Applying a lower bound threshold on a list

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up vote
3
down vote

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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

list-manipulation

share|improve this question

asked Aug 26 at 9:20

jarhead

689412

add a comment | 

up vote
3
down vote

favorite

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

list-manipulation

share|improve this question

asked Aug 26 at 9:20

jarhead

689412

add a comment | 

up vote
3
down vote

favorite

up vote
3
down vote

favorite

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

list-manipulation

share|improve this question

asked Aug 26 at 9:20

jarhead

689412

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

list-manipulation

share|improve this question

asked Aug 26 at 9:20

jarhead

689412

share|improve this question

share|improve this question

asked Aug 26 at 9:20

jarhead

689412

asked Aug 26 at 9:20

jarhead

689412

asked Aug 26 at 9:20

jarhead

689412

689412

add a comment | 

add a comment | 

3 Answers
3

active

oldest

votes

up vote
7
down vote



accepted

You can use Clip, Ramp or 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

share|improve this answer

edited Aug 26 at 10:43

answered Aug 26 at 9:32

kglr

158k8183382

add a comment | 

up vote
2
down vote

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!

share|improve this answer

answered Aug 26 at 9:37

Alexei Boulbitch

20.3k2368

add a comment | 

up vote
1
down vote

You can do this succinctly with the ReplaceAll (/.) and Condition (/;) operators:

list /. x_ /; x < 10^-12 -> 10^-12

share|improve this answer

answered Aug 26 at 14:46

Lee

40817

add a comment | 

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3 Answers
3

active

oldest

votes

3 Answers
3

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
7
down vote



accepted

You can use Clip, Ramp or 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

share|improve this answer

edited Aug 26 at 10:43

answered Aug 26 at 9:32

kglr

158k8183382

add a comment | 

up vote
7
down vote



accepted

You can use Clip, Ramp or 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

share|improve this answer

edited Aug 26 at 10:43

answered Aug 26 at 9:32

kglr

158k8183382

add a comment | 

up vote
7
down vote



accepted

up vote
7
down vote



accepted

You can use Clip, Ramp or 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

share|improve this answer

edited Aug 26 at 10:43

answered Aug 26 at 9:32

kglr

158k8183382

You can use Clip, Ramp or 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

share|improve this answer

edited Aug 26 at 10:43

answered Aug 26 at 9:32

kglr

158k8183382

share|improve this answer

share|improve this answer

edited Aug 26 at 10:43

edited Aug 26 at 10:43

edited Aug 26 at 10:43

answered Aug 26 at 9:32

kglr

158k8183382

answered Aug 26 at 9:32

kglr

158k8183382

answered Aug 26 at 9:32

kglr

158k8183382

158k8183382

add a comment | 

add a comment | 

up vote
2
down vote

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!

share|improve this answer

answered Aug 26 at 9:37

Alexei Boulbitch

20.3k2368

add a comment | 

up vote
2
down vote

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!

share|improve this answer

answered Aug 26 at 9:37

Alexei Boulbitch

20.3k2368

add a comment | 

up vote
2
down vote

up vote
2
down vote

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!

share|improve this answer

answered Aug 26 at 9:37

Alexei Boulbitch

20.3k2368

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!

share|improve this answer

answered Aug 26 at 9:37

Alexei Boulbitch

20.3k2368

share|improve this answer

share|improve this answer

answered Aug 26 at 9:37

Alexei Boulbitch

20.3k2368

answered Aug 26 at 9:37

Alexei Boulbitch

20.3k2368

answered Aug 26 at 9:37

Alexei Boulbitch

20.3k2368

20.3k2368

add a comment | 

add a comment | 

up vote
1
down vote

You can do this succinctly with the ReplaceAll (/.) and Condition (/;) operators:

list /. x_ /; x < 10^-12 -> 10^-12

share|improve this answer

answered Aug 26 at 14:46

Lee

40817

add a comment | 

up vote
1
down vote

You can do this succinctly with the ReplaceAll (/.) and Condition (/;) operators:

list /. x_ /; x < 10^-12 -> 10^-12

share|improve this answer

answered Aug 26 at 14:46

Lee

40817

add a comment | 

up vote
1
down vote

up vote
1
down vote

You can do this succinctly with the ReplaceAll (/.) and Condition (/;) operators:

list /. x_ /; x < 10^-12 -> 10^-12

share|improve this answer

answered Aug 26 at 14:46

Lee

40817

You can do this succinctly with the ReplaceAll (/.) and Condition (/;) operators:

list /. x_ /; x < 10^-12 -> 10^-12

share|improve this answer

answered Aug 26 at 14:46

Lee

40817

share|improve this answer

share|improve this answer

answered Aug 26 at 14:46

Lee

40817

answered Aug 26 at 14:46

Lee

40817

answered Aug 26 at 14:46

Lee

40817

40817

add a comment | 

add a comment | 

 

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