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feat: Added numerical integration of generic functions (#201)

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* feat: Added numerical integration of generic functions

* refactored integration routines

* tests: two trivial tests for integration added.

* docs: quad docstring corrected.

* Small bugfix for integration without obs

---------

Co-authored-by: Fabian Joswig <fabian.joswig@ed.ac.uk>
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s-kuberski 2023-07-14 15:21:59 +02:00 • committed by GitHub
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tests/integrate_test.py Normal file
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import numpy as np
import autograd.numpy as anp
import pyerrors as pe
def test_integration():
def f(p, x):
return p[0] * x + p[1] * x**2 - p[2] / x
def F(p, x):
return p[0] * x**2 / 2. + p[1] * x**3 / 3. - anp.log(x) * p[2]
def check_ana_vs_int(p, l, u, **kwargs):
numint_full = pe.integrate.quad(f, p, l, u, **kwargs)
numint = numint_full[0]
anaint = F(p, u) - F(p, l)
diff = (numint - anaint)
if isinstance(numint, pe.Obs):
numint.gm()
anaint.gm()
assert(diff.is_zero())
else:
assert(np.isclose(0, diff))
pobs = np.array([pe.cov_Obs(1., .1**2, '0'), pe.cov_Obs(2., .2**2, '1'), pe.cov_Obs(2.2, .17**2, '2')])
lobs = pe.cov_Obs(.123, .012**2, 'l')
uobs = pe.cov_Obs(1., .05**2, 'u')
check_ana_vs_int(pobs, lobs, uobs)
check_ana_vs_int(pobs, lobs.value, uobs)
check_ana_vs_int(pobs, lobs, uobs.value)
check_ana_vs_int(pobs, lobs.value, uobs.value)
for i in range(len(pobs)):
p = [pi for pi in pobs]
p[i] = pobs[i].value
check_ana_vs_int(p, lobs, uobs)
check_ana_vs_int([pi.value for pi in pobs], lobs, uobs)
check_ana_vs_int([pi.value for pi in pobs], lobs.value, uobs.value)
check_ana_vs_int(pobs, lobs, uobs, epsabs=1.e-9, epsrel=1.236e-10, limit=100)
assert(len(pe.integrate.quad(f, pobs, lobs, uobs, full_output=True)) > 2)
r1, _ = pe.integrate.quad(F, pobs, 1, 0.1)
r2, _ = pe.integrate.quad(F, pobs, 0.1, 1)
assert r1 == -r2
iamzero, _ = pe.integrate.quad(F, pobs, 1, 1)
assert iamzero == 0