Extract the symmetric matrix built-in another matrix

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up vote
5
down vote

favorite

1

Suppose that I have a matrix M:

M=
 0,1,1,0,1,0,
 1,0,0,1,1,1,
 1,1,0,0,1,0,
 0,1,1,0,0,0,
 1,0,0,1,0,1,
 1,1,1,1,0,0
 ;

I like to extract from M the symmetric matrix symM:

symM=
 0, 1, 1, 0, 1, 0,
 1, 0, 0, 0, 0, 1,
 1, 0, 0, 0, 0, 0,
 0, 0, 0, 0, 0, 0,
 1, 0, 0, 0, 0, 0,
 0, 1, 0, 0, 0, 0
 ;

I do not want to use Do or If commands. I like to implement matrix operations to extract the symmetric part of M.

EDIT 1

In general terms, matrix M is composed of 1 and 0 only, with the condition that the diagonal cells be zeros. My goal is to extract the matrix symM which should only include 1s in the non-zero reciprocal cells (or symmetric cells), otherwise zero.

Example, in the above example, M[[1,2]]=1 and M[[2,1]]=1, then both symM[[1,2]] and symM[[2,1]] should be 1. All other cells which are not qualified should be all zero.

I hope the question is clearer now. Thank you.

matrix

share|improve this question

edited 11 mins ago

kglr

168k8191394

asked 4 hours ago

Tugrul Temel

602113

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Do you have a particular algorithm in mind?
  – corey979
  4 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @corey979: I do not have any algorithm in mind but maybe Scan can be used to collect the non-negative symmetric positions in M.
  – Tugrul Temel
  4 hours ago
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  BitAnd[M, Transpose[M]]
  – Coolwater
  2 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Coolwater That's a good one! Why don't you post it as an answer?
  – Henrik Schumacher
  2 hours ago
  

  
  
  
  

add a comment | 

up vote
5
down vote

favorite

1

Suppose that I have a matrix M:

M=
 0,1,1,0,1,0,
 1,0,0,1,1,1,
 1,1,0,0,1,0,
 0,1,1,0,0,0,
 1,0,0,1,0,1,
 1,1,1,1,0,0
 ;

I like to extract from M the symmetric matrix symM:

symM=
 0, 1, 1, 0, 1, 0,
 1, 0, 0, 0, 0, 1,
 1, 0, 0, 0, 0, 0,
 0, 0, 0, 0, 0, 0,
 1, 0, 0, 0, 0, 0,
 0, 1, 0, 0, 0, 0
 ;

I do not want to use Do or If commands. I like to implement matrix operations to extract the symmetric part of M.

EDIT 1

In general terms, matrix M is composed of 1 and 0 only, with the condition that the diagonal cells be zeros. My goal is to extract the matrix symM which should only include 1s in the non-zero reciprocal cells (or symmetric cells), otherwise zero.

Example, in the above example, M[[1,2]]=1 and M[[2,1]]=1, then both symM[[1,2]] and symM[[2,1]] should be 1. All other cells which are not qualified should be all zero.

I hope the question is clearer now. Thank you.

matrix

share|improve this question

edited 11 mins ago

kglr

168k8191394

asked 4 hours ago

Tugrul Temel

602113

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Do you have a particular algorithm in mind?
  – corey979
  4 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @corey979: I do not have any algorithm in mind but maybe Scan can be used to collect the non-negative symmetric positions in M.
  – Tugrul Temel
  4 hours ago
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  BitAnd[M, Transpose[M]]
  – Coolwater
  2 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Coolwater That's a good one! Why don't you post it as an answer?
  – Henrik Schumacher
  2 hours ago
  

  
  
  
  

add a comment | 

up vote
5
down vote

favorite

1

up vote
5
down vote

favorite

1

1

Suppose that I have a matrix M:

M=
 0,1,1,0,1,0,
 1,0,0,1,1,1,
 1,1,0,0,1,0,
 0,1,1,0,0,0,
 1,0,0,1,0,1,
 1,1,1,1,0,0
 ;

I like to extract from M the symmetric matrix symM:

symM=
 0, 1, 1, 0, 1, 0,
 1, 0, 0, 0, 0, 1,
 1, 0, 0, 0, 0, 0,
 0, 0, 0, 0, 0, 0,
 1, 0, 0, 0, 0, 0,
 0, 1, 0, 0, 0, 0
 ;

I do not want to use Do or If commands. I like to implement matrix operations to extract the symmetric part of M.

EDIT 1

In general terms, matrix M is composed of 1 and 0 only, with the condition that the diagonal cells be zeros. My goal is to extract the matrix symM which should only include 1s in the non-zero reciprocal cells (or symmetric cells), otherwise zero.

Example, in the above example, M[[1,2]]=1 and M[[2,1]]=1, then both symM[[1,2]] and symM[[2,1]] should be 1. All other cells which are not qualified should be all zero.

I hope the question is clearer now. Thank you.

matrix

share|improve this question

edited 11 mins ago

kglr

168k8191394

asked 4 hours ago

Tugrul Temel

602113

Suppose that I have a matrix M:

M=
 0,1,1,0,1,0,
 1,0,0,1,1,1,
 1,1,0,0,1,0,
 0,1,1,0,0,0,
 1,0,0,1,0,1,
 1,1,1,1,0,0
 ;

I like to extract from M the symmetric matrix symM:

symM=
 0, 1, 1, 0, 1, 0,
 1, 0, 0, 0, 0, 1,
 1, 0, 0, 0, 0, 0,
 0, 0, 0, 0, 0, 0,
 1, 0, 0, 0, 0, 0,
 0, 1, 0, 0, 0, 0
 ;

I do not want to use Do or If commands. I like to implement matrix operations to extract the symmetric part of M.

EDIT 1

In general terms, matrix M is composed of 1 and 0 only, with the condition that the diagonal cells be zeros. My goal is to extract the matrix symM which should only include 1s in the non-zero reciprocal cells (or symmetric cells), otherwise zero.

Example, in the above example, M[[1,2]]=1 and M[[2,1]]=1, then both symM[[1,2]] and symM[[2,1]] should be 1. All other cells which are not qualified should be all zero.

I hope the question is clearer now. Thank you.

matrix

matrix

share|improve this question

edited 11 mins ago

kglr

168k8191394

asked 4 hours ago

Tugrul Temel

602113

share|improve this question

edited 11 mins ago

kglr

168k8191394

asked 4 hours ago

Tugrul Temel

602113

share|improve this question

share|improve this question

edited 11 mins ago

kglr

168k8191394

edited 11 mins ago

kglr

168k8191394

edited 11 mins ago

kglr

168k8191394

168k8191394

asked 4 hours ago

Tugrul Temel

602113

asked 4 hours ago

Tugrul Temel

602113

asked 4 hours ago

Tugrul Temel

602113

602113

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Do you have a particular algorithm in mind?
  – corey979
  4 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @corey979: I do not have any algorithm in mind but maybe Scan can be used to collect the non-negative symmetric positions in M.
  – Tugrul Temel
  4 hours ago
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  BitAnd[M, Transpose[M]]
  – Coolwater
  2 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Coolwater That's a good one! Why don't you post it as an answer?
  – Henrik Schumacher
  2 hours ago
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Do you have a particular algorithm in mind?
  – corey979
  4 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @corey979: I do not have any algorithm in mind but maybe Scan can be used to collect the non-negative symmetric positions in M.
  – Tugrul Temel
  4 hours ago
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  BitAnd[M, Transpose[M]]
  – Coolwater
  2 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Coolwater That's a good one! Why don't you post it as an answer?
  – Henrik Schumacher
  2 hours ago
  

  
  
  
  

Do you have a particular algorithm in mind?
– corey979
4 hours ago

Do you have a particular algorithm in mind?
– corey979
4 hours ago

@corey979: I do not have any algorithm in mind but maybe Scan can be used to collect the non-negative symmetric positions in M.
– Tugrul Temel
4 hours ago

@corey979: I do not have any algorithm in mind but maybe Scan can be used to collect the non-negative symmetric positions in M.
– Tugrul Temel
4 hours ago

2

2

BitAnd[M, Transpose[M]]
– Coolwater
2 hours ago

BitAnd[M, Transpose[M]]
– Coolwater
2 hours ago

@Coolwater That's a good one! Why don't you post it as an answer?
– Henrik Schumacher
2 hours ago

@Coolwater That's a good one! Why don't you post it as an answer?
– Henrik Schumacher
2 hours ago

add a comment | 

3 Answers
3

active

oldest

votes

up vote
2
down vote



accepted

Maybe this is what you are looking for. I interpreted your question as if you want to replace all nonsymmetric entries of the input matrix by zeroes and as if the input matrix is not necessarily binary.

A = M Subtract[1, Unitize[Subtract[Transpose[M], M]]];

share|improve this answer

edited 2 hours ago

answered 4 hours ago

Henrik Schumacher

43.2k262127

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Yes...That is what I wanted to have. Perfect...
  – Tugrul Temel
  4 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  @HenrikSchumacher For the symmetric part of M I would have expected something like (M+Transpose[M])/2...Interestingly your result fullfills A==Floor[(M+Transpose[M])/2] !
  – Ulrich Neumann
  4 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  @UlrichNeumann (M+Transpose[M])/2 is the symmetrized part, and in particular the orthogonal projection onto the linear space of symmetric matrices (orthogonal with respect to the Frobenius metric). But as by OP's examples, this was not what the OP asked for.
  – Henrik Schumacher
  4 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Henrik: Referring to your last point, you are right that your code gives me what I wanted. I checked it with other examples and it works.
  – Tugrul Temel
  4 hours ago
  

  
  
  
  

add a comment | 

up vote
5
down vote

Maybe a bit simpler:

M Transpose[M]

Comparing with Henrik's answer:

M Subtract[1, Unitize[Subtract[Transpose[M], M]]] == M Transpose[M]
True

share|improve this answer

answered 3 hours ago

bill s

51.9k375146

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Simpler indeed. But it will work only for binary matrices. Well, actually, it is still somewhat unclear, what the OP's usage spectrum and desired result in the general case is supposed to be. I interpreted it as if the OP wants to replace all nonsymmetric entries of the input matrix by zeroes.
  – Henrik Schumacher
  3 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Henrik -- Agreed, I took the binary example suggested by the OP as indicating interest only in binary matrices.
  – bill s
  3 hours ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Henrik: I wanted to extract binary cells only: that is, if (i,j)==(j,i)==1, then keep them in the output matrix, otherwise place zeros to both cells. What you are saying in your comment is what I actually wanted: replace all non-symmetric entries of the input matrix with zeros. Is Bill's proposal equivalent to your proposal? I want to make sure this because in the original case with n=1000 I cannot check it visually.
  – Tugrul Temel
  2 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  A simple example for which bill's and my proposals lead to different output is the matrix M = 1, 2,1,1. In general it is preferrable to post also all assumptions on the input data already in the question. Moreover your question leave a lot room for interpretation. Please specify exactly what the desired output for a general input matrix should be.
  – Henrik Schumacher
  2 hours ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Henrik: I will edit the question in line with your comment.
  – Tugrul Temel
  1 hour ago
  

  
  
  
  

add a comment | 

up vote
1
down vote

A = Floor @ Symmetrize @ M;

TeXForm @ MatrixForm @ A

$left(
beginarraycccccc
0 & 1 & 1 & 0 & 1 & 0 \
1 & 0 & 0 & 1 & 0 & 1 \
1 & 0 & 0 & 0 & 0 & 0 \
0 & 1 & 0 & 0 & 0 & 0 \
1 & 0 & 0 & 0 & 0 & 0 \
0 & 1 & 0 & 0 & 0 & 0 \
endarray
right)$

Note: This is much slower than the methods in the answers by bill s and Henrik Schumacher.

share|improve this answer

edited 4 mins ago

answered 1 hour ago

kglr

168k8191394

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
2
down vote



accepted

Maybe this is what you are looking for. I interpreted your question as if you want to replace all nonsymmetric entries of the input matrix by zeroes and as if the input matrix is not necessarily binary.

A = M Subtract[1, Unitize[Subtract[Transpose[M], M]]];

share|improve this answer

edited 2 hours ago

answered 4 hours ago

Henrik Schumacher

43.2k262127

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Yes...That is what I wanted to have. Perfect...
  – Tugrul Temel
  4 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  @HenrikSchumacher For the symmetric part of M I would have expected something like (M+Transpose[M])/2...Interestingly your result fullfills A==Floor[(M+Transpose[M])/2] !
  – Ulrich Neumann
  4 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  @UlrichNeumann (M+Transpose[M])/2 is the symmetrized part, and in particular the orthogonal projection onto the linear space of symmetric matrices (orthogonal with respect to the Frobenius metric). But as by OP's examples, this was not what the OP asked for.
  – Henrik Schumacher
  4 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Henrik: Referring to your last point, you are right that your code gives me what I wanted. I checked it with other examples and it works.
  – Tugrul Temel
  4 hours ago
  

  
  
  
  

add a comment | 

up vote
2
down vote



accepted

Maybe this is what you are looking for. I interpreted your question as if you want to replace all nonsymmetric entries of the input matrix by zeroes and as if the input matrix is not necessarily binary.

A = M Subtract[1, Unitize[Subtract[Transpose[M], M]]];

share|improve this answer

edited 2 hours ago

answered 4 hours ago

Henrik Schumacher

43.2k262127

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Yes...That is what I wanted to have. Perfect...
  – Tugrul Temel
  4 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  @HenrikSchumacher For the symmetric part of M I would have expected something like (M+Transpose[M])/2...Interestingly your result fullfills A==Floor[(M+Transpose[M])/2] !
  – Ulrich Neumann
  4 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  @UlrichNeumann (M+Transpose[M])/2 is the symmetrized part, and in particular the orthogonal projection onto the linear space of symmetric matrices (orthogonal with respect to the Frobenius metric). But as by OP's examples, this was not what the OP asked for.
  – Henrik Schumacher
  4 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Henrik: Referring to your last point, you are right that your code gives me what I wanted. I checked it with other examples and it works.
  – Tugrul Temel
  4 hours ago
  

  
  
  
  

add a comment | 

up vote
2
down vote



accepted

up vote
2
down vote



accepted

Maybe this is what you are looking for. I interpreted your question as if you want to replace all nonsymmetric entries of the input matrix by zeroes and as if the input matrix is not necessarily binary.

A = M Subtract[1, Unitize[Subtract[Transpose[M], M]]];

share|improve this answer

edited 2 hours ago

answered 4 hours ago

Henrik Schumacher

43.2k262127

Maybe this is what you are looking for. I interpreted your question as if you want to replace all nonsymmetric entries of the input matrix by zeroes and as if the input matrix is not necessarily binary.

A = M Subtract[1, Unitize[Subtract[Transpose[M], M]]];

share|improve this answer

edited 2 hours ago

answered 4 hours ago

Henrik Schumacher

43.2k262127

share|improve this answer

share|improve this answer

edited 2 hours ago

edited 2 hours ago

edited 2 hours ago

answered 4 hours ago

Henrik Schumacher

43.2k262127

answered 4 hours ago

Henrik Schumacher

43.2k262127

answered 4 hours ago

Henrik Schumacher

43.2k262127

43.2k262127

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Yes...That is what I wanted to have. Perfect...
  – Tugrul Temel
  4 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  @HenrikSchumacher For the symmetric part of M I would have expected something like (M+Transpose[M])/2...Interestingly your result fullfills A==Floor[(M+Transpose[M])/2] !
  – Ulrich Neumann
  4 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  @UlrichNeumann (M+Transpose[M])/2 is the symmetrized part, and in particular the orthogonal projection onto the linear space of symmetric matrices (orthogonal with respect to the Frobenius metric). But as by OP's examples, this was not what the OP asked for.
  – Henrik Schumacher
  4 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Henrik: Referring to your last point, you are right that your code gives me what I wanted. I checked it with other examples and it works.
  – Tugrul Temel
  4 hours ago
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Yes...That is what I wanted to have. Perfect...
  – Tugrul Temel
  4 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  @HenrikSchumacher For the symmetric part of M I would have expected something like (M+Transpose[M])/2...Interestingly your result fullfills A==Floor[(M+Transpose[M])/2] !
  – Ulrich Neumann
  4 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  @UlrichNeumann (M+Transpose[M])/2 is the symmetrized part, and in particular the orthogonal projection onto the linear space of symmetric matrices (orthogonal with respect to the Frobenius metric). But as by OP's examples, this was not what the OP asked for.
  – Henrik Schumacher
  4 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Henrik: Referring to your last point, you are right that your code gives me what I wanted. I checked it with other examples and it works.
  – Tugrul Temel
  4 hours ago
  

  
  
  
  

Yes...That is what I wanted to have. Perfect...
– Tugrul Temel
4 hours ago

Yes...That is what I wanted to have. Perfect...
– Tugrul Temel
4 hours ago

1

1

@HenrikSchumacher For the symmetric part of M I would have expected something like (M+Transpose[M])/2...Interestingly your result fullfills A==Floor[(M+Transpose[M])/2] !
– Ulrich Neumann
4 hours ago

@HenrikSchumacher For the symmetric part of M I would have expected something like (M+Transpose[M])/2...Interestingly your result fullfills A==Floor[(M+Transpose[M])/2] !
– Ulrich Neumann
4 hours ago

1

1

@UlrichNeumann (M+Transpose[M])/2 is the symmetrized part, and in particular the orthogonal projection onto the linear space of symmetric matrices (orthogonal with respect to the Frobenius metric). But as by OP's examples, this was not what the OP asked for.
– Henrik Schumacher
4 hours ago

@UlrichNeumann (M+Transpose[M])/2 is the symmetrized part, and in particular the orthogonal projection onto the linear space of symmetric matrices (orthogonal with respect to the Frobenius metric). But as by OP's examples, this was not what the OP asked for.
– Henrik Schumacher
4 hours ago

@Henrik: Referring to your last point, you are right that your code gives me what I wanted. I checked it with other examples and it works.
– Tugrul Temel
4 hours ago

@Henrik: Referring to your last point, you are right that your code gives me what I wanted. I checked it with other examples and it works.
– Tugrul Temel
4 hours ago

add a comment | 

up vote
5
down vote

Maybe a bit simpler:

M Transpose[M]

Comparing with Henrik's answer:

M Subtract[1, Unitize[Subtract[Transpose[M], M]]] == M Transpose[M]
True

share|improve this answer

answered 3 hours ago

bill s

51.9k375146

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Simpler indeed. But it will work only for binary matrices. Well, actually, it is still somewhat unclear, what the OP's usage spectrum and desired result in the general case is supposed to be. I interpreted it as if the OP wants to replace all nonsymmetric entries of the input matrix by zeroes.
  – Henrik Schumacher
  3 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Henrik -- Agreed, I took the binary example suggested by the OP as indicating interest only in binary matrices.
  – bill s
  3 hours ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Henrik: I wanted to extract binary cells only: that is, if (i,j)==(j,i)==1, then keep them in the output matrix, otherwise place zeros to both cells. What you are saying in your comment is what I actually wanted: replace all non-symmetric entries of the input matrix with zeros. Is Bill's proposal equivalent to your proposal? I want to make sure this because in the original case with n=1000 I cannot check it visually.
  – Tugrul Temel
  2 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  A simple example for which bill's and my proposals lead to different output is the matrix M = 1, 2,1,1. In general it is preferrable to post also all assumptions on the input data already in the question. Moreover your question leave a lot room for interpretation. Please specify exactly what the desired output for a general input matrix should be.
  – Henrik Schumacher
  2 hours ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Henrik: I will edit the question in line with your comment.
  – Tugrul Temel
  1 hour ago
  

  
  
  
  

add a comment | 

up vote
5
down vote

Maybe a bit simpler:

M Transpose[M]

Comparing with Henrik's answer:

M Subtract[1, Unitize[Subtract[Transpose[M], M]]] == M Transpose[M]
True

share|improve this answer

answered 3 hours ago

bill s

51.9k375146

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Simpler indeed. But it will work only for binary matrices. Well, actually, it is still somewhat unclear, what the OP's usage spectrum and desired result in the general case is supposed to be. I interpreted it as if the OP wants to replace all nonsymmetric entries of the input matrix by zeroes.
  – Henrik Schumacher
  3 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Henrik -- Agreed, I took the binary example suggested by the OP as indicating interest only in binary matrices.
  – bill s
  3 hours ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Henrik: I wanted to extract binary cells only: that is, if (i,j)==(j,i)==1, then keep them in the output matrix, otherwise place zeros to both cells. What you are saying in your comment is what I actually wanted: replace all non-symmetric entries of the input matrix with zeros. Is Bill's proposal equivalent to your proposal? I want to make sure this because in the original case with n=1000 I cannot check it visually.
  – Tugrul Temel
  2 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  A simple example for which bill's and my proposals lead to different output is the matrix M = 1, 2,1,1. In general it is preferrable to post also all assumptions on the input data already in the question. Moreover your question leave a lot room for interpretation. Please specify exactly what the desired output for a general input matrix should be.
  – Henrik Schumacher
  2 hours ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Henrik: I will edit the question in line with your comment.
  – Tugrul Temel
  1 hour ago
  

  
  
  
  

add a comment | 

up vote
5
down vote

up vote
5
down vote

Maybe a bit simpler:

M Transpose[M]

Comparing with Henrik's answer:

M Subtract[1, Unitize[Subtract[Transpose[M], M]]] == M Transpose[M]
True

share|improve this answer

answered 3 hours ago

bill s

51.9k375146

Maybe a bit simpler:

M Transpose[M]

Comparing with Henrik's answer:

M Subtract[1, Unitize[Subtract[Transpose[M], M]]] == M Transpose[M]
True

share|improve this answer

answered 3 hours ago

bill s

51.9k375146

share|improve this answer

share|improve this answer

answered 3 hours ago

bill s

51.9k375146

answered 3 hours ago

bill s

51.9k375146

answered 3 hours ago

bill s

51.9k375146

51.9k375146

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Simpler indeed. But it will work only for binary matrices. Well, actually, it is still somewhat unclear, what the OP's usage spectrum and desired result in the general case is supposed to be. I interpreted it as if the OP wants to replace all nonsymmetric entries of the input matrix by zeroes.
  – Henrik Schumacher
  3 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Henrik -- Agreed, I took the binary example suggested by the OP as indicating interest only in binary matrices.
  – bill s
  3 hours ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Henrik: I wanted to extract binary cells only: that is, if (i,j)==(j,i)==1, then keep them in the output matrix, otherwise place zeros to both cells. What you are saying in your comment is what I actually wanted: replace all non-symmetric entries of the input matrix with zeros. Is Bill's proposal equivalent to your proposal? I want to make sure this because in the original case with n=1000 I cannot check it visually.
  – Tugrul Temel
  2 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  A simple example for which bill's and my proposals lead to different output is the matrix M = 1, 2,1,1. In general it is preferrable to post also all assumptions on the input data already in the question. Moreover your question leave a lot room for interpretation. Please specify exactly what the desired output for a general input matrix should be.
  – Henrik Schumacher
  2 hours ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Henrik: I will edit the question in line with your comment.
  – Tugrul Temel
  1 hour ago
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Simpler indeed. But it will work only for binary matrices. Well, actually, it is still somewhat unclear, what the OP's usage spectrum and desired result in the general case is supposed to be. I interpreted it as if the OP wants to replace all nonsymmetric entries of the input matrix by zeroes.
  – Henrik Schumacher
  3 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Henrik -- Agreed, I took the binary example suggested by the OP as indicating interest only in binary matrices.
  – bill s
  3 hours ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Henrik: I wanted to extract binary cells only: that is, if (i,j)==(j,i)==1, then keep them in the output matrix, otherwise place zeros to both cells. What you are saying in your comment is what I actually wanted: replace all non-symmetric entries of the input matrix with zeros. Is Bill's proposal equivalent to your proposal? I want to make sure this because in the original case with n=1000 I cannot check it visually.
  – Tugrul Temel
  2 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  A simple example for which bill's and my proposals lead to different output is the matrix M = 1, 2,1,1. In general it is preferrable to post also all assumptions on the input data already in the question. Moreover your question leave a lot room for interpretation. Please specify exactly what the desired output for a general input matrix should be.
  – Henrik Schumacher
  2 hours ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Henrik: I will edit the question in line with your comment.
  – Tugrul Temel
  1 hour ago
  

  
  
  
  

Simpler indeed. But it will work only for binary matrices. Well, actually, it is still somewhat unclear, what the OP's usage spectrum and desired result in the general case is supposed to be. I interpreted it as if the OP wants to replace all nonsymmetric entries of the input matrix by zeroes.
– Henrik Schumacher
3 hours ago

Simpler indeed. But it will work only for binary matrices. Well, actually, it is still somewhat unclear, what the OP's usage spectrum and desired result in the general case is supposed to be. I interpreted it as if the OP wants to replace all nonsymmetric entries of the input matrix by zeroes.
– Henrik Schumacher
3 hours ago

@Henrik -- Agreed, I took the binary example suggested by the OP as indicating interest only in binary matrices.
– bill s
3 hours ago

@Henrik -- Agreed, I took the binary example suggested by the OP as indicating interest only in binary matrices.
– bill s
3 hours ago

@Henrik: I wanted to extract binary cells only: that is, if (i,j)==(j,i)==1, then keep them in the output matrix, otherwise place zeros to both cells. What you are saying in your comment is what I actually wanted: replace all non-symmetric entries of the input matrix with zeros. Is Bill's proposal equivalent to your proposal? I want to make sure this because in the original case with n=1000 I cannot check it visually.
– Tugrul Temel
2 hours ago

@Henrik: I wanted to extract binary cells only: that is, if (i,j)==(j,i)==1, then keep them in the output matrix, otherwise place zeros to both cells. What you are saying in your comment is what I actually wanted: replace all non-symmetric entries of the input matrix with zeros. Is Bill's proposal equivalent to your proposal? I want to make sure this because in the original case with n=1000 I cannot check it visually.
– Tugrul Temel
2 hours ago

1

1

A simple example for which bill's and my proposals lead to different output is the matrix M = 1, 2,1,1. In general it is preferrable to post also all assumptions on the input data already in the question. Moreover your question leave a lot room for interpretation. Please specify exactly what the desired output for a general input matrix should be.
– Henrik Schumacher
2 hours ago

A simple example for which bill's and my proposals lead to different output is the matrix M = 1, 2,1,1. In general it is preferrable to post also all assumptions on the input data already in the question. Moreover your question leave a lot room for interpretation. Please specify exactly what the desired output for a general input matrix should be.
– Henrik Schumacher
2 hours ago

@Henrik: I will edit the question in line with your comment.
– Tugrul Temel
1 hour ago

@Henrik: I will edit the question in line with your comment.
– Tugrul Temel
1 hour ago

add a comment | 

up vote
1
down vote

A = Floor @ Symmetrize @ M;

TeXForm @ MatrixForm @ A

$left(
beginarraycccccc
0 & 1 & 1 & 0 & 1 & 0 \
1 & 0 & 0 & 1 & 0 & 1 \
1 & 0 & 0 & 0 & 0 & 0 \
0 & 1 & 0 & 0 & 0 & 0 \
1 & 0 & 0 & 0 & 0 & 0 \
0 & 1 & 0 & 0 & 0 & 0 \
endarray
right)$

Note: This is much slower than the methods in the answers by bill s and Henrik Schumacher.

share|improve this answer

edited 4 mins ago

answered 1 hour ago

kglr

168k8191394

add a comment | 

up vote
1
down vote

A = Floor @ Symmetrize @ M;

TeXForm @ MatrixForm @ A

$left(
beginarraycccccc
0 & 1 & 1 & 0 & 1 & 0 \
1 & 0 & 0 & 1 & 0 & 1 \
1 & 0 & 0 & 0 & 0 & 0 \
0 & 1 & 0 & 0 & 0 & 0 \
1 & 0 & 0 & 0 & 0 & 0 \
0 & 1 & 0 & 0 & 0 & 0 \
endarray
right)$

Note: This is much slower than the methods in the answers by bill s and Henrik Schumacher.

share|improve this answer

edited 4 mins ago

answered 1 hour ago

kglr

168k8191394

add a comment | 

up vote
1
down vote

up vote
1
down vote

A = Floor @ Symmetrize @ M;

TeXForm @ MatrixForm @ A

$left(
beginarraycccccc
0 & 1 & 1 & 0 & 1 & 0 \
1 & 0 & 0 & 1 & 0 & 1 \
1 & 0 & 0 & 0 & 0 & 0 \
0 & 1 & 0 & 0 & 0 & 0 \
1 & 0 & 0 & 0 & 0 & 0 \
0 & 1 & 0 & 0 & 0 & 0 \
endarray
right)$

Note: This is much slower than the methods in the answers by bill s and Henrik Schumacher.

share|improve this answer

edited 4 mins ago

answered 1 hour ago

kglr

168k8191394

A = Floor @ Symmetrize @ M;

TeXForm @ MatrixForm @ A

$left(
beginarraycccccc
0 & 1 & 1 & 0 & 1 & 0 \
1 & 0 & 0 & 1 & 0 & 1 \
1 & 0 & 0 & 0 & 0 & 0 \
0 & 1 & 0 & 0 & 0 & 0 \
1 & 0 & 0 & 0 & 0 & 0 \
0 & 1 & 0 & 0 & 0 & 0 \
endarray
right)$

Note: This is much slower than the methods in the answers by bill s and Henrik Schumacher.

share|improve this answer

edited 4 mins ago

answered 1 hour ago

kglr

168k8191394

share|improve this answer

share|improve this answer

edited 4 mins ago

edited 4 mins ago

edited 4 mins ago

answered 1 hour ago

kglr

168k8191394

answered 1 hour ago

kglr

168k8191394

answered 1 hour ago

kglr

168k8191394

168k8191394

add a comment | 

add a comment | 

 

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