Matrix Generation from Other Matrices

Hello everyone, how can I write this matrix?

M = [C*B;

C*A*B + C*B;

C*A^2*B + C*A*B + C*B;

C*A^(n-1)*B + C*A^(n-2)*B ... C*B];

Where A, B, and C are matrices and n is an integer.

Size A = a,a Size B = a,b Size C = c,a

Answer 1

[Stephen23]

F = @(p)C*A^p*B;
M = arrayfun(F,0:n-1,'uni',0);
M = cumsum(cat(3,M{:}),3);
M = reshape(permute(M,[1,3,2]),[],b);

Tested:

>> n = 4;
>> a = 3;
>> b = 5;
>> c = 7;
>> A = randi(9,a,a);
>> B = randi(9,a,b);
>> C = randi(9,c,a);
>> F = @(p)C*A^p*B;
>> M = arrayfun(F,0:n-1,'uni',0);
>> M = cumsum(cat(3,M{:}),3);
>> M = reshape(permute(M,[1,3,2]),[],b)
M =
       62       26       60       54       23
       87       28       84       73       28
       64       32       60       64       26
       91       28       90       69       29
       78       26       84       38       27
       44       28       42       44       21
       39        8       42       17       11
     1097      364     1086      839      363
     1234      413     1197     1024      406
     1310      424     1308      962      430
     1253      429     1215     1045      417
     1173      428     1158      923      407
     1119      364     1134      769      371
      407      157      387      371      143
    15024     5141    14643    12290     5011
    16947     5684    16506    13853     5593
    17592     6090    17118    14508     5898
    17555     5869    17133    14231     5790
    17456     5881    17151    13802     5799
    15148     5313    14763    12446     5117
     6315     2047     6219     4915     2060
   209655    70440   204660   169953    69330
   232333    78197   226401   189661    76832
   247894    83060   242196   200194    81896
   240128    80995   233967   196190    79492
   240835    81632   234924   196069    79970
   216015    72366   211302   173637    71400
    84302    28771    81975    69536    28048

and compare against:

>> C*B
ans =
      62      26      60      54      23
      87      28      84      73      28
      64      32      60      64      26
      91      28      90      69      29
      78      26      84      38      27
      44      28      42      44      21
      39       8      42      17      11
>> C*A*B + C*B
ans =
    1097     364    1086     839     363
    1234     413    1197    1024     406
    1310     424    1308     962     430
    1253     429    1215    1045     417
    1173     428    1158     923     407
    1119     364    1134     769     371
     407     157     387     371     143
>> C*A^2*B + C*A*B + C*B
ans =
   15024    5141   14643   12290    5011
   16947    5684   16506   13853    5593
   17592    6090   17118   14508    5898
   17555    5869   17133   14231    5790
   17456    5881   17151   13802    5799
   15148    5313   14763   12446    5117
    6315    2047    6219    4915    2060

[Saleh Msaddi]

Thanks for your response. Actually my matrices are 2D, the code didn't work when I defined my matrices as:

A = randi(a,a);
B = randi(a,b);
C = randi(c,a);

[Stephen23]

"Actually my matrices are 2D, the code didn't work when I defined my matrices as:"

A = randi(a,a);
B = randi(a,b);
C = randi(c,a);

Of course that didn't work, those commands will produce nonsense matrix sizes that are nothing like the sizes that you specified in your question! In contrast, the commands I used give exactly the matrix sizes that you specified in your question (did you actually check their sizes?):

B = randi(a,b);   % What you did (wrong size) -> bxb matrix max value a
B = randi(9,a,b); % What I did (correct size) -> axb matrix max value 9

The randi documentation explains very clearly that its first input specifies the maximum value returned by randi (its first input does not specify anything about the output size as you have incorrectly assumed). Most likely you mixed up the randi syntax with the rand syntax, but in fact they have different calling syntaxes.

I suggest that you:

• read the randi documentation to know what its inputs actually do.
• take a peek at the sizes of the matrices that you are creating (hint: Variable Viewer).

[Saleh Msaddi]

My bad. I was confused between rand and randi, and I thought that the code produces an array (9,a,a). Anyway thanks Stephen.