import numpy as np
"""
A simple propagation of uncertainty module.
# http://en.wikipedia.org/wiki/Propagation_of_uncertainty
For more sophisticated handling of uncertainties use the `uncertainties`
package.
"""
[docs]def EPadd(a, da, b, db, covar=0):
"""
C = A + B
"""
return (a + b), np.sqrt(da**2 + db**2 + 2 * covar)
[docs]def EPsub(a, da, b, db, covar=0):
"""
C = A - B
"""
return a - b, np.sqrt(da**2 + db**2 - 2 * covar)
[docs]def EPmul(a, da, b, db, covar=0):
"""
C = A * B
"""
return a * b, np.sqrt((b * da) ** 2 + (a * db) ** 2 + 2 * a * b * covar)
[docs]def EPmulk(a, da, k):
"""
C = A * k
"""
return a * k, np.absolute(da * k)
[docs]def EPdiv(a, da, b, db, covar=0):
"""
C = A / B
"""
return (
a / b,
np.sqrt(
((da / b) ** 2 + ((a**2) * (db**2) / (b**4)))
- (2 * covar * a / (b**3))
),
)
[docs]def EPpow(a, da, b, db, covar=0):
"""
C = A ** B
"""
c = a**b
dc = np.absolute(c) * np.sqrt(
((da * b / a) ** 2)
+ (np.log(a) * db) ** 2
+ 2 * b * np.log(a) * covar / a
)
return c, dc
[docs]def EPpowk(a, da, k, n=1):
"""
C = pow(k, A * n)
"""
return (
np.power(k, a * n),
np.absolute(np.power(k, a * n) * n * da * np.log(k)),
)
[docs]def EPlog(a, da, k=1, n=1):
"""
C = n * log(k * A )
"""
return n * np.log(k * a), np.absolute(n * da / a)
[docs]def EPlog10(a, da, k=1, n=1):
"""
C = n * log10(k * A)
"""
return n * np.log10(k * a), np.absolute(n * da / (a * np.log(10)))
[docs]def EPexp(a, da, k=1, n=1):
"""
C = n * exp(k * A)
"""
return n * np.exp(k * a), np.absolute(k * da * n * np.exp(k * a))
[docs]def EPsin(a, da):
"""
C = sin (A)
"""
return np.sin(a), np.absolute(np.cos(a) * da)
[docs]def EPcos(a, da):
"""
C = cos (A)
"""
return np.cos(a), np.absolute(-np.sin(a) * da)
[docs]def EPtan(a, da):
"""
C = tan (A)
"""
return np.tan(a), np.absolute(da / (np.cos(a) ** 2))