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104 lines
2.6 KiB
104 lines
2.6 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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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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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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)
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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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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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"""
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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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