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183 lines
4.8 KiB
183 lines
4.8 KiB
#
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# wpylib.math.fitting.linear module
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# Created: 20121015
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# Wirawan Purwanto
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#
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"""
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wpylib.math.fitting.linear module
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Linear fitting tools.
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"""
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import numpy
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from wpylib.math.fitting import fit_result
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def linregr2d_SZ(x, y, sigma=None):
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"""Performs a linear least square regression to according to a
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linear model
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y(x) = a + b*x ,
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where the input y has uncertainty given by sigma.
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"""
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from numpy import sum, sqrt
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# Based on Shiwei's regr.F code (from email received 20060102).
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# See Linear-regression.txt in my repository of Shiwei's files.
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# See also Numerical Recipes in C, 2nd ed, Sec. 15.2.
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xx = numpy.array(x, copy=False)
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yy = numpy.array(y, copy=False)
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if sigma == None:
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# My addition -- can be dangerous
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# In case of no errorbar, we proceed as if all measurement
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# data have the same uncertainty, taken to be 1.
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ww = numpy.ones_like(y)
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else:
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ww = numpy.array(sigma, copy=False)
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ww **= -2 # make 1/sigma**2 array
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e1 = sum(xx * yy * ww)
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e2 = sum(yy * ww)
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d11 = sum(xx * ww)
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d12 = sum(xx**2 * ww)
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d21 = sum(ww)
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d22 = d11
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detinv = 1.0 / (d11*d22 - d12*d21)
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a = (e1*d22 - e2*d12) * detinv
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b = (e2*d11 - e1*d21) * detinv
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# Shiwei's old method of computing the uncertainty of the
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# y-intersect (sigma_a):
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varsum = sum((xx*d11 - d12)**2 * ww)
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var = varsum * detinv**2
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sigma = sqrt(var)
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# New method based on NR chapter: sqrt(sigma_a2) must give
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# identical result to sigma or else something is screwy!
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sigma_a2 = d12 * (-detinv)
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sigma_b2 = d21 * (-detinv)
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#print sigma_a2
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#print sigma_b2
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return fit_result(
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fit_method='linregr2d_SZ',
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fit_model='linear',
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a=a,
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b=b,
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sigma=sigma,
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sigma_a=sqrt(sigma_a2),
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sigma_b=sqrt(sigma_b2),
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)
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def Test_1():
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"""Testcase 1.
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>>> wpylib.math.fitting.linear.Test_1()
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...
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{'a': -1392.3182324234213,
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'b': -0.82241012516149792,
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'fit_method': 'linregr2d_SZ',
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'fit_model': 'linear',
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'sigma': 0.00048320905704467775,
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'sigma_a': 0.00048320905704467786,
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'sigma_b': 0.080335909573397646}
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My wlinreg tool (via 'dtextrap' shell script alias gives:
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a stats:
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Total number of data : 100000
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Average : -1392.32
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Sample standard deviation: 0.000460341
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Error of the average : 1.45573e-06 (-1.046e-07%)
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b stats:
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Total number of data : 100000
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Average : -0.822099
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Sample standard deviation: 0.0803118
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Error of the average : 0.00025397 (-0.03089%)
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Summary
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a = -1392.31823569246 +/- 0.000460341146124978 = -1392.31824(46)
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b = -0.822098515674071 +/- 0.0803118207916705 = -0.822(80)
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which is close enough for this purpose!
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"""
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from wpylib.text_tools import make_matrix as mtx
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M = mtx("""
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# Source: Co+ QMC/CAS(8,11)d26 cc-pwCVQZ-DK result dated 20121015
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0.01 -1392.32619 0.00047
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0.005 -1392.32284 0.00037
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0.0025 -1392.31994 0.00038
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""")
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x = M[:,0]
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y = M[:,1]
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dy = M[:,2]
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rslt = linregr2d_SZ(x,y,dy)
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print rslt
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return rslt
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def Test_2():
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"""Testcase 2.
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Similar to testcase 1 but with all uncertainties == 1.
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>>> wpylib.math.fitting.linear.Test_2()
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polyfit result = -0.809999999961 -1392.318265
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{'a': -1392.3182649999987,
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'b': -0.81000000006627304,
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'fit_method': 'linregr2d_SZ',
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'fit_model': 'linear',
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'sigma': 1.2247448713915881,
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'sigma_a': 1.2247448713915885,
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'sigma_b': 185.16401995451022}
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This is to be compared with the polyfit output.
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"""
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from wpylib.text_tools import make_matrix as mtx
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M = mtx("""
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# Source: Co+ QMC/CAS(8,11)d26 cc-pwCVQZ-DK result dated 20121015
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0.01 -1392.32619 1.0
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0.005 -1392.32284 1.0
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0.0025 -1392.31994 1.0
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""")
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x = M[:,0]
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y = M[:,1]
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dy = M[:,2]
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rslt = linregr2d_SZ(x,y,dy)
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polyfit_result = numpy.polyfit(x,y,deg=1,full=False)
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print "polyfit result = ", polyfit_result[0], polyfit_result[1]
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return rslt
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def Test_3():
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"""Testcase 3.
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Feed of test from 1/x**3 extrapolation, Ca+4H2 Z=2.3 cc-pCV[TQ5]Z basis
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>>> wpylib.math.fitting.linear.Test_3()
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{'a': -0.92257959784330612,
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'b': 10.193612525866801,
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'fit_method': 'linregr2d_SZ',
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'fit_model': 'linear',
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'sigma': 0.0010352279401853368,
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'sigma_a': 0.0010352279401853377,
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'sigma_b': 0.036555525396641586}
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"""
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from wpylib.text_tools import make_matrix as mtx
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M = mtx("""
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# Source: Co+ QMC/CAS(8,11)d26 cc-pwCVQZ-DK result dated 20121015
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# Groff notebook 1.90, table "testZ23 geometry: Z=2.3 dHH=0.7682", near
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# "/// begin extra (for paper)"
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0.03703704 -0.54533 0.00061
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0.015625 -0.76167 0.00074
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0.008 -0.8442 0.0012
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""")
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x = M[:,0]
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y = M[:,1]
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dy = M[:,2]
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rslt = linregr2d_SZ(x,y,dy)
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return rslt
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