TOMS655_ORIGINAL is a FORTRAN77 library which computes weights for interpolatory quadrature schemes, by Sylvan Elhay and Jaroslav Kautsky. This is the original version of ACM TOMS Algorithm 655.
Thus, the typical use of this library is for the user to specify a quadrature interval, a weight function, and a sequence of abscissas (which may be repeated), and to request the corresponding weight vector so that an interpolatory quadrature rule is produced.
Note that when an abscissa is repeated, this indicates that, at this point, not only the function value but one or more derivatives are to be used in the quadrature formula.
The library is also suitable for the simpler task of computing both the abscissas and weights for a variety of classical Gaussian quadrature rules, including
Name | Interval | Weight function |
---|---|---|
Legendre | (a,b) | 1.0 |
Chebyshev Type 1 | (a,b) | ((b-x)*(x-a))^(-0.5) |
Gegenbauer | (a,b) | ((b-x)*(x-a))^alpha |
Jacobi | (a,b) | (b-x)^alpha*(x-a)^beta |
Laguerre and Generalized Laguerre | (a,+oo) | (x-a)^alpha*exp(-b*(x-a)) |
Hermite and Generalized Hermite | (-oo,+oo) | |x-a|^alpha*exp(-b*(x-a)^2) |
Exponential | (a,b) | |x-(a+b)/2.0|^alpha |
Rational | (a,+oo) | (x-a)^alpha*(x+b)^beta |
The original, true, correct version of ACM TOMS Algorithm 655 is available through ACM: http://www.acm.org/pubs/calgo or NETLIB: http://www.netlib.org/toms/index.html.
TOMS655_ORIGINAL is available in a FORTRAN77 version.
CHEBYSHEV1_RULE, a FORTRAN90 program which can compute and print a Gauss-Chebyshev type 1 quadrature rule.
CHEBYSHEV2_RULE, a FORTRAN90 program which can compute and print a Gauss-Chebyshev type 2 quadrature rule.
GEGENBAUER_RULE, a FORTRAN90 program which can compute and print a Gauss-Gegenbauer quadrature rule.
GEN_HERMITE_RULE, a FORTRAN90 program which can compute and print a generalized Gauss-Hermite quadrature rule.
GEN_LAGUERRE_RULE, a FORTRAN90 program which can compute and print a generalized Gauss-Laguerre quadrature rule.
HERMITE_RULE, a FORTRAN90 program which computes a Gauss-Hermite quadrature rule.
JACOBI_RULE, a FORTRAN90 program which can compute and print a Gauss-Jacobi quadrature rule.
LAGUERRE_RULE, a FORTRAN90 program which can compute and print a Gauss-Laguerre quadrature rule.
LEGENDRE_RULE, a FORTRAN90 program which computes a Gauss-Legendre quadrature rule.
QUADRULE, a FORTRAN90 library which contains information about quadrature rules, both as tabulated values, and as computational procedures.
TOMS655, a FORTRAN77 library which computes the weights for interpolatory quadrature rules; this library is commonly called IQPACK, by Sylvan Elhay and Jaroslav Kautsky. This version of ACM TOMS algorithm 655 has been extensively modified.
TOMS793, a FORTRAN77 library which carries out Gauss quadrature for rational functions, by Walter Gautschi; this is ACM TOMS algorithm 793.
TOMS655_ORIGINAL_PRB is the test distributed with the code.
You can go up one level to the FORTRAN77 source codes.