naginterfaces.library.quad.dim1_fin_bad_vec¶
- naginterfaces.library.quad.dim1_fin_bad_vec(f, a, b, epsabs, epsrel, lw=800, liw=None, data=None)[source]¶
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 usedim1_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
Details of the computation see Further Comments for more information.
- 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 bydim1_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