Implementation of multi-blocks data structure (matrices) for Matlab
This toolbox for Matlab allows creation and manipulation of multi-block matrices, also called "block-matrices". Block-matrices are matrices endowed with a "block-dimensions", that defines a decomposition of the matrix data into several blocks.
The motivation is to manage efficiently concatenation of several data sets while preserving the original structure of the experiment.
The toolbox can be downloaded by cloning the project from the following URL: https://github.com/dlegland/BlockMatrixToolbox.git Then, simply add the path to the "BlockMatrixToolbox/multiBlock" directory to the path.
Let us start with a rather simple matrix:
>> data = reshape(1:28, [7 4])';
>> data
data =
1 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
A Block-Dimension can be assigned to this matrix, using the BlockMatrix class:
>> X = BlockMatrix(data, [2 2], [2 3 2]);
As an alternative syntax, the BlockDimension object can be explicitely created and given as argument:
>> BD = BlockDimension({[2 2], [2 3 2]});
>> X = BlockMatrix(data, BD);
The content of a BlockMatrix can be shown by using the disp function, or simply by omitting the
final semi colon:
>> X
X =
BlockMatrix object with 4 rows and 7 columns
row dims: 2 2
col dims: 2 3 2
1 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
Block-Matrices can be transposed, and multiplied. The block-structure of the resulting block-matrices are preserved.
>> X * X'
ans =
BlockMatrix object with 4 rows and 4 columns
row dims: 2 2
col dims: 2 2
140 336 532 728
336 875 1414 1953
532 1414 2296 3178
728 1953 3178 4403
The content of Block-matrices is accessible by different ways. One possibility is to use the
getBlock and setBlock methods.
>> getBlock(X, 1, 2)
ans =
3 4 5
10 11 12
>> setBlock(X, 1, 2, ones(2, 3));
>> X
X =
BlockMatrix object with 4 rows and 7 columns
row dims: 2 2
col dims: 2 3 2
1 2 1 1 1 6 7
8 9 1 1 1 13 14
15 16 17 18 19 20 21
22 23 24 25 26 27 28
A similar result is obtained by using braces indexing:
>> X{2, 3}
ans =
20 21
27 28
Elements of a block matrix can be accessed using parens indexing
>> X(3, 2)
ans =
16
The toolbox provides support for Block-Diagonal matrices. Block-Diagonal matrices are block-matrices with the particularity that the blocks that are not on the diagonal contains only zero values. An example of block-diagonal matrix is as follow:
>> BD = BlockDiagonal({[1 2 3; 4 5 6], [7 8;9 10], [11 12]})
BD =
BlockMatrix object with 5 rows and 7 columns
row dims: 2 2 1
col dims: 3 2 2
1 2 3 0 0 0 0
4 5 6 0 0 0 0
0 0 0 7 8 0 0
0 0 0 9 10 0 0
0 0 0 0 0 11 12
BlockDiagonal matrices can be multiplied as common block-matrices:
>> BD * BD'
ans =
BlockMatrix object with 5 rows and 5 columns
row dims: 2 2 1
col dims: 2 2 1
14 32 0 0 0
32 77 0 0 0
0 0 113 143 0
0 0 143 181 0
0 0 0 0 265
BlockMatrixToolbox is developped jointly by INRA and ONIRIS. The development started at the occasion of the "CouplImSpec" project, involving also the SOLEIL synchrotron, and during the AI-Fruit project of Region "Pays-de-la-Loire"
Authors:
- Mohamed Hanafi (oniris, mohamed.hanafi, at oniris-nantes.fr)
- David Legland (INRA, BIBS Platform, david.legland, at nantes.inra.fr)
See also:
- http://github.com/gastonstat/blockberry The R implementation of multi-block matrices that inspired this package