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Identify maximum difference in Matrix

Parallelize matrix operationsChecking powers of a matrix for zerosHow to plot a graph from its incidence matrix?Finding maximum value with position from Table of valuesExtract Transfer Matrix from TransferFunctionModelGenerate a simulated covariance matrixChange entire column of matrix using its own elements for calculationsDetermine n related elements with least sum from a matrix?how to derive a conditional covariance matrix (symbolically)Approximate results

3

$begingroup$

i am trying to find the Maximum difference between two matrices and identify where this maximum occurs.

I illustrate what I mean using an example.
Given

X={{3, 1}, {8, 2}, {10, 3}}

Y={{5, 1}, {4, 2}, {5, 3}}

I calculate matrix which has (X-Y) and position as entries, specifically

d={{-2, 1}, {4, 2}, {5, 3}}

As out pout I would like to have

{5,3}

What is the best way to code this?

matrix column

share|improve this question

edited yesterday

Henrik Schumacher

59.4k582165

asked yesterday

AndreasAndreas

1028

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Ordering[Abs[X[[All, 1]] - X[[All, 2]]], -1][[1]] should give the the position 3. The value of the difference can than be found easily.
  $endgroup$
  – Henrik Schumacher
  yesterday
  

  
  
  
  

add a comment | 

3

$begingroup$

i am trying to find the Maximum difference between two matrices and identify where this maximum occurs.

I illustrate what I mean using an example.
Given

X={{3, 1}, {8, 2}, {10, 3}}

Y={{5, 1}, {4, 2}, {5, 3}}

I calculate matrix which has (X-Y) and position as entries, specifically

d={{-2, 1}, {4, 2}, {5, 3}}

As out pout I would like to have

{5,3}

What is the best way to code this?

matrix column

share|improve this question

edited yesterday

Henrik Schumacher

59.4k582165

asked yesterday

AndreasAndreas

1028

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Ordering[Abs[X[[All, 1]] - X[[All, 2]]], -1][[1]] should give the the position 3. The value of the difference can than be found easily.
  $endgroup$
  – Henrik Schumacher
  yesterday
  

  
  
  
  

add a comment | 

$begingroup$

i am trying to find the Maximum difference between two matrices and identify where this maximum occurs.

I illustrate what I mean using an example.
Given

X={{3, 1}, {8, 2}, {10, 3}}

Y={{5, 1}, {4, 2}, {5, 3}}

I calculate matrix which has (X-Y) and position as entries, specifically

d={{-2, 1}, {4, 2}, {5, 3}}

As out pout I would like to have

{5,3}

What is the best way to code this?

matrix column

share|improve this question

edited yesterday

Henrik Schumacher

59.4k582165

asked yesterday

AndreasAndreas

1028

$endgroup$

X={{3, 1}, {8, 2}, {10, 3}}

Y={{5, 1}, {4, 2}, {5, 3}}

d={{-2, 1}, {4, 2}, {5, 3}}

{5,3}

share|improve this question

edited yesterday

Henrik Schumacher

59.4k582165

asked yesterday

AndreasAndreas

1028

share|improve this question

edited yesterday

Henrik Schumacher

59.4k582165

asked yesterday

AndreasAndreas

1028

edited yesterday

Henrik Schumacher

59.4k582165

edited yesterday

Henrik Schumacher

59.4k582165

asked yesterday

AndreasAndreas

1028

asked yesterday

AndreasAndreas

1028

1 Answer
1

active

oldest

votes

5

$begingroup$

Depending on your taste,

d = MapThread[{#1[[1]] - #2[[1]], #1[[2]]} &, {X, Y}]

or

d = Transpose@{X[[All, 1]] - Y[[All, 1]], X[[All, 2]]}

define the differences d, if you need them. The symbol D is already in use in Mathematica, don't use it for variables.

Then you can compute

MaximalBy[d, Abs@*Last]

{{5, 3}}

As @HenrikSchumacher comments you don't really need the intermediate d though, and you don't need the second elements in each entry denoting their position: using Ordering is more elegant:

X = {3, 8, 10};

Y = {5, 4, 5};

j = First@Ordering[Abs[X - Y], -1]

3

(X - Y)[[j]]

5

share|improve this answer

edited yesterday

answered yesterday

RomanRoman

4,51511127

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thank you so much
  $endgroup$
  – Andreas
  yesterday
  

  
  
  
  

add a comment | 

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5

$begingroup$

Depending on your taste,

d = MapThread[{#1[[1]] - #2[[1]], #1[[2]]} &, {X, Y}]

or

d = Transpose@{X[[All, 1]] - Y[[All, 1]], X[[All, 2]]}

define the differences d, if you need them. The symbol D is already in use in Mathematica, don't use it for variables.

Then you can compute

MaximalBy[d, Abs@*Last]

{{5, 3}}

As @HenrikSchumacher comments you don't really need the intermediate d though, and you don't need the second elements in each entry denoting their position: using Ordering is more elegant:

X = {3, 8, 10};

Y = {5, 4, 5};

j = First@Ordering[Abs[X - Y], -1]

3

(X - Y)[[j]]

5

share|improve this answer

edited yesterday

answered yesterday

RomanRoman

4,51511127

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thank you so much
  $endgroup$
  – Andreas
  yesterday
  

  
  
  
  

add a comment | 

5

$begingroup$

Depending on your taste,

d = MapThread[{#1[[1]] - #2[[1]], #1[[2]]} &, {X, Y}]

or

d = Transpose@{X[[All, 1]] - Y[[All, 1]], X[[All, 2]]}

define the differences d, if you need them. The symbol D is already in use in Mathematica, don't use it for variables.

Then you can compute

MaximalBy[d, Abs@*Last]

{{5, 3}}

As @HenrikSchumacher comments you don't really need the intermediate d though, and you don't need the second elements in each entry denoting their position: using Ordering is more elegant:

X = {3, 8, 10};

Y = {5, 4, 5};

j = First@Ordering[Abs[X - Y], -1]

3

(X - Y)[[j]]

5

share|improve this answer

edited yesterday

answered yesterday

RomanRoman

4,51511127

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thank you so much
  $endgroup$
  – Andreas
  yesterday
  

  
  
  
  

add a comment | 

$begingroup$

Depending on your taste,

d = MapThread[{#1[[1]] - #2[[1]], #1[[2]]} &, {X, Y}]

or

d = Transpose@{X[[All, 1]] - Y[[All, 1]], X[[All, 2]]}

define the differences d, if you need them. The symbol D is already in use in Mathematica, don't use it for variables.

Then you can compute

MaximalBy[d, Abs@*Last]

{{5, 3}}

As @HenrikSchumacher comments you don't really need the intermediate d though, and you don't need the second elements in each entry denoting their position: using Ordering is more elegant:

X = {3, 8, 10};

Y = {5, 4, 5};

j = First@Ordering[Abs[X - Y], -1]

3

(X - Y)[[j]]

5

share|improve this answer

edited yesterday

answered yesterday

RomanRoman

4,51511127

$endgroup$

d = MapThread[{#1[[1]] - #2[[1]], #1[[2]]} &, {X, Y}]

d = Transpose@{X[[All, 1]] - Y[[All, 1]], X[[All, 2]]}

MaximalBy[d, Abs@*Last]

X = {3, 8, 10};

Y = {5, 4, 5};

j = First@Ordering[Abs[X - Y], -1]

(X - Y)[[j]]

share|improve this answer

edited yesterday

answered yesterday

RomanRoman

4,51511127

answered yesterday

RomanRoman

4,51511127

answered yesterday

RomanRoman

4,51511127