From 87763d6e57d769d52e566e491dc181dd908585ad Mon Sep 17 00:00:00 2001 From: Wirawan Purwanto Date: Mon, 15 Oct 2012 16:02:41 -0400 Subject: [PATCH] * wpylib.math.fitting.linear: for linear fit methods. First method: linregr2d_SZ() from Shiwei's email in 2006. --- math/fitting/linear.py | 104 +++++++++++++++++++++++++++++++++++++++++ 1 file changed, 104 insertions(+) create mode 100644 math/fitting/linear.py diff --git a/math/fitting/linear.py b/math/fitting/linear.py new file mode 100644 index 0000000..e41e7a5 --- /dev/null +++ b/math/fitting/linear.py @@ -0,0 +1,104 @@ +# +# wpylib.math.fitting.linear module +# Created: 20121015 +# Wirawan Purwanto +# + +""" +wpylib.math.fitting.linear module + +Linear fitting tools. +""" + +import numpy +from wpylib.math.fitting import fit_result + +def linregr2d_SZ(x, y, sigma=None): + """Performs a linear least square regression to according to a + linear model + + y(x) = a + b*x , + + where the input y has uncertainty given by sigma. + """ + from numpy import sum, sqrt + + # Based on Shiwei's regr.F code (from email received 20060102). + # See Linear-regression.txt in my repository of Shiwei's files. + # See also Numerical Recipes in C, 2nd ed, Sec. 15.2. + xx = numpy.array(x, copy=False) + yy = numpy.array(y, copy=False) + if sigma == None: + # My addition -- can be dangerous + # In case of no errorbar, we proceed as if all measurement + # data have the same uncertainty, taken to be 1. + ww = numpy.ones_like(y) + else: + ww = numpy.array(sigma, copy=False) + ww **= -2 # make 1/sigma**2 array + + e1 = sum(xx * yy * ww) + e2 = sum(yy * ww) + d11 = sum(xx * ww) + d12 = sum(xx**2 * ww) + d21 = sum(ww) + d22 = d11 + + detinv = 1.0 / (d11*d22 - d12*d21) + a = (e1*d22 - e2*d12) * detinv + b = (e2*d11 - e1*d21) * detinv + varsum = sum((xx*d11 - d12)**2 * ww) + var = varsum * detinv**2 + sigma = sqrt(var) + + return fit_result( + fit_method='linregr2d_SZ', + fit_model='linear', + a=a, + b=b, + sigma=sigma, + ) + + + +def Test_1(): + """Testcase 1. + + >>> wpylib.math.fitting.linear.Test_1() + ... + {'a': -1392.3182324234213, + 'b': -0.82241012516149792, + 'fit_method': 'linregr2d_SZ', + 'fit_model': 'linear', + 'sigma': 0.00048320905704467775} + + My wlinreg tool (via 'dtextrap' shell script alias gives: + + a stats: + Total number of data : 100000 + Average : -1392.32 + Sample standard deviation: 0.000460341 + Error of the average : 1.45573e-06 (-1.046e-07%) + b stats: + Total number of data : 100000 + Average : -0.822099 + Sample standard deviation: 0.0803118 + Error of the average : 0.00025397 (-0.03089%) + Summary + a = -1392.31823569246 +/- 0.000460341146124978 = -1392.31824(46) + b = -0.822098515674071 +/- 0.0803118207916705 = -0.822(80) + + """ + from wpylib.text_tools import make_matrix as mtx + M = mtx(""" + # Source: Co+ QMC/CAS(8,11)d26 cc-pwCVQZ-DK result dated 20121015 + 0.01 -1392.32619 0.00047 + 0.005 -1392.32284 0.00037 + 0.0025 -1392.31994 0.00038 + """) + x = M[:,0] + y = M[:,1] + dy = M[:,2] + rslt = linregr2d_SZ(x,y,dy) + print rslt + return rslt