Diagnostics

The info object

Every adaptive routine returns (y, info). The integral is y; info is a QuadratureInfo carrying what the solve can tell you about it:

field	meaning
`err`	Estimate of the error in `y`, in the real counterpart of its dtype.
`neval`	Number of evaluations of the integrand.
`status`	Why the routine stopped, as one of the integer codes in `STATUS`.
`info`	The solver’s own state, present only with `full_output=True`. What it holds differs between the adaptive and Romberg routines; see the individual docstrings.

Check status before trusting err, and err before trusting y:

y, info = quadgk(fun, interval, epsabs=1e-10)
assert info.status == quadax.STATUS.normal
assert info.err < 1e-10

Termination status

status is an integer code, so it survives vmap and jit like any other output. STATUS.normal, which is 0, means the requested tolerances were reached; every other code names a difficulty, and looking it up in STATUS gives the member that prints as the message explaining it:

if info.status != quadax.STATUS.normal:
    print(quadax.STATUS[info.status])

Pass throw=True to have the routine raise that message itself rather than report it, for code that should not carry on with an unconverged answer:

y, info = quadgk(fun, interval, epsabs=1e-10, throw=True)

Non-finite integrand values

Points where the integrand evaluates to inf or nan are masked to zero rather than poisoning the result, so an integrable singularity that a node happens to land on does not spoil the integral. Derivatives are masked too, and correctly in reverse mode as well as forward, but what is dropped is that point’s contribution to the derivative: the quadrature is linearized only where the integrand is finite. For an integrable singularity that is the right trade, since a single abscissa carries no weight in the exact integral. It does mean an integrand that is non-finite over a whole region will quietly integrate that region as zero.

The masking costs a second evaluation of the integrand, on the evaluations that are actually differentiated. Values, and derivatives taken in forward mode, are unaffected.