MATLAB: How to store big triangular matrix

MATLABmatrixperformance

I need to store and operate(so time of referencing operations is very important) with thriangular matrix. How to do it effectively? I think that using of sparse matrix is not efficient because we need to store indexes. May be it is better to store as 1-d cell array of 1-d "normal" arrays? Or some other way? Please help. And sorry for my poor English

Best Answer

It depends on what you are doing with the matrices. When you only want to store the matrices, but do not perform any operations, a cell vector seems to be sufficient. When you need column or row operations only, this might be efficient also.

But e.g. for a matrix multiplication this would be a severe disadvantage and a full matrix is much better.

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MATLAB: Triangular surface

Simple example using DelaunayTri. First create a set of points

N = 1000;
theta = 2*pi*rand(N, 1);
phi = acos(2*rand(N, 1) - 1);
x = cos(theta).*sin(phi);
y = sin(theta).*sin(phi);
z = cos(phi);

Mesh the volume using DelaunayTri

Tfull = DelaunayTri(x, y, z);

Find the triangulation on the boundary using freeBoundary

[T, X] = Tfull.freeBoundary();
trisurf(T, X(:, 1), X(:, 2), X(:, 3))
axis equal

MATLAB: I am trying to convert a dense matrix into a sparse matrix to speed up the matrix multiplies, but it is running slowly. How to fix this

The computational bottleneck in this code comes from converting an existing dense matrix into a sparse matrix. If the matrix has only a few non-zero entries, sparse matrix multiplication will indeed be much more efficient. However, there may be a large overhead cost in constructing the sparse matrix from the dense matrix that exists. The cost of the conversion process may therefore negate the savings gained in the multiplication.The best option is to construct the matrix A to be sparse from the beginning, rather than building it as a dense matrix and converting it:

>> A = sparse(i, j, s, m, n);

This will provide the performance gain of the sparse multiplication without the overhead cost of converting a dense matrix into a sparse matrix. However, if it s not possible to do so, then it could prove more efficient to simply perform a dense matrix multiplication.

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