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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"
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 rateLaw(x, y, sigmay=None, order=None, xmin=None, ymin=None, xmax=None, ymax=None):
"""
Perform a fit to y following the specified rate law order
If xmin is not None, x values will be modified by subtraction/addition to
match the desired xmin.
If xmax is not None, x values will be divided by their maximum value and
multiplied by yxax
If ymin is not None, y values will be modified by subtraction/addition to
match the desired ymin.
If ymax is not None, y values will be divided by the maximum value and
multiplied by ymax
"""
x = numpy.asarray(x, dtype=numpy.float64).flatten()
y = numpy.asarray(y, dtype=numpy.float64).flatten()
if xmin is not None:
x = x - x.min() + xmin
if ymin is not None:
y = y - y.min() + ymin
if xmax is not None:
x = xmax * (x /x.max())
if ymax is not None:
y = ymax * (y /y.max())
# we are going to perform a linear fit using different
# transformations as function of the requested order.
ddict = {}
if order is None:
orderList = [0, 1, 2]
else:
orderList = [order]
labels = ["zero", "first", "second"]
for orderNumber in orderList:
label = labels[orderNumber]
ddict["order"] = label
if label == "zero":
# [A] = [A]0 - kt
yw = y
xw = x
elif label == "first":
# [A] = [A]0 exp(-kt)
# or
# ln([A]) = ln([A]0) - kt
idx = y > 0
yw = numpy.log(y[idx])
xw = x[idx]
elif label == "second":
# 1/[A] = 1/[A]0 + kt
idx = (y != 0)
yw = 1 / y[idx]
xw = x[idx]
else:
raise ValueError("Unknown rate law order %s" % order)
if yw.size < 2:
# we cannot perform a linear fit with less than two points
ddict[label] = None
else:
slope, intercept, r, full = linregress(xw, yw, full_output=True)
ddict[label] = full
ddict[label]["x"] = xw
ddict[label]["y"] = yw
if len(orderList) == 1:
return slope, intercept, r
else:
return ddict
def main(argv=None):
if argv is None:
# first order, k = 4.820e-04
x = [0, 600, 1200, 1800, 2400, 3000, 3600]
y = [0.0365, 0.0274, 0.0206, 0.0157, 0.0117, 0.00860, 0.00640]
order = "First"
slope = "0.000482"
print("Expected order: First")
print("Expected slope: 0.000482")
sigmay = None
# second order, k = 1.3e-02
#x = [0, 900, 1800, 3600, 6000]
#y = [1.72e-2, 1.43e-2, 1.23e-2, 9.52e-3, 7.3e-3]
#order = "second"
#slope = "0.013"
elif len(argv) > 1:
# assume we have got a two 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
else:
print("RateLaw [csv_file_name]")
return
result = rateLaw(x, y, sigmay = sigmay)
labels = ["Zero", "First", "Second"]
for key in labels:
print(key + " Order")
print("Interceptt = ", result[key.lower()]["intercept"])
print("Slope = ", result[key.lower()]["slope"])
print("r value = ", result[key.lower()]["r_value"])
print("stderr = ", result[key.lower()]["stderr"])
if __name__ == "__main__":
main(sys.argv)
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