Multi tool use

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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