MATLAB: Query regarding a sparse complex matrix

efficiencysparse

I have a complex matrix, I have to create its sparse form using sparse function. How do I store it in lesser bytes than the original complex matrix? In the first case it is storing in 144 bytes but in the sparse case it is storing in 152 bytes. Any example
A =
   0.1620 + 0.8048i   0.3402 + 0.7727i   0.0000 + 0.0000i
   0.2497 + 0.1178i   0.0000 + 0.0000i   0.0000 + 0.0000i
   0.3937 + 0.6184i   0.4527 + 0.2691i   0.0000 + 0.0000i
>> B = sparse(A)
B =
   (1,1)      0.1620 + 0.8048i
   (2,1)      0.2497 + 0.1178i
   (3,1)      0.3937 + 0.6184i
   (1,2)      0.3402 + 0.7727i
   (3,2)      0.4527 + 0.2691i
>> whos Name Size Bytes Class Attributes
A         3x3               144  double    complex        
B         3x3               152  double    sparse, complex

Best Answer

Hi,
the resulting size of the sparse matrix depends from the number of zero entries. Consider this:
A = randi(10,100);
A(A<=7) = 0;
B = sparse(A);
whos A B
Name        Size             Bytes  Class     Attributes
A         100x100            80000  double              
B         100x100            49096  double    sparse
The code above produced a sparse matrix which has about 60% size then the normal one. There should be about 70% zeros in it.
If we only have about 30% zeros the situation changes:
A = randi(10,100);
A(A<=3) = 0;
B = sparse(A);
whos A B
Name        Size              Bytes  Class     Attributes
A         100x100             80000  double              
B         100x100            113240  double    sparse
Now the size of B is about 40% bigger than A.
EDIT - Now the same example using complex numbers:
about 70% zeros:
R = randi(10,100);
I = ones(100);
C = complex(R,I);
C(real(C)<=7) = 0;
D = sparse(C);
whos C D
gives:
Name        Size              Bytes  Class     Attributes     
C         100x100            160000  double    complex        
D         100x100             71944  double    sparse, complex
and the same with about 30% zeros:
R = randi(10,100);
I = ones(100);
C = complex(R,I);
C(real(C)<=3) = 0;
D = sparse(C);
whos C D
gives:
Name        Size              Bytes  Class     Attributes     
C         100x100            160000  double    complex        
D         100x100            168928  double    sparse, complex
The values differ, but the fundamental effect is the same.
Best regards
Stephan
Related Question