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| Syntax |
gaussq(function fvec, a, b, bound) |
| 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
T
[f(xvec(1)), f(xvec(2)), ... , f(xvec(n))]
n is 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
return cos(x)
end
a = 0.
b = pi / 2
bound = 1.
gaussq(function cosine, a, b, bound)
returns
1
The exact integral is the difference in the sine function
between 0 and pi/2 which is 1.