[Scipy-svn] r2596 - in trunk/Lib/odr: . tests
scipy-svn at scipy.org
scipy-svn at scipy.org
Tue Jan 23 15:14:54 EST 2007
Author: jarrod.millman
Date: 2007-01-23 14:14:51 -0600 (Tue, 23 Jan 2007)
New Revision: 2596
Added:
trunk/Lib/odr/tests/test_odr.py
Removed:
trunk/Lib/odr/tests/test_odrpack.py
Modified:
trunk/Lib/odr/__init__.py
trunk/Lib/odr/setup.py
Log:
more changes to enable tests, created info.py
Modified: trunk/Lib/odr/__init__.py
===================================================================
--- trunk/Lib/odr/__init__.py 2007-01-23 19:45:34 UTC (rev 2595)
+++ trunk/Lib/odr/__init__.py 2007-01-23 20:14:51 UTC (rev 2596)
@@ -1,47 +1,9 @@
-""" Orthogonal Distance Regression
+#
+# odr - Orthogonal Distance Regression
+#
-Introduction
-============
+from info import __doc__
-Why Orthogonal Distance Regression (ODR)? Sometimes one has measurement errors
-in the explanatory variable, not just the response variable. Ordinary Least
-Squares (OLS) fitting procedures treat the data for explanatory variables as
-fixed. Furthermore, OLS procedures require that the response variable be an
-explicit function of the explanatory variables; sometimes making the equation
-explicit is unwieldy and introduces errors. ODR can handle both of these cases
-with ease and can even reduce to the OLS case if necessary.
-
-ODRPACK is a FORTRAN-77 library for performing ODR with possibly non-linear
-fitting functions. It uses a modified trust-region Levenberg-Marquardt-type
-algorithm to estimate the function parameters. The fitting functions are
-provided by Python functions operating on NumPy arrays. The required derivatives
-may be provided by Python functions as well or may be numerically estimated.
-ODRPACK can do explicit or implicit ODR fits or can do OLS. Input and output
-variables may be multi-dimensional. Weights can be provided to account for
-different variances of the observations (even covariances between dimensions of
-the variables).
-
-odr provides two interfaces: a single function and a set of high-level classes
-that wrap that function. Please refer to their docstrings for more information.
-While the docstring of the function, odr, does not have a full explanation of
-its arguments, the classes do, and the arguments with the same name usually have
-the same requirements. Furthermore, it is highly suggested that one at least
-skim the ODRPACK User's Guide. Know Thy Algorithm.
-
-
-Use
-===
-
-See the docstrings of odr.odrpack and the functions and classes for
-usage instructions. The ODRPACK User's Guide is also quite helpful. It can be
-found on one of the ODRPACK's original author's website:
-
- http://www.boulder.nist.gov/mcsd/Staff/JRogers/odrpack.html
-
-Robert Kern
-robert.kern at gmail.com
-"""
-
__version__ = '0.7'
__author__ = 'Robert Kern <robert.kern at gmail.com>'
__date__ = '2006-09-21'
Modified: trunk/Lib/odr/setup.py
===================================================================
--- trunk/Lib/odr/setup.py 2007-01-23 19:45:34 UTC (rev 2595)
+++ trunk/Lib/odr/setup.py 2007-01-23 20:14:51 UTC (rev 2596)
@@ -38,6 +38,7 @@
**blas_info
)
+ config.add_data_dir('tests')
return config
if __name__ == '__main__':
Copied: trunk/Lib/odr/tests/test_odr.py (from rev 2595, trunk/Lib/odr/tests/test_odrpack.py)
===================================================================
--- trunk/Lib/odr/tests/test_odrpack.py 2007-01-23 19:45:34 UTC (rev 2595)
+++ trunk/Lib/odr/tests/test_odr.py 2007-01-23 20:14:51 UTC (rev 2596)
@@ -0,0 +1,316 @@
+# Standard library imports.
+import cPickle
+
+# Scipy imports.
+import numpy as np
+from numpy import pi
+from numpy.testing import NumpyTest, NumpyTestCase, assert_array_almost_equal
+from scipy.odr import Data, Model, ODR, RealData, odr_stop
+
+
+class test_odr(NumpyTestCase):
+
+ # Explicit Example
+
+ def explicit_fcn(self, B, x):
+ ret = B[0] + B[1] * np.power(np.exp(B[2]*x) - 1.0, 2)
+ return ret
+
+ def explicit_fjd(self, B, x):
+ eBx = np.exp(B[2]*x)
+ ret = B[1] * 2.0 * (eBx-1.0) * B[2] * eBx
+ return ret
+
+ def explicit_fjb(self, B, x):
+ eBx = np.exp(B[2]*x)
+ res = np.vstack([np.ones(x.shape[-1]),
+ np.power(eBx-1.0, 2),
+ B[1]*2.0*(eBx-1.0)*eBx*x])
+ return res
+
+ def test_explicit(self):
+ explicit_mod = Model(
+ self.explicit_fcn,
+ fjacb=self.explicit_fjb,
+ fjacd=self.explicit_fjd,
+ meta=dict(name='Sample Explicit Model',
+ ref='ODRPACK UG, pg. 39'),
+ )
+ explicit_dat = Data([0.,0.,5.,7.,7.5,10.,16.,26.,30.,34.,34.5,100.],
+ [1265.,1263.6,1258.,1254.,1253.,1249.8,1237.,1218.,1220.6,
+ 1213.8,1215.5,1212.])
+ explicit_odr = ODR(explicit_dat, explicit_mod, beta0=[1500.0, -50.0, -0.1],
+ ifixx=[0,0,1,1,1,1,1,1,1,1,1,0])
+ explicit_odr.set_job(deriv=2)
+
+ out = explicit_odr.run()
+ assert_array_almost_equal(
+ out.beta,
+ np.array([ 1.2646548050648876e+03, -5.4018409956678255e+01,
+ -8.7849712165253724e-02]),
+ )
+ assert_array_almost_equal(
+ out.sd_beta,
+ np.array([ 1.0349270280543437, 1.583997785262061 , 0.0063321988657267]),
+ )
+ assert_array_almost_equal(
+ out.cov_beta,
+ np.array([[ 4.4949592379003039e-01, -3.7421976890364739e-01,
+ -8.0978217468468912e-04],
+ [ -3.7421976890364739e-01, 1.0529686462751804e+00,
+ -1.9453521827942002e-03],
+ [ -8.0978217468468912e-04, -1.9453521827942002e-03,
+ 1.6827336938454476e-05]]),
+ )
+
+
+ # Implicit Example
+
+ def implicit_fcn(self, B, x):
+ return (B[2]*np.power(x[0]-B[0], 2) +
+ 2.0*B[3]*(x[0]-B[0])*(x[1]-B[1]) +
+ B[4]*np.power(x[1]-B[1], 2) - 1.0)
+
+ def test_implicit(self):
+ implicit_mod = Model(
+ self.implicit_fcn,
+ implicit=1,
+ meta=dict(name='Sample Implicit Model',
+ ref='ODRPACK UG, pg. 49'),
+ )
+ implicit_dat = Data([
+ [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,
+ -0.78,-1.36,-1.9,-2.5,-2.88,-3.18,-3.44],
+ [-0.12,-0.6,-1.,-1.4,-2.54,-3.36,-4.,-4.75,-5.25,-5.64,-5.97,-6.32,
+ -6.44,-6.44,-6.41,-6.25,-5.88,-5.5,-5.24,-4.86]],
+ 1,
+ )
+ implicit_odr = ODR(implicit_dat, implicit_mod,
+ beta0=[-1.0, -3.0, 0.09, 0.02, 0.08])
+
+ out = implicit_odr.run()
+ assert_array_almost_equal(
+ out.beta,
+ np.array([-0.9993809167281279, -2.9310484652026476, 0.0875730502693354,
+ 0.0162299708984738, 0.0797537982976416]),
+ )
+ assert_array_almost_equal(
+ out.sd_beta,
+ np.array([ 0.1113840353364371, 0.1097673310686467, 0.0041060738314314,
+ 0.0027500347539902, 0.0034962501532468]),
+ )
+ assert_array_almost_equal(
+ out.cov_beta,
+ np.array([[ 2.1089274602333052e+00, -1.9437686411979040e+00,
+ 7.0263550868344446e-02, -4.7175267373474862e-02,
+ 5.2515575927380355e-02],
+ [ -1.9437686411979040e+00, 2.0481509222414456e+00,
+ -6.1600515853057307e-02, 4.6268827806232933e-02,
+ -5.8822307501391467e-02],
+ [ 7.0263550868344446e-02, -6.1600515853057307e-02,
+ 2.8659542561579308e-03, -1.4628662260014491e-03,
+ 1.4528860663055824e-03],
+ [ -4.7175267373474862e-02, 4.6268827806232933e-02,
+ -1.4628662260014491e-03, 1.2855592885514335e-03,
+ -1.2692942951415293e-03],
+ [ 5.2515575927380355e-02, -5.8822307501391467e-02,
+ 1.4528860663055824e-03, -1.2692942951415293e-03,
+ 2.0778813389755596e-03]]),
+ )
+
+
+ # Multi-variable Example
+
+ def multi_fcn(self, B, x):
+ if (x < 0.0).any():
+ raise odr_stop
+ theta = pi*B[3]/2.
+ ctheta = np.cos(theta)
+ stheta = np.sin(theta)
+ omega = np.power(2.*pi*x*np.exp(-B[2]), B[3])
+ phi = np.arctan2((omega*stheta), (1.0 + omega*ctheta))
+ r = (B[0] - B[1]) * np.power(np.sqrt(np.power(1.0 + omega*ctheta, 2) +
+ np.power(omega*stheta, 2)), -B[4])
+ ret = np.vstack([B[1] + r*np.cos(B[4]*phi),
+ r*np.sin(B[4]*phi)])
+ return ret
+
+ def test_multi(self):
+ multi_mod = Model(
+ self.multi_fcn,
+ meta=dict(name='Sample Multi-Response Model',
+ ref='ODRPACK UG, pg. 56'),
+ )
+
+ multi_x = np.array([30.0, 50.0, 70.0, 100.0, 150.0, 200.0, 300.0, 500.0,
+ 700.0, 1000.0, 1500.0, 2000.0, 3000.0, 5000.0, 7000.0, 10000.0,
+ 15000.0, 20000.0, 30000.0, 50000.0, 70000.0, 100000.0, 150000.0])
+ multi_y = np.array([
+ [4.22, 4.167, 4.132, 4.038, 4.019, 3.956, 3.884, 3.784, 3.713,
+ 3.633, 3.54, 3.433, 3.358, 3.258, 3.193, 3.128, 3.059, 2.984,
+ 2.934, 2.876, 2.838, 2.798, 2.759],
+ [0.136, 0.167, 0.188, 0.212, 0.236, 0.257, 0.276, 0.297, 0.309,
+ 0.311, 0.314, 0.311, 0.305, 0.289, 0.277, 0.255, 0.24, 0.218,
+ 0.202, 0.182, 0.168, 0.153, 0.139],
+ ])
+ n = len(multi_x)
+ multi_we = np.zeros((2, 2, n), dtype=float)
+ multi_ifixx = np.ones(n, dtype=int)
+ multi_delta = np.zeros(n, dtype=float)
+
+ multi_we[0,0,:] = 559.6
+ multi_we[1,0,:] = multi_we[0,1,:] = -1634.0
+ multi_we[1,1,:] = 8397.0
+
+ for i in range(n):
+ if multi_x[i] < 100.0:
+ multi_ifixx[i] = 0
+ elif multi_x[i] <= 150.0:
+ pass # defaults are fine
+ elif multi_x[i] <= 1000.0:
+ multi_delta[i] = 25.0
+ elif multi_x[i] <= 10000.0:
+ multi_delta[i] = 560.0
+ elif multi_x[i] <= 100000.0:
+ multi_delta[i] = 9500.0
+ else:
+ multi_delta[i] = 144000.0
+ if multi_x[i] == 100.0 or multi_x[i] == 150.0:
+ multi_we[:,:,i] = 0.0
+
+ multi_dat = Data(multi_x, multi_y, wd=1e-4/np.power(multi_x, 2),
+ we=multi_we)
+ multi_odr = ODR(multi_dat, multi_mod, beta0=[4.,2.,7.,.4,.5],
+ delta0=multi_delta, ifixx=multi_ifixx)
+ multi_odr.set_job(deriv=1, del_init=1)
+
+ out = multi_odr.run()
+ assert_array_almost_equal(
+ out.beta,
+ np.array([ 4.3799880305938963, 2.4333057577497703, 8.0028845899503978,
+ 0.5101147161764654, 0.5173902330489161]),
+ )
+ assert_array_almost_equal(
+ out.sd_beta,
+ np.array([ 0.0130625231081944, 0.0130499785273277, 0.1167085962217757,
+ 0.0132642749596149, 0.0288529201353984]),
+ )
+ assert_array_almost_equal(
+ out.cov_beta,
+ np.array([[ 0.0064918418231375, 0.0036159705923791, 0.0438637051470406,
+ -0.0058700836512467, 0.011281212888768 ],
+ [ 0.0036159705923791, 0.0064793789429006, 0.0517610978353126,
+ -0.0051181304940204, 0.0130726943624117],
+ [ 0.0438637051470406, 0.0517610978353126, 0.5182263323095322,
+ -0.0563083340093696, 0.1269490939468611],
+ [-0.0058700836512467, -0.0051181304940204, -0.0563083340093696,
+ 0.0066939246261263, -0.0140184391377962],
+ [ 0.011281212888768 , 0.0130726943624117, 0.1269490939468611,
+ -0.0140184391377962, 0.0316733013820852]]),
+ )
+
+
+ # Pearson's Data
+ # K. Pearson, Philosophical Magazine, 2, 559 (1901)
+
+ def pearson_fcn(self, B, x):
+ return B[0] + B[1]*x
+
+ def test_pearson(self):
+ p_x = np.array([0.,.9,1.8,2.6,3.3,4.4,5.2,6.1,6.5,7.4])
+ p_y = np.array([5.9,5.4,4.4,4.6,3.5,3.7,2.8,2.8,2.4,1.5])
+ p_sx = np.array([.03,.03,.04,.035,.07,.11,.13,.22,.74,1.])
+ p_sy = np.array([1.,.74,.5,.35,.22,.22,.12,.12,.1,.04])
+
+ p_dat = RealData(p_x, p_y, sx=p_sx, sy=p_sy)
+
+ # Reverse the data to test invariance of results
+ pr_dat = RealData(p_y, p_x, sx=p_sy, sy=p_sx)
+
+ p_mod = Model(self.pearson_fcn, meta=dict(name='Uni-linear Fit'))
+
+ p_odr = ODR(p_dat, p_mod, beta0=[1.,1.])
+ pr_odr = ODR(pr_dat, p_mod, beta0=[1.,1.])
+
+ out = p_odr.run()
+ assert_array_almost_equal(
+ out.beta,
+ np.array([ 5.4767400299231674, -0.4796082367610305]),
+ )
+ assert_array_almost_equal(
+ out.sd_beta,
+ np.array([ 0.3590121690702467, 0.0706291186037444]),
+ )
+ assert_array_almost_equal(
+ out.cov_beta,
+ np.array([[ 0.0854275622946333, -0.0161807025443155],
+ [-0.0161807025443155, 0.003306337993922 ]]),
+ )
+
+ rout = pr_odr.run()
+ assert_array_almost_equal(
+ rout.beta,
+ np.array([ 11.4192022410781231, -2.0850374506165474]),
+ )
+ assert_array_almost_equal(
+ rout.sd_beta,
+ np.array([ 0.9820231665657161, 0.3070515616198911]),
+ )
+ assert_array_almost_equal(
+ rout.cov_beta,
+ np.array([[ 0.6391799462548782, -0.1955657291119177],
+ [-0.1955657291119177, 0.0624888159223392]]),
+ )
+
+ # Lorentz Peak
+ # The data is taken from one of the undergraduate physics labs I performed.
+
+ def lorentz(self, beta, x):
+ return (beta[0]*beta[1]*beta[2] / np.sqrt(np.power(x*x -
+ beta[2]*beta[2], 2.0) + np.power(beta[1]*x, 2.0)))
+
+ def test_lorentz(self):
+ l_sy = np.array([.29]*18)
+ l_sx = np.array([.000972971,.000948268,.000707632,.000706679,
+ .000706074, .000703918,.000698955,.000456856,
+ .000455207,.000662717,.000654619,.000652694,
+ .000000859202,.00106589,.00106378,.00125483, .00140818,.00241839])
+
+ l_dat = RealData(
+ [3.9094, 3.85945, 3.84976, 3.84716, 3.84551, 3.83964, 3.82608,
+ 3.78847, 3.78163, 3.72558, 3.70274, 3.6973, 3.67373, 3.65982,
+ 3.6562, 3.62498, 3.55525, 3.41886],
+ [652, 910.5, 984, 1000, 1007.5, 1053, 1160.5, 1409.5, 1430, 1122,
+ 957.5, 920, 777.5, 709.5, 698, 578.5, 418.5, 275.5],
+ sx=l_sx,
+ sy=l_sy,
+ )
+ l_mod = Model(self.lorentz, meta=dict(name='Lorentz Peak'))
+ l_odr = ODR(l_dat, l_mod, beta0=(1000., .1, 3.8))
+
+ out = l_odr.run()
+ assert_array_almost_equal(
+ out.beta,
+ np.array([ 1.4306780846149925e+03, 1.3390509034538309e-01,
+ 3.7798193600109009e+00]),
+ )
+ assert_array_almost_equal(
+ out.sd_beta,
+ np.array([ 7.3621186811330963e-01, 3.5068899941471650e-04,
+ 2.4451209281408992e-04]),
+ )
+ assert_array_almost_equal(
+ out.cov_beta,
+ np.array([[ 2.4714409064597873e-01, -6.9067261911110836e-05,
+ -3.1236953270424990e-05],
+ [ -6.9067261911110836e-05, 5.6077531517333009e-08,
+ 3.6133261832722601e-08],
+ [ -3.1236953270424990e-05, 3.6133261832722601e-08,
+ 2.7261220025171730e-08]]),
+ )
+
+
+if __name__ == "__main__":
+ NumpyTest().run()
+
+#### EOF #######################################################################
Deleted: trunk/Lib/odr/tests/test_odrpack.py
===================================================================
--- trunk/Lib/odr/tests/test_odrpack.py 2007-01-23 19:45:34 UTC (rev 2595)
+++ trunk/Lib/odr/tests/test_odrpack.py 2007-01-23 20:14:51 UTC (rev 2596)
@@ -1,317 +0,0 @@
-
-# Standard library imports.
-import cPickle
-
-# Scipy imports.
-import numpy as np
-from numpy import pi
-from numpy.testing import NumpyTest, NumpyTestCase, assert_array_almost_equal
-from scipy.odr import Data, Model, ODR, RealData, odr_stop
-
-
-class test_odr(NumpyTestCase):
-
- # Explicit Example
-
- def explicit_fcn(self, B, x):
- ret = B[0] + B[1] * np.power(np.exp(B[2]*x) - 1.0, 2)
- return ret
-
- def explicit_fjd(self, B, x):
- eBx = np.exp(B[2]*x)
- ret = B[1] * 2.0 * (eBx-1.0) * B[2] * eBx
- return ret
-
- def explicit_fjb(self, B, x):
- eBx = np.exp(B[2]*x)
- res = np.vstack([np.ones(x.shape[-1]),
- np.power(eBx-1.0, 2),
- B[1]*2.0*(eBx-1.0)*eBx*x])
- return res
-
- def test_explicit(self):
- explicit_mod = Model(
- self.explicit_fcn,
- fjacb=self.explicit_fjb,
- fjacd=self.explicit_fjd,
- meta=dict(name='Sample Explicit Model',
- ref='ODRPACK UG, pg. 39'),
- )
- explicit_dat = Data([0.,0.,5.,7.,7.5,10.,16.,26.,30.,34.,34.5,100.],
- [1265.,1263.6,1258.,1254.,1253.,1249.8,1237.,1218.,1220.6,
- 1213.8,1215.5,1212.])
- explicit_odr = ODR(explicit_dat, explicit_mod, beta0=[1500.0, -50.0, -0.1],
- ifixx=[0,0,1,1,1,1,1,1,1,1,1,0])
- explicit_odr.set_job(deriv=2)
-
- out = explicit_odr.run()
- assert_array_almost_equal(
- out.beta,
- np.array([ 1.2646548050648876e+03, -5.4018409956678255e+01,
- -8.7849712165253724e-02]),
- )
- assert_array_almost_equal(
- out.sd_beta,
- np.array([ 1.0349270280543437, 1.583997785262061 , 0.0063321988657267]),
- )
- assert_array_almost_equal(
- out.cov_beta,
- np.array([[ 4.4949592379003039e-01, -3.7421976890364739e-01,
- -8.0978217468468912e-04],
- [ -3.7421976890364739e-01, 1.0529686462751804e+00,
- -1.9453521827942002e-03],
- [ -8.0978217468468912e-04, -1.9453521827942002e-03,
- 1.6827336938454476e-05]]),
- )
-
-
- # Implicit Example
-
- def implicit_fcn(self, B, x):
- return (B[2]*np.power(x[0]-B[0], 2) +
- 2.0*B[3]*(x[0]-B[0])*(x[1]-B[1]) +
- B[4]*np.power(x[1]-B[1], 2) - 1.0)
-
- def test_implicit(self):
- implicit_mod = Model(
- self.implicit_fcn,
- implicit=1,
- meta=dict(name='Sample Implicit Model',
- ref='ODRPACK UG, pg. 49'),
- )
- implicit_dat = Data([
- [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,
- -0.78,-1.36,-1.9,-2.5,-2.88,-3.18,-3.44],
- [-0.12,-0.6,-1.,-1.4,-2.54,-3.36,-4.,-4.75,-5.25,-5.64,-5.97,-6.32,
- -6.44,-6.44,-6.41,-6.25,-5.88,-5.5,-5.24,-4.86]],
- 1,
- )
- implicit_odr = ODR(implicit_dat, implicit_mod,
- beta0=[-1.0, -3.0, 0.09, 0.02, 0.08])
-
- out = implicit_odr.run()
- assert_array_almost_equal(
- out.beta,
- np.array([-0.9993809167281279, -2.9310484652026476, 0.0875730502693354,
- 0.0162299708984738, 0.0797537982976416]),
- )
- assert_array_almost_equal(
- out.sd_beta,
- np.array([ 0.1113840353364371, 0.1097673310686467, 0.0041060738314314,
- 0.0027500347539902, 0.0034962501532468]),
- )
- assert_array_almost_equal(
- out.cov_beta,
- np.array([[ 2.1089274602333052e+00, -1.9437686411979040e+00,
- 7.0263550868344446e-02, -4.7175267373474862e-02,
- 5.2515575927380355e-02],
- [ -1.9437686411979040e+00, 2.0481509222414456e+00,
- -6.1600515853057307e-02, 4.6268827806232933e-02,
- -5.8822307501391467e-02],
- [ 7.0263550868344446e-02, -6.1600515853057307e-02,
- 2.8659542561579308e-03, -1.4628662260014491e-03,
- 1.4528860663055824e-03],
- [ -4.7175267373474862e-02, 4.6268827806232933e-02,
- -1.4628662260014491e-03, 1.2855592885514335e-03,
- -1.2692942951415293e-03],
- [ 5.2515575927380355e-02, -5.8822307501391467e-02,
- 1.4528860663055824e-03, -1.2692942951415293e-03,
- 2.0778813389755596e-03]]),
- )
-
-
- # Multi-variable Example
-
- def multi_fcn(self, B, x):
- if (x < 0.0).any():
- raise odr_stop
- theta = pi*B[3]/2.
- ctheta = np.cos(theta)
- stheta = np.sin(theta)
- omega = np.power(2.*pi*x*np.exp(-B[2]), B[3])
- phi = np.arctan2((omega*stheta), (1.0 + omega*ctheta))
- r = (B[0] - B[1]) * np.power(np.sqrt(np.power(1.0 + omega*ctheta, 2) +
- np.power(omega*stheta, 2)), -B[4])
- ret = np.vstack([B[1] + r*np.cos(B[4]*phi),
- r*np.sin(B[4]*phi)])
- return ret
-
- def test_multi(self):
- multi_mod = Model(
- self.multi_fcn,
- meta=dict(name='Sample Multi-Response Model',
- ref='ODRPACK UG, pg. 56'),
- )
-
- multi_x = np.array([30.0, 50.0, 70.0, 100.0, 150.0, 200.0, 300.0, 500.0,
- 700.0, 1000.0, 1500.0, 2000.0, 3000.0, 5000.0, 7000.0, 10000.0,
- 15000.0, 20000.0, 30000.0, 50000.0, 70000.0, 100000.0, 150000.0])
- multi_y = np.array([
- [4.22, 4.167, 4.132, 4.038, 4.019, 3.956, 3.884, 3.784, 3.713,
- 3.633, 3.54, 3.433, 3.358, 3.258, 3.193, 3.128, 3.059, 2.984,
- 2.934, 2.876, 2.838, 2.798, 2.759],
- [0.136, 0.167, 0.188, 0.212, 0.236, 0.257, 0.276, 0.297, 0.309,
- 0.311, 0.314, 0.311, 0.305, 0.289, 0.277, 0.255, 0.24, 0.218,
- 0.202, 0.182, 0.168, 0.153, 0.139],
- ])
- n = len(multi_x)
- multi_we = np.zeros((2, 2, n), dtype=float)
- multi_ifixx = np.ones(n, dtype=int)
- multi_delta = np.zeros(n, dtype=float)
-
- multi_we[0,0,:] = 559.6
- multi_we[1,0,:] = multi_we[0,1,:] = -1634.0
- multi_we[1,1,:] = 8397.0
-
- for i in range(n):
- if multi_x[i] < 100.0:
- multi_ifixx[i] = 0
- elif multi_x[i] <= 150.0:
- pass # defaults are fine
- elif multi_x[i] <= 1000.0:
- multi_delta[i] = 25.0
- elif multi_x[i] <= 10000.0:
- multi_delta[i] = 560.0
- elif multi_x[i] <= 100000.0:
- multi_delta[i] = 9500.0
- else:
- multi_delta[i] = 144000.0
- if multi_x[i] == 100.0 or multi_x[i] == 150.0:
- multi_we[:,:,i] = 0.0
-
- multi_dat = Data(multi_x, multi_y, wd=1e-4/np.power(multi_x, 2),
- we=multi_we)
- multi_odr = ODR(multi_dat, multi_mod, beta0=[4.,2.,7.,.4,.5],
- delta0=multi_delta, ifixx=multi_ifixx)
- multi_odr.set_job(deriv=1, del_init=1)
-
- out = multi_odr.run()
- assert_array_almost_equal(
- out.beta,
- np.array([ 4.3799880305938963, 2.4333057577497703, 8.0028845899503978,
- 0.5101147161764654, 0.5173902330489161]),
- )
- assert_array_almost_equal(
- out.sd_beta,
- np.array([ 0.0130625231081944, 0.0130499785273277, 0.1167085962217757,
- 0.0132642749596149, 0.0288529201353984]),
- )
- assert_array_almost_equal(
- out.cov_beta,
- np.array([[ 0.0064918418231375, 0.0036159705923791, 0.0438637051470406,
- -0.0058700836512467, 0.011281212888768 ],
- [ 0.0036159705923791, 0.0064793789429006, 0.0517610978353126,
- -0.0051181304940204, 0.0130726943624117],
- [ 0.0438637051470406, 0.0517610978353126, 0.5182263323095322,
- -0.0563083340093696, 0.1269490939468611],
- [-0.0058700836512467, -0.0051181304940204, -0.0563083340093696,
- 0.0066939246261263, -0.0140184391377962],
- [ 0.011281212888768 , 0.0130726943624117, 0.1269490939468611,
- -0.0140184391377962, 0.0316733013820852]]),
- )
-
-
- # Pearson's Data
- # K. Pearson, Philosophical Magazine, 2, 559 (1901)
-
- def pearson_fcn(self, B, x):
- return B[0] + B[1]*x
-
- def test_pearson(self):
- p_x = np.array([0.,.9,1.8,2.6,3.3,4.4,5.2,6.1,6.5,7.4])
- p_y = np.array([5.9,5.4,4.4,4.6,3.5,3.7,2.8,2.8,2.4,1.5])
- p_sx = np.array([.03,.03,.04,.035,.07,.11,.13,.22,.74,1.])
- p_sy = np.array([1.,.74,.5,.35,.22,.22,.12,.12,.1,.04])
-
- p_dat = RealData(p_x, p_y, sx=p_sx, sy=p_sy)
-
- # Reverse the data to test invariance of results
- pr_dat = RealData(p_y, p_x, sx=p_sy, sy=p_sx)
-
- p_mod = Model(self.pearson_fcn, meta=dict(name='Uni-linear Fit'))
-
- p_odr = ODR(p_dat, p_mod, beta0=[1.,1.])
- pr_odr = ODR(pr_dat, p_mod, beta0=[1.,1.])
-
- out = p_odr.run()
- assert_array_almost_equal(
- out.beta,
- np.array([ 5.4767400299231674, -0.4796082367610305]),
- )
- assert_array_almost_equal(
- out.sd_beta,
- np.array([ 0.3590121690702467, 0.0706291186037444]),
- )
- assert_array_almost_equal(
- out.cov_beta,
- np.array([[ 0.0854275622946333, -0.0161807025443155],
- [-0.0161807025443155, 0.003306337993922 ]]),
- )
-
- rout = pr_odr.run()
- assert_array_almost_equal(
- rout.beta,
- np.array([ 11.4192022410781231, -2.0850374506165474]),
- )
- assert_array_almost_equal(
- rout.sd_beta,
- np.array([ 0.9820231665657161, 0.3070515616198911]),
- )
- assert_array_almost_equal(
- rout.cov_beta,
- np.array([[ 0.6391799462548782, -0.1955657291119177],
- [-0.1955657291119177, 0.0624888159223392]]),
- )
-
- # Lorentz Peak
- # The data is taken from one of the undergraduate physics labs I performed.
-
- def lorentz(self, beta, x):
- return (beta[0]*beta[1]*beta[2] / np.sqrt(np.power(x*x -
- beta[2]*beta[2], 2.0) + np.power(beta[1]*x, 2.0)))
-
- def test_lorentz(self):
- l_sy = np.array([.29]*18)
- l_sx = np.array([.000972971,.000948268,.000707632,.000706679,
- .000706074, .000703918,.000698955,.000456856,
- .000455207,.000662717,.000654619,.000652694,
- .000000859202,.00106589,.00106378,.00125483, .00140818,.00241839])
-
- l_dat = RealData(
- [3.9094, 3.85945, 3.84976, 3.84716, 3.84551, 3.83964, 3.82608,
- 3.78847, 3.78163, 3.72558, 3.70274, 3.6973, 3.67373, 3.65982,
- 3.6562, 3.62498, 3.55525, 3.41886],
- [652, 910.5, 984, 1000, 1007.5, 1053, 1160.5, 1409.5, 1430, 1122,
- 957.5, 920, 777.5, 709.5, 698, 578.5, 418.5, 275.5],
- sx=l_sx,
- sy=l_sy,
- )
- l_mod = Model(self.lorentz, meta=dict(name='Lorentz Peak'))
- l_odr = ODR(l_dat, l_mod, beta0=(1000., .1, 3.8))
-
- out = l_odr.run()
- assert_array_almost_equal(
- out.beta,
- np.array([ 1.4306780846149925e+03, 1.3390509034538309e-01,
- 3.7798193600109009e+00]),
- )
- assert_array_almost_equal(
- out.sd_beta,
- np.array([ 7.3621186811330963e-01, 3.5068899941471650e-04,
- 2.4451209281408992e-04]),
- )
- assert_array_almost_equal(
- out.cov_beta,
- np.array([[ 2.4714409064597873e-01, -6.9067261911110836e-05,
- -3.1236953270424990e-05],
- [ -6.9067261911110836e-05, 5.6077531517333009e-08,
- 3.6133261832722601e-08],
- [ -3.1236953270424990e-05, 3.6133261832722601e-08,
- 2.7261220025171730e-08]]),
- )
-
-
-if __name__ == "__main__":
- NumpyTest().run()
-
-#### EOF #######################################################################
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