Applying a lower bound threshold on a list
Applying a lower bound threshold on a list
Consider the following list
list=0,0,0,10^-18,10^-15,10^-12,10^-10,1,1
How can I apply a threshold on the list that will give a lower bound for the values. For example
ApplyThreshold[list,10^-12];
will yield an outcome of
10^-12,10^-12,10^-12,10^-12,10^-12,10^-12,10^-10,1,1
and
ApplyThreshold[list,10^-9];
will yield an outcome of
10^-9,10^-9,10^-9,10^-9,10^-9,10^-9,10^-9,1,1
3 Answers
3
You can use Clip, Ramp or Max:
Clip
Ramp
Max
Clip[list, 10^-9, ∞]
1/1000000000, 1/1000000000, 1/1000000000, 1/1000000000,
1/1000000000, 1/1000000000, 1/1000000000, 1, 1
Ramp[list - 10^-9] + 10^-9 === Max[#, 10^-9] & /@ list === %
True
Timings:
SeedRandom[1]
lst = RandomReal[1, 100000];
(r1 = Ramp[lst - 10^-9] + 10^-9 ;) // RepeatedTiming // First
0.00017
(r2 = Clip[lst , 10^-9, Infinity];) // RepeatedTiming // First
0.000221
(r3 = Max[#, 10^-9] & /@ lst ;) // RepeatedTiming // First
0.129
(r4 = Map[crit[#, 1*10^-12] &, lst ];) // RepeatedTiming // First (* from Alexei's answer*)
0.185
r1 == r2 == r3 == r4
True
Try the following. This si your list:
lst = 0, 0, 0, 10^-18, 10^-15, 10^-12, 10^-10, 1, 1
This function transforms any number to what you want:
crit[x_, y_] := If[x >= y, x, y];
This applies it to the list:
Map[crit[#, 1*10^-12] &, lst]
(* 1/1000000000000, 1/1000000000000, 1/1000000000000, 1/1000000000000,
1/1000000000000, 1/1000000000000, 1/10000000000, 1, 1 *)
Here is another example of yours:
Map[crit[#, 1*10^-9] &, lst]
(* 1/1000000000, 1/1000000000, 1/1000000000, 1/1000000000,
1/1000000000, 1/1000000000, 1/1000000000, 1, 1 *)
Have fun!
You can do this succinctly with the ReplaceAll (/.) and Condition (/;) operators:
ReplaceAll (/.)
Condition (/;)
list /. x_ /; x < 10^-12 -> 10^-12
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