ILUT preconditioner based on the incomplete LU factorization with a threshold of a sparse matrix.
dcsrilutcomputes a preconditioner
B[ Saad03 ] of a given sparse matrix
Astored in the format accepted in the direct sparse solvers:
Lis a lower triangular matrix with unit diagonal and
Uis an upper triangular matrix with non-unit diagonal.
The following threshold criteria are used to generate the incomplete factors
1) the resulting entry must be greater than the matrix current row norm multiplied by the parameter
2) the number of the non-zero elements in each row of the resulting
Ufactors must not be greater than the value of the parameter
This routine supports only one-based indexing of the array parameters.
- Size (number of rows or columns) of the original squareINTEGER.n-by-nmatrixA.
- Array containing all non-zero elements of the matrixDOUBLE PRECISION.A. The length of the array is equal to their number. Refer tovaluesarray description in the Sparse Matrix Storage Format section for more details.
- Array of sizeINTEGER.(containing indices of non-zero elements in the arrayn+1)a.is the index of the first non-zero element from the rowia(i)i. The value of the last elementis equal to the number of non-zeros in the matrixia(n+1)A, plus one. Refer to therowIndexarray description in the Sparse Matrix Storage Format for more details.
- Array of size equal to the size of the arrayINTEGER.a. This array contains the column numbers for each non-zero element of the matrixA. It is important that the indices are in increasing order per row. Refer to thecolumnsarray description in the Sparse Matrix Storage Format for more details.If column indices are not stored in ascending order for each row of matrix, the result of the routine might not be correct.
- Tolerance for threshold criterion for the resulting entries of the preconditioner.DOUBLE PRECISION.
- Maximum fill-in, which is half of the preconditioner bandwidth. The number of non-zero elements in the rows of the preconditioner cannot exceedINTEGER.(2*.maxfil+1)
- Array of sizeINTEGER.128. This parameter is used to specify the integer set of data for both the ILUT and RCI FGMRES computations. Refer to theipararray description in the FGMRES Common Parameters for more details on FGMRES parameter entries. The entries specific to ILUT are listed below.
You must declare the arrayiparwith length 128. While defining the array in the code asINTEGERipar(31)works, there is no guarantee of future compatibility with.Intel® MKL
- specifies how the routine operates if the value of the computed diagonal element is less than the current matrix row norm multiplied by the value of the parametertol. Ifipar(31)= 0, then the calculation is stopped and the routine returns non-zero error value. Otherwise, the value of the diagonal element is set to a value determined bydpar(31)(see its description below), and the calculations continue.
- There is no default value foripar(31)even if the preconditioner is used within the RCI ISS context. Always set the value of this entry.