Functions/Subroutines¶

subroutine DGETRF (m, n, a, lda, ipiv, info)
DGETRF VARIANT: iterative version of Sivan Toledo's recursive LU algorithm

subroutine DGETRF (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, integer info)¶

DGETRF VARIANT: iterative version of Sivan Toledo's recursive LU algorithm Purpose:

!>
!> DGETRF computes an LU factorization of a general M-by-N matrix A
!> using partial pivoting with row interchanges.
!>
!> The factorization has the form
!>    A = P * L * U
!> where P is a permutation matrix, L is lower triangular with unit
!> diagonal elements (lower trapezoidal if m > n), and U is upper
!> triangular (upper trapezoidal if m < n).
!>
!> This code implements an iterative version of Sivan Toledo's recursive
!> LU algorithm[1].  For square matrices, this iterative versions should
!> be within a factor of two of the optimum number of memory transfers.
!>
!> The pattern is as follows, with the large blocks of U being updated
!> in one call to DTRSM, and the dotted lines denoting sections that
!> have had all pending permutations applied:
!>
!>  1 2 3 4 5 6 7 8
!> +-+-+---+-------+------
!> | |1|   |       |
!> |.+-+ 2 |       |
!> | | |   |       |
!> |.|.+-+-+   4   |
!> | | | |1|       |
!> | | |.+-+       |
!> | | | | |       |
!> |.|.|.|.+-+-+---+  8
!> | | | | | |1|   |
!> | | | | |.+-+ 2 |
!> | | | | | | |   |
!> | | | | |.|.+-+-+
!> | | | | | | | |1|
!> | | | | | | |.+-+
!> | | | | | | | | |
!> |.|.|.|.|.|.|.|.+-----
!> | | | | | | | | |
!>
!> The 1-2-1-4-1-2-1-8-... pattern is the position of the last 1 bit in
!> the binary expansion of the current column.  Each Schur update is
!> applied as soon as the necessary portion of U is available.
!>
!> [1] Toledo, S. 1997. Locality of Reference in LU Decomposition with
!> Partial Pivoting. SIAM J. Matrix Anal. Appl. 18, 4 (Oct. 1997),
!> 1065-1081. http://dx.doi.org/10.1137/S0895479896297744
!>
!>

Parameters

!>          M is INTEGER
!>          The number of rows of the matrix A.  M >= 0.
!> 

!>          N is INTEGER
!>          The number of columns of the matrix A.  N >= 0.
!> 

!>          A is DOUBLE PRECISION array, dimension (LDA,N)
!>          On entry, the M-by-N matrix to be factored.
!>          On exit, the factors L and U from the factorization
!>          A = P*L*U; the unit diagonal elements of L are not stored.
!> 

!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,M).
!> 

!>          IPIV is INTEGER array, dimension (min(M,N))
!>          The pivot indices; for 1 <= i <= min(M,N), row i of the
!>          matrix was interchanged with row IPIV(i).
!> 

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>          > 0:  if INFO = i, U(i,i) is exactly zero. The factorization
!>                has been completed, but the factor U is exactly
!>                singular, and division by zero will occur if it is used
!>                to solve a system of equations.
!> 

Author

Date

Definition at line 135 of file dgetrf.f.