Rows mean collapse in big matrix

Hi,

I have a big matrix (40448x47). I would like to collapse some rows with it mean. For example, if i have:

 avarageNumb = 3
 ma =

    92    99     1     8    15    67    74    51    58    40
    98    80     7    14    16    73    55    57    64    41
     4    81    88    20    22    54    56    63    70    47
    85    87    19    21     3    60    62    69    71    28
    86    93    25     2     9    61    68    75    52    34
    17    24    76    83    90    42    49    26    33    65
    23     5    82    89    91    48    30    32    39    66
    79     6    13    95    97    29    31    38    45    72
    10    12    94    96    78    35    37    44    46    53
    11    18   100    77    84    36    43    50    27    59

I would like 3 to have a matrix 4x10 with rows mean (first row is the mean of the first three, second row is the mean of the 4-5-6 rows, third row is the mean of 7-8-9 rows, and fourth row is the 10 row).

I'm trying to design an algo with nested loop, however i think that Matlab can help me with some function that i do not know (I am a newbie in Matlab)! :)

Thanks, Marco

Answer 1

[Stephen23]

If the number of rows of M was an integer multiple of N then this would be easy to achieve by simply reshaping the matrix M. Because your data does not fit this we have to take into account that there may be from 1 to N last rows to be "collapsed" together. This can be achieved using mat2cell to split the matrix into groups, and then performing the mean inside a cellfun call:

% Number of rows to "collapse" together:
N = 3;
% Your data:
M = [...
    92    99     1     8    15    67    74    51    58    40
    98    80     7    14    16    73    55    57    64    41
     4    81    88    20    22    54    56    63    70    47
    85    87    19    21     3    60    62    69    71    28
    86    93    25     2     9    61    68    75    52    34
    17    24    76    83    90    42    49    26    33    65
    23     5    82    89    91    48    30    32    39    66
    79     6    13    95    97    29    31    38    45    72
    10    12    94    96    78    35    37    44    46    53
    11    18   100    77    84    36    43    50    27    5];
% vector of row counts:
row = N*ones(1,ceil(size(M,1)/N));
row(end) = mod(size(M,1)-1,N)+1;
% scalar of column count:
col = size(M,2);
% split data into cell, with the specified rows and columns in groups:
C = mat2cell(M,row,col);
% calculate mean of each group and concatenate back into one matrix:
out = cell2mat(cellfun(@(m)mean(m,1),C,'UniformOutput',false));

and the output in the command window:

>> out
out =
    64.667       86.667           32           14       17.667       64.667       61.667           57           64       42.667
    62.667           68           40       35.333           34       54.333       59.667       56.667           52       42.333
    37.333       7.6667           63       93.333       88.667       37.333       32.667           38       43.333       63.667
        11           18          100           77           84           36           43           50           27            5

Answer 2

[Andrei Bobrov]

avarageNumb = 3;
ma =[...
92    99     1     8    15    67    74    51    58    40
98    80     7    14    16    73    55    57    64    41
4    81    88    20    22    54    56    63    70    47
85    87    19    21     3    60    62    69    71    28
86    93    25     2     9    61    68    75    52    34
17    24    76    83    90    42    49    26    33    65
23     5    82    89    91    48    30    32    39    66
79     6    13    95    97    29    31    38    45    72
10    12    94    96    78    35    37    44    46    53
11    18   100    77    84    36    43    50    27    59];

ii = ceil((1:size(ma,1))'/avarageNumb);
[jj,kk] = ndgrid(ii,1:size(ma,2));
out = accumarray([jj(:),kk(:)],ma(:),[],@mean);