KLUFactor¶

class sksparse.klu.KLUFactor[source]¶

Class to compute and store the KLU factorization of a sparse matrix.

The constructor computes the symbolic analysis of a sparse matrix \(A\) and determines a fill-reducing ordering such that:

\[L U + F = R P A Q.\]

The numeric factorization is not computed until factorize() is called.

Note

Note that the use of the scale factor R differs between KLU and UMFPACK:

\[\begin{split}L U &= P R_{\mathrm{umf}} A Q \quad &&\text{(UMFPACK)}, \\ L U + F &= R_{\mathrm{klu}} P A Q \quad &&\text{(KLU)}.\end{split}\]

They are related by \(R_{\mathrm{klu}} = P R_{\mathrm{umf}} P^{\top}\).

is_numeric[source]¶

Whether the numeric factorization has been computed.

Type:: bool

lnz[source]¶

The number of nonzeros in the \(L\) factor.

Type:: int

unz[source]¶

The number of nonzeros in the \(U\) factor.

Type:: int

nzoff[source]¶

The number of nonzeros in the \(F\) factor.

Type:: int

nblocks[source]¶

The number of blocks in the BTF ordering of the matrix.

Type:: int

nnz[source]¶

The number of nonzeros in the original matrix.

Type:: int

shape[source]¶

The shape of the original matrix.

Type:: tuple of int

dtype[source]¶

The data type of the matrix entries (float64 or complex128).

Type:: numpy.dtype

itype[source]¶

The integer type used for indexing (int32 or int64).

Type:: numpy.dtype

L[source]¶

The \(L\) factor as a sparse CSC matrix.

Type:: scipy.sparse.csc_array

U[source]¶

The \(U\) factor as a sparse CSC matrix.

Type:: scipy.sparse.csc_array

F[source]¶

The \(F\) factor as a sparse CSC matrix.

Type:: scipy.sparse.csc_array

perm_r, perm_c

The row and column permutation arrays.

Type:: numpy.ndarray

rscale[source]¶

The row scaling array.

Type:: numpy.ndarray

rblocks[source]¶

The row blocks in the BTF ordering.

Type:: numpy.ndarray of int

info[source]¶

An object containing information about the factorization.

Type:: KLUInfo

Notes

This object is an interface to the SuiteSparse KLU library [1].

Added in version 0.5.0.

References

Methods

`__init__`	Compute the KLU factorization of a sparse matrix.
`copy`	Return a deep copy of the current KLUFactor object.
`factorize`	Compute the numeric factorization of the matrix.
`solve`	Solve a linear system using the KLU factorization.