MATRICES with customized sum for rows and columns

I want to create 4 matrices (6x10) with sums of rows and columns as following; in a single program/code.

mat1: sum_row1=sum_row2=......=sum_row6=r(say) sum_col1=sum_col2=......=sum_col6=c(say)&&&&&&& r=c

mat2: sum_row1=sum_row2=......=sum_row sum_col1≠sum_col2≠......≠sum_col6

mat3: sum_row1≠sum_row2≠......≠sum_row6 sum_col1=sum_col2=......=sum_col6

mat4: sum_row1≠sum_row2≠......≠sum_row6 sum_col1≠sum_col2≠......≠sum_col6

Kindly suggest some logic/program

Thanks

[Stephen23]

Duplicate question:

http://www.mathworks.com/matlabcentral/answers/215557-matrices-with-customized-sums-for-rows-and-columns

Answer 1

[Michael Haderlein]

To get mat1, you can use the magic function:

>> mat1=magic(4)

mat1 =

      16     2     3    13
       5    11    10     8
       9     7     6    12
       4    14    15     1

>> sum(mat1,1)

ans =

      34    34    34    34

>> sum(mat1,2)

ans =

      34
      34
      34
      34

mat2, mat3 and mat4 are easy, for instance use randoms and normalize the columns/rows:

>> matrand=rand(4);
>> mat2=bsxfun(@rdivide,matrand,sum(matrand));
>> sum(mat2)

ans =

       1     1     1     1

>> mat3=bsxfun(@rdivide,matrand,sum(matrand,2));
>> sum(mat3,2)

ans =

      1.0000
      1.0000
      1.0000
      1.0000

mat4=matrand;

[MSH]

But magic() command generates only square matrix. How i can get rectangular matrix with magic()?

Regards

[Michael Haderlein]

Oh, sorry, I didn't read that you need 6x10 matrices. However I'm confident that in this case mat1 only exists if all the sums are zero. If this is fine with you, create the matrix with

>> matrand=randi(100,5,9);
>> mat1=[matrand -sum(matrand,2);-sum(matrand,1) sum(matrand(:))];
>> sum(mat1,1)

ans =

       0     0     0     0     0     0     0     0     0     0

>> sum(mat1,2)

ans =

       0
       0
       0
       0
       0
       0

[MSH]

THANKS