Class H2a1a1: Automatic 1-D finite interval quadrature (user need only specify required accuracy), integrand available via user-defined procedure
General Information
- Parent Class
- H2a1a
- Top of Tree
- GAMS
Modules
Package CMLIB (Downloadable; Installed on ITL, ARNO)
- DQAG
- Automatic adaptive integrator, will handle many non-smooth integrands using Gauss Kronrod formulas.
- DQAGE
- Automatic adaptive integrator, can handle most non-smooth functions, also provides more information than QAG.
- DQAGS
- Automatic adaptive integrator, will handle most non-smooth integrands including those with endpoint singularities, uses extrapolation.
- DQAGSE
- Automatic adaptive integrator, can handle integrands with endpoint singularities, provides more information than QAGS.
- DQNG
- Automatic non-adaptive integrator for smooth functions, using Gauss Kronrod Patterson formulas.
- Q1DA
- Automatic integration of a user-defined function of one variable. Special features include randomization and singularity weakening.
- Q1DAX
- Flexible subroutine for the automatic integration of a user-defined function of one variable. Special features include randomization, singularity weakening, restarting, specification of an initial mesh (optional), and output of smallest and largest integrand values.
- Q1DB
- Automatic integration of a user-defined function of one variable. Integrand must be a Fortran function but user may select name. Special features include randomization and singularity weakening. Intermediate in usage difficulty between Q1DA and Q1DAX.
- QAG
- Automatic adaptive integrator, will handle many non-smooth integrands using Gauss Kronrod formulas.
- QAGE
- Automatic adaptive integrator, can handle most non-smooth functions, also provides more information than QAG.
- QAGS
- Automatic adaptive integrator, will handle most non-smooth integrands including those with endpoint singularities, uses extrapolation.
- QAGSE
- Automatic adaptive integrator, can handle integrands with endpoint singularities, provides more information than QAGS.
- QNG
- Automatic non-adaptive integrator for smooth functions, using Gauss Kronrod Patterson formulas.
Package IMSLM (Installed on ITL)
- DQDAG
- Integrate a function using a globally adaptive scheme based on Gauss-Kronrod rules.
- DQDAGS
- Integrate a function (which may have endpoint singularities).
- DQDNG
- Integrate a smooth function using a nonadaptive rule.
- QDAG
- Integrate a function using a globally adaptive scheme based on Gauss-Kronrod rules.
- QDAGS
- Integrate a function (which may have endpoint singularities).
- QDNG
- Integrate a smooth function using a nonadaptive rule.
Package IMSLS (Installed on ITL)
- DQDAGS
- Integrate a function (which may have endpoint singularities).
- QDAGS
- Integrate a function (which may have endpoint singularities).
Package JCAM (Installed on ITL)
- DEFINT
- Uses double exponential transformation of Mori to compute definite integral automatically to user specified accuracy.
Package NAG
- D01AHF
- One-dimensional quadrature, adaptive, finite interval, strategy due to Patterson, suitable for well-behaved integrands
- D01AJF
- One-dimensional quadrature, adaptive, finite interval, strategy due to Piessens and de Doncker, allowing for badly behaved integrands
- D01AKF
- One-dimensional quadrature, adaptive, finite interval, method suitable for oscillating functions
- D01ARF
- One-dimensional quadrature, non-adaptive, finite interval with provision for indefinite integrals
- D01ATF
- One-dimensional quadrature, adaptive, finite interval, variant of D01AJF efficient on vector machines
- D01AUF
- One-dimensional quadrature, adaptive, finite interval, variant of D01AKF efficient on vector machines
- D01BDF
- One-dimensional quadrature, non-adaptive, finite interval
- d01ajc
- One-dimensional adaptive quadrature, allowing for badly behaved integrands
- d01akc
- One-dimensional adaptive quadrature, suitable for oscillating functions
- d01sjc
- One-dimensional adaptive quadrature, allowing for badly behaved integrands, thread-safe
- d01skc
- One-dimensional adaptive quadrature, suitable for oscillating functions, thread-safe
- d01slc
- One-dimensional adaptive quadrature, allowing for singularities at specified points, thread-safe
Package NMS (Installed on ITL)
- DQ1DA
- Adaptive quadrature to estimate integral from A to B to accuracy EPS of REAL FUNCTION F(X). Returns error estimate in E and number of integrand evaluations in KF. Does not require EXTERNAL statement but integrand must be called F.
- Q1DA
- Automatic integration of a user-defined function of one variable. Special features include randomization and singularity weakening.
Package QUADPACK (Downloadable)
- DQAG
- Automatic adaptive integrator, will handle many non-smooth integrands using Gauss Kronrod formulas.
- DQAGE
- Automatic adaptive integrator, can handle most non-smooth functions, also provides more information than QAG.
- DQAGS
- Automatic adaptive integrator, will handle most non-smooth integrands including those with endpoint singularities, uses extrapolation.
- DQAGSE
- Automatic adaptive integrator, can handle integrands with endpoint singularities, provides more information than QAGS.
- DQNG
- Automatic non-adaptive integrator for smooth functions, using Gauss Kronrod Patterson formulas.
- QAG
- Automatic adaptive integrator, will handle many non-smooth integrands using Gauss Kronrod formulas.
- QAGE
- Automatic adaptive integrator, can handle most non-smooth functions, also provides more information than QAG.
- QAGS
- Automatic adaptive integrator, will handle most non-smooth integrands including those with endpoint singularities, uses extrapolation.
- QAGSE
- Automatic adaptive integrator, can handle integrands with endpoint singularities, provides more information than QAGS.
- QNG
- Automatic non-adaptive integrator for smooth functions, using Gauss Kronrod Patterson formulas.
Package SCRUNCH (Installed on ITL)
- SIMP
- Calculates an estimate of the definite integral of a user supplied function by adaptive quadrature. In BASIC.
Package SLATEC (Downloadable; Installed on ITL, ARNO)
- DGAUS8
- Integrate a real function of one variable over a finite interval using an adaptive 8-point Legendre-Gauss algorithm. Intended primarily for high accuracy integration or integration of smooth functions.
- DQAG
- The routine calculates an approximation result to a given definite integral I = integral of F over (A, B), hopefully satisfying following claim for accuracy ABS(I-RESULT)LE.MAX(EPSABS, EPSREL*ABS(I)).
- DQAGE
- The routine calculates an approximation result to a given definite integral I = Integral of F over (A, B), hopefully satisfying following claim for accuracy ABS(I-RESLT).LE.MAX(EPSABS, EPSREL*ABS(I)).
- DQAGS
- The routine calculates an approximation result to a given Definite integral I = Integral of F over (A, B), Hopefully satisfying following claim for accuracy ABS(I-RESULT).LE.MAX(EPSABS, EPSREL*ABS(I)).
- DQAGSE
- The routine calculates an approximation result to a given definite integral I = Integral of F over (A, B), hopefully satisfying following claim for accuracy ABS(I-RESULT).LE.MAX(EPSABS, EPSREL*ABS(I)).
- DQNC79
- Integrate a function using a 7-point adaptive Newton-Cotes quadrature rule.
- DQNG
- The routine calculates an approximation result to a given definite integral I = integral of F over (A, B), hopefully satisfying following claim for accuracy ABS(I-RESULT).LE.MAX(EPSABS, EPSREL*ABS(I)).
- GAUS8
- Integrate a real function of one variable over a finite interval using an adaptive 8-point Legendre-Gauss algorithm. Intended primarily for high accuracy integration or integration of smooth functions.
- QAG
- The routine calculates an approximation result to a given definite integral I = integral of F over (A, B), hopefully satisfying following claim for accuracy ABS(I-RESULT)LE.MAX(EPSABS, EPSREL*ABS(I)).
- QAGE
- The routine calculates an approximation result to a given definite integral I = Integral of F over (A, B), hopefully satisfying following claim for accuracy ABS(I-RESLT).LE.MAX(EPSABS, EPSREL*ABS(I)).
- QAGS
- The routine calculates an approximation result to a given Definite integral I = Integral of F over (A, B), Hopefully satisfying following claim for accuracy ABS(I-RESULT).LE.MAX(EPSABS, EPSREL*ABS(I)).
- QAGSE
- The routine calculates an approximation result to a given definite integral I = Integral of F over (A, B), hopefully satisfying following claim for accuracy ABS(I-RESULT).LE.MAX(EPSABS, EPSREL*ABS(I)).
- QNC79
- Integrate a function using a 7-point adaptive Newton-Cotes quadrature rule.
- QNG
- The routine calculates an approximation result to a given definite integral I = integral of F over (A, B), hopefully satisfying following claim for accuracy ABS(I-RESULT).LE.MAX(EPSABS, EPSREL*ABS(I)).
Package TOMS (Downloadable)
- 614
- INTHP: a Fortran subroutine for automatic numerical integration in Hp. The functions may have singularities at one or both endpoints of an interval. Each of finite, semi-infinite, and infinite intervals are admitted. (See K. Sikorski, F. Stenger, and J. Schwing, ACM TOMS 10 (1984) pp. 152-160.).
- 691
- Two automatic adaptive integration routines, based on QAG and QAGS from QUADPACK. Improvements include replacing the Gauss-Kronrod rules used for local quadrature with recursive monotone stable formulas. (See P. Favati et al., ACM TOMS 17 (1991) pp. 218-232.).
- 699
- QUAD: Performs automatic numerical integration of a univariate function using an improved version of Patterson''s quadrature formulas. (See F. Krogh and W. Van Snyder, ACM TOMS 17 (1991) pp. 457-461.).
- 824
- CUBPACK: Automatic cubature and quadrature over a collection of regions. The region may consist of a union of n-simplices and n-parallelepipeds, such as triangles, rectangles, and tetrahedra. Uses a globally adaptive method. Code is designed to be easily extensible. (See R. Cools and A. Haegemans, ACM TOMS 29 (2003) pp. 287-296.).