MATLAB: Sparse matrix and savings

sparsethresholding

I have a complex matrix which has non zero values only in specific region of the matrix. And most of the remaining part is equal to zero(see the image).The size of the matrix is m x n where m >>>> n eg. 4096 x 256 and I want to carry out element by element multiplication with another complex matrix of same size that has a specific pattern.But here's the problem since the complex matrix has majority of its elements zero (some real some imaginary and sometimes both)I want to store it in sparse form and multiply only the elements which are non zero with that of the pattern_matrix at those positions of non-zero elements in the complex sparse matrix. How do I do it efficiently and save complex multiplications without degradation in quality?

PSEUDO CODE
for 1:value
  while(condition is true)
    Sparse_Matrix = Sparse_Matrix.*Pattern_Matrix(value)
    Another_Matrix(count,:) = sum(Sparse_Matrix)
    Increment count
  end of while loop
  Some operations;
end of For loop

Best Answer

I don't fully understand your pseudo code, particularly your use of value when indexing into Pattern_Matrix(value). If you just want to do element-by-element multiplication with only those non-zero element spots in the sparse matrix, then you can do this:

g = Sparse_Matrix ~= 0; % index spots where you want to do the multipies
Sparse_Matrix(g) = Sparse_Matrix(g) .* Pattern_Matrix(g); % do the multiplies in only those spots

You could also just do it directly as follows (probably faster than above method), but NaN's and Inf's in the non-zero spots will propagate:

Sparse_Matrix = Sparse_Matrix .* Pattern_Matrix;

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MATLAB: Is assigning integers to a complex matrix slow

The difference in performance you observe is a side effect of MATLAB's feature to diligently inspects its complex variables to determine whether they are truely complex (with at least one non-zero imaginary element) or otherwise it will throw away their imaginary part.

MATLAB does this inspection after every modification of the complex variable. The inspection of the imaginary part is a linear scan: scan the imaginary part from the first to the last element until it finds the first non-zero imaginary part. Thus the earlier (closer to the beginning) the first non-zero imaginary part occurs, the less time MATLAB spends on this inspection. The worst case is when all elements have zeros imaginary part except for the last element. In this case, MATLAB has to scan the entire array to determine it is indeed complex, and keeps its imaginary part.

There are several workarounds to speed up the assignment to complex variables:

1. Assign real and complex parts of numbers as two real matrices. Note that this will lead to code that is more complex and harder to maintain, and is not recommended unless absolutely necessary.

2. Initialize complex matrices so that the first element contains the entry '0 + 1*i'. Then, traverse through the matrix backwards when assigning, as shown below:

d = zeros(1e6,20,'single');
v = zeros(1e6,1, 'single'); 
d(1) = 0+i;
for k = 20:-1:1
    d(:,k) = v;
end

3. Explicitly assign complex matrices using the form 'a+i*b', as shown below:

d = zeros(1e6,20,'single') + i*zeros(1e6,20,'single');
v = ones(1e6,1,'single');
for k = 1:20
    d(:,k) = v + i.*v;
end

MATLAB: Multiplication of Sparse complex matrix and a full matrix

The sparse multiplication will skip multiplying the elements that are known to be 0 in the sparse matrix.

Best Answer

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MATLAB: Is assigning integers to a complex matrix slow

MATLAB: Multiplication of Sparse complex matrix and a full matrix

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