self): |
|
def func(b, x): |
|
return b[0] + b[1] * x |
|
|
|
p = Model(func) |
|
p.set_meta(name='Sample Model Meta', ref='ODRPACK') |
|
assert_equal(p.meta, {'name': 'Sample Model Meta', 'ref': 'ODRPACK'}) |
|
|
|
def test_work_array_del_init(self): |
|
""" |
|
Verify fix for gh-18739 where del_init=1 fails. |
|
""" |
|
def func(b, x): |
|
return b[0] + b[1] * x |
|
|
|
|
|
n_data = 4 |
|
x = np.arange(n_data) |
|
y = np.where(x % 2, x + 0.1, x - 0.1) |
|
x_err = np.full(n_data, 0.1) |
|
y_err = np.full(n_data, 0.1) |
|
|
|
linear_model = Model(func) |
|
|
|
rd0 = RealData(x, y, sx=x_err, sy=y_err) |
|
rd1 = RealData(x, y, sx=x_err, sy=0.1) |
|
rd2 = RealData(x, y, sx=x_err, sy=[0.1]) |
|
rd3 = RealData(x, y, sx=x_err, sy=np.full((1, n_data), 0.1)) |
|
rd4 = RealData(x, y, sx=x_err, covy=[[0.01]]) |
|
rd5 = RealData(x, y, sx=x_err, covy=np.full((1, 1, n_data), 0.01)) |
|
for rd in [rd0, rd1, rd2, rd3, rd4, rd5]: |
|
odr_obj = ODR(rd, linear_model, beta0=[0.4, 0.4], |
|
delta0=np.full(n_data, -0.1)) |
|
odr_obj.set_job(fit_type=0, del_init=1) |
|
|
|
odr_obj.run() |
|
|
|
def test_pickling_data(self): |
|
x = np.linspace(0.0, 5.0) |
|
y = 1.0 * x + 2.0 |
|
data = Data(x, y) |
|
|
|
obj_pickle = pickle.dumps(data) |
|
del data |
|
pickle.loads(obj_pickle) |
|
|
|
def test_pickling_real_data(self): |
|
x = np.linspace(0.0, 5.0) |
|
y = 1.0 * x + 2.0 |
|
data = RealData(x, y) |
|
|
|
obj_pickle = pickle.dumps(data) |
|
del data |
|
pickle.loads(obj_pickle) |
|
|
|
def test_pickling_model(self): |
|
obj_pickle = pickle.dumps(unilinear) |
|
pickle.loads(obj_pickle) |
|
|
|
def test_pickling_odr(self): |
|
x = np.linspace(0.0, 5.0) |
|
y = 1.0 * x + 2.0 |
|
odr_obj = ODR(Data(x, y), unilinear) |
|
|
|
obj_pickle = pickle.dumps(odr_obj) |
|
del odr_obj |
|
pickle.loads(obj_pickle) |
|
|
|
def test_pickling_output(self): |
|
x = np.linspace(0.0, 5.0) |
|
y = 1.0 * x + 2.0 |
|
output = ODR(Data(x, y), unilinear).run |
|
|
|
obj_pickle = pickle.dumps(output) |
|
del output |
|
pickle.loads(obj_pickle) |
|
|