Let's see it work

The new Mata class QuadratureVec() is created for the storage and computation of vectorized numerical integration.

Here is an example to approximate the following three integrals:

\[ \int_1^2 2x\ dx\] \[\int_0^{\pi} {\rm sin}(x)\, dx\] \[\int_0^1 \exp(x)\, dx \]

We define evaluator functions f1(), f2(), and f3():

. mata: 
 

             
 
 mata (type end to exit) 
    


: real scalar f1 (real scalar x) {return(2*x)}

: real scalar f2 (real scalar x) {return(sin(x))}

: real scalar f3 (real scalar x) {return(exp(x))}

Having defined the evaluator functions, we follow the four steps that are required each time we use the QuadratureVec() class. First, we create an instance q of the QuadratureVec() class:

: q = QuadratureVec()

Second, we use setEvaluator() to point to the evaluator functions, defined as the column vector evaluator:

: evaluator = (&f1() \ &f2() \ &f3())
: q.setEvaluator(evaluator)

Third, we use setLimits() to specify the lower and upper limits, defined as limits:

: limits = ((1, 2) \ (0,pi()) \ (0,1))
: q.setLimits(limits)

Fourth, we use integrate() to compute the approximations:

: q.integrate()

              1 
1 
            3 
2 
            2 
3 
  1.718281828  

: end

We find that

\[ \int_1^2 2x\ dx = 3\] \[\int_0^{\pi} {\rm sin}(x)\, dx = 2\] \[\int_0^1 \exp(x)\, dx = {1.718281828} \]