Calculating PI using streams, head & tail in DataWeave

Thanks to [head ~ tail] in DataWeave 2.0 we can easily create infinite sequence generators.

In this case we are implementing the Leibniz's series to calculate an approximation of PI.

/**
 * This function returns a stream. We first populate the stream with a
 * head value, and a lazy tail.
 * In this case, we tell the engine the tail is a function call. 
 * That function call will be not be executed UNTIL the value of that
 * call is needed.
 */
fun leibnizTerm(n: Number = 0): Array<Number> = 
  [4 / (n + 1) - 4 / (n + 3) ~ leibnizTerm(n + 4)]
// ^^^^^^^^^^^^^^^^^^^^^^^^^   ^^^^^^^^^^^^^^^^^^
//           head                  lazy tail

/**
 * Now we have the sequence generator, the only thing left is select 
 * the values and aggregate them. We are going to pick a slice of the
 * infinite sequence of leibnizTerm using a range selector.
 */
fun pi(terms: Number = 1E4): Number = do {
  var seriesSubset = leibnizTerm()[0 to terms]
  //                 ^^^^^^^^^^^  ^^^^^^^^^^^^
  //                 series gen   range selector
  ---
  sum( seriesSubset )
}


---
// Then executing
pi(1E4)
// Outputs: 3.1415426585893202

s_j = \sum_{i} w_{ij}.y_{i}

where y_{i} is all the inputs (bias included)

After computing its state, the neuron passes it through its activation function (f_j), which normalizes the result (y_j) (normally between 0-1).

y_j = f_j(S_j)

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