template<typename MatrixType_, typename OrderingType_>
class Eigen::SparseLU< MatrixType_, OrderingType_ >
Sparse supernodal LU factorization for general matrices.
This class implements the supernodal LU factorization for general matrices. It uses the main techniques from the sequential SuperLU package (http://crd-legacy.lbl.gov/~xiaoye/SuperLU/). It handles transparently real and complex arithmetic with single and double precision, depending on the scalar type of your input matrix. The code has been optimized to provide BLAS-3 operations during supernode-panel updates. It benefits directly from the built-in high-performant Eigen BLAS routines. Moreover, when the size of a supernode is very small, the BLAS calls are avoided to enable a better optimization from the compiler. For best performance, you should compile it with NDEBUG flag to avoid the numerous bounds checking on vectors.
An important parameter of this class is the ordering method. It is used to reorder the columns (and eventually the rows) of the matrix to reduce the number of new elements that are created during numerical factorization. The cheapest method available is COLAMD. See the OrderingMethods module for the list of built-in and external ordering methods.
The input matrix A should be in a compressed and column-major form. Otherwise an expensive copy will be made. You can call the inexpensive makeCompressed() to get a compressed matrix.
Note
Unlike the initial SuperLU implementation, there is no step to equilibrate the matrix. For badly scaled matrices, this step can be useful to reduce the pivoting during factorization. If this is the case for your matrices, you can try the basic scaling method at "unsupported/Eigen/src/IterativeSolvers/Scaling.h"
Template Parameters
MatrixType_
The type of the sparse matrix. It must be a column-major SparseMatrix<>
OrderingType_
The ordering method to use, either AMD, COLAMD or METIS. Default is COLMAD
the absolute value of the determinant of the matrix of which *this is the QR decomposition.
Warning
a determinant can be very big or small, so for matrices of large enough dimension, there is a risk of overflow/underflow. One way to work around that is to use logAbsDeterminant() instead.
Analyze and factorize the matrix so the solver is ready to solve.
Compute the symbolic and numeric factorization of the input sparse matrix. The input matrix should be in column-major storage, otherwise analyzePattern() will do a heavy copy.
To get error of this function you should check info(), you can get more info of errors with lastErrorMessage().
In the past (before 2012 (git history is not older)), this function was returning an integer. This exit was 0 if successful factorization.
0 if info = i, and i is been completed, but the factor U is exactly singular, and division by zero will occur if it is used to solve a system of equation. A->ncol: number of bytes allocated when memory allocation failure occurred, plus A->ncol. If lwork = -1, it is the estimated amount of space needed, plus A->ncol.
It seems that A was the name of the matrix in the past.
Reports whether previous computation was successful.
Returns
Success if computation was successful, NumericalIssue if the LU factorization reports a problem, zero diagonal for instance InvalidInput if the input matrix is invalid
Inheritance diagram for Eigen::SparseLU< MatrixType_, OrderingType_ >:
1.14.0