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I want a way to rotate a list to the right by a fractional amount, i.e. I want a function fractionalRotateRight[data, 2.3] that would rotate data two positions to the right, and then an extra 0.3 positions.

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  • $\begingroup$ What does it mean by "0.3 positions"? $\endgroup$ Mar 26 '20 at 3:27
  • $\begingroup$ I imagine that the list is the values of a periodic function sampled evenly. When I 'shift' by 0.3 positions I want to estimate from the current sample, what the sample would have been, had I shifted my sampling positions by 0.3 units. That's how I think about it anyway. $\endgroup$
    – Tom
    Mar 26 '20 at 16:48
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  fractionalRotateRight[data_, shift_] := Module[{n, f, nShift},
      n = IntegerPart[shift];
      f = FractionalPart[shift];
      nShift = RotateRight[data, n];
      If[shift >= 0,
         MovingAverage[Prepend[nShift, nShift[[-1]]], {f, 1 - f}],
         MovingAverage[Append[nShift, nShift[[1]]], {1 - Abs[f], Abs[f]}]
      ]
  ]

Example (1): The input fractionalRotateRight[{0, 0, 1, 0, 0}, 1.7] produces the output {0., 0., 0., 0.3, 0.7}

Example (2): The input fractionalRotateRight[{0, 0, 1, 0, 0}, -1.7] produces the output {0.7, 0.3, 0., 0., 0.}

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Another approach is to use interpolation.

list = RandomInteger[{0, 10}, 10]
int = Interpolation[list, InterpolationOrder -> 1];
shift = 0.2; 
int[# + shift] & /@ Range[10] // Quiet

list is the list that you want to rotate, shift is the amount to rotate. int[x] is a function that you can index into at will, in particular at all the shifted locations. The Quiet is needed because at the ends you are extrapolating, and this generates a warning (but not an error).

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