MATLAB: Does MATLAB version 6.5 (R13) allocate large amounts of memory when I copy a row of data from a sparse matrix

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I am performing operations on sparse data. When I copy a single row of my sparse matrix, the resulting sparse matrix allocates far more memory than is actually needed. When I copy multiple rows of data from the sparse matrix, MATLAB allocates a segment of memory that is larger than the block of memory taken up by the original sparse matrix. However, when I copy a column from my original sparse matrix, MATLAB allocates the right amount of memory.
The following code illustrates the problem:
A=sprand(100,1000,0.01); %Create a random sparse matrix.
[mA,nA]=size(A);
Nbites_A = 8*nzmax(A) + 4*(nzmax(A)+nA+1); %total number of bytes required to store a sparse matrix 
B=A(1,:);   %Copy one row from A
[mB,nB]=size(B);
Nbites_B = 8*nzmax(B) + 4*(nzmax(B)+nB+1); %total number of bytes required to store a copy of one row of a sparse matrix 
C=A([1 1 2 2 3 3],:); %Copy six rows from A
[mC,nC]=size(C);
Nbites_C = 8*nzmax(C) + 4*(nzmax(C)+nC+1); %total number of bytes required to store a copy of six rows of a sparse matrix 
D=A(:,10); %Copy one column from A
[mD,nD]=size(D);
Nbites_D = 8*nzmax(D) + 4*(nzmax(D)+nD+1); %total number of bytes required to store a copy of a column of a sparse matrix
whos A B C D
In the above code, I create a sparse matrix A. The variable B is a copy of one row of A. The variable C is a copy of six rows of A. The variable D is a copy of one column of A. The output of WHOS indicates that B and C allocate far more memory than is required to store the elements of the sparse matrix A. Why is MATLAB allocating so much memory for B and C?

Best Answer

When you create a sparse matrix such as A in the above code in MATLAB, the variable A is a pointer to the columns of the sparse matrix. Hence, when you copy a column out of A, you are just copying the pointer to that column. MATLAB already knows how much memory to allocate for that column.
However, when you copy a row out of a sparse matrix, MATLAB has to first allocate memory before it can copy the contents of that row. It does not have information about how many non-zero elements are stored in that row and thus makes a worst case scenario guess.
More information about how MATLAB allocates memory for sparse matrices can be found in the MATLAB Documentation obtained by typing the following command in the MATLAB Command Window:
web([docroot '/techdoc/math/sparse3.html#19608'])
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