LUfactorization of a general n-by-n banded distributed matrix.
LUfactorization of a general
nreal/complex banded distributed matrix
n-1) using partial pivoting with row interchanges.
The resulting factorization is not the same factorization as returned from the LAPACK
?gbtrf. Additional permutations are performed on the matrix for the sake of parallelism.
The factorization has the form
Qare permutation matrices, and
Uare banded lower and upper triangular matrices, respectively. The matrix
Qrepresents reordering of columns for the sake of parallelism, while
Prepresents reordering of rows for numerical stability using classic partial pivoting.
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Notice revision #20110804
This notice covers the following instruction sets: SSE2, SSE4.2, AVX2, AVX-512.
- (global)The number of rows and columns in the distributed submatrixINTEGER.A(1:n,ja:ja+n-1);.n≥0
- (global)The number of sub-diagonals within the band ofINTEGER.A