dim1_fin_bad_vec is a general purpose integrator which calculates an approximation to the integral of a function over a finite interval :

Deprecated since version 27.1.0.0: dim1_fin_bad_vec will be removed in naginterfaces 31.3.0.0. Please use dim1_fin_general() instead. See also the Replacement Calls document.

For full information please refer to the NAG Library document for d01at

https://support.nag.com/numeric/nl/nagdoc_30.1/flhtml/d01/d01atf.html

Parameters
fcallable fv = f(x, data=None)

must return the values of the integrand at a set of points.

Parameters
xfloat, ndarray, shape

The points at which the integrand must be evaluated.

dataarbitrary, optional, modifiable in place

User-communication data for callback functions.

Returns
fvfloat, array-like, shape

must contain the value of at the point , for .

afloat

, the lower limit of integration.

bfloat

, the upper limit of integration. It is not necessary that .

epsabsfloat

The absolute accuracy required. If is negative, the absolute value is used. See Accuracy.

epsrelfloat

The relative accuracy required. If is negative, the absolute value is used. See Accuracy.

lwint, optional

The value of (together with that of ) imposes a bound on the number of sub-intervals into which the interval of integration may be divided by the function. The number of sub-intervals cannot exceed . The more difficult the integrand, the larger should be.

liwNone or int, optional

Note: if this argument is None then a default value will be used, determined as follows: .

The number of sub-intervals into which the interval of integration may be divided cannot exceed .

dataarbitrary, optional

User-communication data for callback functions.

Returns
resultfloat

The approximation to the integral .

abserrfloat

An estimate of the modulus of the absolute error, which should be an upper bound for .

wfloat, ndarray, shape

iwint, ndarray, shape

contains the actual number of sub-intervals used. The rest of the array is used as workspace.

Raises
NagValueError
(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

Warns
NagAlgorithmicWarning
(errno )

The maximum number of subdivisions () has been reached: , and .

(errno )

Round-off error prevents the requested tolerance from being achieved: and .

(errno )

Extremely bad integrand behaviour occurs around the sub-interval .

(errno )

Round-off error is detected in the extrapolation table.

(errno )

The integral is probably divergent or slowly convergent.

Notes

No equivalent traditional C interface for this routine exists in the NAG Library.

dim1_fin_bad_vec is based on the QUADPACK routine QAGS (see Piessens et al. (1983)). It is an adaptive function, using the Gauss -point and Kronrod -point rules. The algorithm, described in de Doncker (1978), incorporates a global acceptance criterion (as defined by Malcolm and Simpson (1976)) together with the -algorithm (see Wynn (1956)) to perform extrapolation. The local error estimation is described in Piessens et al. (1983).

The function is suitable as a general purpose integrator, and can be used when the integrand has singularities, especially when these are of algebraic or logarithmic type.

dim1_fin_bad_vec requires a function to evaluate the integrand at an array of different points and is, therefore, amenable to parallel execution. Otherwise the algorithm is identical to that used by dim1_fin_bad().

References

de Doncker, E, 1978, An adaptive extrapolation algorithm for automatic integration, ACM SIGNUM Newsl. (13(2)), 12–18

Malcolm, M A and Simpson, R B, 1976, Local versus global strategies for adaptive quadrature, ACM Trans. Math. Software (1), 129–146

Piessens, R, de Doncker–Kapenga, E, Überhuber, C and Kahaner, D, 1983, QUADPACK, A Subroutine Package for Automatic Integration, Springer–Verlag

Wynn, P, 1956, On a device for computing the transformation, Math. Tables Aids Comput. (10), 91–96