QUADPACK

QUADPACK is a FORTRAN 77 library for numerical integration (quadrature) of one-dimensional functions. It was included in the SLATEC Common Mathematical Library and is therefore in the public domain. The individual subprograms are also available on netlib. The GNU Scientific Library reimplemented the QUADPACK routines in C. SciPy provides a Python interface to part of QUADPACK.

QUADPACK is a FORTRAN 77 library for numerical integration (quadrature) of one-dimensional functions. It was included in the SLATEC Common Mathematical Library and is therefore in the public domain. The individual subprograms are also available on netlib. The GNU Scientific Library reimplemented the QUADPACK routines in C. SciPy provides a Python interface to part of QUADPACK. ==Routines== The main focus of QUADPACK is on automatic integration routines in which the user inputs the problem and an absolute or relative error tolerance and the routine attempts to perform the integration with an error no larger than that requested. There are nine such automatic routines in QUADPACK, in addition to a number of non-automatic routines. All but one of the automatic routines use adaptive quadrature. | | | | | |} ===General-purpose routines=== The two general-purpose routines most suitable for use without further analysis of the integrand are QAGS for integration over a finite interval and QAGI for integration over an infinite interval. These two routines are used in GNU Octave (the quad command) and R (the integrate function). QAGS : uses global adaptive quadrature based on 21-point Gauss–Kronrod quadrature within each subinterval, with acceleration by Peter Wynn's epsilon algorithm. QAGI : is the only general-purpose routine for infinite intervals, and maps the infinite interval onto the semi-open interval (0,1] using a transformation then uses the same approach as QAGS, except with 15-point rather than 21-point Gauss–Kronrod quadrature. For an integral over the whole real line, the transformation used is x = (1-t)/t : \int_{-\infty}^{+\infty} f(x) dx = \int_0^1 {dt\over t^2} \left(f\left(\frac{1-t}{t}\right) + f\left(-\frac{1-t}{t}\right)\right) \;. This is not the best approach for all integrands: another transformation may be appropriate, or one might prefer to break up the original interval and use QAGI only on the infinite part. ===Brief overview of the other automatic routines=== QNG : simple non-adaptive integrator QAG : simple adaptive integrator QAGP : similar to QAGS but allows user to specify locations of internal singularities, discontinuities etc. QAWO : integral of or over a finite interval QAWF : Fourier transform QAWS : integral of from to , where is smooth and , with and QAWC : Cauchy principal value of the integral of for user-specified and ==See also== List of numerical libraries List of open-source mathematical libraries ==References== ==Further reading==

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