Edit detail for NumericalQuadrature revision 3 of 3

Numeric integration routines

)sh NumericalQuadrature

 NumericalQuadrature(F: FloatingPointSystem) is a package constructor
 Abbreviation for NumericalQuadrature is NUMQUAD 
 This constructor is exposed in this frame.
------------------------------- Operations --------------------------------

 aromberg : ((F -> F), F, F, F, F, Integer, Integer, Integer) -> Record(value: F,error: F,totalpts: Integer,success: Boolean)
 asimpson : ((F -> F), F, F, F, F, Integer, Integer, Integer) -> Record(value: F,error: F,totalpts: Integer,success: Boolean)
 atrapezoidal : ((F -> F), F, F, F, F, Integer, Integer, Integer) -> Record(value: F,error: F,totalpts: Integer,success: Boolean)
 romberg : ((F -> F), F, F, F, F, Integer, Integer) -> Record(value: F,error: F,totalpts: Integer,success: Boolean)
 rombergo : ((F -> F), F, F, F, F, Integer, Integer) -> Record(value: F,error: F,totalpts: Integer,success: Boolean)
 simpson : ((F -> F), F, F, F, F, Integer, Integer) -> Record(value: F,error: F,totalpts: Integer,success: Boolean)
 simpsono : ((F -> F), F, F, F, F, Integer, Integer) -> Record(value: F,error: F,totalpts: Integer,success: Boolean)
 trapezoidal : ((F -> F), F, F, F, F, Integer, Integer) -> Record(value: F,error: F,totalpts: Integer,success: Boolean)
 trapezoidalo : ((F -> F), F, F, F, F, Integer, Integer) -> Record(value: F,error: F,totalpts: Integer,success: Boolean)

Example

f(x) == sin(x)

-- aromberg(fn, a, b, epsrel, epsabs, nmin, nmax, nint)
-- uses the adaptive romberg method to numerically integrate function
-- \spad{fn} over the closed interval from \spad{a} to \spad{b},
-- with relative accuracy \spad{epsrel} and absolute accuracy
-- \spad{epsabs}, with the refinement levels for convergence checking
-- vary from \spad{nmin} to \spad{nmax}, and where \spad{nint}
-- is the number of independent intervals to apply the integrator.
-- The value returned is a record containing the value of the integral,
-- the estimate of the error in the computation, the total number of
-- function evaluations, and either a boolean value which is true if
-- the integral was computed within the user specified error criterion.

aromberg(f, -%pi, %pi, 0.0001, 0.001, 2, 5, 20)

Compiling function f with type Float -> Float

(1)