# Moore-Penrose Generalized Inverse of Sparse Matrix

Is there any package that provides a function to calculate a generalized inverse of a sparse matrix? I know the `LinearAlgebra` package provides `pinv` and the `SparseArrays` provides capabilities for the creation of sparse matrices but have not been able to find any the calculate the psuedo-inverse of a sparse matrix

The pseudo-inverse of a sparse matrix would almost always be dense, wouldnâ€™t it? Given that, it seems like it doesnâ€™t make too much sense to have a sparse pinvâ€”or if one does it would be equivalent to converting to sense first.

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You almost never compute the inverse (pseudo or otherwise) of a sparse matrix because the inverse is generally dense.

On the other hand, you do compute the application of the inverse to a vector, and you often precompute factorizations that let you apply the inverse more quickly.

In the case of the ordinary inverse, you can apply a sparse inverse with `A \ b` and compute the factorization with `lu(A)` etcetera. In the case of the pseudoinverse, applying it computes the least-squares solution, and the corresponding factorization is usually `qr`.

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