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""" This sub-module contains various mathematical functions that do various
things, variously.
"""
import numpy as np
def slope(x, y):
""" Take a simple derivative, dy/dx.
The derivative is centered and it has the same number of points as the
original x/y data.
Args:
x (ndarray): x data
y (ndarray): y data
Returns:
ndarray: derivative
"""
der = np.zeros(len(x), dtype=float)
rise = y[2:] - y[:-2]
run = x[2:] - x[:-2]
with np.errstate(divide='ignore'):
der[1:-1] = rise / run
der[0] = (y[1] - y[0]) / (x[1] - x[0])
der[-1] = (y[-1] - y[-2]) / (x[-1] - x[-2])
return der
def slope_span_n(x, y, n=11, nozeros=True):
"""Simple derivative, except the derivative is over a -N/2 to N/2 span.
This helps with noisy data.
This function also deletes zero values since the results of this
function are usually used to divide other values (i.e., to avoid div. 0
errors).
Args:
x (ndarray): x data
y (ndarray): y data
n (int, optional): span, must be odd, default is 11
nozeros (bool, optional): don't allow der=0 results, default is True
Returns:
ndarray: derivative
"""
assert n % 2 == 1, "N must be odd."
n = (n - 1) // 2
der = np.zeros(len(x), dtype=float)
rise = y[2 * n + 1:] - y[:-2 * n - 1]
run = x[2 * n + 1:] - x[:-2 * n - 1]
with np.errstate(divide='ignore'):
der[n + 1:-n] = rise / run
for n in range(1, n + 1):
rise = y[2 * n + 1:] - y[:-2 * n - 1]
run = x[2 * n + 1:] - x[:-2 * n - 1]
der[n] = rise[n] / run[n]
der[-n] = rise[-n] / run[-n]
der[0] = der[1]
der[-1] = der[-2]
if nozeros:
der[der == 0] = 1e-10
return der
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