iterate

iterate(init, coeffs, input)

init a scalar or a vector.

coeffs a scalar or a vector. init and coeffs have the same length.

input a scalar or a vector. If input is a scalar, it must be an integer and it means the number of iterations; if input is a vector, its length means the number of iterations and each element of input is added to the result of the corresponding iteration.

If init, coeffs and input are all scalars, return a geometric sequence [init*coeffs, init*coeffs^2, init*coeffs^3, …]. The length of the sequence is input.

If init and coeffs are scalars and input is a vector, return an array x with x[0]=init*coeffs + input[0] and x[n]=x[n-1]* coeffs + input[n].

If init and coeffs are vectors and input is a scalar, return an array x with x[n]=y(n)** coeffs, y(n)=y(n-1)[1:].append!(x[n-1]), y(0)= init. The length of x is input. ** returns the inner product of 2 vectors.

If init, coeffs and input are all vectors, return an array x with x[n]=y(n)** coeffs + input[n], y(n)=y(n-1)[1:].append!(x[n-1]), y(0)= init. The length of x is input. ** returns the inner product of 2 vectors.

iterate(1, 0.8, 3);
// output
[0.8,0.64,0.512]
// 1*0.8=0.8, 0.8*0.8=0.64, 0.64*0.8=0.512

iterate(1, 0.8, 0.1 0.2 0.3);
// output
[0.9,0.92,1.036]
// 1*0.8+0.1=0.9, 0.9*0.8+0.2=0.92, 0.92*0.8+0.3=1.036

iterate(1 1, 1 1, 10);
// output
[2,3,5,8,13,21,34,55,89,144]
// this is the Fibonacci series: 1*1 + 1*1=2; 1*1+2*1=3; 2*1+3*1=5; 3*1+5*1=8; ... ; 55*1+89*1=144.

iterate(1 1, 1 1, 1 2 3 4 5);
// output
[3,6,12,22,39]
// 1*1+1*1+1=3; 1*1+3*1+2=6; 3*1+6*1+3=12; 6*1+12*1+4=22; 12*1+22*1+5=39.