What are the ways to sum matrix elements in MATLAB

Question

Given the matrix   A    1 2 3  4 5 6  7 8 9      How could you use a for loop to compute the sum of the elements in the matrix  Write a one line MATLAB command using the function sum to sum the matrix elements in A    My answer   1    for j 1 3      for i j 3          A i      A i    A j 1    A j 2        end end   2   sum A    Are these the correct answers  I didn t know how to use if  while and for  Can anyone explain it to me

User · Answer

Another answer for the first question is to use one for loop and perform linear indexing into the array using the function NUMEL to get the total number of elements   total   0  for i   1 numel A    total   total A i   end

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1   total   0  for i 1 size A 1    for j 1 size A 2      total   total   A i j     end end   2   total   sum A

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The best practice is definitely to avoid loops or recursions in Matlab   Between sum A     and sum sum A     In my experience  arrays in Matlab seems to be stored in a continuous block in memory as stacked column vectors  So the shape of A does not quite matter in sum     One can test reshape   and check if reshaping is fast in Matlab  If it is  then we have a reason to believe that the shape of an array is not directly related to the way the data is stored and manipulated    As such  there is no reason sum sum A   should be faster  It would be slower if Matlab actually creates a row vector recording the sum of each column of A first and then sum over the columns  But I think sum sum A   is very wide-spread amongst users  It is likely that they hard-code sum sum A   to be a single loop  the same to sum A       Below I offer some testing results  In each test  A rand size  and size is specified in the displayed texts   First is using tic toc   Size 100x100 sum A     Elapsed time is 0 000025 seconds  sum sum A   Elapsed time is 0 000018 seconds   Size 10000x1 sum A     Elapsed time is 0 000014 seconds  sum A  Elapsed time is 0 000013 seconds   Size 1000x1000 sum A     Elapsed time is 0 001641 seconds  sum A  Elapsed time is 0 001561 seconds   Size 1000000 sum A     Elapsed time is 0 002439 seconds  sum A  Elapsed time is 0 001697 seconds   Size 10000x10000 sum A     Elapsed time is 0 148504 seconds  sum A  Elapsed time is 0 155160 seconds   Size 100000000 Error using rand Out of memory  Type HELP MEMORY for your options   Error in test27  line 70  A rand 100000000 1     Below is using cputime  Size 100x100 The cputime for sum A     in seconds is  0 The cputime for sum sum A   in seconds is  0  Size 10000x1 The cputime for sum A     in seconds is  0 The cputime for sum sum A   in seconds is  0  Size 1000x1000 The cputime for sum A     in seconds is  0 The cputime for sum sum A   in seconds is  0  Size 1000000 The cputime for sum A     in seconds is  0 The cputime for sum sum A   in seconds is  0  Size 10000x10000 The cputime for sum A     in seconds is  0 312 The cputime for sum sum A   in seconds is  0 312  Size 100000000 Error using rand Out of memory  Type HELP MEMORY for your options   Error in test27 2  line 70  A rand 100000000 1     In my experience  both timers are only meaningful up to  1s  So if you have similar experience with Matlab timers  none of the tests can discern sum A     and sum sum A      I tried the largest size allowed on my computer a few more times   Size 10000x10000 sum A     Elapsed time is 0 151256 seconds  sum A  Elapsed time is 0 143937 seconds   Size 10000x10000 sum A     Elapsed time is 0 149802 seconds  sum A  Elapsed time is 0 145227 seconds   Size 10000x10000 The cputime for sum A     in seconds is  0 2808 The cputime for sum sum A   in seconds is  0 312  Size 10000x10000 The cputime for sum A     in seconds is  0 312 The cputime for sum sum A   in seconds is  0 312  Size 10000x10000 The cputime for sum A     in seconds is  0 312 The cputime for sum sum A   in seconds is  0 312   They seem equivalent  Either one is good  But sum sum A   requires that you know the dimension of your array is 2

User · Answer

You are trying to sum up all the elements of 2-D Array  In Matlab use   Array Sum   sum sum Array Name

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Avoid for loops whenever possible   sum A       is great however if you have some logical indexing going on you can t use the     but you can write     Sum all elements under 45 in the matrix sum   sum   A      A  lt  45       Since sum sums the columns and sums the row vector that was created by the first sum  Note that this only works if the matrix is 2-dim

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For very large matrices using sum sum A   can be faster than sum A        gt  gt  A   rand 20000    gt  gt  tic  B sum A      toc  tic  C sum sum A    toc Elapsed time is 0 407980 seconds  Elapsed time is 0 322624 seconds

[matlab] What are the ways to sum matrix elements in MATLAB?

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