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Ratios

Ratios

Ratios[list]

gives the successive ratios of elements in list.

Ratios[list,n]

gives the n iterated ratios of list.

Ratios[list,{n₁,n₂,…}]

gives the successive n_k ratios at level k in a nested list.

Details

Ratios divides successive elements by preceding ones, so that Ratios[{x₁,x₂}] gives {x₂/x₁}.
If list has length s, Ratios[list,n] has length s-n.
Ratios[m,{1,0}] or Ratios[m,1] finds the successive ratios of rows in a 2D array or matrix m. Ratios[m,{0,1}] finds the ratios of columns.
Ratios[list,{n₁,n₂}] is equivalent to Ratios[Ratios[list,n₁],{0,n₂}].

Examples

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Basic Examples (2)

First ratios:

Second ratios:

Scope (3)

Ratios of rows, within each column:

Ratios of columns, within each row:

Ratios of a TimeSeries:

Properties & Relations (2)

First ratios are constant for a geometric sequence:

FoldList with Times acts as an inverse of Ratios:

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