Functions/Subroutines¶

subroutine zgetrf (M, N, A, LDA, IPIV, INFO)
ZGETRF VARIANT: iterative version of Sivan Toledo's recursive LU algorithm

subroutine zgetrf (integer M, integer N, complex*16, dimension( lda, * ) A, integer LDA, integer, dimension( * ) IPIV, integer INFO)¶

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

 ZGETRF 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 COMPLEX*16 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 136 of file VARIANTS/lu/REC/zgetrf.f.