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#/*##########################################################################
#
# The PyMca X-Ray Fluorescence Toolkit
#
# Copyright (c) 2004-2016 European Synchrotron Radiation Facility
#
# This file is part of the PyMca X-ray Fluorescence Toolkit developed at
# the ESRF by the Software group.
#
# Permission is hereby granted, free of charge, to any person obtaining a copy
# of this software and associated documentation files (the "Software"), to deal
# in the Software without restriction, including without limitation the rights
# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
# copies of the Software, and to permit persons to whom the Software is
# furnished to do so, subject to the following conditions:
#
# The above copyright notice and this permission notice shall be included in
# all copies or substantial portions of the Software.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
# THE SOFTWARE.
#
#############################################################################*/
__author__ = "V.A. Sole - ESRF Data Analysis"
__contact__ = "sole@esrf.fr"
__license__ = "MIT"
__copyright__ = "European Synchrotron Radiation Facility, Grenoble, France"
import numpy
from numpy.linalg import inv
import sys
def linregress(x, y, sigmay=None, full_output=False):
"""
Linear fit to a straight line following P.R. Bevington:
"Data Reduction and Error Analysis for the Physical Sciences"
It tries to be an improved version of scipystats.linregress
Parameters
----------
x, y : array_like
two sets of measurements. Both arrays should have the same length.
sigmay : The uncertainty on the y values
Returns
-------
slope : float
slope of the regression line
intercept : float
intercept of the regression line
r_value : float
correlation coefficient
if full_output is true, an additional dictionary is returned with the keys
sigma_slope: uncertainty on the slope
sigma_intercept: uncertainty on the intercept
stderr: float
square root of the variance
"""
x = numpy.asarray(x, dtype=numpy.float64).flatten()
y = numpy.asarray(y, dtype=numpy.float64).flatten()
N = y.size
if sigmay is None:
sigmay = numpy.ones((N,), dtype=y.dtype)
else:
sigmay = numpy.asarray(sigmay, dtype=numpy.float64).flatten()
w = 1.0 / (sigmay * sigmay + (sigmay == 0))
n = S = w.sum()
Sx = (w * x).sum()
Sy = (w * y).sum()
Sxx = (w * x * x).sum()
Sxy = ((w * x * y)).sum()
Syy = ((w * y * y)).sum()
# SSxx is identical to delta in Bevington book
delta = SSxx = (S * Sxx - Sx * Sx)
tmpValue = Sxx * Sy - Sx * Sxy
intercept = tmpValue / delta
SSxy = (S * Sxy - Sx * Sy)
slope = SSxy / delta
sigma_slope = numpy.sqrt(S /delta)
sigma_intercept = numpy.sqrt(Sxx / delta)
SSyy = (n * Syy - Sy * Sy)
r_value = SSxy / numpy.sqrt(SSxx * SSyy)
if r_value > 1.0:
r_value = 1.0
if r_value < -1.0:
r_value = -1.0
if not full_output:
return slope, intercept, r_value
ddict = {}
# calculate the variance
if N < 3:
variance = 0.0
else:
variance = ((y - intercept - slope * x) ** 2).sum() / (N - 2)
ddict["variance"] = variance
ddict["stderr"] = numpy.sqrt(variance)
ddict["slope"] = slope
ddict["intercept"] = intercept
ddict["r_value"] = r_value
ddict["sigma_intercept"] = numpy.sqrt(Sxx / SSxx)
ddict["sigma_slope"] = numpy.sqrt(S / SSxx)
return slope, intercept, r_value, ddict
def main(argv=None):
if argv is None:
# Bevington data of Table 6-2
x = [0, 15, 30, 45, 60, 75, 90, 105, 120, 135]
y = [106, 80, 98, 75, 74, 73, 49, 38, 37, 22]
sigmay = numpy.sqrt(numpy.array(y))
slope, intercept, r, ddict = linregress(x, y, sigmay=sigmay, full_output=True)
print("WEIGHTED DATA")
print("LINREGRESS results")
print("SLOPE = ", ddict["slope"], " +/- ", ddict["sigma_slope"])
print("INTERCEPT = ", ddict["intercept"], " +/- ", ddict["sigma_intercept"])
from PyMca5.PyMcaMath.linalg import lstsq
derivatives = numpy.zeros((len(y), 2))
derivatives[:, 0] = numpy.array(x, dtype=numpy.float64)
derivatives[:, 1] = 1.0
print("LEAST SQUARES RESULT")
result = lstsq(derivatives, y, sigma_b=sigmay, weight=1, uncertainties=True)
print("SLOPE = ", result[0][0], " +/- ", result[1][0])
print("INTERCEPT = ", result[0][1], " +/- ", result[1][1])
print("\n\n")
# Bevington data of Table 6-1
x = [1, 2, 3, 4, 5, 6, 7, 8, 9]
y = [15.6, 17.5, 36.6, 43.8, 58.2, 61.6, 64.2, 70.4, 98.8]
print("UNWEIGHTED DATA")
slope, intercept, r, ddict = linregress(x, y, sigmay=None, full_output=True)
print("LINREGRESS results")
print("SLOPE = ", ddict["slope"], " +/- ", ddict["sigma_slope"])
print("INTERCEPT = ", ddict["intercept"], " +/- ", ddict["sigma_intercept"])
derivatives = numpy.zeros((len(y), 2))
derivatives[:, 0] = numpy.array(x, dtype=numpy.float64)
derivatives[:, 1] = 1.0
print("LEAST SQUARES RESULT")
result = lstsq(derivatives, y, sigma_b=None, weight=0, uncertainties=True)
print("SLOPE = ", result[0][0], " +/- ", result[1][0])
print("INTERCEPT = ", result[0][1], " +/- ", result[1][1])
print("\n\n")
elif len(argv) > 1:
# assume we have got a two (or three) column csv file
data = numpy.loadtxt(argv[1])
x = data[:, 0]
y = data[:, 1]
if data.shape[1] > 2:
sigmay = data[:, 2]
else:
sigmay = None
slope, intercept, r, ddict = linregress(x, y,
sigmay=sigmay,
full_output=True)
print("LINREGRESS results")
print("SLOPE = ", ddict["slope"], " +/- ", ddict["sigma_slope"])
print("INTERCEPT = ", ddict["intercept"], " +/- ", ddict["sigma_intercept"])
else:
print("RateLaw [csv_file_name]")
return
if __name__ == "__main__":
main(sys.argv)
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