auto_correlation takes as argument a complex vector v of length n and returns its cross-correlation with itself as the vector v⋆v of length 2 n−1 (see the cross_correlation command, section 5.25.1). For example, input :

auto_correlation([2,3,4,3,1,4,5,1,3,1])

Output :

[2.0,9.0,15.0,28.0,37.0,44.0,58.0,58.0,68.0,

91.0,68.0,58.0,58.0,44.0,37.0,28.0,15.0,9.0,2.0]

91.0,68.0,58.0,58.0,44.0,37.0,28.0,15.0,9.0,2.0]