summation operation for a matrix?

x = (1:36)+(1:36).' % some 36-by-36 matrix
x = 36×36
     2     3     4     5     6     7     8     9    10    11    12    13    14    15    16    17    18    19    20    21    22    23    24    25    26    27    28    29    30    31
     3     4     5     6     7     8     9    10    11    12    13    14    15    16    17    18    19    20    21    22    23    24    25    26    27    28    29    30    31    32
     4     5     6     7     8     9    10    11    12    13    14    15    16    17    18    19    20    21    22    23    24    25    26    27    28    29    30    31    32    33
     5     6     7     8     9    10    11    12    13    14    15    16    17    18    19    20    21    22    23    24    25    26    27    28    29    30    31    32    33    34
     6     7     8     9    10    11    12    13    14    15    16    17    18    19    20    21    22    23    24    25    26    27    28    29    30    31    32    33    34    35
     7     8     9    10    11    12    13    14    15    16    17    18    19    20    21    22    23    24    25    26    27    28    29    30    31    32    33    34    35    36
     8     9    10    11    12    13    14    15    16    17    18    19    20    21    22    23    24    25    26    27    28    29    30    31    32    33    34    35    36    37
     9    10    11    12    13    14    15    16    17    18    19    20    21    22    23    24    25    26    27    28    29    30    31    32    33    34    35    36    37    38
    10    11    12    13    14    15    16    17    18    19    20    21    22    23    24    25    26    27    28    29    30    31    32    33    34    35    36    37    38    39
    11    12    13    14    15    16    17    18    19    20    21    22    23    24    25    26    27    28    29    30    31    32    33    34    35    36    37    38    39    40
% add first row and first column (exlcuding first element)
sum(x(1,:))+sum(x(2:end,1))
ans = 1402
% or add first row and first column then subtract first element because it
% was included twice
sum(x(1,:))+sum(x(:,1))-x(1,1)
ans = 1402

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Torsten 2022-4-4

编辑：Torsten 2022-4-4

I have a matrix with dimensions 36x36. what i want to is this;

x(1,1)+x(1,2)+...+x(1,36) +x(2,1)+x(3,1)+x(4,1)+...+x(36,1) <= (somevalue)

You don't have this matrix.

You must construct the matrix which implements this constraint.

In the matrix I set up for the other constraint, just set the ones at the correct positions, and you'll get the above constraint implemented:

https://de.mathworks.com/matlabcentral/answers/1687409-dependent-variable-operations?s_tid=srchtitle

There is no simpler way to do so.

You can have a look here for a simple example:

https://de.mathworks.com/matlabcentral/answers/1688434-how-can-i-define-a-lower-bound-of-the-lp?s_tid=srchtitle

Azime Beyza Ari 2022-4-4

Yes, i tried that but since my objective function only uses 1296 variable adding y's to Z caused too much error. Instead i wanted to eliminte y and work on x's. Since the whole idea behind y's are being equal to x's summation.

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