Mdtryhht

Overlay of two functions leaves gaps

Classification of surfaces

Can someone publish a story that happened to you?

What is causing the white spot to appear in some of my pictures

Map of water taps to fill bottles

How could Tony Stark make this in Endgame?

Critique of timeline aesthetic

How to stop co-workers from teasing me because I know Russian?

How to pronounce 'c++' in Spanish

Dynamic SOQL query relationship with field visibility for Users

Initiative: Do I lose my attack/action if my target moves or dies before my turn in combat?

Does a large simulator bay have standard public address announcements?

Do I have an "anti-research" personality?

Implications of cigar-shaped bodies having rings?

Coordinate my way to the name of the (video) game

How to prevent z-fighting in OpenSCAD?

What happened to Captain America in Endgame?

How does Captain America channel this power?

Why does nature favour the Laplacian?

Pulling the rope with one hand is as heavy as with two hands?

What term is being referred to with "reflected-sound-of-underground-spirits"?

How can Republicans who favour free markets, consistently express anger when they don't like the outcome of that choice?

can anyone help me with this awful query plan?

Could the terminal length of components like resistors be reduced?

Apply MapThread to all but one variable

How do you efficiently return all of a List but one element?All values for a function with two arguments without OuterEfficiently finding the maximum value of a column in a matrixnested use of Apply/Map/MapThread in pure functionsMapThread AlternativesFinding neighbors from listMapThread problemapply binary operation to all adjacent pairsFlip sign of one variable in listFind numbers from Mean, Variance and Correlation coefficient

2

$begingroup$

I would like to know what is the most efficient to implement the following computation. Given three lists

 a = a_1,a_2, a_3, …, a_n
 b = b_1,b_2, b_3, …, b_n
 c = c_1,c_2, c_3, …, c_n 

and a function $f(x_1,x_2,x_3)$, obtain

 f(a_1,b_1,c_1) f(a_1,b_1,c_2) ..... f(a_1,b_1,c_n) 
 f(a_2,b_2,c_1) f(a_2,b_2,c_2) ..... f(a_2,b_2,c_n) 
 ..... ..... ..... .....
 f(a_n,b_n,c_1) f(a_n,b_n,c_2) ..... f(a_n,b_n,c_n) 

I cannot find a solution not using For.

list-manipulation

share|improve this question

edited 3 hours ago

corey979

20.9k64382

asked 3 hours ago

SmerdjakovSmerdjakov

1305

$endgroup$

add a comment | 

2

$begingroup$

I would like to know what is the most efficient to implement the following computation. Given three lists

 a = a_1,a_2, a_3, …, a_n
 b = b_1,b_2, b_3, …, b_n
 c = c_1,c_2, c_3, …, c_n 

and a function $f(x_1,x_2,x_3)$, obtain

 f(a_1,b_1,c_1) f(a_1,b_1,c_2) ..... f(a_1,b_1,c_n) 
 f(a_2,b_2,c_1) f(a_2,b_2,c_2) ..... f(a_2,b_2,c_n) 
 ..... ..... ..... .....
 f(a_n,b_n,c_1) f(a_n,b_n,c_2) ..... f(a_n,b_n,c_n) 

I cannot find a solution not using For.

list-manipulation

share|improve this question

edited 3 hours ago

corey979

20.9k64382

asked 3 hours ago

SmerdjakovSmerdjakov

1305

$endgroup$

add a comment | 

$begingroup$

I would like to know what is the most efficient to implement the following computation. Given three lists

 a = a_1,a_2, a_3, …, a_n
 b = b_1,b_2, b_3, …, b_n
 c = c_1,c_2, c_3, …, c_n 

and a function $f(x_1,x_2,x_3)$, obtain

 f(a_1,b_1,c_1) f(a_1,b_1,c_2) ..... f(a_1,b_1,c_n) 
 f(a_2,b_2,c_1) f(a_2,b_2,c_2) ..... f(a_2,b_2,c_n) 
 ..... ..... ..... .....
 f(a_n,b_n,c_1) f(a_n,b_n,c_2) ..... f(a_n,b_n,c_n) 

I cannot find a solution not using For.

list-manipulation

share|improve this question

edited 3 hours ago

corey979

20.9k64382

asked 3 hours ago

SmerdjakovSmerdjakov

1305

$endgroup$

 a = a_1,a_2, a_3, …, a_n
 b = b_1,b_2, b_3, …, b_n
 c = c_1,c_2, c_3, …, c_n 

 f(a_1,b_1,c_1) f(a_1,b_1,c_2) ..... f(a_1,b_1,c_n) 
 f(a_2,b_2,c_1) f(a_2,b_2,c_2) ..... f(a_2,b_2,c_n) 
 ..... ..... ..... .....
 f(a_n,b_n,c_1) f(a_n,b_n,c_2) ..... f(a_n,b_n,c_n) 

share|improve this question

edited 3 hours ago

corey979

20.9k64382

asked 3 hours ago

SmerdjakovSmerdjakov

1305

share|improve this question

edited 3 hours ago

corey979

20.9k64382

asked 3 hours ago

SmerdjakovSmerdjakov

1305

edited 3 hours ago

corey979

20.9k64382

edited 3 hours ago

corey979

20.9k64382

asked 3 hours ago

SmerdjakovSmerdjakov

1305

asked 3 hours ago

SmerdjakovSmerdjakov

1305

4 Answers
4

active

oldest

votes

4

$begingroup$

Here's one way to do it with Outer:

n = 3;
l1 = Array[a, n];
l2 = Array[b, n];
l3 = Array[c, n];

Outer[
 f[#1[[1]], #1[[2]], #2] &,
 Transpose @ l1, l2,
 l3,
 1
]

Out[25]= f[a[1], b[1], c[1]], f[a[1], b[1], c[2]],
f[a[1], b[1], c[3]], f[a[2], b[2], c[1]], f[a[2], b[2], c[2]],
f[a[2], b[2], c[3]], f[a[3], b[3], c[1]], f[a[3], b[3], c[2]],
f[a[3], b[3], c[3]]

share|improve this answer

answered 3 hours ago

Sjoerd SmitSjoerd Smit

4,610817

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Or Outer[f[Sequence @@ #1, #2] &, Transpose@l1, l2, l3, 1] so you don't need to unravel #1 manually.
  $endgroup$
  – Roman
  3 hours ago
  

  
  
  
  

add a comment | 

2

$begingroup$

a = a1, a2, a3, a4, a5;
b = b1, b2, b3, b4, b5;
c = c1, c2, c3, c4, c5;

Table[f[a[[j]], b[[j]], c[[k]]], j, 1, 5, k, 1, 5]

share|improve this answer

answered 3 hours ago

corey979corey979

20.9k64382

$endgroup$

add a comment | 

2

$begingroup$

Another possibility is to use the 3-arg version of Thread. With Sjoerd's example:

n = 3;
l1 = Array[a,n];
l2 = Array[b,n];
l3 = Array[c,n];

Using Thread:

Thread /@ Thread[f[l1, l2, l3], List, 2]

f[a[1], b[1], c[1]], f[a[1], b[1], c[2]],
f[a[1], b[1], c[3]], f[a[2], b[2], c[1]], f[a[2], b[2], c[2]],
f[a[2], b[2], c[3]], f[a[3], b[3], c[1]], f[a[3], b[3], c[2]],
f[a[3], b[3], c[3]]

share|improve this answer

answered 2 hours ago

Carl WollCarl Woll

75.9k3100198

$endgroup$

add a comment | 

0

$begingroup$

Another way with Curry and Through.

Through /@ Apply[Curry[f, 2, 3, 1] /@ c] /@ Transpose@a, b

Hope this helps.

share|improve this answer

answered 18 mins ago

EdmundEdmund

26.8k330103

$endgroup$

add a comment | 

Your Answer

StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "387"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);

else
createEditor();

);

function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);



);

draft saved

draft discarded

Sign up or log in

StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);

Sign up using Google

Sign up using Facebook

Sign up using Email and Password

Post as a guest

Name

Email

Required, but never shown

StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f197144%2fapply-mapthread-to-all-but-one-variable%23new-answer', 'question_page');

);

Post as a guest

Name

Email

Required, but never shown

4

$begingroup$

Here's one way to do it with Outer:

n = 3;
l1 = Array[a, n];
l2 = Array[b, n];
l3 = Array[c, n];

Outer[
 f[#1[[1]], #1[[2]], #2] &,
 Transpose @ l1, l2,
 l3,
 1
]

Out[25]= f[a[1], b[1], c[1]], f[a[1], b[1], c[2]],
f[a[1], b[1], c[3]], f[a[2], b[2], c[1]], f[a[2], b[2], c[2]],
f[a[2], b[2], c[3]], f[a[3], b[3], c[1]], f[a[3], b[3], c[2]],
f[a[3], b[3], c[3]]

share|improve this answer

answered 3 hours ago

Sjoerd SmitSjoerd Smit

4,610817

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Or Outer[f[Sequence @@ #1, #2] &, Transpose@l1, l2, l3, 1] so you don't need to unravel #1 manually.
  $endgroup$
  – Roman
  3 hours ago
  

  
  
  
  

add a comment | 

4

$begingroup$

Here's one way to do it with Outer:

n = 3;
l1 = Array[a, n];
l2 = Array[b, n];
l3 = Array[c, n];

Outer[
 f[#1[[1]], #1[[2]], #2] &,
 Transpose @ l1, l2,
 l3,
 1
]

Out[25]= f[a[1], b[1], c[1]], f[a[1], b[1], c[2]],
f[a[1], b[1], c[3]], f[a[2], b[2], c[1]], f[a[2], b[2], c[2]],
f[a[2], b[2], c[3]], f[a[3], b[3], c[1]], f[a[3], b[3], c[2]],
f[a[3], b[3], c[3]]

share|improve this answer

answered 3 hours ago

Sjoerd SmitSjoerd Smit

4,610817

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Or Outer[f[Sequence @@ #1, #2] &, Transpose@l1, l2, l3, 1] so you don't need to unravel #1 manually.
  $endgroup$
  – Roman
  3 hours ago
  

  
  
  
  

add a comment | 

$begingroup$

Here's one way to do it with Outer:

n = 3;
l1 = Array[a, n];
l2 = Array[b, n];
l3 = Array[c, n];

Outer[
 f[#1[[1]], #1[[2]], #2] &,
 Transpose @ l1, l2,
 l3,
 1
]

Out[25]= f[a[1], b[1], c[1]], f[a[1], b[1], c[2]],
f[a[1], b[1], c[3]], f[a[2], b[2], c[1]], f[a[2], b[2], c[2]],
f[a[2], b[2], c[3]], f[a[3], b[3], c[1]], f[a[3], b[3], c[2]],
f[a[3], b[3], c[3]]

share|improve this answer

answered 3 hours ago

Sjoerd SmitSjoerd Smit

4,610817

$endgroup$

n = 3;
l1 = Array[a, n];
l2 = Array[b, n];
l3 = Array[c, n];

Outer[
 f[#1[[1]], #1[[2]], #2] &,
 Transpose @ l1, l2,
 l3,
 1
]

share|improve this answer

answered 3 hours ago

Sjoerd SmitSjoerd Smit

4,610817

answered 3 hours ago

Sjoerd SmitSjoerd Smit

4,610817

answered 3 hours ago

Sjoerd SmitSjoerd Smit

4,610817

2

$begingroup$

a = a1, a2, a3, a4, a5;
b = b1, b2, b3, b4, b5;
c = c1, c2, c3, c4, c5;

Table[f[a[[j]], b[[j]], c[[k]]], j, 1, 5, k, 1, 5]

share|improve this answer

answered 3 hours ago

corey979corey979

20.9k64382

$endgroup$

add a comment | 

2

$begingroup$

a = a1, a2, a3, a4, a5;
b = b1, b2, b3, b4, b5;
c = c1, c2, c3, c4, c5;

Table[f[a[[j]], b[[j]], c[[k]]], j, 1, 5, k, 1, 5]

share|improve this answer

answered 3 hours ago

corey979corey979

20.9k64382

$endgroup$

add a comment | 

$begingroup$

a = a1, a2, a3, a4, a5;
b = b1, b2, b3, b4, b5;
c = c1, c2, c3, c4, c5;

Table[f[a[[j]], b[[j]], c[[k]]], j, 1, 5, k, 1, 5]

share|improve this answer

answered 3 hours ago

corey979corey979

20.9k64382

$endgroup$

a = a1, a2, a3, a4, a5;
b = b1, b2, b3, b4, b5;
c = c1, c2, c3, c4, c5;

Table[f[a[[j]], b[[j]], c[[k]]], j, 1, 5, k, 1, 5]

share|improve this answer

answered 3 hours ago

corey979corey979

20.9k64382

answered 3 hours ago

corey979corey979

20.9k64382

answered 3 hours ago

corey979corey979

20.9k64382

2

$begingroup$

Another possibility is to use the 3-arg version of Thread. With Sjoerd's example:

n = 3;
l1 = Array[a,n];
l2 = Array[b,n];
l3 = Array[c,n];

Using Thread:

Thread /@ Thread[f[l1, l2, l3], List, 2]

f[a[1], b[1], c[1]], f[a[1], b[1], c[2]],
f[a[1], b[1], c[3]], f[a[2], b[2], c[1]], f[a[2], b[2], c[2]],
f[a[2], b[2], c[3]], f[a[3], b[3], c[1]], f[a[3], b[3], c[2]],
f[a[3], b[3], c[3]]

share|improve this answer

answered 2 hours ago

Carl WollCarl Woll

75.9k3100198

$endgroup$

add a comment | 

2

$begingroup$

Another possibility is to use the 3-arg version of Thread. With Sjoerd's example:

n = 3;
l1 = Array[a,n];
l2 = Array[b,n];
l3 = Array[c,n];

Using Thread:

Thread /@ Thread[f[l1, l2, l3], List, 2]

f[a[1], b[1], c[1]], f[a[1], b[1], c[2]],
f[a[1], b[1], c[3]], f[a[2], b[2], c[1]], f[a[2], b[2], c[2]],
f[a[2], b[2], c[3]], f[a[3], b[3], c[1]], f[a[3], b[3], c[2]],
f[a[3], b[3], c[3]]

share|improve this answer

answered 2 hours ago

Carl WollCarl Woll

75.9k3100198

$endgroup$

add a comment | 

$begingroup$

Another possibility is to use the 3-arg version of Thread. With Sjoerd's example:

n = 3;
l1 = Array[a,n];
l2 = Array[b,n];
l3 = Array[c,n];

Using Thread:

Thread /@ Thread[f[l1, l2, l3], List, 2]

f[a[1], b[1], c[1]], f[a[1], b[1], c[2]],
f[a[1], b[1], c[3]], f[a[2], b[2], c[1]], f[a[2], b[2], c[2]],
f[a[2], b[2], c[3]], f[a[3], b[3], c[1]], f[a[3], b[3], c[2]],
f[a[3], b[3], c[3]]

share|improve this answer

answered 2 hours ago

Carl WollCarl Woll

75.9k3100198

$endgroup$

n = 3;
l1 = Array[a,n];
l2 = Array[b,n];
l3 = Array[c,n];

Thread /@ Thread[f[l1, l2, l3], List, 2]

share|improve this answer

answered 2 hours ago

Carl WollCarl Woll

75.9k3100198

answered 2 hours ago

Carl WollCarl Woll

75.9k3100198

answered 2 hours ago

Carl WollCarl Woll

75.9k3100198

0

$begingroup$

Another way with Curry and Through.

Through /@ Apply[Curry[f, 2, 3, 1] /@ c] /@ Transpose@a, b

Hope this helps.

share|improve this answer

answered 18 mins ago

EdmundEdmund

26.8k330103

$endgroup$

add a comment | 

0

$begingroup$

Another way with Curry and Through.

Through /@ Apply[Curry[f, 2, 3, 1] /@ c] /@ Transpose@a, b

Hope this helps.

share|improve this answer

answered 18 mins ago

EdmundEdmund

26.8k330103

$endgroup$

add a comment | 

$begingroup$

Another way with Curry and Through.

Through /@ Apply[Curry[f, 2, 3, 1] /@ c] /@ Transpose@a, b

Hope this helps.

share|improve this answer

answered 18 mins ago

EdmundEdmund

26.8k330103

$endgroup$

Through /@ Apply[Curry[f, 2, 3, 1] /@ c] /@ Transpose@a, b

share|improve this answer

answered 18 mins ago

EdmundEdmund

26.8k330103

answered 18 mins ago

EdmundEdmund

26.8k330103

answered 18 mins ago

EdmundEdmund

26.8k330103