Recommended direct solver for sparse positive definite linear system in scipy?

问题

I'm sorry if this is explained clearly in the scipy.sparse documentation.

When using scipy, what function would you recommend using to solve a sparse positive definite linear system of equations? I want to use a direct method, and I want the columns to be reordered so as to preserve sparsity as much as possible in the Cholesky factorization of the coefficient matrix. Ideally I'd be able to experiment with various options for reordering.

Does a direct solver for sparse positive definite systems exist in scipy.sparse? Is scikit.sparse the way to go?

回答1:

scipy.sparse.linalg.spsolve is clear enough, but it seems that for speed you must

pip install scikit-umfpack

or else

1. build UMFPACK and AMD from SuiteSparse
2. then rebuild scipy from source, with [umfpack] umfpack_libs = ... in site.cfg .

otherwise scipy.sparse.linalg defaults to the slower SuperLU.

Is scikit.sparse the way to go?

Compared to what, with what criteria ? If C / C++ is enough for you, use SuiteSparse directly. Any tool depends on what you're comfortable with, and on users: one, two, many. Maybe better visualization would help your project more than faster spsolve.

Some pretty obvious pluses and minuses of scipy.sparse:

+ python for fast development, data input -- matrices -- visualize
+ several packages have built on scipy.sparse; ask around in your application area (which is ?)
- rough edges (matrices are a pain), with afaik no wiki to collect hints and code snippets
- layers upon layers, scipy.sparse -- SuiteSparse -- ... BLAS ... make timing and debugging tough.

Fwiw, solver times vary a lot on my iMac. These are all with default args, without umfpack.
(This is NOT a realistic testcase; but satisficing is often good enough.)

X = sparse.rand( m, n, dens, format="csr" )
A = 1e-6 * sparse.eye(m) + X * X.T
linalg solvers( A, b )

(5000, 5000)  density 0.42 % --
   51 msec spsolve
    5 msec bicg
    3 msec bicgstab
    2 msec cg
    4 msec cgs
    3 msec gmres
    4 msec lgmres
    1 msec minres
    6 msec qmr
    5 msec lsmr
(5000, 5000)  density 0.84 % --
  428 msec spsolve
   12 msec bicg
    7 msec bicgstab
    5 msec cg
   10 msec cgs
    6 msec gmres
    8 msec lgmres
    2 msec minres
   13 msec qmr
   12 msec lsmr
(5000, 5000)  density 1.3 % --
 1462 msec spsolve
   16 msec bicg
    9 msec bicgstab
    7 msec cg
   11 msec cgs
    7 msec gmres
   10 msec lgmres
    1 msec minres
   18 msec qmr
   14 msec lsmr

来源：https://stackoverflow.com/questions/17962403/recommended-direct-solver-for-sparse-positive-definite-linear-system-in-scipy