Averaging elements of a list of matrices over time

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Suppose that I have a time series of a matrix, say, for 3 periods.

t1=0,3,0,6,0,0,3,6,0;
t2=0,6,0,3,0,3,0,6,0;
t3=0,3,6,3,0,6,3,3,0;

I want to take the average of each cell [i,j] over time by considering the number of non-zero elements only as follows:

I went through the documentation of Matrix Operations but I could not find any thing close to what I describe above. Of course, one can use Flatten, Sum and Partition to accomplish what I want. However, I like to have a more elegant way to do the job using matrix structure.

matrix

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asked 53 mins ago

Tugrul Temel

525113

add a comment | 

up vote
2
down vote

favorite

Suppose that I have a time series of a matrix, say, for 3 periods.

t1=0,3,0,6,0,0,3,6,0;
t2=0,6,0,3,0,3,0,6,0;
t3=0,3,6,3,0,6,3,3,0;

I want to take the average of each cell [i,j] over time by considering the number of non-zero elements only as follows:

I went through the documentation of Matrix Operations but I could not find any thing close to what I describe above. Of course, one can use Flatten, Sum and Partition to accomplish what I want. However, I like to have a more elegant way to do the job using matrix structure.

matrix

share|improve this question

asked 53 mins ago

Tugrul Temel

525113

add a comment | 

up vote
2
down vote

favorite

up vote
2
down vote

favorite

Suppose that I have a time series of a matrix, say, for 3 periods.

t1=0,3,0,6,0,0,3,6,0;
t2=0,6,0,3,0,3,0,6,0;
t3=0,3,6,3,0,6,3,3,0;

I want to take the average of each cell [i,j] over time by considering the number of non-zero elements only as follows:

I went through the documentation of Matrix Operations but I could not find any thing close to what I describe above. Of course, one can use Flatten, Sum and Partition to accomplish what I want. However, I like to have a more elegant way to do the job using matrix structure.

matrix

share|improve this question

asked 53 mins ago

Tugrul Temel

525113

Suppose that I have a time series of a matrix, say, for 3 periods.

t1=0,3,0,6,0,0,3,6,0;
t2=0,6,0,3,0,3,0,6,0;
t3=0,3,6,3,0,6,3,3,0;

I want to take the average of each cell [i,j] over time by considering the number of non-zero elements only as follows:

I went through the documentation of Matrix Operations but I could not find any thing close to what I describe above. Of course, one can use Flatten, Sum and Partition to accomplish what I want. However, I like to have a more elegant way to do the job using matrix structure.

matrix

matrix

share|improve this question

asked 53 mins ago

Tugrul Temel

525113

share|improve this question

asked 53 mins ago

Tugrul Temel

525113

share|improve this question

share|improve this question

asked 53 mins ago

Tugrul Temel

525113

asked 53 mins ago

Tugrul Temel

525113

asked 53 mins ago

Tugrul Temel

525113

525113

add a comment | 

add a comment | 

2 Answers
2

active

oldest

votes

up vote
3
down vote



accepted

Quiet @ Block[Indeterminate = 0, Total[#] / Total[Unitize @ #]] & @ t1, t2, t3

% // MatrixForm // TeXForm

$left(
beginarrayccc
0 & 4 & 6 \
4 & 0 & frac92 \
3 & 5 & 0 \
endarray
right)$

Also

Total[t1, t2, t3] / (Total[Unitize @ t1, t2, t3] /. 0 -> 1)

same result

share|improve this answer

edited 16 mins ago

answered 43 mins ago

kglr

167k8189392

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Your answers are perfect, just the type of answers I was thinking of. The first answer looks more elegant, though.
  – Tugrul Temel
  27 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thank you @TugrulTemel for the accept and kind words.
  – kglr
  25 mins ago
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  First solution gives a warning on M11.3 Power::infy: Infinite expression 1/0 encountered.
  – Okkes Dulgerci
  21 mins ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thank you @OkkesDulgerci. Forgot to Quiet.
  – kglr
  15 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @kglr: Yes, I was going to ask why we receive warnings from the first method. There is no room for warning because if all elements are zero, then the average is zero.
  – Tugrul Temel
  14 mins ago
  

  
  
  
  

 | 
show 1 more comment

up vote
2
down vote

Total[t1, t2, t3]/Clip[Total[Unitize@t1, t2, t3], 1, Infinity]

share|improve this answer

answered 29 mins ago

Alan

6,0541124

add a comment | 

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2 Answers
2

active

oldest

votes

2 Answers
2

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
3
down vote



accepted

Quiet @ Block[Indeterminate = 0, Total[#] / Total[Unitize @ #]] & @ t1, t2, t3

% // MatrixForm // TeXForm

$left(
beginarrayccc
0 & 4 & 6 \
4 & 0 & frac92 \
3 & 5 & 0 \
endarray
right)$

Also

Total[t1, t2, t3] / (Total[Unitize @ t1, t2, t3] /. 0 -> 1)

same result

share|improve this answer

edited 16 mins ago

answered 43 mins ago

kglr

167k8189392

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Your answers are perfect, just the type of answers I was thinking of. The first answer looks more elegant, though.
  – Tugrul Temel
  27 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thank you @TugrulTemel for the accept and kind words.
  – kglr
  25 mins ago
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  First solution gives a warning on M11.3 Power::infy: Infinite expression 1/0 encountered.
  – Okkes Dulgerci
  21 mins ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thank you @OkkesDulgerci. Forgot to Quiet.
  – kglr
  15 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @kglr: Yes, I was going to ask why we receive warnings from the first method. There is no room for warning because if all elements are zero, then the average is zero.
  – Tugrul Temel
  14 mins ago
  

  
  
  
  

 | 
show 1 more comment

up vote
3
down vote



accepted

Quiet @ Block[Indeterminate = 0, Total[#] / Total[Unitize @ #]] & @ t1, t2, t3

% // MatrixForm // TeXForm

$left(
beginarrayccc
0 & 4 & 6 \
4 & 0 & frac92 \
3 & 5 & 0 \
endarray
right)$

Also

Total[t1, t2, t3] / (Total[Unitize @ t1, t2, t3] /. 0 -> 1)

same result

share|improve this answer

edited 16 mins ago

answered 43 mins ago

kglr

167k8189392

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Your answers are perfect, just the type of answers I was thinking of. The first answer looks more elegant, though.
  – Tugrul Temel
  27 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thank you @TugrulTemel for the accept and kind words.
  – kglr
  25 mins ago
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  First solution gives a warning on M11.3 Power::infy: Infinite expression 1/0 encountered.
  – Okkes Dulgerci
  21 mins ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thank you @OkkesDulgerci. Forgot to Quiet.
  – kglr
  15 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @kglr: Yes, I was going to ask why we receive warnings from the first method. There is no room for warning because if all elements are zero, then the average is zero.
  – Tugrul Temel
  14 mins ago
  

  
  
  
  

 | 
show 1 more comment

up vote
3
down vote



accepted

up vote
3
down vote



accepted

Quiet @ Block[Indeterminate = 0, Total[#] / Total[Unitize @ #]] & @ t1, t2, t3

% // MatrixForm // TeXForm

$left(
beginarrayccc
0 & 4 & 6 \
4 & 0 & frac92 \
3 & 5 & 0 \
endarray
right)$

Also

Total[t1, t2, t3] / (Total[Unitize @ t1, t2, t3] /. 0 -> 1)

same result

share|improve this answer

edited 16 mins ago

answered 43 mins ago

kglr

167k8189392

Quiet @ Block[Indeterminate = 0, Total[#] / Total[Unitize @ #]] & @ t1, t2, t3

% // MatrixForm // TeXForm

$left(
beginarrayccc
0 & 4 & 6 \
4 & 0 & frac92 \
3 & 5 & 0 \
endarray
right)$

Also

Total[t1, t2, t3] / (Total[Unitize @ t1, t2, t3] /. 0 -> 1)

same result

share|improve this answer

edited 16 mins ago

answered 43 mins ago

kglr

167k8189392

share|improve this answer

share|improve this answer

edited 16 mins ago

edited 16 mins ago

edited 16 mins ago

answered 43 mins ago

kglr

167k8189392

answered 43 mins ago

kglr

167k8189392

answered 43 mins ago

kglr

167k8189392

167k8189392

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Your answers are perfect, just the type of answers I was thinking of. The first answer looks more elegant, though.
  – Tugrul Temel
  27 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thank you @TugrulTemel for the accept and kind words.
  – kglr
  25 mins ago
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  First solution gives a warning on M11.3 Power::infy: Infinite expression 1/0 encountered.
  – Okkes Dulgerci
  21 mins ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thank you @OkkesDulgerci. Forgot to Quiet.
  – kglr
  15 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @kglr: Yes, I was going to ask why we receive warnings from the first method. There is no room for warning because if all elements are zero, then the average is zero.
  – Tugrul Temel
  14 mins ago
  

  
  
  
  

 | 
show 1 more comment

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Your answers are perfect, just the type of answers I was thinking of. The first answer looks more elegant, though.
  – Tugrul Temel
  27 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thank you @TugrulTemel for the accept and kind words.
  – kglr
  25 mins ago
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  First solution gives a warning on M11.3 Power::infy: Infinite expression 1/0 encountered.
  – Okkes Dulgerci
  21 mins ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thank you @OkkesDulgerci. Forgot to Quiet.
  – kglr
  15 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @kglr: Yes, I was going to ask why we receive warnings from the first method. There is no room for warning because if all elements are zero, then the average is zero.
  – Tugrul Temel
  14 mins ago
  

  
  
  
  

Your answers are perfect, just the type of answers I was thinking of. The first answer looks more elegant, though.
– Tugrul Temel
27 mins ago

Your answers are perfect, just the type of answers I was thinking of. The first answer looks more elegant, though.
– Tugrul Temel
27 mins ago

Thank you @TugrulTemel for the accept and kind words.
– kglr
25 mins ago

Thank you @TugrulTemel for the accept and kind words.
– kglr
25 mins ago

2

2

First solution gives a warning on M11.3 Power::infy: Infinite expression 1/0 encountered.
– Okkes Dulgerci
21 mins ago

First solution gives a warning on M11.3 Power::infy: Infinite expression 1/0 encountered.
– Okkes Dulgerci
21 mins ago

Thank you @OkkesDulgerci. Forgot to Quiet.
– kglr
15 mins ago

Thank you @OkkesDulgerci. Forgot to Quiet.
– kglr
15 mins ago

@kglr: Yes, I was going to ask why we receive warnings from the first method. There is no room for warning because if all elements are zero, then the average is zero.
– Tugrul Temel
14 mins ago

@kglr: Yes, I was going to ask why we receive warnings from the first method. There is no room for warning because if all elements are zero, then the average is zero.
– Tugrul Temel
14 mins ago

 | 
show 1 more comment

up vote
2
down vote

Total[t1, t2, t3]/Clip[Total[Unitize@t1, t2, t3], 1, Infinity]

share|improve this answer

answered 29 mins ago

Alan

6,0541124

add a comment | 

up vote
2
down vote

Total[t1, t2, t3]/Clip[Total[Unitize@t1, t2, t3], 1, Infinity]

share|improve this answer

answered 29 mins ago

Alan

6,0541124

add a comment | 

up vote
2
down vote

up vote
2
down vote

Total[t1, t2, t3]/Clip[Total[Unitize@t1, t2, t3], 1, Infinity]

share|improve this answer

answered 29 mins ago

Alan

6,0541124

Total[t1, t2, t3]/Clip[Total[Unitize@t1, t2, t3], 1, Infinity]

share|improve this answer

answered 29 mins ago

Alan

6,0541124

share|improve this answer

share|improve this answer

answered 29 mins ago

Alan

6,0541124

answered 29 mins ago

Alan

6,0541124

answered 29 mins ago

Alan

6,0541124

6,0541124

add a comment | 

add a comment | 

 

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