Product Fn
Product Fn is a direct subtype of Real To Real Function
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TYPE INCLUSION RELATIONSHIPS
AVAILABLE FUNCTIONS
AVAILABLE CREATE FUNCTION KEYS
TYPICAL OBJECTS OF TYPE Product Fn
This type represents a function ƒ that maps u real variable numbers x₁, x₂, ..., xᵤ to one number, as folows:
ƒ(x₁,x₂,...,xᵤ) = (m₁xₑ₍₁₎ + c₁)(m₂xₑ₍₂₎ + c₂)...(mᵣxₑ₍ᵣ₎ + cᵣ) + c
where m₁, m₂, ..., mᵣ and c are given fixed constants and e: i -> e(i) is a given integer mapping.
It turns out that when r < u, not all of the x₁, x₂, ..., xᵤ variables contribute to the function output.
In typical usage though, r = u and e is the identity function: e(i) = i, 1 <= i <= u, so that the formula becomes:
ƒ(x₁,x₂,...,xᵤ) = (m₁x₁ + c₁)(m₂x₂ + c₂)...(mᵤxᵤ + cᵣ) + c
and the function expects an input array of u numbers, which implies a domain dimensionality of u
But when e is not trivial, the domain dimensionality becomes u', where:
u' = max{ e(1), e(2), ..., e(r) }
Note that u' may then also be less or greater than u, as explained further at Input Variables