|See Also||trapz , gaussq2d , gaussleg , quadint|
f(x)over the interval
[a, b]. The return value is a scalar with the same type as a. The function call
fvec(xvec)returns the column vector
with the same type as xvec, where
[f(xvec(1)), f(xvec(2)), ... , f(xvec(n))]
nis the dimension of the column vector xvec. The column vector xvec will have the same type as a. The real or double-precision scalar a specifies the lower limit for the integration. The scalar b has the same type as a and specifies the upper limit for the integration. The scalar bound has the same type as a and specifies an upper bound for the quadrature interval size. As this bound gets smaller, the integration becomes more accurate and the number of necessary function evaluations increases.
pi/2. The integration interval is broken into sub-intervals each of which is at most 1 unit long and a fifth-order (three point) Gaussian quadrature approximation is used on each sub-interval. A special version of the cosine function is defined because O-Matrix intrinsic functions cannot be passed as arguments.
function cosine(x) begin
a = 0.
b = pi / 2
bound = 1.
gaussq(function cosine, a, b, bound)
The exact integral is the difference in the sine function between 0 and
pi/2which is 1.